D I A L I S I S Y V E J I G A U R I B A R I A . J

J ALFCNSO R. ROMERO AXGNUIS

MAT. 81325704

m S E. PAUlMINO MARQUE2

U T - 'f6113354 M U I A CRUZ AMDALUZ VERA MAT. 81323968

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A LOS ESTUDIANTES

DE

INGWIERIA BI OpñEDIC A.

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PREFACIO

Hasta l a Última mitad Cel s i e l o XIX, todavía no se rea-

zaban investigaciones con e l f i n de determinar e l mecanismo - de Ir formación de l a orina, s¿lo ex is t fan h ipótes is basadas - en los conocimientos anatómicos de l a época.

Hace algunos años, Galeno, Malpighi, Bowman entre mchos - otros constituyeron poco u poco un estudio más preciso de las-

funciones d e l sisteiiia urinario..

E l f i n que persigae este trabaja, es l ograr que l o s estudi

antes de ingenier ía biÓm8dica &en entender l a anatomía y - f i s i o l o g í a d e l sistema urinario. Sin embargo, se desea primcr-

dialnente que se comprenda e l fenómeno de d i á l i s i s , e l cual d e

sar ro l l a una tarea de v i t a l importancia er. l a regulación de - l a s concentraciónas osmóticas de,] medio interno. Además de un- conocimi~ento más detal lado sobre el funcionamiento de l a v e j i -

ga urinaria.

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E l ostudiünte de ingenier ía bioniRdica debe -crearse una idea

queirelacione l a s funciones de dscho aparato con sus conocimi- - a s í conjugarlos y obtener una apl icación más ventajosas en l a

instmmentación jr técnicas utilizaddas para tener medicionea - sác precisas sobre l o s p a r b e t r o s de las fmc i ones de l a v e j i -

ga, Tizón, uretra,,etc. y ciiéDÓdos que den una solución z l o s

problema^ planteados.

entos f í s i cos , matemáticos, e iáctrónicos, etc . para l o g r a r

Xoy en 2 ía , como un e j w p l o my común, se emplean riEones-

a r t i f i c i a l e s para sus t i tu i r l as funciones real izadas por los - riñones normales en personas con insuf ic ienc ia renal.

Z l estudiante no deberá o lv idar nunca que sólo por exigen-

c i a s de carácter diPdáctico se r e e l i z a un estudio por separaro-

de l o s d i s t in tos Órganos, como si pudieran considerarse aisla-

dos . Tal separaci¿n es muy a r t i f i c i a l ya que todo ser vivien-

t e forma una unidad anaDÓmiaa. y funcional.

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I B D I C E

IIJTRLü3UCCION ..................................................... 5 PARTE I I ANATOMIA

W O N .... ......................... ................................ 7 URETER ........................................................... 16 VEJIGA USINARIA .................................................. 18 URETRA ........................................................... 20

PARTE 111 J?ISIOLOGIA

INTRODUCCION ...................................................... 23

PROCTSOS RENAL3S RASICOS .......................................... 24

TASAS DE FIIIIFUCION GLOMERULAR ...... ! .............................. 27

MICCION ........................................................... 29

FIIIIPRAC'ION GLOMERULAR ............................................ 2~

REGULACION EEL SODIC Y 3L EQUILIBRIO ijEL AGUA .................... 30

REWIACION RENAL I)E LA OSMOLARIDAD ?WI'RACEIULAR .................. 31 REGULACION DEL POTASIO 31 ........................................... REGULACION DEL CALCIO ............. ., .............................. 33

PARTE 111s DIA IXS IS

D I A L I S I S ......................................................... 36 EL IXQUIU~O DE LA D IAL IS IS ........................................ 38 EFICACIA IJEL RIEON ARTIBICIAL ..... ., .............................. 40

PARTE I V I VEJIGA URIEARI. . . , . , , .

VEGIJA URINARIA ................................................... 43 OBlNA ............................................................. 43 EL TRANSPORTE DE LA ORINA POR M S URETERES A LA VEJIGA .......... 43 INVERVACION DE LA VEJIGA .......................................... 44 W L D O DE LA VEJIGA ............................................. 45 EVACUACION DE LA VEJIGA .......... ri,... ........................... 47 MECANISMOS REFLEJOS DE LA MICCION ................................ 4a INFIUjE$?CIA DEL SISTEMA NERVIDSO SOBm U F'UNCION VEESCAL ......... 49 TRASTOREOS DE LA IMWION ......................................... 49

PARTE V I CONCLIJSIONES

CONCIUSIONES ..................................................... 52

BLSUOGRAFIA ..................................................... 54

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E l sistema rend está constituido por : los riñones, ureteres, v e j i ga

y -2retra. Los r izcnes contribuyen a l rnmteriiniento de l a hornsostasis ex--

cretEndo orina, a través de l a cual se eliniinan diversos residuos d e l Lie

tabc1i;mo jur:to con 1.0s excesos d e l <.,qua, e l e c t r ó l i t o s y rio e l e r t r ó l i t o s

d.el z.sd io ir-terno. b orina ex i re ta la por l o s rii;.oncs pasa por l o s urctg

r e s

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a 1.s v3 j i ga y es eliminada -1 exter io r o iedimtelz uretra.

En e l hombre adulto, e 5 t h coInpletúrnente sepürtados ICs ór,yw!ss uropo-

yé t i cos rie l o s órganos cue preparm l o s ?r@uctos mxuales; 3010 t i m e n - en común 10s órgmos gcn i ta l es externos.

Fig . 1 Sinopsis del apazcto uroger?it: 1; i 1; izqu:cvrda cl r?t,sx:l.ino; ci

l a derecha, e l fcrmriino. & :ojo: Órginos urinarios; en negrc: Erganoh

kpnitr. leo.

En l a f ig. 1 se ofrece un;

nos ur incr iosr ri.ñón, ure te r y

sinopsis d e l sistern:. urogenit t l . b s &a-

ve j i ga son iguales en m o * sexos.

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P A R T E I

A N A T O M I A .

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I ANATOMIA:

Riñón: E l rinÓn e s e l Órgano de mngor tamaño de l a cavida.d retroper i tonepl .

Es un Ói-ríano par. E l riñón izauienio e s un poco más grande que e l r izón - de-echo. Su forma se parece a. l a de una judía. E l borde convexo mira ha--

c i a atrás y afuera. Los e j e s longitudinales de ambos riiiones no son para-

l e l o s sino que divergen hacia cbajo. E l peso de un riñón sanc e o de 120 a

200 gramos. E l Órgano mide aproximadmente de 11 z 12 centímetros de lar- go, de 5 a 6 centfmetros de ancho y de 3 a 4 centímetros de espesor.

En ccda riñón se distinguen una cara anter ior , máa abombada, y una 02 r a poster ior , un bords l a t e r a l O extlerno y un borde medial o interno, un- polo, superior y un polo infer ior . &; los polos superiores se asientan l a r

g l &dulas suprarrenale s.

Le superf icie de2 riñón es l i s a muestra pocas abolladuras externas.

221 e l borde medial es tá situado ' e l h i l i o renal. Eb l a regi6n h i l i a r - exhibe e l riñón una fosa pro fwda, seno d e l riñón, cuyas dimensiones se - r e v e l m sólo cuando se eliminan to6a.s l a s estructuras que entran en e l hL l i o y selen de 61, o bien en e l cort8e transversal (Figura 2). Por e l hi--

l i o se interna l a a r t e r i a renal y sa le l a . vena renal y e l ureter. Ue es--

t a s t r e s estructuras e l ure te r es la, más dorsp.1.

E l rizón está rodeado por una c8psula de t e j i d o conjuntivo denso . Po see una capa suner f i c ia l res is tente , cápsula. renal, que consta de doe tú-

nicas, m a ext.erna ( f ibrosa ) , s una interna (subf ibrosr o muscularis) , l a

cual, se& indica su nombre, es portadora de la. mscula.hara l i sa .

La cápsula conjnnIive está redeada:.por l a cápsula adiposa. Esta forma

un compartimento acolchado. E l todo está contenido en e l saco aponeuróti-

0 0 d e l riñón e1 cual por arr iba se fusiona con e l diIf.ragma y por el l a d o

medial y caudal con l a aponeurosis psoaci l iaca. De esta manera se f i j a e l

riñón a l a pared abdominal poster ior , sin embargo, -sede l o suf ic iente pú-

r a que se desplace una distancia de uno a dos centímetros con l o s movimie

entos respirator ios.

E l riñón derecho se ha l l a situado siempre más abajo que e l izquierdo,

debido a l a s dimensiones d e l hígado. E l h i l i o renal se encuentra aproxima

demente en l a a l tura de l a segunde vértebra lumbar. Hacia arriba, el r i 4 ñÓn sobrepasa e l l ím i t e i n f e r i o r de l a Oleura. Es necesario rechazar l a -

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pleura hacia aiwzba cuando se requiere l l e g a r a l polo superior d e l rinón-

desde atr,"s.

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Fig. 2 . Las cápsules renales.

E l parérquima d e l riñón t a l coma se ofrece en e l corta frori?zal a &'a-

vés d e l rilíón ( f i gu ra 3, lámina l), 'permite d i s t ingu i r dos capas mxroscb

pica.sr l a m s t m c i a medumlr y lz sustmcia oortical.¿Es verdad que 12- sus t m c i n c o r t i c a l rodea l a susts ic ia aedular en forma concéntrice, pero se-

prolonga en l a s columnas de Sert in h;asta e l seno d e l riñón. Por l o tanto,

1í: sustrncia mehilar dispuestas en l a s llamadas pir jmides rena.les, está - circundada por todos l o s lados por k s t a n c i e cor t i ca l , excepto en l o s vé; t i c e s pir,amideles que se proyectai e~ e l seno d e l r isón, apareciendo en C

61 Como pepi las renales. C a d a pir;mi.de m,-du1a.r con Is. envcl turt c o r t i c r l

forme un lc'bulo. A ceda psp i la l e pertenece un c á l i z de la p e l v i s renal . L;i sustancia cc r? i ca l niiiestre un asppsctc p a u l o s o f i c o , trí.spa.se.i.a -

?or e r t r í e s rad~ i r l es apenas v i s ib l es , rd i o ! ; riedsleres o p i rzh idrs 01 Fe--

r r e in que l a s subdividen en 'Lobuli l los cor t i ca l i s . Entre l o s r& io meduls

r e s se e.?racián f inos puntitos sánpineos, 1.0s córpu3sculos renales o de-

Malpighi. Est& situados en e l 1lama.do laber into corticu.1 de l o s lobuli--

110s co r t i ca l e s . ~a sustmc ia medulm const i tuye l a - to ta l ida- do 1a.s pir:.'rnioes separg

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43s entre sí ? o r l as columnas de Bertin, presenta hecia e l seno d e l r iñón en 1e.c papi las, un co l o r más c l e r o que l a sustancia c o r t i c a l (zona i n t e i i

na). hi l a zona de transic ión a l a sustancia c o r t i c a l (zona exterric) .u+

co l o r es más subido, cas i siempre r o j o azulado. E l número de pir&idns re n d e s es qmeralmente de 10 a 15 . Algunas veoes, dos pirámides se unen - en una pag i la (lámina 1).

Hefrón.

Cor.sti.tuyen l a unidad estructural y fumiona l de 1os:riñÓnes se e s t i k

ma que su número osc i l a entre 1 a 2 OCO O00 por riñón. Cae.a nefrón ? s t 6 4

fornado, por una parte rlilatada, e l oÓ.Fpusculo de Malpighi, por el túbulo

contorneado proximal, segmetoéi delgado y grueso d e l as2 de Henle y túbulo

contonieado disttt l . E l corpúsculo renal comta d e l glomc'rulo y l a cáptm+ 1; d e Rm,ma? mc! l o ervuelve. su di&etro es de 0.1 a 3 mm.

Fig. 3 . Esquemc Se1 riñón. En rojor sustancia co r t i ca l , punteaao te-

j i d o adiposo d e l seno d e l riñ6n.

CorpÚsculo de Malpighi; Está formado por un o v i l l o de capi lares enwe l~ tos

por l a cágsula de Bowman que posee dos hojas, un8 interna adossd.2. a l o s - capi lares y otra externa fornian.;o l os l ími tes d e l corpúsculsde Malpighi-

F ig . 4 . También se les denomina hojas v i s e r o l y pa r i e t a l de l a czpsula - de Bournan entre e l l a s ex i s t e un espacio ca,psuler que rec ibe e l l íquido ++ f i l t r a d o a t revés de l a pared de l o s capi.lares d e l Rlomérulo y d.e l a hoja

v i s e ra l .

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%ins. 2 .- Diagramas de l a estmctura del riñón.

C& corpÚsculo de Mlapighi t i ene un po lo vascular por e l oual pene--

t r n l a a r t e r i o l a aferentey sa le l a e r t e r i o l a e ferente y un po lo urinario,

donde se i n i c i a e l tubo coiitornaado proximal. La a r t e r i o l a e ferente se dL v ide en var ios capi lares qu'! constituyen asas. Las asas capi lares or ig ina

das de una misma rama se mastomosan enrre sf pero no con l a s de otras ra mes. Además hay conecciones d i rec tas con e l vaso e ferente y e l aferente - mediante l a s cuales l a sangre puede c i rcu lar incluso sin pasar por e l g l o

rnéruio. -

Eh l o s capi lares glornerulares c i r cu la sar:gre a r t e r i a l cuya presión hA

drostát ica es regulada por l a a r t e r i o l a aferente que t iene mayor cmtidad

de d s c u l o l i s o que l a eferente, pudiendo va r i e r a s í su diámetro, mien---

t r a s que e l de l a Última permaneoe constante.

d b u l o contorneado proximal; Comprende una parte i n i c i a l contigua a l cor-

púsculo de Malpighi y una parte r e c t i l í n e a que penetra en l a medular ne--

d iante una extensión muy cor ta continuandose con e l segmei;to delga6o del-

asa de Henle ( f i gura 5). La pared d e l tubulo contorneado proximal está formado por una epite--

i i o cúbico simple.

Los túbulos proximales poseen una luz amplia como puede apreciarse en

e l riñón i n vivo.

Asa de Henle. Los CorpÚsculos situados cerca de l a región medular (más n s

merosos que l o s superf ic ia les ) poseen asas de henle mayores que l a s de -- los corpúsculos l o c d i z a d o s cerca de l a cápsula. Cada &a de Henle tiene-

forma de U con un brazo delgado y o t r o grueso. En i a s asas largas (más n%

merosas) l a curvatura está siempre en e l s e p e n t o delgado, en cambio en -- l a s cortas se loca l i zan en e l segmento Trueso. Por consiguiente, l a mayor

porción d e l segrneEto delgado es descente y l a mayor porción de l a parte - gruesa es ascendente ( f i gu ra 5).

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La porción delgada t i ene un d i b e t r o ex te r io r de cerca de 12 micras - pero laluz es a. ip l ia puesto que sÚ pared está formada por cé lu las aplana-

das con núcleos que sobresalen hacia l a luz.

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Fig. 4.- CorÚsculo de Malpigki. En l a parte superior de la f i gura aparece

en e l polo vascular con sus arterimlas eferentes y aferentes y l a mácula-

densa. La pared d e 1; a r h & o l a aferente muestra l a s cé iu ias yuxtagiome-

lares. Observese l a forma de l o s podositos y las aaracter ís t ic ; s de les - cé l u l as de l a hoja pa r i e t a l de la cgpsulñ d e Bowman. En l a parte infe-

r i o r de l a f i g . apirece en e l polo ur inar io con e l túbulo contomeado tu- ¡ I bular. I

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Fig . 5. Local ización c o r t i c a l y medular de los componentes d e l nefrón y - d e l sistema cia l o s ductos colectores; estos últ imos est& representLdos - en negro. I

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'Rsbulo oor,torneado distal.-Cuando l a porción gruesa d e l asa de Eienle pens

' tran en l a co r t i ca l , conserva. la misma estructura histo lbgica; s in embar-

eo, se vuelve tortucsó y pasa a llamarse túbulo contorneado d i s t a l , que - e s e l Último segmento d e l nefrón, estando igualmente revestie'o por epite-

l i o cúbico simple.

E l túbulo d i s t d esta junto a l oorpÚsculo de Malpighi d e l mismo ne+&

frón, frecuentemente inmediato a l a s a r t e r i o l as e ferente y aferente. En - es te punto la pared del túbulo d i s t a l se modificar s u s células se vuelven

c i l indr i cas .

TÚbulos colectores.- k orina pasa de los túbulos contorneados distales-

a l o s túbulos co lectores que en l a médula se unen unos a o t r o s forniando - tubos cada ve z de mayor c d i b r e que se dir igen a l a s papilas. La mayor -- parte de l o s tubos co lectores est& en l a médula y siguen un trayecto r e g

I íneo loc tubos colectoren de qmor ,diámetro se ha l l v r revest idos por epL

t e l i o cÚhico y tienen un d.iárnetro as 40 micrzs eproxinadainente. A medid¿.-

que se unen y se aproxi:nan a lás papi las aumenta e l d i h e t r o Uel tubo que

en l a s inmediaciones de l a papi la l l e g a alcaxzar 200 mioras.

Aparato yuxtaglome%Ular.- Muy cnroa d e l corpúsculo de Malpighi l a arte--

r i o l a aferente presenta una modificación en su cupa media; posee células-

epite1ioidk;i en vez de f i b r a s musculIires l isas. La arteric. la aferente pug

? e ser yu,@aca merced al apari.to yuxtaglomerulár.

Sistema vzscular de l riiiÓn.- A l i gual que e l hígado también e l rilión en-

su microestmctura esta o rgan isdo 3e&. la oonotnicción de su oistzma w-

vascular ( f i gu ra 6) . La arteriz: r e n d , arteri:. mug gruesa SO x m i f i v a en

e l h i l i 0 d r i riñón en numerosos ramos que entre l a s papi las renales se in tnrnan como ar te r ias inter lobulares o peripiramicales. Em e l l ím i t e entre

l a sustmcih oiedular y l a ocrt , i cá i se producen una nueva r a i f i c L c i ó s ;--

emergientio l a s a r te r ias arciformen que por últimc despiden l a s ya nenoio-

nadas a r t e r i a s i n t e r l o b i l i l l a r e s qnca entre l o s radios medulares se d i r i y e

gen hacia l a pe r i f e r i z . De e-,tas ürt?r ias i t l t e r l obu l i l l a res penden l o s '7

glornérulos mediante sus s r t e r í a s af9rentes. Las ; . r ter ías eferentes se res.

sueihren *.e nuevo, esta v e z en una Fed cap i la r terminal. Los c q i l a r e s vea

nosos vue?.ven a juntar l a :sangre y l a conducen ii lo largo de las arteritcs

in t e r i obu l i l l a r es y l ob i i l i l l a r es a IC, vena renal.

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Fig. 6 Sieteme v z s x l a r d e l riiíbn. En rojos arter ías.

Vias urinarias eferentes.

Las v í a s ur inzr ias efereiiptas Qai:iienzan v ir tualxente con los túbulos - co lectores d e l parhquiinii rensl.. Xstos se reUI?en en un conducto pap i l z r - de l o s cuz les entre 10 a 30 desembocan en zr vé r t i c e p i r a i d a l c pagi lñ - rsr.rl ofreciendo e l aspacto rls m c peque56 criba, &e¿ , cn jbos i a z I r pzpi-

la. Uía o v;riss pepi las son tcnidús >or u11 c 5 l i z rer:sl, uni de lo:: rami-

ficecic7:es ue IC pe l v i s renal, que recoge l a orirc. cc:i!o vn pequeso embudo

( i5mina 1). La p e l v i s renal.- k p e l v i s renal t im4 a&:; o nienos e l aspectc infwdibu-

l i f o r im fle l o s cCl iccs, pero su fcr!oa e r apliinalla. La forma de 1;'. re@$:- rt?i;rl pii+Ce v:.rikr ~ u c h o . 6o:::o extre:.ius opuestos pueden ds~rse formes de - t i p o ü.entrít ico :i' t ipo ampolloso ( f i gura 7), sier:?& e 1 t i p o r w i i f i c d o e l

mEs frecuente.

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Lus papi las renales est& reveat idzs por ? p i t e l i o cúbico simple, qGe-

er. el p l i egue de t r m c i c i i n hacia el c & l i z se w a l v e p lur iestrat i f i cado.

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Los c z l i c e s y l a p e l v i s renal est& tapi icdos por e l 1lam;do e p i t e l i o de-

transición de l a s v í a s ur ixar icn eferentes. En t o m o a l niisnio se sr.cuez--

t r a t e j i d o cor.ectivo con rniocitos y f i b r a s e lás t i oas j por fuers w ü adven -

Fig . 7 .- Tipo den t r í t i c o ,y ampolloso de l a p e l v i s renal.

I üréter.- Xida aproxi!np.damente 30 cent&etros de largo. Es un conducto que

I l l e v a le orina de l a p e l v i s renal a l a ve j iga. Fin su comienzo est2 situa-

I do en l a cavidad abdoiiiinal ir.mediatamente p o r debrjc de l peritoneo y en - ' su porción abbd.c:ninal se l o obsorva en e l r e l i s v e i i e l a pared abi.iomina1 -- , poeteriorgstvlr io eviscruda l a cavi,ií!.li peritoneal. En l a l ínea i leopectí--

nea se acode &:o si@ier:do lusgo en su porción j e i v iana l a pared de l a

p e l v i s inenor sobrecruzmdc l a ar t e r i a '

i l í a c a COI& muy en le proxinidad-

j de d iv is ión. Por último trmAscurre en direcciór. a lgo s ed ia l desocibien - , do un l eve arco, intercruza, en e l hombre e l conduoto deferente, en l a mu- 1 j e r l a a r t e r i z u t e r i n a en e l t e j i d o conectivo pelviano, y per fora en di--

I r w c i ó n cblioue, l a pared de lz v e j i g a en UT: s i t i o Tróximo a su base que , ! dentrm de l a misma, es e l &&lo l a t e r a l d e l tr ígono ves ica l . I

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La pared d e l uréter conste &e tÚnicó mcosa, tÚnica muscular y tÚnica

adventicia. E l e p i t e l i o ure tL l mest:a m a estmctura especií i l . En estado

de contracción ureta l , el ' ep i t e l i o es p lur i es t ra t i f i cado , volvi&&ose bi-

=l.

ER

SUSTAüCIA C D R W A L

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SECM DCC R I M N

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VENA REWAL 13OáA DE UNA PAPILA

Lámina 1.- Riñón. Recorte oblicua pars

parénquima renal , e l peaículo r a d y

representar conjuntmente e l - 12 p e l v i s renal.

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es t ra t i f i cado en l a di latación. L-a capa superior no es plana sino que -- forma rodetes de cé lu las relativamente grandes recubiert : . ,~ por co'lulás - subymentes. Ha rec ib ido e l nombre de e p i t e l i o de transición y se encuen-

t r a desde l a p e l v i s renal hasti; l a uretra inclusive. k. túnica muscular - consta de una capa muscular longitudinal ia tema, ide Iinaieapa c i rcu lar mz d i a y de una cap; longitudinal externa que f a l t a en l a porción abdominal-

que está situada inmediatamente debajo d e l peritoneo. L-, f a l t a l a membra-

na basal y l a muscularis mucosae.

La ve j iga .

k v e j i g a (lámina 3) e s un órgano iravitariomusouloso que junta i a -- or ina que gotea rítmicamente d e l u r é t e r . Está situada en e l p e l v i s menor,

detrás de l o s pubis, y en estado de vacuidad. no sobrepasa e l borde supe--

r i o r de l o s mismos. Su capacidad varáa en l os .dos sexos y de un individuo

a otro , pero se puede d e c i r que una v e j i g a sma aún colmanso su máxima cz pacidad no l l e g a hasta e l ombligo.

En l a v e j i g a se kistinguer, e& fondo vesicular , e l cuerpo ves i ca l , y e l

vér t ice . E l v é r t i c e mire hacia arrib'a y adelante, e l fondo mira haciü ato,

j o y atrás, de suerte que e l e j e del , Órgano transcurre en l a l ínea media

dende arr iba y delante hasta abajo y atrás. k veg i j a está suspendida por

e l v é r t i c e mediante e l ligamente umbi l ical med.iano o cuerda de uraco., - que se t iende en l a pared aodoroinal ,anterior harta e l ombligo y es e l -- r es to d e l conducto vesicoalantoides f e t d obliterado, Uraco.

Iia veaiga está recubierta por e l peritoneo solamente en su sector pos

t e r i o r . E l espacio subperitoneal entre l a pared ves i ca l anter ior , l a s í f i

s i s y l a pared abdominal anter ior está ocupado por t e j i d o coneotivo laxo9

se llama espacio retropúbico o pevesical , y permite e l desplazamiento de-

l a pared ves i ca l ouando e l Órgano se l lena. D e l lado de l a pared pos t e r i c -

or, e l peritoneo l l e g a en e l hombre hasta los v é r t i c e s de l a s vesículas - seminares; aquí se rep l i ega sobre la pared anter ior d e l recto formando l a

excavación rectovesical . En l a mujer, se interpone e l útero entre e l rec-

t o y l a ve j i ga , de suerte que e l peritoneo se pepl iega desde l a v e j i ga - desde e l cuerpo d e l útero formándose l a excavación vesioouterina. :

mcmsa de l a v e j i g a es gruesa y pletór ica. E l e p i t e l i o e s e l mismo

que ex i s te en l a p e l v i s renal y en e l ureter , o sea e l llamado e p i t e l i o -

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IELUE UttETERAL

R I ú 0 0 V6álCAL

U W L A V 0 S I C A L

MS0#3OCAOUnA DEL CONOWTO WAEULADOR -U MONTANUM

O E ~ D C A D W A DEL UWCULO PIIDSTA W m A L DE LA FURC(0K *8)3RANOSA DE

L A 3ULJOUffETRAL 3JL30 DEL PEN

-3OCAUJIIA DE LA úLANDULA 3 U L m W C T R A L :ONDO DE SAGO DEL SIL3

Lámina 3.- Vej iga masculina y parción superior de l a uretra (abiertas

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de transic ión de l a s v í a s ur inar ias eferentes. E l r e l i e v e de l a mucosa d$

l a mayor parte de l a superf ic ie interria se la v e j i g a es e l mismo. Sl v e r tive d e l t r í g m c apunta hacia abajo y e s e l o r i f i c i o endovesical de l a

uretra. b pared poster ior de este o r i f i c i o t i ene una eminencia más o me-

nos marcada, l a ú k l a vesical; e l l a corresponde a l lóbulo medio de la '..:--

próstata.. Lce &gulos superiores d e l tr ígono son los o r i f i c i o ureta les .- Un pl iegue .transversal, p l i egue ureta l , ensancha e l tr ígono algo hacia - ambos lados; se destaca más POT e l uré te r que perfora 1? pared ves i ca l en

dirección oblicua. A d i f e r e r c i a rlel res to de l a !mcosa ves ica l , e l trígc-

no es h ís t t i i to sensible a l dolor.

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Ia msculnture de 1+ v e j i g a está dispuestrí en forma de red y está -- mezclada con f i b r a s nl&tir,n,s. Convencjonalmente se dist ingie i , tires ca.pss

se& l a disposic ión que muestra le porción paravesica.1 del. uréter , pero-

estas c a p s no pueden ser dife:cenciadb.s coa precisión. Eh c m b i o l a rmiscg

ls ture dol t r ígono ves i ca l consta de un c o l c h h grueso d.e f i b r a s f inas -- que t i ene :por función f i jar mediante l a modificeción de su tono l a pos ic i

Ón de los o r i f i c i o s u r o t d e s . %cia abajo l a s f i b ras musculares d.el t r í g o - nc acrsic&l se cort inúm forman.o us asa muscular que enlaza a modo de hon - da l a pcrción i n i c i a l de l a uretra, miÍsculo es f in te r ves ica l . Este ezf in-

t e r 5 s , 'e iiusci?~iitura Lisa. Lo acompaña en BW M c i ó n un .segundo m''scuio-

c i r cu la r y esqriado, músculo elsfinter ureti-21 que enlaza l a porción nem-

branosa de l a uretra; ente dscuLo groviene de l o s inÚsculos 301 Terinco . De es te modo en l c oclusión y eel vacicmientc cooperan mÚsc6los voluntari-

os e involunterios.

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Uretra.- Es u11 coriducto que l l e v a l a orina de l a v e j i g a a l ex te r io r me-

diante el zcto de l a micción. En el sexo masculino l a u-etrs da también-

pcso a l espernc durante l a eyarulación. En e1 sexo femenino es un óraelno-

exclusivamentecel a y 2 r ~ t 0 urinario.

uretra masculi.na. Est6 fornaua por Ins porciones; prostát ica, me&-

brenosa y cr?vernosa. o peniana.

ie próstata está situ3,ic- muy cerca de l a ve j i ga , y en su in t e r i o r se-

encuentra l a parte i n i c i a l de :la uretrE,. Los coriductos que t rmspcr t in l a

secreción de l a próstata se abren en l a uretra prostática.

% l a pcrciÓn d.orsal de l a uretra pros t z t i ca hay una elevaciónrque se

pro-recta hacia 911 in te r io r , e l verumontanum. ?Zn e l 6pice d e l veromtanum

se a h r e un tubo c i ego sin funoidn (desconocida) , e l a t r í cu lo pros$&ioo.

A l o s lados d e l veruinontmum se abren dos conductos eyaculadores, por -- l o s cuales pasa e l esporrná. Ls uretra prostát ice e s t á revestida por epi-

1 i o fie trexsic ión.

k uretra menbranosa ~ 6 1 0 t i ene 1 cm de extefisión >r e s t i revestide - nor onitel . io seudostrati f icado columnar, ex i s tkndo en esta zona, un e s f í n

ter l’e :,:Úsculo eGtriado, e l e s f ín t e r externo de l a . uretra.

La uretra civernosa se 1oc;iliza en e l cue-rpo cLverncso d e l pene. C e r

ca de su extremidd externa, l i i luz ae l a ure t ia cavernosa se d i l a ta , far

man:!o l a f osa caiiicular. ~1 e p i t e l i o de l a uretra czvernosr es suedostra-

t i f i c a d o columnna.r, con <reas <?e e p i t e l i o p&vi !.cr.toso estri t i f i c ~ . d o .

bas glándulas de L i t t r é sori &e1 t i po musculosorg se encuentran en to-

cia la extensión &e l a uretrt;, wn,me precorni.n;n en 12 uretra penianz.

A l g u ~ a s de est: s glSn6ulas tienen sus partes aeoretorss incluidas en

e l ep i t e l i ode revestiuiiento de la uretr;., rnientxs que 0trc.s ?oseen eo=--

dhct os excret ore s.

Üaetra femenina. Es un conducto de 4 a 5 cm de longitud revest ido nor

e p i t e l i o p lmn . estrat i f ic ; ido, con zonas de e p i t e l i o seudoatratificac?o co-

lumnar. Cercc Le su aberture a l exter ioT, l a uretra femenina t iene un es-

f írtnr de n6sculo ostriEdo, e l es f ín te r externo de 1,. i iretra.

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P A R T E I1

F I S I O L O G I A .

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FISIOLOCIAr

introducción I

Auzrte de clgunos experhentos real izados por Galeno puede decirse - 9ue hasta l a Última mitad d e l s i g l o XIX no se r e l i m r o n investigaciones - con el f i n cie determinar e l mecanismo de 1:. formación C.e orina. Previa---

mente no ex is t ían más ~ u e hi&esis basadas en l o s conocii..ientos anatómi-

cos de l a &poca. Qaleno, convencido de 1á verdad de l a sentencia de Aris-

t ó t e l e s de que “ l a naturdeza no l?.áce nada en vanott, decía, a l hablab de-

l a c arter i i . s renales, “ s i no es para pur i f i ca r 12 sínzre que l levan, que-

se me d ige norqué l a naturaleza las ha creado tan consi lebables y por que’ l a s ha prolongado y rimif icado a l igual quc l a s venas, hzste l e cavided - miama de l o s rii5ones”. MalpiThi descubridor de l a corteza renal y 6.e pe--

que?as c$psulas globulosas conteniendo im nudo de capi lares, dedujo que - en estas cgpsulas se formrbz la orina Gue era conducida hasta la pe l v i s - r e n d por l o s túbulos. Bowman en 1842, demostró l a ccntinuidad de Ir. csp-

sula ~ u e l l e v a su nombre con los tubos ur in f f e ros , y estudió l a estmctu-

re d e l e p i t e l i o de éstos, f a l l una hipÓDesis segÚn 1+ cual 12s cglulas-

riel híbulo serían l a s encar:adaa d e el iminer de l a s t r i v e l o s principios-

espec í f i cos de l a ori.na.

Dos &os in& tarde, Iudwig, e l cé lebre f i s i ó l o g o dem& opuso a esta

t e o r í a una t e o r í a puramente mec5nica. Considero a l o s giomémios como apa

ratos de f i l t r ac i ón .

En 1874 Reidenhain modif icó l a t e o r í a de Bowman, sostenienbo que 10s-

glomémlos sepegabm agua y algunas sales y ope l a s cé lu las tubulares h=

cian l o mismo con otras excretando también productos d e l nett-bolismo y - sustáncia,s extrañas.

Cushny (1917) propone u o r Últ imo, l a er.tonces llamada t e o r í a moderna,

eb l a que admite que e l primer proceso en la formc.ción de l a orina es la-

f i l trú.ciÓn, a través d e l glomérulo, d e un l íquido cuya composición es siw

mi lar a l a d e l plasma sanguíneo en cuanto a su proporción de agua y sus--

tancias c r i s ta lb ides y que este u l t ra f i l t r ado se concentra en e l tubo u- n í f e r o por l a absorción de un f lu ido de composición constante, quedando - en e l tdbulo y concentrandose en 61 l a sustancias de desecho que se eiimL

nan con l a orina; tuvo que admitir que esa absorción de un f l u i d o Óptimo

ten ía que deberse a una

capacidad excretora de l a s oé ln las tubulares.

“actividad v i t z l d e l e p i t e l i o tubular”, nego la-

Procesos renales básioos.

La formación de l a orina empieza por l a f i l t r a c i ó n d e l plasma esenci-

almente l i b r e de proteínas, a través de l o s capi lares glomerulares, hecia

e l i n t e r i o r de l a cápsula de Bowman. La orina f i n a l que entra a l a p e l v i s

renal d i f i e r e completamente d e l f i l t rado glomeniral porque a l f l u i r e l lí -ido f i l t r a d o de l a cápsula de Bowman a través de l a s partes r e s t a t e s - d e l túbulo, se a l t e ra su composiciÓn. Este cambio ocurre mediante dos p rg

ceso8 generales, l a reabsorción tubular y i a secreción tubular. E l túbulo

se ha l l a en todos sus puntos, intimamente relacionado con los cspi lares - peritubulares, l a re lación que permite l a transferencia de los materiales

entre e l plasma ger i tubular y e l i n e t r i o r d e l túbulo (lumen tubular). Cu-

a d o l a d i recc ión de l a transferencia va d e l lumen tubular a l plasma capi

l a r peritubular, e l proceso se denomina reabsorción tubular. El moviwien-

t o en d i recc ió i opuesta, es to AS, d e l plasma peritubular a l lumm tubular

se denomina secreción tubula. (No cor,fundirse este termino con excreción;

d e c i r que un2 sust nc ia ha sido excretaaá e s afirmar solamente que e l l a - aparece en &a orina f i na l ) . La f i gura 8 i lus t ra estas relaciones.

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1 R L T R A C W WOt4Elh)I.M L SCIIÍCIOW 7UIULAn

T<HULAn

Fig. 8 .- Los t r e s elementos basicos de l a función renal.

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Las relziciones in& comunes entre estos procesos renales bzsicos -fil-

tración glomerui&, reabsorción tubular, y secreción tubular aparecen en-

1 a ~ f i gura 9. E l plasma contiene las sustancias X, Y, y 2 entran a los c g

p i l a r e s glomerulares. C ie r ta cantid?!d de plasma desprovi:ito de proteínas-

que contienen est;s sustancias se f i l t r a a l i n td r i o r de l a cápsula de Bow m a n entra a l tÚbulo proximal, y empieza BU f l u j o a través d e l resto d e l - túbulo. E1 res to d e l plasmr, que contiene tembién X, Y, y 2 abandonan - l o s capi lares glomerulares a través de l a a r t e r i o l a e ferente, y entran - los capi lares peritubulares. Las c ~ l i i l a s que componen e l e p i t e l i o tubular

pueden t rmspor t s r en form:. act iva X, d e l plasma peritubular e l in t e r i o - d e l lumen tubular, pero no en dirección opuesta. Medimto esta cornbinacii

6n de 1: f i l t r a c i ó n y 12 secreción tubular todo e l plasma que inicialmen-

t e entro a l a a r t e r i a renal se l i b e r s de la sustancia X l a cual sale del-

cuerpo en l a orina. S i e l tcbulo fuera incapaz de reabsorción l a Y y 2 - inicialmente f i l t r a d a s en e l glomérulo también saldrían d e l cuerpo en la-

l a orina, pero e l túbulo puede transportar l a s susti l lc ies Y y 2, d e l 111--

men tubular nuevmente a l inber ior & e l plasma:per3-tubular. La cs i t i5ad de

reabsorción d.e Y es pequeña de t a l mulelea que l a mayor parte d e l material

f i l t r d o se l e clel cuerpo.; pero respecto de 2 e1 mecanismo de reabsorción-

e s trn poderoso que virtual.,:ent,e la totc.lid,d d e l material f i l trado f luye

a t ravés de l a vena renal nuevmente n l a vena uavci.

E l riñón tarabaja solamente sobre e l plasma. C2ea sustancia d e l plasma

e s maipulzda por e l nefrón de una menera caracter íst ica. E l punto c r í t i -

co con;iste en que l a s tasas de avance de l o s procesos pert inentes est&-

sujetas e l contro l f i s i o l óg i co . E l desencadenamiento de cmbios dn l a fil-

tración o reabsorción segulan 19. concentración -.de l a sustancia en e l p lag

nia.

F i l t r ac i ón glomerular.- e l $íqiiido que fml tra a t ravés d e l glomérulo ha--

c i a l a cápsula de Bowman se denomine f i l t r L d o glomerular; l a membra3 de-

10s capi lares glomemlares rec ibe e l nombrn de membrana glomenihr. Fin @

nera l es t2 membrana e s anábga a la de los d.em& cspiLares, presenta..aly_

nas d i f e re rc i es . En primer lugar, t i ene t r e s capas Srincipaies: 1) l a en-

d o t e l i a l d e l propio c;gilar; '2) una baatal, 3) una capa de cé lulús epite-

l i a l e s que r e v i s t e Is super f ic ie de 12 c ~ p s u l z de Barman. A pevar d e l I&-

yor nri'mro d~e caplipas, l a poo-osiri.r.d de l a mernbrma g1o:nerular es de 100 a -- 1000 veces mzyor que l a de l o r capi lare- usuales. Así rues, e l Ei ltrrdo-

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La 2resiÓn cLpi1s.r Elcinaruler e ? ~ zeneralmente de unos 50 mm Eg . &to L

r es, aproximadamente l a nit& de l a 5resiÓn a r t e r i a l media y considerable- i mente superior a l a de otros capi larbs d e l cuerpo. La presi6n hidrcstát i -

cap i l a r que favorecr I r - * i i t rbs i6n no sí:rec: co.xllet. serite i;c oposición . Pcr otr . p i s t e 1a gresión colmidornEfir i de l a siir,:re y l a aresick en l a -

cíissula <e 3o:rman se oponen z 13. f i l t rc ,c ión. La o r d i n i r i o , l i szztit?e.-i r1.e

proteín?. qx.e k j r PE cLgsIi1L t!e Poimr;? e s :qeinLsi$!o pequefiagarc. trrnr s i - b

nif ic: ,crox; Tnro en csso de üunent.:Ti ccnsidercb~c:nonte, su Cresi6n cc lo i -

dcs:iCtica cviden+ei,iente i n t e r v e r d r x ~2 n i v e l d e LL ~ e n h r i ~ l e z lomrulcr ir. -

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o e l ?aso d e l líqcir!c a trw +?L - n!ernbrma.

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Composición < e l f i l t r a d o glomeiu1ár.- Tier.2 .\-si exactanerite l a sisa; que

e l i i q i i d o xu,? e::.ni.?i <<e l cu xtremos ari ;eri :%les ,'.e l o s capi lar-s hzci;! - lo-, líqii'iilo ; i n t e i s t i c i . les. No coi.tienn ~ l o b u i o o rojos, 3- meros de .O5 - po r 100 de proteína y menos del. 1/2C0 de 1; ::roteína Cel plas.:.a.

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b cc:q,osición en el .ectr6l i . tos j. otros solutos d e l di1 trúrio ~ l o m ~ r u - -

l a r e s s:milar i IC r?el l íqu ido i n t e r s t i c i a l . Bebido i 12, pobrazz ae io--

nes 2e proteínas c, r@os negetivrmente en el f i l t rudc , se esteblece un - qGui l ihr j~c que hace que le ccricrntrüción &e l o s demás ione i nogativoo in-

c l u p n ? o e1 c lon i rc y e l bictrboneto sea &proxiru R lente 5% mayor t,mto-

en e l 14quicio i n t e r s t i c i 1 corn en e 1 glomerular, que en e l plasma; l a e-

conc+I:+,yúciÓn de ionei, pos i t i v os e s eproxiin&amente 5% menor, la u cor-cen-

tracicn-s de sustmcias c r i s ta lo ides no i on i z as, como ure?., creatinína,

y alucose 3 9 t h aumantúda.8 aproxima.r?arnente 4 $ debir;o a 1; munnncii ci,si-

t o t a l d e proteínzs.

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: c c -h resumen, przct icaxer te e i E1trad.o glomerular es i;,Qal ai plasma, -

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s i n conteliido inmii ' iesto *e proteínns.

Temas de f i l t r a c i ó n .:loneiulur.- En e l ho::ibre e l vol.unen promedio c i ~ 1 lf quicio f i l t r a d o d e l plasma il in . ter ior de l a c6psulz r!e Bowmvl e s de lC40 - l i t ros/ d i n , el. volumen t o t a l ? e l plasma es f i I t r i l r io por l o s rii<ones unas

60 veces a1 di?.. Esta capacidt-d de procesar voluinenes tm i;rzndes de p l a s

mn es, en parte , l a que ok~.paciea a l o s riñones para exoretar capacidzrI;:3

enormes de desecho yzegular l o s elemento;; d e l arnbiente interno en forma - tan precisa. LE persona promec".io excreta entre 1 y 2 l i t r o s Ce or ins por-

d ía , e l 99 $ d e l a,@a f i l t r z d t , debe s.zr reabsorvido. h a i ü e l i n f e r i o r de-

l o s capi lares per i tuñi lares, ü..:liendo d e l cuerpo e l l $ restante en forma

de orina.

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En i ~ n peri6do de 24 hrs se recoge l a orinb d e l sujeto, se nide en es-

t e voluzen d.e orin?. l a cmti6ii.ú ae ins:;¿ por l i t r o y se encuentra que es - de 72C mg/litro, por l o t:lr,to, a f i n de eaoretan ?Coma de SSLS; en 24 hrs

e l su?.?to debe h:.ber fStr:-clo 720 mg e= e l üiismo periódo de 24 hrs. En - ot ros términos pare exp l i car I n a.9-riciÓn de 720 mg Ce nasé en 1~ orina - f i n a l deben habsrso f i l t r d o en un periÓdo i e 26 hrs 180 l i t r o 3 de plasm?"

-e conlienei. un& conr.en+r.;ción cie 4 mg/:/litro.

Rormaliiente e l f i l t ra r ' o ,g.!omerular ccrisiituye m;'s o nonos una quinta-

purte (le1 plasma t o t z l que entra. a l rii7,c'n. En est& forma, e l flujo plzsmi

t i c o renal t o t a l es ip,ual a 900 l i t ro/día o 0.61C litros/min. P o r l o tm-

t o l o s riñones reciben ii3 una -:uinta a una cu.arta parte d e l debito curdi5

co t o t a l ( 5 litros/min.), aunque su peso combinado e s i n f e r i o r &l 1 5 del

pee0 tot8.l d e l cuerpo estas r o l r c i cne i ?.parecen en la. figur;. 10.

Rssbsorción *bular.- El filt.rcido clonieruls-r que penetra en l o s túbulo.: - del nefrón sigue; 1) ncr e l tÚh.ilo proximal; 2) a&xivér. de 1a.s a s i s de -- Henle; 3) hacis e l tÚbulo diste1 y 4) por e1 tubo co l ec tor hacis, l a pel-

V i s d e l riñón. A l o lareo cie este trayecto algunes sustsxcirs son reabsor

vi!ias o 3ecretada.s selectiv-mente por e l e p i t e l i o tubular e l l íqu ieo

tante que penetra en l a p e l v i s es l a orina. La reabsorción &esempeñz un - papel mucho menor quo l a secreción en esta formación de orina, pero l a se

creción e s p, rticularments importtnte para r e g i r cuales ser'n l a s crnt ids

des de ione:; de pot?,sio, ionea de hick6genc y unas cuantaa suatuicias más-

-

-

~ en l e orina. i

De o rd im i o más d.el 99 $ de e.ga d e l f i l t r a d o glomenilar e s reabsorbi-

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SETANCIA Y

~

O R I N A O R I N A O R I N A

Fig. 9 Manipulación renal de tres sistemas X, Y, y z

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do en l o s túbulos. Por l o tiinto, s i al&n constituyente d isue l to d e l f i l-

trado glomerular no es reabsorvido a l o k r g o de su trayecto por los tú- los , .esta reabsorción de agua evidentemente concentra l a sustancia más de

99 veces. Por o t ra parte, algunos componentes como glucosa y asinoacioos-

son reabsorvidos c i , s i totalmente de manerú. que su concentraciór. baja casi

hasta cero anbes que e l l íqu ido se transforme en orina. &h esta forma l o s

tu'bulos separvl l a s sustancias que deben conservbrse por e l cuerpo de lae sustancias qut2 6eben el iminarse con l a orina.

Los mecmismos bgsicos para ,Bransportarse a través cie la. membrana tu-

bular son enencialmente l o s misnos que l o s ñe t rmspor te a través de o t ra

membrana, corporal. Pueden d i v id i r s e en transporte act ivo, transporte pas&

vo o di fusión.

l-

t VDCUHEN TOTAL DE

TE AL RWt4 ViA DE L A A R T E mJos out wmm n u n s m L

100 LITROS OIA

7 2 0 L i t n o s OIA c 140 L m o s DIA

I FLUJO SANWINEO RENAL T O T A L 1 O40 LITROMIP

PLA YIP TOTAL FILTRA00 OIANYIEIITE HACIAEL wrenion DE L A CAPSULA 1 DE 3DU)AN. t iFú1

Fig.l@.- Rlairnitud de l a ta.ssL de f i l t rLc iÓn glomerular.

Micción.

De los riñones, f luye la orina a l a v e j i g a ii través de l o s uréfecs -- impediba por l a s chntr;cciónes p e r i s t a l i t i c a s que forma l a =red uretera l

y que t i ene como otros d s c u l o s l i s os , r i tmisidad inherente. b. ve j i ga es

una estructura en forma de bomha de peredes constituidas por estratos - gruesos de mÚsculo l i so . A l contraerse l a s paredes comprimen hacia l a pa-y

t e interna aument,mdo ;vqf 12 ures1Ón de l a orlnn que hay en l a ve j i ga .

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La micción es basicamente un r e f l e j o espire1 l o c d que puede sometez se a l i f i f h j o I!e l o s centros cerebrz~l-es superiores. E l m'sculo de l a v e j i

ea rec ibe un abundante sumriistro de nervios parasimpáticos. -

Cuz:do la v e j i g a contiene solainente cantid: des pe,:ueñas de orina su p

presión interna es bnjc., es POCG la ec,timulz.ciÓn :le l o s receptores de es-

tirPmiento de l a ve j i ga , l o s nerv ios p6resimpáticos se h a l l a rels.tivumen

t e inactivos. -

Eh l o s adultos se tubene le capacidad de dem0rr.r 18 micción o inducix

l a volunta.rimsnte. En un adiJlt0 e l VChmen de orina que se requiere en

l a vediga pc.ra i n i c i a r e l r e f l e j o esriinal de contracCiÓn de l a misma es - a.proximadaiflente de 300ml. E l aplazmiento en l a s v i a s descendentes se --- l l e v a a cabo medimte l o s estímulos de l o s nervios motores que vm a l ss-

t í n t e r externo, c0ntrarrectand.c s,sí e l estímulo sin&ptico opuesto, ?roce-

? m t e d.e los resentores de e s t i r m i e n t o de 1- vej iqa.

Regulación d e l sofiio y enui l ihr io de! agua.- l o que a l agua se r o f i e c

Fe, 1~~ ecrcreción d e l sod.io 2 trwr.'.; de la p i e l y d a 1 t racto E-strointesti-

na.1 es, g o r l o Fenerzl, realmente pn~us i i i pero puerl.e incrementarse en f o z

a: not9bln diimmte el sudor, vómito o diarree en proporciones considera,--

bles.

c .

E l corterol d.e l e excrqción renal d.el sodic Y f ie l qa. constituye 107:-

rnecmisrnos ids import:nte:; jar ; - l a mgulacic% d e l sodio y Cel egua en e l -

ciierpo. L s t;*s¿r, excrito2is.s (::e e5;tc.s sustinaaas pueden texer :.iiz. vFrja-

ciÓri conc,ider:..ble; p o r ejwnplo, UP. g r n cor.wtf:idor de se.1 2ueC.e i n j e r i r - de 20 a 25 cr de NaCl el r l í i . , mientrcs un ?p.ciente sor~etido a un; d ie ta - i3.e poca w,i p e d e i p r e r i r dolmimte 50 mg. En t a l rango ? u d e e l risén - ro::nii~l a l$erar facilmente su excrei-ióc ? e sal. Tie manera s imi lar , 1 ~ , ex--

creci6n v r iner i edc q ~ c a puede v c i a r f j .c i&logicz.wnte desde unos 400 m l - / d & hzsf.: 25 l i tros/?<& , ~ ~ q g h so h í l l s . la :>exon& i '~; Qe.:ier:.c\ 3 p w

tic,ipiz:<o 25 xn;< cc ipetencis t i ? '2ehidz.

~ -.

Teblr 1. Rutas rcri:i.lcs de le in,qestión : pér<!idr C ? P so+io.

10.5

0.25 r.25

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R e ; p l x i & re:?:, 1 1; os::iolaridad ext:*;:cclulLr.- s'o?.vl:ms la ¿;ten-

ción F. 1z comper.s:ción renal ci4 1 ~ s p Q d i d a s 3' gweac ia ; se a;yua pur?,, - +>o-- ejenplo, una persona que bebe 2 l i t ro -s d.e rips, sin l i le ocurra cam-- k io r.I?ins en c l 7cr~teniCo to'ul d i s d d o l cuemc sino +:,n solo *ir1 -- ew.8 tott.1. E l mecmj smo ccmpens8.toric mols e f h i i n t n consiste e~ e x c r ~ t ~ r

10s riñonn,: e1 cixceso de qp2, sir. alterar su excreción od inar i c? cic Ss-1 esto prQciszaente 10 aue e l l o s hacen. La permeabilidtd de l o s t~:h~zlm,

d inta l es y ductos co lectores 8.1 a~puc. i56 kace inuy brijL, lz rscbsorci6n ($9-

rad io p r o c d s normalmente pera e l :SF; e s incapii: c?e c n c a r , y ::e e ~ c r e t a

ür. p n n volumen 6 e orina ertremadanecte~ disuelte . 2 s er ta mimera, se el&

m i - e r l FXCUSO d e +pa pra. Lon riñones producen 'ma orina final $.e csmo

lúridcd i gua l c, la d e l olásma o i n f s r i o r a la de éste (or ina hiycoinót ica)

ocurriendo 1á &tima ci?andc quierr cpe l e ?eohsorni& d e l agia p e 6 a rem

@.da con r e l . i6n a 1.i reabsorción del. scluto, es to es, cum60 1.13 reduce- 12, HA2 pl; fimstica. 3st; ??-?-o cue 1- f c rmc ió - O e LIP? ori,na. hopoos:fi;'ti.ca-

cwstiti::.Fe iir,í< h u w * cornpenapci66". (I+] s s x ~ s o de riyu; en $1. cuerpo.

-

Re,ml,-ciÓYi del ?otri.si~o.- L? concentr?.ciÓn de potiasj.n d e l l f ? i i i d @ S Y ~ P P C ~

l n l a r e s ext-echz-norte rerplwdi en su cnn+idr<. La iniportrr:cie de w.rte--

ner "eta concectreciór en ni ; ,nbi.e~te Zntnmo SQ r'eriva prirnordia.lmente - d e l papel d e l gc tec io en l a excits.bil idad de lor, nervior, y múcc.clo8. 'la - e

l ev : ción de I r cc? r~ r t rnc i ón externa de pct.acio reduce e l potencial de - IF, membrm:: en rspoqo, a1mentazc2o ;..sí 1c e m i t ; bi1id:g.d cel.i:l~ar. Y >l. l a - irvers;: , la reducción f i e l potaaio .externo hinel'poiariza l a s membrannas

1i;lares 27 rechice su exci tehi l idad.

U200 que le mayor per te d e l potasio d e l cuerpo se enccentrz dentro de

18,s células, ante todo como resGlt8,dc de l o s n is t ems de transporte act i -

vo d e l ion localizar?os en l a s membranas ce lulares, auri una l i g e r a a.lter2-

ciÓn de l a s t::sas Oe transporte .;el ion 2 través de l s s membranas celula-

ren puedo producir un gran cambio en l a can?5?.rd de pote.sio ex t r i ce lu le r .

La person; normal per~,iünece en e:lui.librio So ta l de potasio mediante - 12 excreción d i a r i a de unít ci.ntidad de potasio i p e . 1 a l a cantidac ingerL

dz lnencs l a s car.ti.dzdes re2ucidl.s que se eliminan en l a s materias f e o d e s

y e l sudor. Las pérdidas d e l pott,sio á. tr;.vés d e l sudor y d e l t r t c t c Sas-

t r o in t es t ina l son normalmente pequeñ-as.

E l poto,s i r es comp1et;:iiiente f i l t r a b l e en e l glomérulo. Las cmtidades-

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de potasio excretado en 1;- or ine son generalmente une parte reducida, ( d e l

10 a l 15 $) de la cantió:c! f i l tr ; ,da, estableciendose a s í &a re<.l i*Ld d.e - l a mzbsorción tubular d e l potasio. Los cL,mbios que se producen en l a ex-

cTeciÓn d e l pothsio obedecen i l o s cmbios producidos en l a seoreción üe l

mismo.

La horinona aldosterona controla l a secreción d e l potasio, además de - a p d a r a l a reabsoroión tubular d e l sodio, aumenta l a secreción tubular - d e l potasió. Dicha hormona e:; secretada por l a s cé lu las de l a corteza su-

pzarrenal que son sensibles en s í mismes, a l a ccncentraoión d.e potasio - d e l l íqu ido extracelular que l a s baña. E l control y l o s e fectos tubulares

r e ra l e s de l a aldosterona aparecen resumidos en l a f igura 11.

I A L ICSTERDEA PLASNATICA

I

Fig. 11 .- Resumen del control ae l a aldosterona y sus

funciones.

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Regdación d e l calcio.- b. concentración de l c:.lcio se mantiene de ordins

r i o relativamente constant??, ?.erivándose 1; exieencia de la re,placiEn -- precisa. primPrdialrnente -de l o s efectos profundos que causii e l ca l c i o en ., l a e x c i t i W l i d a d neuromuscular. Una baja coricentración de ca l c i o aumenta- l a exc i tab i l idad de l a s membranas ce lu lares nerviosas y musculeres de tal

manera que l a s personas aquejadas de enfermedades en que se presenta nia-

v e l bajo de c s l c i o sufren de t é t m o hipocalcémioo. E l c t l c i o a s í mismo - e s importante en l a coagulación de l a sangre, pero e l n i v e l bajo d e l cal-

c i o .no e s nunca, desde el uunto de v i s t a c l ín i co , causa de coagulación - nnormal porque l o s n ive l es requeridos pera esta función se hal lan consid2

rablemente por deba jc de l o s Gue producen e l t é t m o f e t t l . b. hipercalce-

mia es también pe l igrosa en cuanto oausa arritmias c; rdísca.s como también

d i-,mir.uciÓn de l a exc i tab i l idad neurc:nuscular.

Por l o menos t r e s s i t i o s e featores se hallan implicados en la regula-

ción de l a concentración extr; :celular d e l c d c i o r e l hueso; e l ririón y e l

t r a c t o east ro in t e c t ina l . E l hheso. Aproximaiiainerite e l 99 por c iento d e l c a l c i o t o t a l d e l cuerpo

de un marco de m Ó 1 2 se ha l l a en e l hueso, e l cual consta primordialmente

culas ó r g h i c i s en que se depositan cristc:!es de fos fato c d c i o .

li.1 t r sc to gastrointestir lal . La absorción de ca l c i o está sujeta a un - contro l hormonal de gran presisión.

E l ri;iÓn. E1 rilÓn manipula e l c d c i o por f i l t r a c i ó n ;r reabsorción . E l manejo de f o s f a t o es import,znte en l a regulación d e l c r l c i o extracelu-

lar.

Los +res s i t i o s descr i tos anteriormente están sujetos ;1 control .!e - una hormona prc te i cc d ominad:< Hormona paratiroiae;, protucid?. T)or l e s - cl&dulas parotiroideas. La producción de 1.. hormona. pws. t i roi6r.a est6 - cor,trclzíi;:. airectamente por l a concentración ae ca l c i o d e l l íqu ido DXtT3.e

cel?>. lar que ban2 1s.s cé l i i las de dichas g'.&diil.%s. Ie. reducciór de c,: lcio-

estimula 1s prccción y l ibert.ci6n de l e h.ormona. parat iro idea, y una meyor

conosntra.ciÓn hace l o contrario.

LE vitamina '> estfmul; la. n3sorciÓn d e l c ; i l c io por oa.rte d e l in tes t i -

@ acti,vid;:d en 6 I t i - a insfancia e s cnr'trcli-d? .por c l c:,lcio p l asmát~ no, co.

~ z , :"oymonfi c i ~-citoninp. e; ; s:si:retada ucr Inn cé1rila.c: ?lie se hs.ll'W

t r o de l a nlándu??, ti.roidoc la. 51121 rode:-n, oero se dif3zRncj.m :or-letr.-

mente rln 1.0s f o l f cu l os que secretan l a t i roxina. k cs.lcitonina reduce el cs.lcio pl;.smz.tic.o primordiaimentf? i .nhi biend~o 12 reabsorción por ,,?.,-te $ e l

huesc. Su secreción es ccntroloda direot;imsnte por IC ccnrsE tr:,.ciÓn del. - -:am:. que :.b.zstece tl ir%ctxnente la cl&dtla t i ro idea .

Regulación d e l ion hidrógeno.- La mayoria de l a s rec,.cciones metwbólices * son dn delic&;!. sensibi l idad ii l a concentración de l ion hidróceno d e l 15 qiiido en clue ocurren. Ta l sensibi l idad se uebe ante todo a1 marcdo i n f &

jo de l a fuLir!ciÓn enzimática ejercidc. por el ion hidrógeno. La concentraci

Ón de ion hidrógeno d e l 1í i iuido.extri icelulYr e s una de l a s cantiilrtdes q u i

nicr:r, más desicivits y estcechmente r ew ladas de t o d o el cuerpo.

.- -

-

La centidad de ácido fosf&ico, sulfGt.ico y or&ico que se form, en-

l a serccria normal, depende primorc'ialmente d e l t i p o y l a cmt idad de a l i -

mento ingerido. S i ha de mantenerse e l equ i l ib r io d e l ion hidrógeno, debe

el iminarse d e l cuerpo cada díe. l a misma cantidad. La pérdida ocurre a trs v6s de l o s riñones. Ademis éstos deben ser capaces de a l t e ra r su excreci-

ón de ion hidrógeno es resxest ; . , a l o s cambios que se presentan en l a pro

ducción de ion hidrógeno por p a r t e tiel cuerpo sin importar 16 fuente. Los

r iños deben ser 8,s; mismo cspticer; de compensar cui- lquier pérdida o ganan-

c i e gastro intest ina l d e l ion 1?irGrÓ$enc.

-

Virtualmente l a to ta l idad d e l ion hidrógeno excretado en l a orina en-

t r a a !.os túbulos en l z secreción tubular ; :el e f e c t o de control de l áci-

do result:! primordialmente e jerc ido de mznerá d i rec ta en l a cé lulas tubu-

lares , sin nerv io u hormonL alguna de por medio. Gbvimente, un sistema - tíil es e f e c t i v o pare Ba estü.%ilizaciÓn. de l a concentración a e l ion hidrÓ-

genoen su v a l o r nomal. + k oapacid.ad de los riñones para excretar H depende t m ? o de 1;- secre

c ióntuai lar d e l ion hidrógeno como de los amortiguadores de l a orina.

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P A R T E I 1 1

D I A L I S I S .

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Ahora hace ya unos 25 230s que se emplean riñones e r t i f i c i e l e s para - t r a t a r pa.cientes que sufren g r i v e insuf ic ienc ia renal. En a l e n o s t ipos - de inmf i c i8nc ia r e n d eguda, como. e l resultente de intoxicscióh merci~ri-

:.l. o e l choque c i rcu lá tor io , e l riñón 5 . r t i f i c i a l so u t i l i z a simpaenente - para poder consenrar en v ida a l paciente durante unas semanes, hasta que-

l a l es ión rena.1 haya c u r d o y los rinones puedan asumir nuevmente SUS -- funciones. E l riñón a r t i f i c i a l set ido perfeccionando hasta e l punto que - >ay n i l e s de persopas con i n s u f b i e n c i a renal pe-mrnentemente, i w l u s o jt

' . imen extrisa6os totclmente mbcs riñones, y que siez;en en her. 2sta

do de s;.lufi, a Treces durmte sños; su vi.dz d-epende tot;..lmmte d e l r i ñ & - a r t i f i c i a l . Otro recurso es:.el transplant:? +.e riñón, hasta enero ?.e 1981-

en MI'xicc se real izaron en e l Instituno Nacional de Nutrición 100 trans--

plantes, BE! de l os casos provinieron de aonadores vivos, 12 d4 gersonas

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que mrieron. Easta l a fechú sólo han muerto 23 pacientes ya sea por re--

chaúo o ir.fecaión, 11 viven con c i d a de riñones a r t i f i c i a l e s y 66 con - buena fUnciÓn renal (1).

51 pr inc ip io brcsico d.el r5Ón a r t i f i c i a l est,riba en hacer c i r cu lar 1;

-,;rigre por unos conductos muy f inos de membranes muy delgLcias. Sn e l otro

la30 de e:s'us nembrrnas hay un 1ícpid.o d i c l i zante k c i k e l cia1 l a s u s t e

c i s indeseable de l a sangre puss por d.ifusiÓn.

i,a f i gura 12 i lustra. un r i zón e r t i f i c i a l en e l ciicil IC sangre corltinuc,

mente pzst. 1. tr:ivéu de doc Fiojí.:3 del~t.d(!i?s ce c e l o f h y en e l lado e-xterno-

de c?rle l&i.na hay 111: l íau ido dia l izante. E l celo?& es sufioientesente -

31,

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aquipos mcdezms, se t i e r en l i s s i .p ientes ccrec+eríst icasr operación 2-u-

tomatizdu, nuevos e l e w n t o s ccsnductorea <e smgre , al ta se,%rid:.ci en l o s

i rocesos de puri f icr .c i fn, real izados >ara tener los en c l in l cas c en casa-

de l o s pacientes. Sin embargo nuevas invert ig. .ciones p o s i b i l i t a , 1á. e x i s

tenc ia <e n%evos &todos t e u l t ra f i l t rac ión , difusión y hemofi l tración, - que pueden ser pue.,-:os en estos equipos. Los avances incorporatoe tr;en - c i e r t a s desvmta jas &ales comos l a conplejirlrd de l o s sistemas de ?roces2

mirnto y imiestreo dg C ~ t o s , l a necesidad de unu maxor difusim’n, atención-

y cladic-oión en e l uso p opereoión de estos cparútos.(2).

8 .

I . / Un inc.trumento QUS pronorcionaun i.ndics de u l t ra f i l t r ac i ón 3n hemodis

l i s i s por membrrnas ha sido de.:&rrollad.o debido ?, l a necesidxi de un con-

trol e s t r i c t o en e l proceso. E1 monitor de u l t ra f i l t r ac i ón para hemodiáli-

s i e rec ibe t-ns señales de ertrzda que sons l a variación de l a s presiones

de entrcd;, al sistene de hemodiSlisis por membrtna, la v, r iac ión fie l a s - preoicnes 6.- sa l id& C.al mismo y l a v¿r iaciÓn en e l volumen entre e l f l u j o

s in &ia i i i?ar y e l fJujo dializadm; y con éztos, monitorea la pre;zi& en l a

nembrani., $1 volumen ultrsfi l trado .y 01 índice de u l t ra f i l t r z c i ón . (3)

Cusldo +err 91 riñón a r t i f i c i a l normalmente, l a i sangre s:Le continu-

meste de una arteria., a t róv iesó e l Ctispcsitivo, y e s devuelto a u.na vena.

~i volumen t o t a l de sangra en e l ri’ibn a r t i f i c i a l en todo momento es de - unos 500 ml; l a intenaidPd d e l flujo puede ser de Varios centena re^: +.e m i

por minuto, y In super f ic ie de d i fus ión t o t a l suele hal larse entre 10,000-

y 20pO0 cm . Pera e v i t a r l a co:,,*la<;iÓn de l a s a p r e en e l ri56n ct i f i -

c i a 1 so int ioduce xeparina en e l l a cuando penetrc en e l ririón. L e g o , pa-

rá e v i t a r l.;% hemorr:gia en el pEciente e consecuencii de l z t acción de la-

heparins, se inyecta una s u s t m r i i antiheparínica, l a protamina, er! l a - sangre devuelto. a l enfemo.

2

Observando 1, ncturo.lezi+ de 12 ooncucción eaéctr ic¿ en e l ouc-rpo k u c ~

no se sabe que ex i s t e u ~ a corrier.te con ima frecuencia abajo de l o s 1-z

a trave‘s d e l f l u i d o extrace lu lar este e f e c t o puede ser u s d o parü medir - l a s d i ferenc ias en e l f l u i d o en l o s espac ia in t e r i o r es d e l cuerpo, e s 62

c i r , podemos implementar un método que u t i l i c e l a dmpedzrcia p a r estim;tr

l o s cambios en n i to t i i l de p.gu?. d e l cuerpo. Para. una mzyor exactitud. se - hzcen l a s nesiciones a dos freciiencizs, e l cambio de la. impednnnia es ir2

"

38

c

i r i

r i

.-

r i

L

r L

1-

L

c

i

L c c c r

porcional a l cFmbio de volumen, l o s d: t os obtenidos deb?n ser microproce-

ssiioi par un monitoreo continuo (4) .

+

.%l. dislizrinb fresca tamp. constante Ussd8

Fig. 12 .- Esquema de un riñón a r t i f i c i a l .

E l l íqu ido de diáJ!i&,.- 4. tabla 2 compara l a composición de un l íquido

d ia l i zante t:pico con l a de l plasma normal y e l plasma urémico. Observese i

que l a s concentraciones de sodio, potasio y c loruro en l íquido d ia l i zante

, y en e l plasma normal son idénticos, pero en e l plasma urénico las conceg

I t raciones d,e po-tasio y de cloruro est& corsmderablemente elevadas. Este-

1 i&n difunde a t ravés de l a membrana d ia l i zante con t a l rapidez * . que SU c o ~ I I

I

centración

t e en plazo de t r e s a cuatro horas de exposición a l mismo.

cae hasta quedar igual R. l a que t i ene en e l l íqu ido d i a l i z a n i

Por o t ra parte, no hay fosfato, urea, urato n i creictinina en e l 1fquL do dia l izante. Por l o tanto, cuando e l paclente urénico se somete a diál j-

s i s esta sustancias se pienlen en gran cantided hacia e l l iqu ido de l a - sangre, con l o cual se eliminan grandes cantidildes d e e l l a s existentes en

e l plasma,

Así pues, los constituyente,, d e l l íqu ido d ia l i zante se e l i gen de mane

en cü-

so de uremia. pueda suprimirse con gran r&idez, mientras que los e1ectrÓA

l i t o s normales pers isten en f o w e esencidmente normal.

- r a que l a sustancialse Fb ha l l a en exceso en e l l íqu ido extracelular

* Plasma l íquido Plasma

Constituyentes normal d i a l 1 zan t e urémico

E l e c t r ó l i t o s (mes/ 1)

Na+ 142 142 142

K+ 5 5 8

c a++ 3 3 2

%++ I.. 5 1.5 1.5

c 1- 10 7 10 7 10 7

"XI) 27 27 14 -

Lactato 1.2 t.2 1:2

IiP04 3 O 9

--

Urato 0.3 O

O S i l f a t o 0.5 -- 2

3

~. - I I 1

40

E Constituyente Plasma Líquido Plasma

nnrmal d ia l i zante urémicc

c

r i

i

c c

- i

i

c t-

No e l e c t r a i i t o s

(mg por 100)

Glucosa 100 125 100

.Urea 26 O 200

Creatinina 1 O 6

J

Tabla 2 .- Comparación d e l l íquido d iP l i zante

con e l plasma normal y e1 >lama urémicc.

Se ha encontredo clue e l r eml tado de Is descom?osiciÓn de l e urea es-

principzJmenta una. funcidn de entrada de energía a l a cé lula, con aumento

de PH, fcrmxción de cotnpuestos c lorares t F 1 C O ~ O c1or;'minc.s.

E l conocimiento de la- re::cciones de desconposición de la urea posib& l i t a e l r e c i c l o ds1 l íquido d i d i z t d o r . Li: urea puede ser oxid:,da, e l e c t r g 7

I . liti.camnntn en una solución d i i i i m c o r a con 1s aplicación de energía y -- con ternperrtura; s in embmgo, se h:. encontrado pequeños prodi.ictcs secund-

que se disuelve en e l 2inl i .zador y - r i o de c lo rzn ine i e hidracinas,

una, oxid&rj.Ón sustmci;.l de Zluccs? y acetatc presentes er n l d . i a l j .

especialmarte a altor. n i v e l e s t ie ensrg í i . Easta &or?. 12. a.plicación cl . ini - cíi de este sistema. cuede ser ir .coqari :do mediznte l:.,. climini.ciÓn 6e éstas

co2

.cienes intermeaias. (5)

Eficacizi, < e l riñón art; f j c id . - k a f i c x i s . &e iin ri.5Ón a r t i f i c i ñ l su

r--,.P "-..~, .-,, ~.

tF3ci.s ?or minuto; s i rwcr2:rnos l o d i c h o mtericrmente, e l l o tzmbiéi.,

ronct.ituye la form: mas i q c r t a t e de e q r e s : r 1,. cfici..r:i: Ciinsional * e 4

l o s ,úropios riñones. k mayor pn.rte pecien ; e l a r a r 'or minilto 100 a 200 - m l tie plasma <IC i i .re~., l o cual Sermiestra,, que, por l o nencs en l o que se - ref j-ere R 1.3 excreción de estas s i ist 'ncias, e1 riñón 3r t i f i c i e . i p~tnr'e fun

oionar m5.s dos veces más rápi<...ments que 10s &os rizome- normal.mente ;iun

se,::h 91 vo!.~:njr. (!il - ! am zue puede aclkrarse de l f i ferentes sus

I

c

L r L

r i

c

i i

r L

- i L

I tos, cuyo aclsrimiento de ~ I . T ~ ? F solo ea 2e 70 m l por mi.nuto. Sin enbargo,-

0 1 ri5Ón a r t i f i c i a l no puede iit i l io:.rse DOT' más rie doce hores czds. t r e s c

cii;tro d i a s ?or el pe l i g ro de exceso cie hper ina , hemóliz is e i r f e c c i fn . Fn ?onneci:encia, $1 aclarpmiento pl&mico tot:-1 se h a l l a todrx íe alKo li-

mitado cumdo e l riñón a r t i f i c i a l d s t i t i i y e a l o s riñones nrrmales.

h s ?rocesoo, d.e d i z l i c i r ; son muy costoeos principalmente qor el d t o -

prec io *.e Ic.3 membroni.s para filtrar l a sengre debido a *-to, ee deben 5.2

s;,rroll.ar mé~odot: para limpi zr l es ruembronas dia l izadoras para que puedan

ser reusdas. las procesos incluyenr lavado con ácido c lorh ídr ico , despub

& con u n . solución de peróxidc de hidrógeno que actus como selvente de-

l a sangre, luego enjuagado nuevaente con água y finalmente se e s t e r i l i z a

con una solución di luida% de formaldehido.(6)

I

La pr.idicoiÓn de desarro l lo de un hemodiaiilkdor e s importante ya que

es un probl.ema. c l fnico. E1 modelo de ecuaciones parcia les d i i f e renc ides - en dos v¿,riables; y generalmente requiere de solución numérica.

E l cimbio d e l l íquido d i e l i zbdo implica. un problemz de va lores la - f ront era.

Un método a l ternat ivo para e l an&l i s i s d e l comportamiento d e l hemodia

l i z - d o r modelo de parai'ietros conocidos de este modelo resulta una solucicn

Ó a ana l l t i ca a\@. problema, d e l cual l a concentración e e l soluto en sm--

g re puede ser calculado.

-

~i mo2elo p u d e ser aplicado a complejos geométricos .y m& complica--

dos sistemi;s paciente-riñón e r t i f i c i s l . ( 7 ) - Un m 5 1 i s i e te6r ico ' t : ~ o 1 4 1~ tra,:;fcrericic $e mz;?':: en un- cavidad-

d i tiel- , ? e l ri=ión ar t i f i c i c .1 con ültraf i l . t raci6n par ir a)

& cc IC ;5.:2j.sis constante; b) ur.i ccnc>3zitreciÓn c m fa ~ i c l i s i s \-arj.&s1c

a IC Icrt;o l e 1.2 lon,T:iti.id diel tubo. La solución li t,3nei>ios ;;ir $1 mótcco- 2,. s e p ~ z . cin'r: c<s vr.ri;bleu i:ss^ni.o unc. se r i e d- exTnr:siiC ini ' inits. 61 re-

s x l t i d c ins i c¿ que e l t i po d e c i t ,nnf i i tsac i&, 1~ pc?ri;1cLbili:'d de la ,['- hranna y 2~ eonczntrúsión. cn l a L i s l i s i s d i s t i r t s de cero t. iece ur! 9fecto-

s i + y i f i c a t i v o en l a clearance d e l . soluto.( 8)

<;c,i:car'tr:..cj.&, -

..

.. P A R T E I V

i

r-

i

L

P

V E J I G A U R I N A R I A .

L

r- r i

r i L

c

L

.... c

‘L

c

L

c

i

c

i

c

i

r L

I

í L

c

i

,-

t 1 4 4

r i P

L

c

I

L

r L

I

i

- L

- L

- L

r

L

i

c L

r L-

fod.?; su longitud.

Cuar.?o se rcur.en o r i m en ?.L pe l v i s , ’.A prsuión L;uiiiintt en el].a-, y se

i n i c i a un¿ con t r sc i ón pe r i s t á l t i ca , que co::iiertna sfi l a p e l v i s y CiifllC

de hc,cia abejo siguiendo e l urétnr púr, impulFshr 1; orina hacit. 1 . vejiga.

Apórace un;: and:; per is t6Zt ica que s- desplnz:: cen velocidad de unos 3 cm/

zog desde c d i . 10 se,?. hia.;ta.cz&. 2 ó 3 minutos. Lz onda p e r i s t á l t i c a -- puede dexpla-ar or inr contrá una obstrucción con prer;iÓr .h.zst;. de 25 m,&g

La estimulación parasimp?tica aumenta, y la estii!nil.coión siupáticc. dizmie

cuye dichz. frecuencia. LÚ. trar-s:niciÓr. Ue I&. onda. per is tGl t ica deper.de pro

ba3lemer.t.c rle iinpulsos nerviosos que p e s a a l o largo ciel plexo intram--

r d en la iiisma formú. como Jfunoionan e l plexo intrúrnural d e l intest ino.

su extreno i n f e r i o r e l i i réter per;etia en 1á ve j i gb 2 trav6:: de t r i

rlono se,&. se i l u s t r a en 12 fimra 13. i 3 l uréter sigue unos centímetros - por <:ebajo Le1 e p i t e l i o vas i cz l , de rnanere que 1ú pr.esiÓn en l e vejiga. l o

coriprirne y e v i t s as í e l f luJc ?.$trÓgrído de orina oumio üumenta 1z presA

ór en &.;tú duruite 1~ micción.

IneIvsciÓn de l a ve j ig i . - Según se in i i s?b en l a f i í p r a 13, la -veJigc u r i -

nar is , enenci;:lmanfs una vesícula de m<sculo kiso, es tc foriusL por dos-

partes pmincipalesr z) e l cuerpo, Que compreziie prirncipalaente e l rr6ucuio

detrusor, b) e l tr ígono, pe<;ukia zona t r i á l gu la r cerca .{.e le . boca. tie 1, vz jiFm a travéi . de 1~ c u d p~3a.n ambos urdteres y 1~ L-Tetra. Cuaniio 1; v e j i

ga se d i l a ta , e s e l cuerpo de la mi.sma e l que se disti.ende; durmte e l -- flujo de l a micción; es e l tdsculo detrusor e l que se c0r.trs.e ?ara vaciar

l a v e j i g r .

-

E l znísculo d e l tr isono e:rtC eritrelbzi.do alradedcr ie lá &hrt i^ ra de l a

ur::tr; y mcntienc un c i e r r e ion.ico r i e l r s s m a hastiL que 16 . ;>resi& Ue la-

m i . s m a se e leva t m t o que vence e l tonc miiscul.ar. Por l o tzritc, e l nnísccio

d e l tr íyono rec ibe e l nombre de esfi:.inter i c terno @.e l a ve j iga . Unos cell-

t ímetros :.& Lila ds l z ve j i ga , 1s. uretra atrrviect. e l Ci@rarrua uro:%ci-

t a l , c u p m.isouláturá constituye e l es f ín t e r externo de Ir vesiza. Sete - m’sriilo es esquelét ico voluntLrio, en contraste COK e l re:to de L , musci.1-

l , t u r i + r!e li, v e j i g e , constituid:? totalmente por e l m’~cu10 l i so . 221 estad

do norm=] este es f ín te r externo se cons9rvz. Fin contracción tórice. c p n imy

picie e l goteo constmte de orii-’a. pero puede r e k j s r s e voluntarianente o

en forma r e f l e j a ;.1 tiempo de 1i inicción.

Lt! fiqurU. 13 también i lus t ra l a s conexiones nerviosas fundmentóles en

I I I

45 c c r L

L

r L

r i

r L

r L

r . .-

niéduia espinrrl ?ara control de l a v e j i g e . La exci tación parasimpática p a

voca contracción d e l músculo depresor y quizá c i e r t a abertura d e l e s f i n t g

inberno. Las f i b r a s sensit ivas nerviosas abandonan la ve j i ga principalvie2

t e wompaiíando a. l o s nervios parasiizpat5cos médulü. es-

pine1 por l o s nervios pelv iancs y e l ?lex0 sacro. E l es f ínter externo de-

la ve j i ge , músculo esquelét ico voluntario, es controlado por e l nerv io p~

dendo que t i ene su origen en l o s dos primeros segmentos sacros de l a médu - l a espinal. La niisrne f i gura muestra f i b r a s simpáticas que pasan de l a s r e - qiones lumbares de l a médula siguiendo e l plexo hipoggstr ico hacia l a ve- j i ga . La estimu3aciÓn de estos nervios hace que se r e l r j e l a v e j i ga , o -- sea un e fec to OpUeStO a l de l a estiuula.ción parasimpática. Sin embergo, - en estado normal los nervios :;impáticos no interwienen en e l control de - l a micción.

y p e n e t r a en 1;

ESFlNTEn EXTEilNO

F i z . 13 Ve j i ga ur inar ia :r su i n e r v x i ó n

k i n grcpiedr. r?s de band; s de mÚsculo l i s o de la ve j i ga (en un cerdo)C.

fueron inves t i gd i i s meiiante 1;:. medición iie acortamiento y alargamientos- rápidos con di ferentes n i v e l e s de fuerza. Un modelo por medio d e l cual - puede e m l i c a r s e e l comportamiento de l a propiedades e lás t i cas es e l mode

r i i

L

F

L

i

P

i

r- 1 L

i

c

l o de f ib ras des l i zab les d e l músculo contrLct i1 (Y ) . Llenado de la vejiga.- La o r i n i que penetra a l a v e j i g a i:jipulsada rítmi--

cemente por l a s cont rac iones pe r i s t á l t i cas d e l uréter , llenR, aquélla, en-

forme lenta y l a d i l a t a progresiva:iiente. La musculatura de l e ve j i ga , tie ne l a propiedad de adaptar su capacidad a l o s ctimbios de su contenicio s in

que va r í e myornente l a presión interna.

La l ínea cor.tiniia. de l a f i g i r a 14 rec ibe e l nombre de cistomegrmr d e

la ve j iga . &best -a l o s cr:.ibios de presión i r t rnves i ca l es a medida que se-

l l ena l a v e j i g c con orina. Cuando no hay nada de orint- en la ve j i ga , l a - presión intraves ica l es aproximé..damente nula, pero cuando se he. reunido - en e l l a 100 m l de orina, Ir? presiÓn'habV& aumentado hasta aproximadamente

10 cm 2.e agua. La l legada adicional de orina hasta 400 ml puede acumular

se sin aumento importante depresión; l a pre.;iÓn se conserva todavía en 10

cm de agua, l o cual depenae d e l tono intr ínseco de l a propia pared ves<--

c e l . ?Gs a l l < de este punto, 1? acumula.ciÓr. d . e orina hace que l a r,ri::sión-

se ele eve mug rRpidmente,

Suuerpuestos a, l o s cvmbios de pre,;iÓn tónica mientras sue vc llenando

l a vejiga., hay aumentos a p d o s per iódicos de presión c:ue durui de5de unos cumto. se:qmdon a más da un minuto. Ls. presión puede e levarse solzmente

uno^ pocos centínntros de >,ni?, o hs.st= mss de 100 cm de a. F s t x scn-

on6r.s < e mj-cción en e l cisto:netogr;ima, cau.&adas por el r e f l e j o en l a mic-

ción.

En esta eCe,pa exi.-,ten proniedades 9asivas eil 1í1 vejiga, que ?iis+en se-

8.ercrit::s en terminos de l e re lación volumen-nresión. bicho sintsnr: de - subr!j.vir'? snr a) dscendencia d P 1 ti.em,no ron 1~ pared. ne vej iqs. (?irer?e-

s e r ax?!icyin usando un mo4elo ?i?cdniástico) ; b) deoendenci?. de 1- ion-

,-itud d e I í ;wrd de l a veJigi , ( 9s mostr3'io en un :ródulo e?1á?$ico a . ! imi t i

do, el ciia.1 depende biexponenci?lmenitede 12 tensión); c ) geometría de 1,

v e j t j i i : r ina .r ia , ( e s dosrr i t? . como tin^ es fera dense crrc;idu d e t e j i d o oe - volumen constante), F i i mcdn2.o r : o r t i . e n ~ 14 pzrÉmetros, p r d i c e 1: forma -- d o l cistoyrymr prpcis : melifs. Los vr loreu SOR obtecidos ?or var iar %&ni--

cas de medición y son independientes d e l lugar y In dirección en que son-

tornados. Li re la jac ión constant9,ei módulo e l f n t i c o r e l a t i v o en su a t i c i -

Ón son constoEtes, l o c u d implica. una d.ependencia d e l tiempo l inea l . E l

volumen d e l t e j i d o en l a pared es constiinte, l a v e j i g a ur inar ia es esf+

ca. (10)

- 47

r-

L.

r

L

c

.. O t u l 200 300 o m

VOLWEN t m o

L

- L

i

Fig. 14 .- Cistonegrama norioál, mostrando tambign 0n'ia.s agutes de

pr i s ión (curvas de trezos) causadas por r e f l e j o s üe micaión.

' EvaouacHÓn de 18. vejiga.- fii acto da l a micción , zuncpe de naturaleza re f l e j a , se i n i c i s por l o general voluntarimente. Dicho mecanismo es pura-

mente r e f l e j o únicamente l o s niños o en aquellos C ~ I S O S patológicos, en l o s que l a v e j i g a e n t i á is ladr de l o s centros supericres. Cuana.o sobreviene - e l d.eceo de or iner en e l uduito, s s t e interv iene coq. su voluntad para re-

pr imir e l deseo o biex para c d e r a 61. E l grimer casg,inhibe parcialmen-

t e de l a micción J Se contr:a.e e 1 e s f í n t e r externo; l a presión ves i ca l < i s - minuye y e i deseo de or inar cesa. momantár?eamente. Se puede vencer voluntg

riarnente e l heseo de or inar hast;: que l a ve j i ga contiene unos 7OOml, en - cuvo CLSO aquél se vuelve imperioso y va acompañado de una sensación d o l 2

m s a en e l hipogastrio. Cuando e l sujeto cede a l deseo de orinar, se su-- prime i a contracción voluntaria a e l e s f í n t e r externo y se in i c ia , una oade

na de r e f l e j o s que terminar por váciar l a vejiga.. S in enibareo, puecie de-

tenerse a volunta& l a micción una y otra, vez por l a contracción ::el o s f í n

t e r externo. Durante 13. micción se contraen los músculos ves i ca l es (detrusor), se-

,, .

r I i

L

c

c

L

i

i

r e l a j a e l e s f í n t e r interno y l a orina es expel ida con fuerza considera--

b l e , pudiendo l a presión in t raves i ca l alcanzer una c i f r a de 130 cm de -- agua. E l comienzo de l a micción se h a l l a precedidg por l o general, de una

contracción 6e l o s mu-sculos abdo:iiin?,les y un paro inspirator io con l a ~12

t i .s cerrada. Este esfuerzo f a c i l i t a l a micción, pero no es indispensable-

par::, que e l l a se produzca. La contracción abdominal weae continuar duran

t e l a micción para ace lerar l a expulsión de la orina. En e l hombre, e l 2

!núscuio bulbocavernoso se contrae rítmicamente a l f i n a l de ia micción, con

l o que se expulsan l a s últimas gotas de or ina contenidas en l a uretra. - En l a mujer , l a micción termina bruscamente.

Mecrinisrnoa r e f l e j o s de l a miscciÓn.- Las investigaciones de ñarrinfiton en

e l gato hm revelado l a intervención de una. :serie de r e f l e j o s coordinados

en e l acto de l a micción. t os soni

1) Contracción de l a rnusculetura v es i ca l (detrusor) cuando l a presión in-

terns al 'anza a 10 cm de agua. Las vía; a ferentes de e r te r e f l e j o siguen-

e l trayecto de l o ; nervios pe.lvianos; su centro re encuentra en l a región

biilboprot1,berancial. En l a pared. v e a i o d parecen e x i s t i r rsce$ores sen--

sibl.es a 1: dfstenhión.

2) Contrhcción de 12 msculztura. v es i ca l c;iisadti por l a entres de orirla-

en l a uretra. Las ví2.s aferentes de es te r e f l e j o , qlie eseg.1ran e l vtcia--

miento veTica1 una vez comenzdo, es e l nerVio pudcnd.0, y su vía eferente

pondiente e l riervioxélvico; su centro se encuentra en l a región hi-

bo nrotuberancial.

3) Contracción dáb i l y t rans i to r ia de l a v e j i g r , c;uc4adá por l a clistanci-

ón c e la pri:n.:ra, porción <e 1 á uretra. Las v í as aferentes &e este r e f l e j o

s iq ien e l traiyectc '.el hipogáotrico.

4) ~ s l a j e c i ó n d e l es f ín ts r externo i t i a n e ~ pase. l íqu ido por l a uretra. Am-

bas v ías a f e r e s t i y e ferentes, siguen e l nerv io palendo.

5) af.?j'enfe r:j e l nerv io pé l v i co ; l a e fsrentc e l pudendo.

6) Rela5acibn del mv'sculo l i s o de 1.a i i retra en su t e r c i o su2erior cumdo-

se distisii<?e lz vaj iga. Ambas vías, aferente y e ierente, s i w s n rl nervio

p ~ l v i a n o . E l centro de estos cui t ro últimos r e f l e j o s se encuentra en l a T

médula s;,.crü.

Relajación del r:sf ínter externo cu3mio se c0ntrt.e l a vejig?,. b. v í a -

En el. ecto normal de Is mioción o&&¿ uno de estor r e f l e j o s , s?.lvo e l+

L lu!ga.r a que se estc;blesca e l s i s i e c t e , ase&zirmrír &sf que ze

- 1

4 9

57

P

L

F-.

L

c

i

c

C OnC IIJSI(EiE3 La función d e l apark.to ur inar io se resume en dos Krandeo -

ñmposi

i) notable part ic ipación en l a r egdac i ón d e l :nadio - interno ( smgrs, linf;, l íqu idos in t e r s t i c i c l a s ) que-

baña a l conjunto de cé lulas .-.el organismo.

ii) b. excreción de l o s desechos mstabo?icos-.

E l in i inx ión de deseetos.- cutitro sust.,tncir,s, refl.u.jo

de 12. act iv idwl d e l orgúnismo qus 84 excreta de mmer

r¿r regular en la oriEa ( i a lire& y e l ácir?c urícn, que

constituyen l a iíltiina etapa de l;, depulac ión (:e l m -

proteínas, 1~ . cre;t inins y l a creatina). También e l - desa lo jo de vitsrninas, enzimas, horconas ? e g r d d a s , i

g l&u ics ro jos y algunas cé lu las por medic de la ori-

na,. &e. concentración de esos minerales, e*tU' cjn film&

ón & e l equ i l i b r i o h idro l e l éc t r i vo Cc l plesna,

i c

L

- L

l a supresión d e l control voluntario de l a micción. S in embargo, en este--

caso e l ton? ves i ca l suele estar aumentadoprobablemente por líi aotividzd-

d e l p lexo nervioso::perivesical. La v e j i g a presenta d é l i l e s contracciónes-

cuando 1ñ cantidad de or ina que contiene es aun sscasa l o que da origen a

l a evacuación de volumenes ur iner ios que no exceden de l o s 100 ml. b. sección de l a médula. espina1 por encima de l a región s%cri. de ja in

tac to e l mecanismo r e f l e j o de l a micción, pero éste queda independiaado - de todo contro l voluntario.

Durente e l periódo de Shock medular e l r e f l e j o de l a micciCn está su-

primido y 6sta t i ene lugar por rebosaniento. Pasado este periÓdo, e l re--

f l e j o reaperece y 1,- v e j i g a se evacue en formz intermitente, s i bien sue-

l e !ped?-r un residuo in& o menos importate .

En alCmnos casos, l a estimiilación cutanea de la zona per inea l despie;

t a e l r e f l e j o , mecanismo que permite a los enfermos c i e r t o control de?su-

micción .

.

r L

c

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I

P A R T E v

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i

c

r-.

P

C O N C L U S I O N E S .

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H. Voss R. Herr l inger

Anatomís. humana. Tomo 1 y 2

Ed i t o r i a l e l Ateneo.

Suenos Aires,Lrgentina. 1968

L. C. Junqueira, J. Carneiro.

H is to log fe Básica.

Ed i t o r i a l Salvat

Barcelona, EspaEa. W72

B. A. Houssay, R. Caldeyro-Barcik

F i s i o l o g í a Humana

Ed i to r ia l " E l Ateneo".

ñuenos Aires, A r :entina. 1974

Arthur C. Guyton.

Tratado de F i s i o l o g í a medica.

Ed i t o r i a l interaméricana

México. 1976

J. L. Locsow

Anatbmía y f i s i o l o g í a humana

Ecl itorial i.nteram6rican.a

México, U.F. 1982

Vander, Sherman, Iuciano

F i s i o l og í a humana

Ed i t o r i a l MacGraw-Hill

México.1983

(1) Transplantes de riñón en el Ins t i tu to N x i o n a l de Nutrición. Arturo - 1 Dib Kuri.

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(9)

Medios contemporñneos pr?: la pur i f i cac ión extra renal en l a sangre

Yu. G. Kozlov, G.K. L is i ts ina. IEEE Enginaering Biomedical. 1981 Invest igación de un monitor de u l t ra f i l t r ac i ón ;>ara hemodiálisis . D. Gisser, 0. S t ra i t , A. Zelman. IEE Transduction on Biomedical - engineering. 1983 Uso d e l e s técnicas de impedancia para e l r eg i s t ro automaticode -- cambios en los volumenes de los f lu idos durante l a hemodií l is is.

B. Tei?ner. Medical and bio logY Engineering ui& comput. mqro 1983

Modelo de parámetros para hemodializbdor.

P. A. Ramacharndran, R.A. idashelkar. Medical & b i o l o m Eng. & compt

Vol. 18 . 1980

Reuso de una m&uina prcprPmeble cara a i g l i s i s .

X. Gentles, L. F. Braganza, C . S. Saiphoo, M a A. Manus1 . Xed & - Biol.' Ene. & Cornput. Novienibre, l9&0-

Recic lo de d ia l i zado par; e1 rilión a r t i f i c i 2 1 por degradación Plec-

troquímico de metr!icl itos inut i les : investigz2cicr:es do reecciones - continuas. M. Fels. Med. & Biol . Ihng. & Comput. Vo l 20. 1982

MHlis iE; de Un hemodi6lieador tubular - e f e c t o d e la ultra . f i l t rac i -

Ón y concentración sn l a d i j l i s i s . R Jagannathan, U. 9. Shhettigar

Med. & Biol. Eng. & Comput. Vol. 15 . 1977 Prppiedades semia last~eas de l a s banaas de n6sculo en l a veji ira u- nF.rir de un cerdo. R. van Mestrigt, E. A. Tauecchio. Med. & B i o l

~ n g . & Comput. Vol. 20 , 1982

Propiedades panims en 1,: v e j i g e ur inar ia en 1; fase d e colección.-

R. A. MastriEt, B. L. R . A. Coclsaet, W. A. van Diiyl. Med. & Biol.

Eng. & Comput. Vol. 16 1978

Pro?j.adatfea fie 1i.activintlad mecánica rlnl nlisculo l i s o 8.e 1;:. v..j;qa-

urinxr is . U. J. .Gr i f f i thn, R V ~ I M r s t r i @ , W. L. Van IjuDUyl , B. L. / R. P.. Ccolsret. Ked. & Bioi. En,?. & Corinut. Vol. 17,1979. C u m r p s d e l f lu ido de Ir- orinñ de hombres sanosi un noc:9lo matemgtico

de 1;. vejin;;., y r i q 1:- fvr i r ión urqtrd h r a n t e 12 micción. Meü. & - 3101. Ene. & Compt. !l. J. Gr i f f i ths , i:. J. Rollern:~.. Vol. 19-

is, 79

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BIOMEDICZNA Trasplantes de riiion en el Instituto Nacional de Nutrición

trición.

Los primeps 100 casos de transplantes de riñón rcaliza- dos en el Instituto Nacional de Nutrición fueron evalua- dos recientemente. El estudio lo realizó el doctor Arturo Dih Kuri, dirqtor de la Unidad de Trasplantes del De- partamento de Mcdicina Experimental del INN, fun- dado par el doctor Federico Chávez Peón. actual'subse. crerario de salubridad y asesor de ICyT.

El elevado número de pacientes con insuficiencia renal crónica, explicó el doctor Dib Kuri. ha obligado a mejo- rar y ampliar los programas de tratamiento. AI pruente, quienes sufren insuficiencia renal temiinal son tratados básicamente con tres programas: a) hemodiálisis crónica. b)diálisis peritoneal crónica y c) trasplante renal.

Los tres programas están relacionados entre sí. Sinem- hargo. el trasplante renal es el que más ventajas ofrece, tanto en materia económica a mediano y largo plazo, como por las posibilidades de rehabilitación psicosocial del paciente. -

Hasta la fecha sc han realizado ,100 en el,.INN trasplan- tes renales. En 88 casos los donadores fueron personas vi- vas. familiares de los pacienres; los restantes 12 órganos se obtuvieron de donadores que murieron. Las edades de los receptores variaron entre los I3 y los 50 aríos.

En 98 casos la enfermedad causal fue la glornerulone- fritis crónica; nueve sufrían glorneruloesclerosis; los restantes estaban enfennos de gota, lupus y nefrono- psitis. En todos los casos se utilizaron esquemas de i n - munización con base en esteroides (metilprednisolona y prednisorra) y azatioprina con las dosis convencionales..

La técnica quirúrgica consistió en llevar a cabo la ne- frectomía en el donador, hacer la perfusión del rifión con

96; J

. . solucio,nes frías, para después colocarlo en la fosa iliaca dd receptor mediante anastomosis de la vena renal a la iliaca en forma terminolateral y de la arteria renal a la hipgástrica en forma terminoterminal. El ureter se anas- tomma a la vejiga mediante la formación de un túnel su bmucoso .

Las complicaciones médicas observadas fueron: sin- drome de cushing en 26 casos; infección urinaria suhcli- nica en 19 ocasiones: ncrosis ruhular aguda en 12: hepái titis en cinco; citomegalovirus en cuatro; neumonía en tres; y herpes zoster también en tres casos.

Las complicaciones quirúrgicas consistieron en: ohs- trucción urinaria por coágulos en I ocasiones. fístuh un- naria en 5, infección de la herida en 4, esrenosis,de la anastomosis arterial en 2. linfoceles en 2. y hematoma pe- rirrenal en uno de los c a m . En 42 pacientes se presentó

" rechazo agudo del nuevo riñón; en 29 casos el rechazo fue L crónico y sólo en una ocasión hubo rechazo hiperagudq El 80 por ciento de loa casos de rechazo agudo fueron re. sueltos con el tratamiento previsto.

Hasta hoy han muerto 23 pacientes, 19 por rechazo o sepsis. 2 por insuficiencia hepática. uno por infarto de miocardio y uno por accidente.

&tos resultados indican. observó el doctor Dib-Kuri. que el Instituto Nacional de Nutrinón sc encuentra a la altura de los mejores institutos del mundo en transplantes de riñón. El promedio de muertes y comp-caciones en México es considerablemente más bajo que m u r o s pai-

La causa del txho sc debe, según el doctor Dib. a la -correcta evaluación de los candidatos y laclccción de los- donadorn que en la mayoría de.lor c a m "n familiares del enfermo, lo que ham que .aumenten las posibilidades de Funcionamiento del injerto y. por ende, de superviven-

SeS.

cia de los receptoru.D . Evolución global Porcentaje de pcienta

Muertos ........................................................ 23 Viven en diálisis ........................................ 11 Viven con buena función renal ....... ........ 66

.

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qi i i i . i l "y i s~i>l:~~~6%~,!ii < . I l~i ' i l L - Y . C ~ ~ ' I , / I i. r t , t > , , t i o ! ,.,I t i ' , .

s o f patients w i t h ?!ironic. renaJ i i i iuf i j .c ici icy. i v ion o f b!hod was c a r r i ed out 2 - 1 times per week [ r r i i i

oted Liie fiiri.ous tempo o f work i n th i s iipherc O I mi

cchnolagy and < urreut 2evelopmental t r

i t ed a t Lhe "T'uhlic Hi:;il.tli-Rfl" irit~erriacional o i ! i i i , i i 'i'n i contemporary apparatuscs i s c1i;iracterized by i . i i i , ' LI.-

i , ! . , 1 ~ t , ~ . m ~ , 'i,.it wt<li.Iy ustx ciitrit>g :I !vng:~l!:: pci-im! (LO-I '> .. * I / " 1 , \ ' :

ductl.ng blood (d ia lyzers , Lieniofiltratiiiii uiiiis, :iiid C I ~ I

if t l i c im<!liiod of extra-renal pur1 f l ra t i o i i 01- blood ( r e J e c t i m ( ' 1 i ~ mire aniS more widespread existence of apparatuses belonging t,'i

i ri ; i i t.ii the sa fe ty OS the procedure o f pur i f i ca t i on ;

. i g a (modelr of' portable apparatuses were not presente<!). rI?sign í o r an apparatus that can he used i n f ixed locations - - i r

Ri*ir,:!r,l I ~ I ; , , d~:vi,!<i!i,:~ t i t ; i l . ¡rends Tor these apparatuses, one slioilld note the. followinp

I ) Beside.s tiir me: Iiuids of hemodialysis and peritoneal d i a l y s i s wlii~ch have a l ready l x x n r t r , , < I i ! i < ~ ~ i , ~ l , ~ i i $,, i i i ~ ~ l i o i l s oí zil.iradiffiisloii Liiid !i<,.iiiiiFI1trüLi.i;ii t i y e b e i n g piit Inti - 1 1 . { ? i ? < . ~ i n cIic$;(? , ~,;ia.ratuses;

2) rcquiri-ineiits t.1 e t the p r i x e s s of puri f ic.at ion i)? physiologic are being strerigthi,iieil

1) t u a greater ai i greater degree, the parameters which d i r e c t l y or ind i rec t l y chttrac. t & r i z e tiw norn. i . i i i n g action o f ext.ra-renal pur i f i ca t i on of blood on the human iirgai ism iire heginrii?:: to be defined;

c i t i n g and processing information are being made s i gn i f i can t l y niore q>! ing analysis of iii€ormatioii i s becoming more videspread.

pi>iri i-C :

5) :I !;resit d e a l ( 1 1 attei i t ioi i i s being devoted to the imp1.eiiientatioii o f the external des:ign o f apparatuses w i t h the aim of increasing the e.ase w i t h which they can bci used.

In coiite.mporary "a1 t i f i c i a l kidney" apparatuses meant t o he used f o r extra-renal piirif cation ( I F blood I i y tlie method o f hemodialysis, deaerated idi.alysis s o l u t i m s (d ia lysate ) of u pi-rstribcd compusitirm and teniperature can be automatically prepared, hlood and dialyt;atr+ can he moved through tlie d ia lyzer a t prescribed rates , and the operating m n d i t i o i i n can he cnii t r o i led uutom;iti<i;iI iy.

I n the iipparatiises, t:he followi.iig functions are automatically contro l led : the prcssiir, on t i l < I n p i i t arid tI:v iwipiit o f t.hc pcrfiisioii piimp; the lev1.1. of h iood iii tlic 0 . t ~ trap; I t i ~ TLuw rat.<!. tcmnerature. aiid conduct;ince of dia lvsate : and tlic leahüee o f b l o o d i n t c the die'.vsn

All-Union Scientii ir-Research Ins t i tu t e o f Medical Instrument Construction, Moscow.. Translated f r r in i IlediLs:iiiYk.ayii Tektiiiika, No. 2, pp. 32-15, March-Aiiril, :IS81. Originnl iiri I C L C .;iliiit)itted i leceinbcr U, 19~0.

48 0006-3 i98/(~1/15OL-0048$0!.50 Q 1981 Plenum Publishing Corporation

'To ac~.compL.L!;ti this, Sirst and foremiwc the operator m u s t be prrivided w i f t i i l i i . ~ p a r m c ' l ~ ' r + ; c h a r a r t e r i z i n g :lie normaliz!ng a c t i o n of thc ex t ra - rena l p u r i f i c a t i o n o f hloh>d i>n i.hc h u n x i n orfiitii!~iii. SiiiiIi p:iranici.crR i t i r l i i d c the i l i i i lywii i t i i n i s , I hc rntc ni' I111w~l I l o w . 11x r : i i< ' o i ult i :a ! i l : rat ion, bind the u l t r a r i l t r a t e voliime.

i i l . t r a f i l t r n t i o n . Methods presupposing the automatic col1 ,ect ion 01: the neccssiirv inf<irni: i t i o n . . i ts automatic process ing , and the subsequent v i s u a l i z a t i u n o f t!ic r e s u l t s through the use o ? numbered i l luminated dials have replaced c a l c u l a t i o a methods t o drtermirie the mte i > f u1 t r a - í i . l ~ r i ~ t i i m , wlilcti were bnsed on lie col lect . i» i i oi datu thy t.lic opi:r:i~or uhiiui I l i t , ! r:iosiiicm- braiie pressure i i i the d i a l y z e r and on the process ing of t h e s e d a t a by hand.

'The automit1.c contro l o l the method o f u l t r a f i . l t r ; i t i o n has hccii piit I n t o c , I ~ I L ' , ' L iii t i i c , m;i.i<irity o f apparatuses represented a t the e x h i h i t i o n . I n the YC I30017 ; ipp;l ! -atw' ni i.hi, "i. .!eansolan S. A." firm (Franc.e.j, i n the A 2008 <: apparatus o f the Wl: firm ( i TR ) , aiid in the " S i ra t ron 1'M" apparatus o f the "Cordis Daw" f irni (USA) an isovo1iinietri.c niei.liod o l roil- triil was used. [n the 7200 apparatus of t h e "Drakr.Uil.Iock" ii.rm ( U S A ) , the piir;imr:ters

' i . l inracterizing tlie method o f u l t r a f i l t r a t i o n a r e determined I n a computer :>lit i i u!iiosí' Inpai t iii'e fed sfgmi1.s ; i b « u t the pressures o f blood and d i a l ~ y s a t e on the i n p u t and o i i i i i u t i>f Lhe d i a l y z e r , as w e l l as data about t h e tvpe o f d i a l y z e r used.

oi assumptions re[!arding. f o r example, the law O S <ii .s tr lb i i t ion o f pressures i n the d i a l y z e r , tiie determined rG>iiductivi~ty for water of the d i a l yzcr nieiiihranc. and tlic hylxiClir.!;i:s atioiit thi. i , i i I i r ~ r i i i dlstrll:iii I t in U T i i l í ~ ~ i l i i ~ i b i i i g the menil>rrine surr; ic ,o* hind uhoiir ilii' i l < ~ ~ i ~ i - r r i i i ~ v < I i~!;i~;iii t i i d < . <,I< i t s e f f e c t i v e :mrf:ice aren. The e x i s t e n c e o f tlit'si! assumptions d w r i i i i w s I lie rc.! 1:iliIi I Ly 0 1 lnfnrmat Ion ri ,pirdlng Clir opcriiting coiidltl»nn nf ii1.t r a f i l t r a t i m .

Here the volumes o f prepared and expended d i a l y s a t e a r e equalized aut«mati.c;il l y ' ani! the excess f l u i d ( d i a l y s a t e ) i s measured by a speci .a l ized device .

i n g the des i red c l . i n i c a i e f f e c t o f ex t ra - rena l puri f icat i .or i .

s ive ly . The outi'ut of t h e s e pumps depends on t h e speed rif rotat ir in o f the d r i v e slinít. tis

well a s on parameters c h a r a c t e r i z i n g t:he kinematics or the pimp and on the t i i b i n ~ used i n the pump -- i t s degree o f c.ompression. There fore , w1if.n r o i i t r o l l i n g the output o f a r o l l e r type pump on t h e h a s i s o f information about tlie speed o f r o t i t i o t i of the d r i v e ! < h a i l , i t i.,

s u l t , i n not one o f the apparatuses i n which t h e Flow r a t e of b1.ood i s cnntro'lled, i s the

'The g r e a t e s t progress !las been achieved i n the sphere n f automating< tiie control 01 ~ r'

'r!ie c i i l < : u l ~ t i o r i metl iod performed both manually and automat.ic.aJ.1y i s

The dlrect c,ontrol of u l t . r a f i l t r a t i o n by the isovol i imetr ic method i s more proini~sin&;.

Information regarding the r a t e o f hlood fl.«w i s very important t o the process o f obtain-

T r i foreigi i " a r t i f i c i a l kidne.y" apparatuses , roll.er type perSiisi.«ri pumps ai-e i i s t ~ d cxcl u-

ary t o use assumptions which m a t e r i a l l y i~nf luencf the accuracy o f cnntro l . As il re-

,. degree of e r r o r of this contro l fiuaranteed.

The use of p e r f u s h n piitiips of the r o l l e r type l.e:rds not on1.y 10 an iriidc,ier-riiiiir,<l <IC>(;I.*!E of e r r o r in t h e c o n t r o l of blood f l~ow, b u t a l ~ s o t o r!n ampl i f i ca t ion o f the control of pres- sures a t the i i i p u t and output o f the perfusion systrm; t o guarantee that t i i i , system i s :iter-- i l e , i t i n necessary t o use s p e c i a l d iv id ing chambers, which srp;.r;itc the h l o o d (~ondui~Li . i ix

~ connecting l i n e s From the contro l . l in8 devl.ce.

i

4 9

i '1

L T

, 11 = the magnitude o í an 8 kHz signal, picked iip by thc

electrode pair 1-2

With ~niixiinuni sweating, K I~ coriics down lo ahout 20 kn. and K2] and R1, arc also reduced (approxinintely 31 kS1eech). The control voltage to the automatic gain-cuntrol amplifier (AGC) is proportional t o u, which varies alniust linearly (Fig. 51 Ii>r ii linear change In K, , , H 1 3 , nnd RSi in tho ahova- iiiciiti<incd r:iiiges. 'l'lie A M used In this experiiricnt tieeded the control voltagc of increasing magnitude to pruvide higher gain. This was suitably matched with the help of a slope- cliitiigcr.

However. the overall gain of the EMG channel can be kept constant l iy lhis scheme only i f the level of muscular contrnc- Iioii ruiiuins the suiiic cvcry liinc. Tliu spccil'ic resintaiice of thc v<>Iumr conductor i~ iay he taken as 0.5 $1' ni 161. But, when the muscle cont.racts, it is hardened end the specific re- sistanci is inrreased. tlenco, the 8 kHz charinel picks up morc

voltapc. Ilut. lhis variation is i i i inll c:ni>uRii , m i i

viiriulioii c!i vciiidge ol?teituihiv I r w tiir L h t i i y 11% I>:'<(:'

ilowcvci. t h i s type of g:"n coiiilicnnatril 1:MG ,~!¡mt not find its US? for general diagnostic prncet!iirir I> tht 8 kH7, signal injection.

':,

1

>! [ I 1 I:. Sli\\ii.iIyA. 11, Il.ilii*iiiirni,iai,i.iri. aiitl K. , ,

tiiinary u ~ w t d io! thr i.lri.lri,n,).o~r;iii;," i l+~g.,vol. IlME-24,Scpi. 1917.

121 1'. A. Parker, 1. A. Stuller. und Ii. N. Scnii

674, May 1971. [ I 1 I f . Roeslcr ,~ i id W. Decker, "iiivcrtlgi~iion 0 1 l p d - : w p

pulse lensth spectra ofyross-EMG signals by m u l t i : : l ~ ~ n tion,*' in ddvonces in Exreinni Control of Hiit:,on €x:rN'' M. M. Gavriliivic and A. B. Wilson, Eds. üubiovwc, I Y X

141 V. Dunfleld and E. Shwedyk, "DiRitd EMG-pnicsw~" Ilr;i' I' En)!. ('ompitr..vol. 16. pp. 745-751. 1978.

[ S I í:. Alinstrorn, P. Herberts, ;md P. Ksdefars, "Pat1 cOn!ro! af a mulrifuiiciional h m d prurthesia." p Electrw!. I>cr. Aspects Etir. Conf. Elrctrutechniqti 14 Dip., Aiiirterdnin,Tlie Netherlmds, Apr. 22,-?6.

161 R. Pli>nrcy, Rioi.lee:rie Ph<viornetm New i 'ork. M

thc ii,ulllsi"lo in)."oloclric Ch1in110i:~ l'?"?. ;

, , ,,; ,í jlll j,

1969, p. 204.

,l , ni 46 1 I l l <>ti:,

An Ultrafiltration Monitor for Hemodialysis Research In 0, DAVII) tiISSI:R. GARY STICALT, ALLEN ZI:I.MAN. I r;tPurl,c

VICTOR BASTIDAS. JKFFREY HARROW. CARL KABLITZ, AND

ROBERT STEPHEN

,4brrroc:-Tlic ullraiillrniioii mte of hemodidyda mcmbmrs hr bo c n r z ~ y cuiitriiiicii lor mwimuiii imiiont bcnoñt. A sppcc~il Q I J ~

instrument is ilosciiiwi üiat takes in iiidog presurc iniormaiifi' the analog output of nn appropriate weighing syrtam and produceb: di&W displays and andog OUtpUtJ (for a stdpchiri recorder)ol iillralion ralo and uliraflllr~lion index M well us ihc averrgcd tranmembrane Iiydmstilic prearure drop and volume of u i d The instruniant nornially uscs M rvornging lime olibuut 1 mln.

vduen oí several Iiigli-flux dinlyzcrs. After thaw dialyzer ca'fflCit'' YTP incarumd. patients niay be mansgod by the uae nt prcmure moniP*: and controls dono, despite coiiddciable dccreiw in uilnriltrttiun hiin

during didysis.

! r ~ s

.hie

' b!ncp The monitor was uscd cllnicnlly lo evaluate membrane p W r ' ii thtac

llFIl t ~$1,~ ju

rill. nai pi 1 pati

lNTRODUCTlON for h. During hemodialysis, the patient's blood washes one

n membrane. The other sidc is wnstied hy a snit solu dialysate. The transport of blood plosma solutes throu

Manuscript received February I? . 1982;revissd September 24. This work wns riiplrortud In 1mrt by W. J . KNr,niioctor ur tlin Ili of Artüicid Organs, School of Medicino. Unlveiafiy al Utnh, S City, UT 84112, and by P. Thomson. President, Aimex Cc Boston. M A 02109.

I>. Ginaer, i;. Sirnit. find V. 11us1idn~ ni@ with the I>cpurtmont tried, Camputor, and Systems Cnginecring. Rcnsseiisr Polytcc

A. %oinion IT with tho ron ic i for iiiiimcdiui ihpinocriiie. üonrrsw ,,s-T I'olylcclinlc Iiistltu to, Troy, Ni' 1219 I.

1. Harrow, <:. Kabütz, and R. Stcplitn are with the Division a l A d ' I ¡ "Int cid Orgaris, School of Modicine, llnivcrsity of Utah. Snlt Lake CitYjrn , :Ii,'c, 84112. 8 ' Ihc ~

s i i tute ,noy . NY 1 2 1 ~ 1 .

l . L. is priniarily controlled by the concentration gradient

and it$ perincability coefficient,. Ilowcver, tho , or ullraNtraiion rato, is mostly dependent trammembrane hydrostatic pressure and the

a S W of the membrane in a particular dialyzer

n in a seriis of articles [2]-(41 that for "hi i.e.,didyzen for which Lp > 6 ml ' h'l ' m -

ultraliltration rate averaged over a short time in- &)] is related to the mean transmenilmine hydro-

.,; pressure drop averaged over the same short time interval [he patient's plasma mean oncotic pressure IT; by the

P

--. IJLl'RATll.1 I?ATION MONlTOii

OFF Q Q O O c 4 0 0 ,UP",S RFCORDCR OYliili is -- _I_

Fig. I. Front panal arrangement of the iiilraíitrshun nionitor.

c d instrument. Of course, generaüzatioii of tile e to all dialyzers would also he txtremeiy uselul

>filtration rate is directly available, in principle, @te of patieill weight loss. Weighing systems capahle

ir the rnornentary ultrafiltration index of the =A,nI,"(l - w). Since O,, and solutc r0- fur all fwiiioilialysis iiienibraiiei, knowledge

useful in predicting dinlyzer performance iii

¡:LB. 2. Hlock dlrwarn afthe rystcrn.

r3Lx IS primarily controlled by theconcentration gradienf

y;c ilavc shown in ii series of articles LZl-[41 that for "hi h

(, the ultrafiltration rate averaged over a short time in- (Q,)(i)] IS relatod t o thc mean transmeinhranr: hyiiro- mure drop averaged over the sanie short time inieival

the patieni's piasma mean oncotic pressure n: by the

diaivzers," i.c.,dialyzers for which L, > 6 ml ' h-' m 4 :

lormuia ,,,>" ,,I ticak-ampiituda ai:^ '4

:F.;< I,) ,nuiricliannei snalyrp. @")(!)=A", I,;<! - Wj((T(P;n)(I) - 7 ; ) (1) e area, 1,: is the initial hydraulic pir-

e membrane, and OL is a constant indicating the which thc hydraulic permeability is decreasing with

,, $ ( I - at) is the ultrafiltration index of the nction of time. A s time goes on, Breater values equired to maintain a constant e,. Since njs

ux dialyzers, (TrJwz) i iliirliiy II 5 1 1 dlulywia 111

i. ant. Often "staiidard Iicrno- . xhihit this tiine dependence during

6 the paticnt to an optimum "dry weight," ,wriciicid dialysis @CrSonnel conimonly readjust the mean ,,,,,,ci;ibrane prcosurr. in rdspoiiso to clianges in patient rtlght and blood pressure. Clearly, a method for continuous

rate could result in a most Of course, genPraiization of the

zers would also he extremely useful

n rate is directly available, in principie, ient weight loss. Weighing systems capable rams i n a few hundred kilograms are avail-

ht movements of the patient result in ap. weight, and even the forces due to air

a chair can causc output changcs. uantity is tlie rate of change of weight, nts will be acccniuated unless they can

hey vary so slowly that this initial filter-

onitor t o be described is basically a sig- ning Valid Ultrafiltration rate data from

~ ,.(,I o ! iiiririuii I;xrrcmiri,i,

hranes with L, i2i 2-3 ml ,

'TION

, J. Kullf, üirector o Tiis; ULTKAIILT'KATION HATli MONI'FOK

purpose instrument has three input signals as front panel sketch in Fig. I . Two are 0--10V 250 torr from each of the two differential pres-

c i "IC with the Deparfmc lerinR, üenaselncr Poly

ius with tWe Dlvidon 'wrr,ty d iit~ti, Salt Like

-- Fig. 2. Hock diagram of the systcin.

no) or momentary ultrafiltration index A, I.,, í r j . .I II ago provisions fur multiplexing all four o f these lor disi a singlechannel strip-chart recoriirr.

There arc also ihrec four-digit displays (in ilic friiiii They normally indicate averaged mean pressu~c (Sn; aged flow rate (Q"), and the momentary ultrafiltraii«i A," Lp. In the. "calibrate" mode they indicate insti mean pressure a, the V ~ I U I I I C i, anti tilc iiliic ill

volume (Y), respectively. Fig. 2 shows the block diagram lor tlie sysiiiir. 'The I /

filter in the pressure channel has a time constant o1 ah,

as

1000 n,,~,,((chp;n)- .p,= 1000 (e,) (2h)

since onc is interested in determining A,L t o i/iOOO. 1000 (0,) is generated tiy using i024@,)- 16 <a$- 8 (QJ, produced by shifting bits and then subtracting. An initially reset accumu. !ation register then t ias <pnT) - R; repeatedly added until i t s valuc rcachcs lMt0 !Qo), The nurnher of additions required is I000 ,4,,,Lp(f). This, along with the other two digital outputs, is lalched hcfore presentation t o the DAC's for conversion.

'l'lic, digilal displays roquirc inputs i n BCV form and all the digital processing has been in the binary system. Drcoding is accomplished in the following way. Both a binary and a BCD countcr. iniiially reset, count clock pulses until the binury cciuntcr value equals the binary quantity to be displayed. 'The DC:i> counter output is then latched for display. I'or cases wliero thr Icast significant digit is to be omittcd. the BCD counter is driven by the clock sigrial after division by 10. Roundoff is accomplished by presetting the divide counter at 5.

'Shc various operations are synchronously c.«ntrolled by three scparate scqucncing systems each composed of a counter, a riiiilllplrxt~r, m d a decoder o r two plus any appropriate logic, One o f : h i x operalks the inpul niultiplexiiig systcin, one con- trols the ni m o r y operations, and the thud is the master of the

Most of the digital logic and memory has been implemented in ChlOS or MOS technology since there is no requirement for high-aprcd operation. There are a total of 230 integrated cir- cui t package? mounted on six plug-in boards in addition to the

display syrlrni .

Fig. ?. Ultraliltration monitor uscd with weighing system and 11 Uial~ds patient.

power supply and display pnncl. A sot ol I.ED iiidicnliii possible over-range conditions is also provided. The rcsi~I'!tlk on all ranges excecds that of the sensor transducers.

RiiStiL'l'S A N I ) DISCUSSION

tanks may change only duc t o water loss hy thr patient 01

rnation. Unfortuiiutely, uny sudden changa In a vur cause a transient that takes u full averaging period to üisiip~ua Such transients were usually observed to be related to palie movement. They begin with pressure changes. and resu11 temporary change in dialyzer prime volunie. Much oí the da was excluded froni analysis for this reason.

In regions without obvious transients, data points were iakc from the strip chart recordings al successive 2 min inteNgi.

The daln were ohtainrd froin a nuriiher i if pnticriis n l I University of Utah Medical Center (Salt Lake City) in an elf to characterize dialyzen of several nianufacturers. With excep:iorr. they were used in the single-pass co-current mode. Flut-plate high-flux dialyzers cannot l ie used in cuun dialysate blood-flow systems without expensive ultrafiltra control systorns because of excessivc ininimuin ultrafiltrnli«~ rates. Co-current dialyzer operation minimizes water from the patient and permits use of the high-flux dial

but the dccreasc In small molecule clearance of about I cent resulting froni co-currrnt operation can be avoided, sired, by increasing the dialysate flow rate.

Data reduction was carried oul a l Iknssclaer Polytech stitute (Troy, NY) using a n IBM 3033 computer and sla packages BMDPIK and BMOP3R (revised April 1977) Health Science Coqputing Facility, University of Cali Los Angeles. Since measured oncotic pressures showe variation during a dialysis and tlie sensitivity t o vanatio is small, all parameters u'ere calculated for an average

.

L.

C"

LI *ptern and hem?

P

E TIIANSACTIONS ON HIOMEUICAL ENGINEFRING. VOL. RME-30. NI>. 2. I'IiRHIIAUY 198.1 1.1s

SAP., -*- I I . A d

20 30 40 W' 60 10 Ha O0 1 m 1

1

2slari r- c_I_

I -1 80 90 ilx) 110 IZO 130 140 150 llio

DlbLYSIS TIME IN MINUTE5

Fig. 4. Andog outpul of dlgitnlly averaged prossure and flow (2 min ovoraging timc) during most o f one dialysis.

TABLE I ULTWLPILTHAT~ON PARAMETEES OP HiaH-FLrx DIALYZERS

4 tV"

t percenta m l . h - l h NDP hi 1.P

n i l . 1,-' . m-' . nimHg-' i percent' __ ._._l.___l___.--- __.__ ~

CHI'. I .36 mz R.09 f 1.1 peiceiii 0.0616 i 4.0 percent t 72 57s 8 (co-currcnt) .~~ ~ ~~~~~~

,, ... ~r.610. 1.0 2 17.4 t 2.0 percent 0.0107 f 6.0perccnt i 101 4x0 8

CDAK 1.8 ma 6.17 t 2.5 percent 0.0657 t 8.0 peiccnt i. R8 29s 4

7.28 i 4.5 pcrcenl 0.0597 t 12 perccnt t U6 ?O9 2

(co~urteiil)

(co-currcni Ci)hK I .H rn

I counlcr-current)

"Stand.ird errar of uiefiicieiit of curve fit. b~t i in<~ard error cf curve tit,

4 .__.I.___-.. I ~.. "_ .__

ic pressure no = 21 mmllg . Table I shows the results for dialyzers. Tie number of dato points used and the num- dialyses arc indicated by NDPandN, respectively. These af LL are consistent with a 30-40 perccnt reduction in ring a 5 h dialysis. We ihink the causc niay be protein p on the .iiembrane surface.

ing deterniined values or n and np for a number of coni- used dialyrers, it i s now possihlc for any hemodialysis

to more acciiratcly adjust the ultrafiltration rates of its ala provided by this instrument also make pos- ~1 rdinicni use of high-lliix dialyiers. which ure eahle than standard dialyzers and therefore,

the patient a more thoroiidi dialy All that U needed monitor a n d adjust the average transnienibrnne preusiirc these data lind tho clopscd iiiiie. No hcd scales are rc- [61. Our staff currently obtains dry weight of the eight

protocol to within 200 nil lor cach dialysis and scs have been completed witholil a single tech-

& slro worth noting that the monitor niay he useful lor physiological measurements whenever a weighing systeni

can he empioyed. Thc determinalion of insensihle water loss IS one such possibility.

[ I I E. Klein, IM., Ewrlu~rion of iltmodrpljzers und Didjsis M e w hranirs, National Institutes a l l.lealth DHEW Publ. (NIH) 77-3294.

121 A. Zelman, I:. Bullock, R. Stephen, C. Kablitz, D. Duffy, and W. Kolff. "ControUed ultrafiltration during ~ i n p l e - p a ~ didysis wilt? lhe RP6 dialyzer and evillustinn of its iimsdepcndcnt uitrafiltr;i- lion indox."Arrijicid Or,wris. pp. I Mi-186, Aue. 19HO. A. ZehZJ. R. Stcphon, D. C.irser.C. Kabkfl, J . &liirow, 8. Decter, G. Strail, V. Bastidas. and W . Kolff, "Prossurc control of ultmlillr8- lim rule during Iirniiidi;ilyris wiih hlgli fliix diiilyxrx iind l imo dc. pendenir or mciiihraiio ircnspvrt paruiniirn." in S?itilwiic Moil- hranes: Volurnc Ii, Ilyyper. ond l~itmIil!m!iort mes, A. I:. ' r u r h d k , C.A. Nrw York: Arnciican Chernicul Swiety, 1981, pp. 61-74.

141 A. Zolman. M. Wliilc. K. Ackcr ,T. Wed. R. Parsons, and D. Gisser, "A simple method h r lncorpoiatiiiy. sinnle p;ar di;ilysais delivery a n d controllcd uitrafiltrdiioii with the Kl'd l,igll flux dialyzer:'^ iXal.isds. vul. 3, pp. 219.-235, 1979.

[SI 1'. U. Kcshiiriah, I:. ü. Constantini, D. A. I-uchrnann, and 1:. 1..

131

Equipgent using an impedance technique for automatic recording of fluid-volume changes during haernod - _ ¡a lysis.

Abstract-An instrument lor continuous monitoring of fluid- voiume changes hws been developed. A rstrspoiat whole-bo* impedance technique is employed with a constant w m n t of lwp4 at 1.5kHz and 150tHz. A micropmcessor automfiully cwlculw,l.hr changes in fluid volums from changes in whole-body impebn6'e. Eody-rudace "ea is uredwtw nornulisinp hcior together W¡lh an empinOl& ktermined con?iam to obtain r d i n ~ s expmssd in IIvsr. Estimrws oiiluid-volunn champs ObLLYd by the method w u e rompsred with concomitant changes in the body weight of ten p . i i w ~ ~ s undugoing hema& &si& and * ccw&ion corlfirrn! oi 04iS was iomd.

. . . .

.. . . . .+: - ,

. .

C- .I

haemdialysis was delermined with precision sales (Stamos m d e l 340)., Several mathematical models were tried for describing the relationship between impedance change a d , ?eight change.

The following equatlon was selected because it yielded strong correlations in combination with a low

~ sensitivity to movement artefacts.

where AV = nuid-volume change k = proportionality factor s = body-surface arca

z,,,, z , ~ ~ = impcdanm at 1.5 and 15OkHz : zl.,,, z,iOf = corresponding impedanm from base-

line determinatim.

i vaiue tor body-surfaa arca used in the ~ cnluiiatiom was obtainad from

: s=(W+H-60))100 . . . . . 4 2 )

uhefe S = body-surface ared in m' W = uaeight in kg H = heioht in cm

Regression oí calculated nuid-volume change on change in weight during hacmodialysis treatment u'as tested by analysis of v a r i a m .

A special-purpose impedance instrument was designed using eqns. 1 and 2 to compute fluid-volume c h a w . This instrument was tken tested in a second group of ten patients. The design and properties of the instrument are described in detail below, whereas the medical and physiological aspects of the investigation are discussed clsewhere (TEDNER and LINS, 1983). .

2.1 Procedure Ten randomly selsted patientSgave their informed

consont to participate in the study. The p l i c n t s u'ae weighed before and after the h a e m d i a l p i s and a rigorous r s o r d vas kept on their intake of fluid and solid i d . Two tape ekctioda (3M M 6001) were applied to one arm and another pair was appld to the

FILTER 1.5 ldll

t

contralateral ankle (Fig. I). Before application the skin was cleaned with alcohol. A baseline determination Of total body impedance ..as made immediately upon the start of the dialysis procedure and a second reading was made immediately prior to the end.

2.2 Equipmmt A tetrapolar impedancc technique was d with a

constant current of I C 0 4 at l5kHz and 1SOkHz The measuring quipment - ir controlled by a microprocessor and comprises oscillator circuits, detCcfor circuits and digital Circuits, including a digital display (Fig. 1 ).The oscillatpr and detector circuits are working continuously and arc unatTecicd by the microproccssor program. ~

2.2.1 Osciikgor circuits. The lrequmcy from a 1.5 MHz crystal oscillator is divided by IO three ti- in a frequency divider (Fig. 2). The IMkHz and l.5kHz signals arc U m n d to l o w p s í f i l t m uansiorming the.yluaraa>avc from the dividcr to sine wave. Thc signals are added in a summing mplihar

and converted to constant current. The vanation in amplitude and frequency ofthe constant current is l e s than 0.02% and O.OOi%, rcspectivcly, within the normal operating temperature range. The conslant- current circuit can drive a load of a few ohms to several kilohms. The patient is comected ‘to the constant- current circuit by coaxial cables, where the shields are dnven to signal potential by two voltage followers to minimise capacitive losses.

- 2.2.2 Defector circuits. High-impedamr low-noise

voltage followers with an input impedance of I0”fl are mounted on the measuring cables close to the electrodes (Fig. 3). A dillerence amplifier feeds the signal to narrowband active fillers of the INK type (G~~~~~et~l.,1971)withaQvalueof2Oandagainof 3 0 d B tuned to 1.5 and IWkHZ, rspcctivcly. L F 3 5 7 operational ampliñcrs with a gabbandwidth product of 20MHz and high performance resistors and capacitors are used in the filters to minimise drift with temperature and time. Two fullwan rectifiers detect the ampiitu& that is proportional to the impedance at

BANWASS RECTIFIER

flLTER 1% w7. - CIRCUIT -0

150 WIZ -

RECTIFIER UIIOPMS - FILTER 1.5 I<H2 ClRWll d 4 I S WIz -_

Fi. 3 Block iiiaermn of detector cirairr

. .*.

I

' b

" kach frequency. The circuits have a total gain

of 40dB. ,is:

2.2.3 Digital circuits. A 280 mino ocessoi Fontrols the measuringr)suena and cal r ulales the fluid-volume chanie (FÍ 1).

The detector circuits arewnmctcd to an analogue 6wiich which sequentially feeds the detected amplitude Xrom .the iew-'and .high-frequency rect¡Km lo an analogue-to-digital convertor. The switch and the .analoguc-to-digital convertor are umtrolled b y the ,microprocessor program. Two seis of thumbwheels for entering therpaticnt's weight and height are also connected to the microprocessor. A reset switch sets ,the display to zero at the baseline determination. ~ 'The program is stored in an e.p.r.o.m. and the !impedance values from the baseline determination are jstored in a m.os. memory. The memory is battery I powred to protect the initial values in C B B ~ o( power- /iinc failure. This arrangement also makes it possible to /measure over several days, úna the baseline values are , no1 lost when tbc power ¡s turned d. Fluid-vdume 1 change in iibes is calculated by the microprmcslor j program using q s . 1 and 2. T h e U W c d value is 1 p-ud on a 3digit 1r.d. dinpky.

i . , . . -DATA FLCU

j ' .-

2.2.4 Microprocessor program. When the power switch is activated an initiating program is executed, which sets the program counter lo the starting point Of the main loop in the program (Fig. 5). The program is continuously repeating the main loop if the reset switch is nor activaled. The cycle time is then ZMms, mainly dependent on the analoguehodigital conversion.

First. the analogue switch is set to connect the low- frequency detector to the analogue-todigital coBvertor. The analogue impedance value at the ,output of the detcclor circuit is digitised and stored in the memory. This sequena is then repeated for the high frequency. "hereafter the microprocessor senses if the reset switch is activated. If this is not the case weight and height values are entered from the thumbwheels and the initial impedana values are entered from the initial value mtmory. The fluid- volume change is then calculated and presented on the disolav. Finallv the Dromam returns t o the starling . , point of the main loop.

If the met switch is activntd the program leaves the main loop and the impcdana va¡ues from the two deistor outputs at 1.5 and i M k H z arc digitid and stored in the beat-line memory. The display is set to zero, and h a l l y the program returns to the starting point of the main h p .

lmipaiam readings in ohms can also be obtained. By entering numba ccdcs to the wight thumbwbals thc.program jumps to a subloop. The mcasurrd impedance at the high or low frequency is now pmebtcd on the display, instead of cakuiated fluid- voiume c h F g e .

3 Rar)b Qt method w & s c d in 38 mensu-ts on ten

patients. Most. of the paticat8 were s t u d i i during more than one hacmodial)%¡s p r d u r e . Only the

. .

,'*, a tht t h , ch si$ TI

lir Ci de lir in ci F

21 h;

S i l

Vi

Cl m (S

Bi O tl

4

C

o b

E C .* C

a

C

a .' 1

1 7

L - 1

I < i

values for impedancc and weight changes obtained on the fir's1 occasion in each @t¡ent were nscd for testing the regression of cakulaled fluid-volume change on changs-in body weight. The regression was found sicnihcant when tested with an F-test at the I% level. Thecorr~IationcocmcieritwasO-89 (P < OiX)I).Arno sinnificant ordinate interceptwas found the regression line was f o d through &e: origin (SNEDFJ~R and COCHRAN, 1980). The proportionality factor k was dcterkncd as the inverse of the clope of thc regression line of the impedance function ( q n I ) against change in weieht IA = 9 621 Calculated valuesolfluid-volume - ~ - ~ . . ~ I ... change used lor the statistical evaluation are shown in Fig.'6 together with the total material.

It is clear irom the analysis of variance that about WLof thevariation incalcniated fluid-volunicchange has other origins than real change in fluid volume. This variation r&ts the total m o r of the method and comprises mtasurement uncertainties. All measuremais were done with the following accuracies (stnndnrd d+nations):

EX uryrpcy or the impedance maauicaients dcncads on thc stability oíthc constant -1 .nd the YOAlncy 0 r t b e . A t of thc voltage bc<wecn tbt mmr akti.&. 7hc siaolityd the ~n of tbt hodpsr 6Itm is importmt for thc nccumq oftba vottap marnnmcnls. ' h e h n of the fitten U MdB and the maximum gab of the LF357 operational amdiñcr is Y dB i t ISOkHZ, gjvmS only 8dB of

. .

- . hcádroom. T o improve the pccuracy of the ds\eclor circuits c m t a l filters or a phase-lak ishniquc may be a M e r Cbo~c.

The outpt signal -from the low-psss fi1cuS in the d a t o r eirnllts is only approximateiy sinuiadil,

. . This bas no effst'on the measurements as long as t h t amplitudeUconstant,siaccan distortcdsinewnveir obumed whcn the signal is pnsscd through the narrowband ñItcrs in the dc(ector circuits.

"b,....

~

. .

, .

The constant prrcnt oi 100 pA is sufficñntty low to be ~ I C S S to the patient at the irquariar wed, since tht d&uode des are distant from the hsnrt region. At the mme time the c u m n t U suífmiently high t o give a

reasonable signal-to-noise ratio (30dB) in the detector circuits.

Hum and other unwanted'signals picked up by natient cables tend to cancel since the two sipnals from ;he voltage followers are subtracted in the-dilíerence amplifier.

The input impedance oi the voltage followers is i0''fi Consequently, the current drawn from the patient is so low that the potential drop over the skin/electrode region can be neglwtcd. The input bias currmt oithe voltage followers islcss than SOPA. This, together with the high input impedance, makes the dstrodc polarisation negligible.

Other investigators have also used impedance methods for dei;rmination of fluid-volume changFr Patientstrcated uithdiureticr were inve~tigated witha bipolar whok-body impedance techniqÜe at 5 k H z (IENIN et al., 1974) #vinq a correlation &ent of r = 0.85 between changes in .impadnna and weight. This method was dcvelopsd by THOMASSET (1965). and is invasive, using n d c electrodes This might, constitute an inconveniena for repPted applicptonr on Lmtients.

Ágronp ofpatients treated w t h hnemodialyiu were iavgtigatcd with a tetrapolar wbdc-body impcdana tschniquentSOkHz(SEoENZXY andNYBOER1976).A c o d a t i o n oír = 064 bctvkn chances in imucdnna - and weight w u found. The noninvasive method d m i b c d here shows a

slightly higher correlation (r = 089). It also bas the sdvnntnge oí k i n g reiatively insensitive io movemCnt artefacts, since impcdunx differtsas are maa~urcd. Tbc eaumment was found convenient to use by the

stali mi .easily tokrated by the patients;'Thc itnlltivity a l lovrdetst ion of fluid-volume chan~ea u smaUu~~l.ItphouMbeposcibktnwcthcmcthodin other forms of intensive u r e , but the proportionality rictm may then hive to bc changed or other combinations oi írcquencics may be rcquircd.

Res- BOLOT, I., BERNARD, C.' LAUREk G., ROBElr, A;

CALEUAW, E., ]WIN, P., LLNOIII, I. Ud THOMAPEJ, A.

GO. H o r n ,E., MEAWII, C. and SIMPSON, D. (1969) A

relationship betw-n wblc M y irnpsd.na and told body watu volume. Ann& of the N.Y. Acdmy OI socncCr, Intcrnntiond Confer-. on BinekcIriul Impedina, MARKWCH, S. E. (Ed.), 170, 452-461.

TH~MAESET, A. (1974) Vliiation dc I'imp8dracc buu JENIN, P, LENOIR, J., BOLOT. 1, BERNAW, c. ind

289 .

Programmable machine for dialyser reuse

W. Genrles L. F. Braganza

D.putmim o( Bion*d¡c*l Ew"rnw. Swm*brook Wul Cintn. Unk.1iy oi Tolomo. T a m o . Canada

C. S. Saiphoo M. A. Mmiuel -

0epm-m ot M.disina. UnIrrmiw ot Tolmo. oivbion d %h&gy. Sunn*brw(i Madd l Csnm. TOIMO. Crnad.

. AbstrKt-Beuvff d the high cost of di+&. m n y cemres h u e developed methods of cleaninp

diarsWr cufridgcs so fhat they n u y be reuaed. This paper describer 8 mchinc which cleans dulvser m r i d p s ~utonutic.ltv. The m i n dillerence behve-en f+s machine and others reponed in fhe karcme ir iis .My to ten rufomfidly f a leeks 01 obstruction and sound an alnm il the die+- is un&& f a mur the wuh@ pocas. The dwelopmsnr of these rnts ndsrsnb.d . in &d. ?he inawpawáh d rims te* ¡ma rim dim *-rem of the nuciúm WM m& the muse c4 M w e r s shuhr , s J u and nnm cwlrimm.

.([.ruOrd.--Di*llaniu

~

traces of lorouldchydc. The flushing is continued untü aii trates of formilldctiyde have been m o v e d .

Tbc pna*c or d- reusr, aithough widespread, $6 enatk in many un& b r a number of reasons. FAltly. i t is un- and time wnsurnh and in b q c r uNis additional star may he oecded to per- form tk produre. Inothu umts it rc~l~oyc~ a nunc from ber dmiy&L dutia. .For üu h e dialyeis pt*ot it prw the t h e of prrpintion for

a i p i t e i b a diikdh, it bas bten m p m d tht

of European uDiu(VsrcnuwaPI;l978)and61% of dialpin .milo .m' the, UK (Wmo a d, 19%)

. prrtrC thc reuse ofdirpub*diil+. WOÍO et d. (1978) hn'h WrM -wits o l a survey which

Some motbidity binrnmomüty. ' 7 ' - '

in ordq u> ovc~conx the unpks~aat ind iime mmumiq 'upsti of reuse, a numbcr or automated reuse machmet bvc bacn dcvciopd and reported in ihc litcraturc (AIYITAZZI n d, 1975; De PALMA et d., 1974). Thac rnachiaa use a number of-ddiflcrcnt tshMgva to rvuh the d@ and then BU it with r S & b ¡ q solution b r st-. They all lack the ~bw to tesi the didym and pmviac some indica- lum of when it has dctmontai to the extent that i t may no longer be 'adviarbk to reuse it. Tatkg preecdures desmital in the litcriturc (FAR= a al., 1974; GaniH ef d., 1972) arc t h e consuming and require cxpcnsivc 'mc.8uremcnt apparatus a h r h d e s tbm ~iatriiubk b r 4c by home dllyais pt- ¡en%.. in grdmr to ovuwme the dimnilties oí luting

h dial- is then axlnc&d to theprunt Po Wurl.

dd+ ied if requires idditw urchnicii aiu. 17.zxoí us di.iriii luib (&Am R al, 1978), 311%

. . . .

'.* .-. , .. - . " . .. . .. .. . ' .~ . ,

. . . . . -.

. -. .

the dialyser membrane. a machine has been developed at Sunnybrook Medical Centre which not only performs the washing proeas automatiailly, but itso evaluates the integrity of the membrane. The qnachirie incorporates a sophisticated alarm system w h r h halls the washing p m s ifthcre is any abnor- mal los of fluid pressure. A photograph ofthe mach- ine is shown in Fig. I.

i Darrip<ion 'ol Irrti*+ Themachineconwits ofuidq@Picmodulecon-

laioiog the control circuitry and a plumbing module ontajning solenoid valves, interconnecting tubing nd pressire sensors used in the alarm system. Fig. 2 i a block diapram which will assist in understanding

may be activated by inserting diodes in the appro- priate positions of the matrix. T h e program board also contains active circv'íry to perform complex functions within a given washing cycle for the pur-

R E S E MACHINE MOCK DIAGRAM

CMITIOL LOGIC

CYCLf T l h w s

.................... U3ARD

he operationof the machine. The first block mntains the mntrol bg¡~ and cydc

mien. This block ensures that the vanous qdS of he wmhmp moas6 are pñonned in the comct t DINER

DUD I IIII ................... E M - *uik

)(riir *bw.

I

I' I

SOLENOID VALVES ..

. her, I

forr d

The total duration of the washing process described is ap$oximaiely 18 minutes.

4Ahi.insygao ' The alarm sysim has two separate functions. The

6rst is lo monitor fluid presura during each step of the w,uhmg procus, and sound an alarm if there is

ny abnormal los of fluid pssure . The sewnd &ion 16 to evaluate the membrane and sound an

Phnn if leaks or cuMivc obstruction oí the mcm-' bane developed. This evaluation is p d o d in &CIS 2 and 6 of the washing precess.

The first Junction of the a h system will now be described in more detail. The ouipu(s from the pro- pam board mntrol which solenoid valve is open at

+ny given time. Thae outputs a n also fed to the board, providing it with infornution on whm

lour ports of the machine. For exampie, when the yde veive ir opened to st& the bbod

$ ' .

akrm ia indiaid.

t o c w rem, m whieh dl burd&vi)vsiIrc ppcncd. In dd i t i n~ an audibk dami is soundmi.

.~ ,

't ... An ohsewation of the pressures at the venous pon ""n, by

+,; I:: 'I .4 . cai

i '"*.. ¡ne '%e@= Tir

of the reuse machine during the 'dynamic rinsing' of cycle 2 led us to develop a simpler and less expensive technique for estimating flow resistance.

u ~ ~ c L i w a < . ~ l y m i n p l i . a t t i t b m g a v s c d . ai ihewncypd to kmase ua&wue, Prrrurc i

ruricd,and the paDnrc rrlired by,opDaing the mooitorrdaithevawwcnd.Nthk~~pro- .

d n m at the a n d d,u ia done mdynsmic rim¡¡ . cyck (cy& 2). the quaiion describing the prrcrrure d m y ai the venous end i u Iollows: . .

. . P(t) = P(t = . -

wh = prrsrure r=time

. . K = cumpiinrice of dklyeer and mnnening

. . . tubing .,

diaiyscr . ,.. . R resist- to Row of water throieh ventional method of measuring this resistance has

been to piso wata through the blood comprtment ' "

at a constant rate offlow and lo measure the pressure Thii quition ir a ~ l o g o u r to the quation daCnbiog drop across the dialyser using a dikrmtial pressure the dudurgc of capacitor through a resistor. From transducer. This tahnique is upensive and únpncti- the quition it can be kan tht the time amstmi of 1-1 for home dialysis patients. .the prarurc decay, produa RK, u dirktiy intluaicrd 1 I

jp Mdiul I Biologiwi Enginoaring 6 Computing I ' . Nowamber lSa,

'

. . ~

by the resistance lo flow through the dialyier. Meas- urement of the time constant in the equation shown can be implemented simply in our machine using an inexmnsive nressure switch. set to ocen at lle of the

mean value-between first and founh use was statist- ically signifcant at 5% level.

6 sour el^ of error in ihe timesomtint measurement ~.~~~~ peak prrssuk which is controlled by'a pressure regu- Mor. Fig. 5 shows the exponential pressure decay during the dynamic rinse cycle. The time from the opening ofthe revemdrain valve at the point D until the opening of the pressure switch at l/e of the pcak pressurc is a measure of the time constant,lnd hence a measure of the resistarm to fiow through the dialyser. A simple timing circuit is used lo trigger an . a b if this time i n t m a l c a d some prde1ermincd vdue v t h g an uripcceptably higli value of resistance. . '

It is clear from the formula for the pressuredecay curve that the observed changa in time constant could have been caused by (a) changes in the com- piisnce or resistance io flow through the reuse mach- ine itself o r (b) changa .in compliance or resistance to flow through the dialyser. To control for changes in eitheF resistance or com-

pliance of the machine and connecting tubing, the time constant of , the machine itself, with no dialyscr connected, was measured before each t i m e a n s t a n t measurement used in this studv. To obtain this

8 t \ \ I I

,\,-E, , '-

~~ ~~~~~~~

If the membrane dcvebgl: a leak, the resistance will decrease and the rate o f pressure rise will increase. This rate oí pressure rise can be estimated simpiy with one o f the pressure sensors on the blood side of the system. The time interval bctwam closing all valves. on the blood side until the pressure rim to

. .

. . ,

numb., o1 UYI " . .

- - iZ__=... ._j. .. . ~ ~ .. . ' . ' ~ #-' .. I

I ,. ,. ' . I, . : ._. . . . ' - z . ~ ~ ~ .- ---- , t; .$',,.. ., * .-':i -

> ,

Eacept for this one i n d e n t , the machine time coilstants were obscrva~p remain stable at 490 ms, , indicating that the comfliance of ihc fluid circuit io the machine was not ,undergoing any progressive change. Therefore it can be concluded that changes in the observed time copstant are caused only by hhangcs in the dialysen themselves. , From the formula for the pressure dccsy curve, it can be wen that thesc chsnnes IMV be caused by

*

kither a change in comptiam- or a &mge in resisi- a m to flow throuah the dialvrer. To lest for chinas in didyser compl ikee after &use, comph~na &- uremmis were taken on a set of five new dialysen, and on a set of five dialysm which had been used four times: '

The method of measuring compliance will now be p~ribcd. The section of highly cornphiant tubing kas removed from the,rcuse machine, as this tubing we it difficult to observe small changa in com-

I ¡ ¡ of the blood mmpanmnit of the dialyscr achine fluid circuit. The dialyser was U>MCC~@ to the rcw machine

flushed with water to rhoovc all air bubles from he bbad cozqnrihacnt. The mue machinc~~asthau w i t c w OR sepiirrp the blood cqnpmaent. The idyute c o m ~ t was opmd to .InHmpheric

we. A pressure t n n d ~ was amnatd to the I d rmnpartmcot, 5 ml of watm WIO Qjcctd into

tbc wrnpartmmi, and thc duiy io prusum was &. The ratio of &&&e in volume to c h i n e

n pmcure .(AY/AP) ia then a measure o i thc corn- üancc of the system. SincdY is constant at 5 m l the bserved prmsurcdrangcs arc imcndy proportionai

The mclll ehw in pressure for the d i a l y s a was 54.4 I J03 kPa Ud :the mean

in pmrun br the urd didyrenwu64Q f .7 kh. ?he iocrorcd prusm indkatc a kwe -1% with reme. uring a t ~ ü d r - q .

I

the change in observed pressure, and hence in ob- served compliance, was not significant ai the 5% level.

: This data indicates that aner four uses there is a tendency io reduction in compliance, although it is not statistically signiñcant. Posihle reasons for It decrcnsc in compliamx are (a) changes in the struc- ture of the membrane following exposurc to hydrogen peroxide or formaldehyde or (b) fibrin deposition on the inner walls of the hollow f ihm. Prclminary data indicate that new dialysen sub- pad to the washing proass , without being used on- a patient. d o not show any decreare in complisnce.

Since decreased compliance would cause a decrcnsc in time constant, we may conclude that the obsmed increase in time constant with each reuse has becn caused by an increase in res is tam to Row through the dialyser.

Fig. 7 show that, although thefime constant has i n c d , the ellickncy o f the membrane hasnot yct decreased IO a levd where it ir añecting claranai of urca and creatinine from the blmd. The changes in mean damna from the first to the burth me lor both mbduieer are not rc i t i . td ly rigaitiem.

This preümimary data mnñrms two things. Fim, that tk w h h g procm performed hy the nuchine s d in getIing the membrane dean enough 'lo - maintain d e a r a n a s at a utiaiactory kvcl. Secondly. that the .time consimt.is a mu& more sensitive mdiutor of membrane obstruction than. m3'asure- mnit of clearances. Thus, it can not only bc used as i n iccapt/rcject test ofthe dialyacr M o r e subsequent we. it also has value,as a method of evaluating improvrmcnts in the washing procm which may be impicrnentad by chugcp inrdhe .pogram board of 'the rewe machine.

step 6 of the washing prmsF fs a prrPsurc test which tab for perforations of the membrane, an oeariod problcm with rcw of dialysen. To ex- pkin how this test deiecb perforations or leaks. refer bpcL to the plumbing schematk of Fig. 3. If the dialyaale compRwnt ir prrtuirissd by opening the w a i a vaive. but kaving di drains 'closai, and

.lhc .&¡lbod~mmpnipcnt ir wed by daing all the valves, water will flow across the membrane due to the pressure gradknt. The pressure in the blood compaflment will rise exponentially until it is q u a l io the prcssure in the dialysate compartment. Thia situation is analogous to charging a capacitor through a resistana from a mnstant voltage source. In this c ~ s e the membrane itself is the resistance clement.

;

~

-

'

t 1

.

Th the

rat thi

the CY< dc thi rei rei Fc sw tw no cle

Vdl

pn

thl dd IM

thi vl Ch

7 ,

i

I I i

I

L

J

Thus a simple alarm may bc implemented to reject the dialyser if this time interval is abnormally shon.

The venous pressure switch is used lo monitor the rate of pressure r k in the blood compartmcni. Since

leaks. The tremendous cost savings realised by reuse are,well documented and the features ofthis nachine contribute significantly to ihe salety and consistency of the procedure.

WING, A. 1. BRUNN~L. F. P. Ud BRYNGEI. H. O. A. et d.

.

M d h l I Biotogiwl Enginwring 6 Computing . . N0vqmb.r 1- ' '

- . . > .

-1 1 - -

Mcd h 8w tnP drc-pui 1981) la 1 7 Y ixx

, - 1 - Lumped-parameter model for haemodiaiyser with

r" system appiica'tieñ-ts sinnrlation of patient-artificial-kidney

L. P. A. Ramachandran R. A. Masheikar

L - Natanal Chemical LabOmtor~ Poona 411 O08 l&ia .-

mu the Derformance Aí& l i c a l s o l u t ? o . i a r p " e ~ r r ~ n - o f solute m b K d

Abstract-A s m , e lumped paramerer merhr?mai,calmod-d f r- leaving rhe haemodialvser. A-- a Driori

rhemodel is illusrra3ed bv comparing ir with the num#icalsolurion of su9uested. mole exacr 2-diniensional modeis and some ex erimenral data on commerckl diafyysers. lhe ulilllv of Ihe modelis illusIrared by an appl icat io~to lh'e s i m u ~ p a r i e n r - g n 7 / i c 5 a f - i l t d m v

m m w . .

system. wherein compact analytical expressions are shown IO describe the whole comple; -- system.

Keywords-Artificial Pidney, Haemodialysis, Modelling c

List of symbols

a parameter defined in eqo. 14

A,,, A,> parameters defined by eqor 32 and 33, rejpectively

C b concentration of solute in blood, rnoleicrn'

Cbt concentration o f solute in the blood enter- ing the dialyser, molejcm'

C., concentration of solute in the blood leaving the dialyser. mole/crn'

Cd concentration of solute in the dialysate fluid. rnolelcni'

CA concentration of solute in the dialysate entering. mole/cm3

C,, concentration of solute in the dial>sate leaving. mole/cm3

C., conCentration of solute at the wall in con- :act wirh the dialysate, mole i rni

concentration of solute in the inrracellular fluid. molelcm'

c, concenrration or solute at the wall in con- tact with the blood. niole/cm'

u molecular diiiusivity of solute in blood,

. c',

Cm'k .- Flrr i receireC !2<h February snd accepled I . final fo,m 3rd September 1279

molecular diffusiviiy of solute in dialysate fluid, cm'ls

axial dispersion coefficient, cm'is

haifchannel width of a parallel plate dialyser, cm

rate of production of urea in the body, mole/s

permeability of the tube wall, cmls

effective mass-transfer coefficient for the dialysate side fluid, c m l s

effective mass-transfer coefficient from the blood to the tube wall. cm/s

exchange coefficient between infra and extracellular compartments. h- ' or s- '

length of the dialyser. cm

rate of removal of urea in the dialyser. mole s parameter detiiied by eqn. 12 parameter defined b!~ eqn. 13

m i u of floii ratio. Q,Q,

voliirnrtrii flow rare of blood. cni'ls \,olumetric tlow rate of dialysate. cni31/r

ra(!ius of the fubiilir haemodialyrer. c n l

time elapsed r i m start of dialysis. s

average velocity of blood, cmls

total volume of intracellular compart- ment, cm'

total volume of extracellular compart- ment. cm'

width of the dialysate groove, cm

axial distance, cm

dimensionless axial distance,' x / L

dimensioiilcss axial length of the dialyser (LDlu,R' for tubular and LD/u.hf for flat plate dialywrs, respectively)

parameter defined in eqn. 15 or 16

parameters dciined in eqns. 42 and 43, respectively

geometry factor (= i for flat plate, 2 for cylinder)

roots ofeqn. 38

dimensionless wall permeability kR/D

illustrari.re example of this using a simple 2-compart- men1 model for the palien1 is precented andanal>+cal solutions are deri\ed to describe the proczsq.

2 .\lode1 equations In the lumpd-parameter model, the radial varia-

tion in concentration due to finite solute transport through the wall is assumed to be confined entirely to a small region near the wall. Thus the raisrance to mass transfer r n the blood side is assumed io be present only in this small region and is characterised by an effective mass-transfer coefficient, k,.. Thus the rate of dialysis per unit wall area of the dialyser is given by:

R A = k L ( C b - C , I . . ~ . . . . (1)

where Cb is the local volume average concentration of solute in the blood at any axial position and C , is the conmntration at the wall in contact with blood. Further, solute transfer t a k a place through the membrane and to the dialysate fluid. These are given by:

R A = kíC,- Cdw) . . . . . . . (2)

= kAC,,- C,) . . . . . . . (3)

where C, is the local volume average concentration of the solute in the dialysate fluid and Cd, is the concentration at the wall in contact with the dialysate side.

The schematic diagram of the model and the various t r a n s w n resistances are shown in Fiz. I .

1 Introduction

~L ~

If eqns. 1-3 are combined, the rate of solute transfer per unit wall area of the dialywr is given by:

k

I + - + -

~~o~ eqn. 4. t h e mass &lance for

RA = (4)

( ~ k~ ka I). DAVE and P.e.ms-O+i (1970).] Further

arise whe:? the concentration of the so~,,te i n ysate fluid is also changing significantly. The blood can f o r m u l a t ~ a function of

nbathematical niodel ated boundary axial as:

v p i c pjohlem [Coo.

;:X!R

k (C,-C,I I this y a v i an alternative method of analysirig B, -- d' c, -~,~- dC* =

d I

. . . . (ij

mhere ::is a geometry factor uhich has a ialur ofoiie

some experimental dala I O illustrate thc validity fora flat-plat< diaiyser and txo for a tubular dialyser.

this approach. An approximotc method for an in eqn. 5 the term DE is an ahid diswrsion

tubular and flat-plate haemodialysers is discussed. 71h model can he applied easily to uther equipment

ii wvl id :1ko be mciul . ~ t ! a s diiiii4oii. The asi:il dispenioii coefficient has a niore complicated Men useu conin?only i n ctlenlical enzi~eerim:

Further, for a flat-plate dialyser, the term R (radius, is replaced by h (half-channel width).

coefficient which takes into account the e!kt% n i nonuniform radial velocity profile and radial inole-

. (14)

Q D u ~ L

. .. / membrane'

-fig. I Schematic of haemodialyser showing con- 0 = centrarion profiie of solure -

\ RAMACH~NDRAN and MASHELKAR (1975) and

authors have compared their results with more h<ASHEl.KAR and RAMACHANDRAN (1975). These with 'Or a diaiyser, defined -

k L involved numericdl computations of the exact z-- - differential equations and the agreement i n all the R Uh

"-:ases is found to be excellent. z = , . . . . . (15) 'The mass balance for the dialysate side assuming

,-plug' flow is as follows:

and, for a flat-plate dialyser, as

k L z = -

~-,,. -Q.K L5 = - Q B dx -

! p h e r e QD and Q , are the volumetric flow rates of :I ihe dialysate fluid and blood, respectively. Eqn. 6 is ,"eased on the countercurrent flow of the two streams. 1 The boundary conditions for the solution o f extent of solute removal in the dialyser: b q n s . 5 and 6 are as follows:

If the blood and dialysate Ruid are flowing wn- currently the following equation (which is derived in an analogous manner) can be used to predict the

(- dC. '1.t

Al .i = 1, - y ~ = O . . . . . . (SI

b) For thc dialysate Ruid

AI .Y = o. rd =- c.du . 8- (5!

41 .Y = L . c< = Cdi . . . . . . ( I O ) I

Solution to the model equations Soluiion of eqns. 5 and 6 can be obtained

inalytically and can be expressed i n the followirig

orward marhemaricaal nianimlations and the details

c form l r l i c solution involves straight-

The quantity Qn!QD is ascribed a negative viluo for concurrent flow for the purpose of calculations of P. and R from eqns. 13 and 14. The parameter P in eqn. 17 is given by eqn. 12.

Eqn. 1 i enables one to predict the concentration of the solute in the h!ood leaving the haemodialyser, provided that the model parimcters Dmkr, k,,and the membrane perineabiiity k are known. An approximate n priori mctliixi of es!imation o f the model parameters D E , h , arid k, is presented i n the next Section. It will Ire shown that the prediction of Cbo, based on these npproximdte mode¡ parameters is sufficiently accurate for all prarrical purporer.

T A Y ~ O R (1953) in any equipment in which rhr radial , elocity distribution is known. F-or a I*jeu.i<inian ,uid flowing in a circular tube, under Iaminar-llo~v onditions DE is given by:

(18)

: Eqn. 18 is based on the assumption that no wall inass transfer exists. Thc value of DE is modified

, when there is a solute transfer across the wall as hown by SAKKARASURRAMANIAN and GILL (1974).

, .lowever, this refinement introduces a large number of mathematical complexities and is probably not

,..sery necessary in the context of the present simple iiodel. The approximate value of D, given by

, .. qn. 18 will be shown to predict the haemodialyser performance accurately. Similar analysis for a

,parallel-plate haeinoüialyser giver Tor a laminar low of a Newtonian fluid:

Iic flow of blood exhibits non-Newtonian behaviour ,nd !he rheological datacan be analysed in termsofa

Casson model (LIGHTFOOT, 1974). The values of D , or the flow of such a Casson fluid through a tube

L : R D m E N (19671. and can be used if the rheological properties of blood are known. However, this refinement may not be necessary to describe blood Iuw in relatively high shear situations encountered II a haemodialyser (KCQUMAN, 1972). The values of L E in an equipment in which the velocity distribution

, is not known can be determined experimentally by ricer experiments (LEEXSPIEL, 1972). Some work in the transient response of a haemodialyser has een done by R A h i A c ~ N D R A N and MASHELKAR

(1978) and this analysis may be useful in evaluating e model paramcters from the exwriniental data.

$ ,f circular cross-section have been. reported by

L ," .2 B l o o ~ l - s d ~ ~ ~ U S S - I T I I X . ~ ~ ~ ~ coqficicicni (k,)

The blood-side mass-transfer coefficient kr for a pul ly developed laminar flow is a function of the 1 $,all flux, ¡.e. the rate of mass transfer through the tmembranc and the dialysate as measured by the 1 permeability coefficient k and the dialysate-side

oefficient kd (C«ONEY et of., 1974). KOOIJMAX (1973) ias compiled the information on the blood-sidi ass-transfer coefficient as a function of the

i dimensionless wail pernKahility 11 defined as k R I D . p imi la r information is also available in the paper by ' ~ L T O N PI al. (1970) for a flat-plate dialyser. Two

imiting cases can easily be identified. For q -t O, the , condition of consrant wall flux is approached and 6 l i e limiting value of the dimensionless blood-side

-tl.iimíer cn-Hicient defined as kL RID is 24;l 1 L , r 2.18 for this case. For 7,- r, the conditions of

i; . ; ,

.kL R/b I s 1.g3.tka U&+& ~ n k v ~ 8 b ctrcs\.

h%n%%l>vs \ b i l l be general!) less than four and for t l i i l : ca\e the valuc ofk, R.1) is !not much differs-: íroin lhe kaliie ínr -, o. Herice a value of k , R I D of 24, I I can lbc a~sutiieil as a simplification to simulate tuhular haemodialyser performance. I f a more accurate value is dcsired then the theoretical data of KIMXIMAY (1973) can be used. I t should be also noted that this Yalue is applicable only for fully developed Row, ¡.e. when the dimensionless length of the ddyser ( L D / u , R*) is greater than 0.2. This restriction is not very critical. since in practice the value of L DIUb R2 is generally greater than one.

Similarly, for a parallel-plate haemodialyser the value of the blood-side mass transfer can be approxi- mated to that Tor a flow of a laminar Newtonian fluid with a constant mass flux at the wall and this value is given as (KOOIJMAX, 1973):

(20)

3.3 Diaiysaie-side mass-rronfer coefficieni (k,) If the dialysate-side fluid is assumed to be in

laminar flow, the following equation can be used to obtain an approximate a prioriestimate of the value of the dialysate-side mass-transfer coefficient.

where W is the width of the dialysate groove and D , is the moecular difusivity of the solute in the dialysate fluid.

Eqn. 21 is based on the assumption of a Rat

0 2 O 4 O 6 O B 1 0 dlmCnSIMte55 length Y

Fig 2 Dimensionless outlet concentration for tubular haemodialyspr

x x x lumped parameter mooel. ~ comt:int w;~ll crmposiiion are rciched and ilie value nimeiical solution of Daws and Parkincon (ni%

Constant wall flux. - If the flow of the dialysate-side fluid i s likely 10 be in the turbulent regiiiie, the contriDlition of :he dialysate-side mass-transfer resiStailCA would be negligible in comparison with the blood and membrane r e s i s t a m . The order of magnitude o f the dialysate-side cocficient can be obtained from the correlations similar to heat transfer lor Row i n annuli. Some correlations for this pirpose ha\,e been summarised by KNUVSEN and KATZ (19581. In the foilowing Section, the validity of the pro-

posed model is illustrated and the w o f the% - approximate model parameters given above is shown to be sufficiently accurate for the prediction o f the haemodialyser performance.

F

' - c

-

!- 4 Validity of the lumped-parameter model 4.1 Co~isronr-dioi~v~me-ronreni~ation case

The accuracy of the limped-parameter model uas examined by considering a case of constant dialysate composition C, equal tozero. The model predictions - were compared with the numerical solution of the exact 2-dimensional model reported by DAVIS and PARKINSON (1970). 7he results are shomnfn Fig. 2: where Can/Cal is plotted as a function of d mension less length y defined as L DIU. R'. For this com- parison the model parameters kL and De were estimated a priori. The agreement between the r lumped model and the distributed-parameter model ' is excellent, pariicularly for the practical range o f

ti < 2 and large !;slues of y í y > 0.6).

L

I

....

4.2 i ' ~ ~ ~ ; , ~ ~ - ~ l ~ ~ , l l . ~ , ~ l ~ - ~ , , , ~ ~ ~ , ~ l ~ ~ , l in,, <-air

~Tb.3 iprohleiii lhas been solved by C~OUEY el u¡. ll9T11 hy a iiiinierical procedure for the case Of cuncrirrent flow of the two fluids. The comparison of the lumped parameter model (eqn. 17) with this solution is shown in Fig. 3. The comparisons were made using a priori values for the parameters k,., k , and DE. The other pafameters were chosen to be the same as in Table 1 of COONEY P I ol. (19741. The

i

&E 1

I ook-

3 46 I

! o 2;

I 2 3 dimensionless length y

Fig 3 Eflect of retm of blood to dialysate flow rates on outlet concentratmn of solute

-_present work x x x numerical solution of Cooney el ai

(1974)

7 Table 7 . Parameters used in illusuaiive simularion of pat ient-arul ic ial -ke" system

L_

Initial concentration of urea in body

Blood flow rate !n haemodialyser

Flow rate of dialysate

Permeability

Diffusivity of urea i n blood

Length of dialyser

Width of dialyser , Half-channel width

Volume of extracellular compartments (blood)

= 2 mglcm3

= 200 cm3Ímin

= 424 crn3/min

= 1 . 2 ~ 1 0 - 3 cm/s

= 2 ~ 1 0 - ~ c m Z Í s

= 84-77 cm

= 14-76 c m

= 0.008 cm

= 101

Volume of intracellular compartments = 20 I

Exchange caefficent between infra- = 50 lih (and 10 lih lor and extracellular mmpanments the second case)

Rate of cree production = O 0629 grn h .1 kg body Weight

8-

8- €I,&&- we/ glrf c p p

rgreement is eiceilciit and i,cr.,c the prescn' tmx!~ ! an be conveniently used for all ~al~iilutii>ns ii\ i t

-oes not require a numerial solution. N o niiiiierical solution has been presented for coiiniercurrent flow

+n the past in the literature and the luinped-paid- ~ ieter approach is useful for this case. L

5 Comparison with e x p e r h a i d data - The theoretical predictions for a parallel-plate taeinodialyser are now checked with the experi-

-nental dota o f GRIMSRGD and BABB (19661. The coniparison with their da:a was made ior the system

.-&odium chloride and water. The estimated value o f g ;as 0.12. Experimentally, Cirimsrud and Babb

-hanged the value of y by changing both the solution llow rate as well as tlie channel height. A comparison

'&tween their e x p e r h t a l data and the luiiiped- lardmeter-model predictions of this work is shown

-n Fig. 4. Very good agreement is found to exist rip to a value of ,y = 5, hut at higher values of y the experimental data points are somewhat higher than

~ he theoretical predictions. Comparison between the -xperimerital data and theoretical predictions of a

' 've accurate model showed similar trends. This 'F he attributed to the possible boundary-layer

r i f e s t s due, to the presence of the side wall. -1 he theoretifal predictions with variable dialysate

%oncentration are now t a t e d by using the data of ~ RAMIREZ tTI d. (1971) on a commercial Kiil dialyser. ' F h e dialyser had a length of 84.772cm, width of . 14.764cm and the height of the blood half channel

r-

.-<vas S x IO--' cm. The Fewrted permeability of urea

,I Two values o f D of I x IO-'cnils and \\as I .2 v 10- ;mis.

r- climensron!ess lenoth v

valuc 01' I1 is lihelr t i i bc i t i thi , TYII~L.~ i o r c~riri.ple, CULTO& P I ril. (19711 obtained a d u e of I Y cm2/s for D for a \iall shear ratc o f ?O to 50 s-'. The diffusivity of urea i n blood i s shear-rate dependent [see for example, HYhiAS (1975)). In clinical dialysers, the wall shear rate is of the order o f IOOS-' or higher and hence the diñusion co- efficient is likely to be augmented over i t s value at zero shear rate. Hence the range of D in normal diaiysers is likely to be between 1 x lo-" to 2 x iO-5cnP/s.

The theoretical predictions of the lumped-para- meter model for varying dialysate concentration (based on eqn. 11) are plotted as curves in Fig% 5 and 6 so as to enable an easy comparison with the data obtained by RAMIREZ era/ . (1971 i. Fig. 5 shows the data obtained by maintaining the dialysate flow- rate constant at 424 cm'jmin and varying the blood flow rate. whereas Fig. 6 shows the data obtained by maintaining the blood flow rate consfant at 206 cm'lmin and varying the dialysate flow rate. The agreement between theoretical predictions and the experimental dala is found to be excellent. The sensitivity of the model to variations in D i s not very large for this case and is of the order of 20%.

6 Simuiaiion oi a patient-ariiücial-kidney system

The results of the model prediction o f a haemo- dialyser can be extremely useful lo the clinician. if a theoretical evaluation of the in tiro performance of the dialyser can be made. Such a model would enable the clinician to predict the time required for haemodialysis treatment and thereby save time-

I o L:

, - . F~,Q. 5 Effect of blood flowrate on outlet concentration

Of So,'l,te

4 :/at pia:* LllalysP, rnodelpiediclions, O0 = 424 cm','m;n '-F,g. 4 Compai,Jan Of model with experimenialdata on

0 6 t

>p o 5. 1

200 300 Loo 500 dialysate rote Q,,crn3/min

Fig. 6 Effecl of ddysale f/ow rafe on oul/et con- cenlration of soiule - model. c i a = 206 cm3Imin -, ~. i_ experimental data of Ramirer el al.

(7971)

discrete homog+oeous compartments separated by semipermeable membranes. The transfer of solute takes place from the various compartments such as the interstitial fluid, intracellular fluid and red cells into plasma and subsequently the solutes are removed from the plasma in the haernodialyser. A complete theoretical model of the patient-artificial-kidney system should account for the transfer between the various compamnents, removal of solute in the haemodialyser a i d , t h e rate of production o f solute i n the body.

A number of investigators haw modellcd ~ l i c patient-dialyser system hased on a simplified 2-compartment model for the patient [BELL el ni. 11965): KING rr al (1968): DEDRICK and BiSCHoFF 11968); \\'0~~~1d1(1969) ; GORMLEY and BELL (1970); ABBRECHT and PRODAW (197111. .As shosn by PAPPEXHEIMR t 1957) significant concentration .

differences exist for solutes such as urea ktween only the intercellular fluid and the plasma, and hence rhc 2-compartmental model may be satisfaanory. Recently SHrrricm el al. (197n have presemed a more complex 5-compartment model for the sysieni and have presented a numerical sohiion to the problem.

In this work the problem of simulation of parient- artificial-kidney system is illustrated using a Zcom- partment model (Fig. 7). Analytical solutio^ are presented for the transient concentration of Una in the blood and tissues as a function of haemo- dialyser operating variables and various physio-

timeof dialysis. h

u2 5 '.Oo 1 2 3 4

timeof dialysis. h

Fig. 8 Predicrions of palienl-arrilicial-kidney model, K = 50 I lh

Vg transient mass balance for the blood compart- r nt assuming complete mixing is:

References ABRRECHT. P. M., and PKODASY, N. W. (1971) A model

of the Datient anificial kidney system. IEEE Tram. .- acctlmuldtion = mass exchanged from tmues+

production --removal in :he dzlyser

- -i;iathematically

r_

i

where, I is the rate of production of urea in the body r h i c h is assumed constant, K is the interchange : iefficicnt for urea between the blood and tissue i i d VE is the total volume o f hlood. A transient mass balance for the concentration of urea in the intra-

,&llular fluid in the tissues C, assuming complete : i ix ing is: L

Vc d- = K(C",-c,> . . . . , 12-51 dl -

The simultaneous solution of eqns. 24 and 25 .,¡cid Chi and C, as a function of time. The equations

can he solved analytically and the details are ~ presented in Appendix 2. In particular, eqns. 39 8 J I d 44 enable direct calculation of the concentration ' d i urea in the t*o compartments at m y given time. ' A s an illustration, a patient~ariificial-kidner ;+stem is simulated for the \slues of the various

)arameters surnrnariscd in Table 1. The results a i r sbhown in Figs. 8 and 9 and two values of the ' exchange coefficient o f 50 a r i 10 I jh. respecti\el?. ~ + t i s seen that the difference in the concentralion i n 8 : the two compartments is not very large when the ii:xchange coefficient is large (K = 50 1/11) hut for 1 K ~= lil l / h the dilferences k o m e fairly large. It i s I interesiing to compare Figs. 8 and 9 and note iha!. , alrlioiigh tlir cmcmtration of urea in the plasma 1.' drops to almobt the sanle value in a given timc :i,r

of urea in the intra- cw &' = In Iih. ThiL

IC

.~ B M E - I ~ , 251.

BEL(., R. L.. C i ;~ns . F. K . and B~ns. A. L. (1965) Aiialng simulation of the patient art i f id kidiiey system. Trnns. Am. Soe. AT, . Inrwnal Organr. 11, 183.

Cocron. C. K. (19h7) A review of the development and performance o f haemodialysers. NIH. US PHS, Federal Cleariiie; House Accession PB-182-281

CULTOS, C. K., Suirri, K. A,, MERRILL, E. W. and RFKE, I. M. 11970) Diffusion of orsanic solutes in stagnant plasma and red cell suspensions. Chenr. Em Prof . Sym. Serks, 66, (991, 85.

COLTOX. C. K.. Sumi, K. A., STROEVE, P. and MERRILL, E, W. (1971) DiRurion of urea in flowing blood. Ani. Inr<. Chem. Ens 1.. 17, 773.

CDONEY. D. O., DAWS. E. I. and Kizr, S. S. (19741 Mass transfer in parallel plate dialyurr-A conjugated boundary value problem. Chem. fig. 1. 8,213.

Dhvrs, H. R. and PARKINSOS, G . V. (19701 Mass riansfer f r r in .;mall cqiilaries with wall resistance in the laminar now regime. aPpi. sei. R K , 22.20.

DFDRICK, R. L. and BIscttom. K. B. 11967) Pharmaco- kinetiir iii application of artificial kidney. C-hhrm. Ew. Prof. S y % p Scrim. 64. (84). 33.

EwaGm, M . E. 11967) Dispersion of matter in Non- Newionian flou a i I O U tiow ialc<. lrzd. Enp. Cheri. Fund., 3, 463.

GORVLEY. Y. W. and BELL, R. L. (1970) The dynamics ni u:- iranifsr and iclehral presjure during rapidly chacgiiig urea levels in the h ! d . C k n ~ Eng. Prov.

Baau, 4 . C. (1966) Velocit! and con- IC lor laminar flow of a Ns~xtoniali

fluid in a dialyrcr. Chon. Etw Pro?. (iiiw Suriri. 62, 10.

HYMAV. W. A. 11975) Au~rnenicd diliuriiro in Rouing !>locd. Tronr. .<S.ME. 58.

Ktw;. P. H.. B w t ~ . W. K., GI\\ , M . E. and FROST. A. B. (1968) Computer optiniizatlcm of haenii*lialysis.

K<KXJVA\, J . \1. 119721 Flow and Ma,s transfer in haeniodialysrrs~lnfluence of non-Ncuioninn blood

K<iii$iva%, J . 51. 11'173) Liiminsr heii or mas, innsfer in rectangular channcls and in cyliiidxica! iuix.- for CUI!! dcvelo~cii flow'. Clwii,. /:,!P. Sci.. 28. 1149.

K K i m F \ . J . Ci. .ii!d K % r z . D. 1. !IcJ?S1 Fluid d!nani¡i.s and hmi iram!cr, M c ~ ~ r ~ ~ ~ ~ - l ~ l i l ! , Neb> Ymk, 403.

I 1 ~. ! .V<P~I I 0~ I I<>??> C'hcmicnl Reaction Enyinecring~

si<»i,7. Series. 66. 99.

rrc><ini A,,,. so< hi. rr,ier,,d orponr. 1.1. itr9.

no,,. ~ i ~ ~ ~ ~ > . E , , ~ .i , 4, 1x9

I__

“-LIGIITFCV~, E. y. (1974) ~ r an r po r i Dhhenmena in living s y s t c r ~ . \v;Ic). x e u i o r k .

8 - \ l . ~ s ! , ( t L A X , R .I ~!ac! KAV\<H*UT>KAX. P. A. 11975) \ inrw model for hollow fibre enrymc reactor. J. .4l>i’l.

L-

PAPPFYHHW R. J . R. (1557) Parrage ofmolffulcr through capillary +ail\, Ph.vsiol. Ret‘., 33, 387.

i - R & ~ a r ~ i ~ u n a ~ . i . P. A. and MASHELKAR. R. A. 11975~ 1- Axial dispersion model analysis of homugeii+our-.

hetcrogcneovr reactions in a tubular reactor. Lrrr. tie.qr & Moss Transfer, 2, 213.

RAMKHANDBAS. P. A. and MasHfLaAa. R. A. (1970 Trancient anaiy~is of a haenmdialyser. Unpublished work.

RaMinir. VI. F., MICKLCY, 41. C. and LFWIT. D. N.

l i rw. & hi<,. Twh., 25, 867.

I-.

9-

(1071) Mlnthematical Moácf;L,ts c,. i: ,::.c dialyrsr. Chcnr. En#. Prop S y n v Sei¡?.% 114, (67) . 116.

S A \ K A K ~ F I BKA\I.\YIAU. S. and G i l , W. U. (19711 L<iriszil> C ~ ~ I ~ Y ~ C I ~ Y ~ diliu\ion with interphaie rnav transfer. Proc. /I. .%c., A333, 115.

S i i r r r i a A R , I.!. R.. DW-PAK. D. and GHISTA, D. N. (19771 A model ni the patient-dialysis treatment to study the dynamic< oí mitahoiic waste concentrations. Med. & Bioi. E m & CmrjxL, IS. 124.

TAYLOK, G. I. 11553) Dispersion o í soluble matter in I U I I - ~ I J flouhp slowly i h w u e h a pine. Proc. R. Sor.,

Woi.,, M. B.. W~isov, P. D. and DARBOUR. P. H. (1969) Thcorrtical e-i.~luation of a poticnt artificial kidney ~ystem using a Kill dialyrer. Rand Cvrpoialion. Santa hlonica, California, Memo RM 5955, N1M.

,4219, 186.

1- Appendix 1 ,

1- Solution of the lumped-parameter baeumdialyser male1

from the literature (LEvmSmL, 1972). ?he solutian may 8 1 be expressed as:

~~

Q. If the mass-transfer terms ale eliminated from eqns.

__ .~ -~ I‘ . . , (30) 1- 5 arid 6 we obtain:

Integrating once and using the boundary condition at is defined by eqn. 12. x ~7- L and rearranging gives: Rearranging eqn. 30 we obtain:

ai:

k I. Y 2 ’ &

A h ‘ A: I , Similxíi) eqn. 25 may hc written as:

(3A)

c

3

11 B @en the solution for C, as a function of time can be - - . , . . . (43) rimen as: lA,t+A12)(A2-A,)

(39) B i c, = 8,exp(A,1)-t8~exp(A*I)-------

( A L , i , A , 2 ) where - c&j and Cr(c) are the ~on~entrations at I == O.

ne solution for the transient concentration of solute in the blood a n be obtained as:

c,, =--~. . {p, . i~exp(A,i)+pIAiexp(AlI) ;

B

T h e r e

I - p, and f12 are the integration constants.

The boundary conditions are as follows:

. . . . . . . At I = O C, = Cdo) (40) VC 7

K -xi, from eqn. 25,

. . . . . . . :~ p, exp(A,r)+& exp(A.r)- . (44) y&- dc* = -jc {cbJ(oj-~c,(o)) (41) (A,,S.4,*)

~

i

r

'i r

Recycie of dialysate from the artificial kidney by electrochemical degradation of waste metabolites: continuous reactor investigations

I

M. Fels Depanmeni of Chern~cal Engineering. Lakehead Univeisily, Thunder B a y Oniario. Canade

Abstract-Experiments are deroibed on the conlmuous eleclfoiylic decomposition a i urea in diawsace and ,: ddysale minus glucose andlor acelale. 11 was found lhal in addirion lo*:he urea removed. rh

wasanexcess ofCIO-. CIO;andCIO;,onsproduced. A p H d m p ofabout 1 unir /sce&upiiP;eni) and 3 4 um15 (acelaie sbsenr) was also observed. I1 is concluded lhal lhese side diecis woiiid preclude climcal applicalion.'and lhal iimre work should Concenlrale on methods of elim,nai,ng fhese effects

glucose andacelale were oxidisedsobslanrially. especdly al the higher power levels, andthar &d 7"

Keywords-Amficial kidnay. EiecVo!yIic d,ssoc/arion

1 Introduction H ochloriie (as NdOCI or HOCI) has been r-td THIS paper is a repon on continuing work on the b ~ A U ~ ~ 1 9 ~ 3 ) l O . b e P I O a Ü C ~ i O ~ concept oían electrolytic oxidation scheme to rcmove ofJkiE?!nt !eCeSSXY-lO o ~ í ~ ~ ~ e organic toxins from the artificial kidney dialysate to allow metabolites. To remove the hypochlori1ea;eifucin: recycle. Initial research on the concept was reported ?cent such LU.G& o r b i c A X w a s ested. - previously by FELS (1978). and i t is useful at this point stage 10

to summarise briefly previous work in this field. inves&kate lurtho@es& ceactions?mdmffa%mg Several workers (TUWINER, ..1966; BIZOT and ~. urea I decom khP osition, ' ' becausuin less . -malysa ie

SalssE, l9i3; YAO ef oí.. 19731 have reported that c o u d e d A harmful b y - p r @ u c t s , m Ñ E a l toxins such as urea. creatinine and uric acid could be usefuiness of an el~ctroly~~~r~yclcscheine woÜT¿CE <iiidisrd hy passao_s an electrjc through a irnpwsible. TaJhis-c& the objectives o1 the research solutkm cmt.iining chloride ions. -e a r e to quan=fhc . -. a m b ü n t ~ ~ t &

Generally i t has k e n found t m h e raie oí urea A d e oxidation reactions. and to analyse for the decompositioTbainly a function of the pow= Presence, Of potenti& mxic by-pC?.lücts Such Ithecell. The gases iven o r consisted o1 nitrogen, .GzramineS. arbon d i o x i J e 5 E Z k & sition I: oxyge-

hndhyaroaenro rn the e l e c t r - a t u d o e a s e in DH was also observed. In addition to urea dryom ositiiin w i 0 n U a i . c b c e ñ ~i; íaS¿;rai i¿fr>bd?&ER (19661 p a d t h ~ ~ i o ñ ~ l o r i n a t e d comp=s SÜTY~S chjms?>m-y_durine electrolysis h y the ln!lowng reaction s c h e m e r

Thus. ih!!?sar%L important

v

- ~

2 Thwretical coiaideratians The electrolytic reactions involved have been

discussed previously by FEI.S (19781 and thus will on!y he srirnn>ariscd briefly hcre. Essentially i t is postulated that a solution oí sodium hypochlorite (NaOCI) I S

formed as ,u, intermediate nhich then reacts o i t h urea tc. form U,. CO, 2nd i1,O. the NaOC-I hiing c imver t rd back to 3aCl

.. t k ¡ ¡ n i \ / pr<di ic i s : ,

? O t l l lNCOYiI , -- IV2+C0,+?H,0 . '5)

I t i s convenient to :onsider the oxiddiion hy this rhi.mc hecdiise by mt:asurinL the amount orhydrogen g a h given off. the amount of oxygen available ¡or o\itlation can be calculated.

.There are several potential Oxidation reaclicm % h i d can occur in the dia1)sate solutioti:

t I I oxidation <if urea as in eqn. 5. This reacti i in rotild yicid 3 moles of hydrogen per molc o í urca.

( 2 ) ionnation of oxygen gas by the combination of two oxygcn atoms:

O+O-O+* . . . . . . . 16)

I:) formation oí chlorine-oxygen ions:

CI -+o ..+ C I O ~ ~ . . . . . . . (7)

cIr+~?0 - cio; . . . . . . . (81

CI- +30 - c10; . . . . . . . (9)

Reactions 1.8 and 9 would result in 1.2 and 3 moles of hydrogen given OK respectively.

(4) oxidation of glucose to gluconic acid, a monocarboxylic acid

HOCH,iCHOH),CHO+O - HOCH, (CHOH),CO, ti í I O )

eqiiipmcni i\ shown in Fig. I . Theelectrol~ticceilisahowoio Fig.2. Itconsistedof

a p r s p x cylinder. 57 mm in diameter and 125 m m in height. Inlet and outlet connections were provided to enable the cell to be run as a continuous stirred tank reactor. The elestrodes were concentric cylinders, the outer one being 25 m m diameter and the inner 20 mm. Each is 5Omm in length and constructed of 52-mesh platinum gauze. A magnetic stirring bar was placed in the bottom of the cell to provide mixing

1

3.2 Soluiions used Four solutions were used for the decomposition

studies, each had an initial concentration oí500 mg I ~~ ' of urea. The solutions were

I S ) oxidation o f acetate. Sodium acetate present in the dialysate acts as a bufer: that is. hydrogen ions added to the solution will react to form acetic acid which is weakly ionised. Thus. in the present case. where there are indications of a fair amount af hldrogen ions ahnut (because of thc pH dropl. it uould he cxpected that acetic acid would k present. Oxidation of acetic acid to carbon dioxide and water,,, phdek$,'c QJ/

( I ) normal (2 ) dialysate without the glucose

(3) dialysate without the acetate 14) dialysate without acetate or glucose.

Table 1 gires the compositions oí the four typqs of solutions used.

can occur: oar Olrier

C H , C C ) , I - I + 2 0 - . 2 C O , + ~ H ~ O . . ¡ I l l ~1 m r - - , . In the present expsriment. the amount n f oiygen

a\ailable for the abovc reactions was obtained by measuring the quantity of hydrogen gas evolved, The estent oí rezctions 5 to 9 was calculated by direct measurement of the products. and the extent of reactions 10 and I I obtnined by dilierencc

3 F~perimenriil

tii,idi.ilei

3. i i2iiiiixiciir lhs expciirnental ret-up consisied mainly of nn Auid ourler

3 . 3 I r , < v l <,>i"lJSi.S

Deiermination oi urea was done using an analytical procediire described by CEROTTi (1971). Essentially, the method consists oí reacting a small amount of solutior (2Opli with a diacetylmonoxime-antipyrene reagentaltheboilingpiintlor 15min.Ayellowcolour then develops. the intensity oí which is related to the concentration of urea in solution. The absorbence of the siiniplc is read at 460nm using a Spectronic-70 snectrometer.

hi h e 1 hi* .Analyse. oí the three anions werc done uckg

nandard analytical techniques lkieny. CIO- was obtained by reaction with a known eAcess oí sodium arsenite (Na,As,O,) and the unrcacted arsenite determine<' by titration uith an iLAine solutton. Titration d a sample in ac>difiec pi.tassium iodine solution with s<xliurn thiosulphate yields the amount olthe two anions CIO- and CIO;. The quantity ofall three ions was ,abta xed by reacting the Sample with NaBr and concentrated hydrochloric acid, adding KI and titrating with sodium thinsulphate. The individual

. . *'> . ..

:e .%>,

nicq 1-1 $"in 1 ruln 2 a soin 3 ,0111 4

\a 1341) I3411 1340 1340 i

Ca 31) 31) 3 0 30 K I .O 1 -0 11) I O % 1.S 1.5 1-5 I5 Cl 102.5 102.5 139-5 139.5

~~ ~~ Acelate 37u 370 Gl"C0Se 2-5gi.' 2,5pl-' - . > ~ ~

3.4 Gas analyses The gaseous ellluent from the cell was analysed by

gas chromatography using a PYE Model 105 chromatograph with a thermal conductivity detector. The major components of the effluent were CO,. O,. N, and HI. Carbon dioxide was analysed in a 2 m long, 3 mm diameter column packed u'ith Poropak-Q. The O? and Ni were analysed in a 3 m long, 3 mm diameter column packed with molecular sieve 5A. Helium was used as the carrier gas lor the above three gases. The Poropak-Q column was used to analyse lor hydrogen. but. in this case, nitrogen was used as the carrier gas because the thermal conductivities of helium and hyirogen are so ciose. The flow rate of the carrier gas -as set at 30mlinin.' lor all analyses.

The cell gases were passed through a cold trap kept at ~ 1O'C prior to entering the chromatograph 'to remove the \rater vapour. The flow rate Jl the gases was measured using a wap-bubble flow meter. Standardisation oí the EX chromatograph was perlormed urth gas mixtures oí known coffiposition h:!vine approximately the same percentages as would hc expected lrom the crli.

3 . 5 i J e ~ w m i ! r ~ m m ufCiO-, C1O;ond CiO; The C I W ion (as NaOCl or HOC'II. being an

tnierniediate in !he rextion icheme, uoiild be i'xpected I O be pccsrnt to some extent in the exit stream Ironi the CCI: iíi addirion to hypochioritc. !I was postulated tha! some hirhcr oxidation Droducts such

aiiions were then obtained by subtraction. Detailed descriptionsolthese procedurescan be found in CPPA ~ 3 )

3.6 Analysisfor hydrazine and chioruminrs Beside the major components of urea and CIO, ions.

analyses were done to determine the presence of hydrazine and mono and dichloramines in the solution. The hydrazine was determined by two methods, one based on the reaction with KIO, ~VOGEL, 1961). and the other based on the reaction uith iodine (SIGGIA, 1949). The chloramines were determined by an amperometric titration. details al which can be round in GREENBERG er al. (1975).

3 7 E.qwimeniul procedure The dialysate solution was made up by dilbtion o l a

concentrate and addition of urea to a concqtration of XWmgl- ' . The electrolysis cell was filled. and the pumpset todeliver 100mlmin~ ' .Thevoltage w a s w to a given value, and alter the steady stale was rcdched. samples were removed lar analysis. At this time, the effluent gas composition and rate were measured. All analyses nerc done at least in triplicate.

. , . . .

4.1 Urea decornposiiioti The composition o1 urea in soluli<in I< :% fil?::i!r,n

mainly of the power input to the cell. the typr o¡ solution used, and the temperature. Figs. 3 and 4 show

r

power. w Fig. 4 Brr.urnposl,ion ugaiasr power inpur at 31c

the dwomposition as a function o1 power input for the four solution^ used at a cell temperature of20 C and 37~C. respectively. I t is readily apparent that the major paraincter influencing the decamposilion rate is the puaer input to the cell. because. as uill he discussed l i lzr . the production (and consequentl) l h e concentration) uithe hypochlorite ion increases with power input Competing oxidation reactions account

Tiir a I O W ~ rate of depradation whcn thc solution r:,mtains ~liii.cnr and,or aictate: ir:- uili he discur-Ci! lnox fuI!y later

4 . 2 G m er0Iu1ion Measurement ol the pas composition of the gases

evolved from the reaction indicated several interesting observations. The only compnenis which were found to any extent were CO,, O,, N, and H,. Previous results (FELC. 1978) had indicated that there were small amounts of additional gaseous by-products present. However. these data were obtained on a hatch system, and proh:ihly indicated secondary reactions when the urea concentration was iery low and power levcls high.

Thcoreiically, one molt ofCO, and one mole of N, should be given orrh every mole of urea decomposed. With regard tc ihe N, pas. it wai round that generally the flow rate wasabout 10to20'~~lowerthanexpected. It was felt that the reaSons for this anomaly were inaccuracies in the gas flow values and the likelihood that someolthegasnowed out ofthecellwith theexit liquid.

The measurements oiC0, showed that most ofthe CO, given o f did not appear in the emuent gas stream. Representative data at x) W are shown in Table 2. It is apparent that most of the CO, (Mi to 87";) is dissolving in the solution. The solubility ofthis gas is a function of many Cactors, notably pH, salt

Fie. 3

concentration. temperature and parrial pressure of the f:i' i t ~ l ? . 4n idea <!í the arnount oíC0, which would d i ~ w l ~ c ~ ~ ~ n be ehtaincd from thc \ohhilit? in water at 211 C: and A i C for a typical Cu, composition of 5:ó. This figure is about 0 2 and 0-1 rnmolmin-', respectively. The experimental data are somewhat higher than these numbers, again probably owing to inaccuracies in the measurement oí gas flow.

Overall. typically, gas compositions were about: C0,-~4",: 0,--..6%; N,-IT4 and H,-SO".ó. 'rabie 3 shows rates oí gas evolution at M W :or tsmperatures of 20 c and 3 7 r .

'I uhie .l. G U S m i u r m ~ C . I a i 5ow t ~ n nimoimin 'I

O, gas, in forming excess CIO; and in oxidising the glucose and,'or acetate. Figs 7 to 10 show these results ?or thc ?our solutions employed at 37 C.

Rclerring to Fig. IO. which gives the percent oí oxidation used lor glucose andlor acetate. it is =sen that there is a relatively larse amount oioxidatioo of both thesr organic suhstances, especially at the tiisher power levels. As would be expected. in solution I . having both glucose and acetate present. the oxidation requirements ale the highest. Comparing solution 2 (no glucose) and solution 3 (no acetatej gives a measure iiíthe relative ease oí oxidation oíthe glucose

Solution Temperature lire= coi

37 0.25 ,, o.O<)i

~~~ ~ ~~~~~ ~~~~~. ~ ~~~ ~~

I 20 0.22 11.043

20 0-26 0-030 17 0.27 0.070 ?O 0.31 0.080 3 i 0.36 0-IW

4 ?O 0.3 I 0-057 37 U38 0-170

0 1 N*

0. I 36 0-210 0.163 0.220 0,123 0.243

o-om 0.261 0-102 o 304 0069 0.312 0-078 0.370

~ ~~~ ~

0.195 (1.240

4.3 CIO; resulis Three species oí CI0;ion in the cell solution were "reo

'. .. . ~

-d

j -. ..

i.---i-- L l-~--d-...L on m

measured. namely C1W. CIO; and CIO;. Fig. 5 (in rn mol miti ~ ' )and Fig 6 (in mg 1 - ')show the resui ts as a function of power input for the dialysate solution at 37C. The data at 20'C and for the other three 3 60 solutions showed very similar trends: that is. the amount of ('10- was higher than either the CIO;.or the CIO;. On the average. about 25"; of the total CIO; was ClOiand IY'J~ was CIO;.

4 . 1 Owr<r// oridarion 20

.o 4 0

5 g 4o

i O 20 dC At this point. one can present the total oxidation

generated I S iitiliscd in oxidising the urca. in iorming picture. that IS. how much oí the orvgen atoms p o w w

Fh. 7

oxidations ellectively do not occur al powcr than about I O W . Naturally, the paa l t ) u much lower rate of urea decomposition and consrquently a larger and more expensive device.

Considering the results for solution 4 in Fig. IO. it appears that even though there is no acetate or glucose present, there is some oxidation unaccountcd for: this discrepancy is probably due to experimenlal emor. Considering .the accuracy in the gas flow, urca concentration and gas composition measurements, an 8", error is not unreasonable.

With regard to the urea oxidation results shown in Fig. 7 , it cm be seen that thc oxida!ion is mosi efficient in a salt solution and least efficient in the dialysate itself. This is understandable because the salt solution would have no competing side oxidation reactions frornglucoseand acetate.Theother twosolutions with une extra oxidisable component lie in between the IWL' e::treme cues. The oxidation efficiency of Ursa Pdk as the power to the cell iucreses due to the incriawd extent of the other oxidations.

The percent of oxidation allocated to the formation of O, (Fig. 8) and to CIO; (Fig. 9 ) is not a strong function oíthe power input. Also, in the caw oíthe O, data. the amount of O, produced seems to be a function of the solution type.

The current efficiency was calculated on the basis of the total amount of H , produced, considering that I Faraday (Y6000As) would be required theoretically for each moic of H,. Calculated this way, it was found that !he efliciencies for all cases were remarkably constant at valucs ranging 'between 4ü and .W per cent The remaindel-,ofcourse. appears as heat due to ohmic resistance of the solutions.

1 . 5 Hii!i;i;iii,, ",id cf!!,,r'l":d*!c !r\L<.'!.

were ncgativc. I i wac calculnied thai !hi, nican5 thai !he soiution contained less than lOmp1-I oí hydrazine. The quantatitive determination of

I /ir a,i.ii?tic;il k,t> ;or l i i C ,pTc\í:.-~ of lh>drd,i*c

Po- W

Fig. R

I ohle 4. pH cflecrs during urea oxidmirin

Solution LO w YO w

O 20 40 6.9 80

power iv

Fig. 9

chloramines in the sample could not be perfurined because of the relative!y high concentration oíC1O;in the sample. However. i t can be stated qualitatively that the chloramine concentration would he at least an order o í magnitude less than the Cl0;concentration. which would mean a concentration less than IOmgl-'.

4 . 6 pH eflects The initial pH was about 7-1, and i t was found that

upon oxidation, there was a drop in pH for all solutions. In general the drop was more pronounced at the higher power inputs. The lowering of pH is probably due to the following factors:

( I I formation of HOC1 and resulting breakdown to

(2) lormation ofgluconic acid by reaction I O (3; loss of buffering capaciry due to oxidation of the

(4) formation of H,CO, by reaction of the solution

HCI and O

3 c e 1 a 1 e

with CO, gas.

Representative p H results at 37'C are shown in Table 4. I t can be seen that the acetate in solution doe, provide stihrtantral biillering. With acetate present, a p H drop of about 1.2 units was observed. hui with no

jrc 'tm. thc drop was from 3 to 4 units. The solution c ~ ~ n t : i i ~ ~ m g giiicose hui no acetate ch<>ued the largest drop in p1.i values presiitnahly bccause oíthe gluconic aiid niid no buiTering capacity.

, /- 1

Fig. to

5 Conclusions At this point, the following conclusions on the

results can be made: ( I ) l lrea can be onidised electrol~tically in a

dialysate solution, the rate inneasing with applied power aiid with temperature.

(2) Under conditions studied, little secondary products of chloramines and hydrazine were found.

(3) Most of the carbon dioxide formed dissolves in the didysate.

(4) 7here was substantial oxidation al both t h e glucose and acctate present in the dialysate especially HI higher power levels.

(5) An excess of CIO-, ClOIand CIO; anions was formed, with the CIO- being the major component This excessis proportional tothe power inpu1,givinga cnnccntration of ahout ZOrngl-' at I O W and I 7 5 m g l - ' at XOW. Therefore. clinical application o1 such a device must incorporate a means of removiiq [hese oxidation intermediates.

( 6 ) A p H drop wah evidenr in all cases the decreasr being higher ;at hiehcr poner lei,eli. I t should be relatively easy to counteract this effect b? the addition of a small amount of NnOH III the final pfoduct.

I n summary i t appears that. although the present scheme c3n indeed rcmove organic toxins i i o m thc di;ilysate btream. i t would require some basic niodifications to eliminate the side oxidation effects k f o r e being considcied C m LIY on a clinical scale.

6 Future work

Future work will concentrate on minimising ridc oxidations. and eliminating the excess Cl0;ions from solution. Schemes such as Dulsed current and ver i cloce electrode spacing (10 keep power levels low) \vil!

be tried. Suitable reducing agents to remove Lile CIO, such as ascorbic acid will he souBht. and experiment- danc to deierminc the kinetin of this reduction rcaction. In addition, experiments on ihc eifect oí the addition of NaOH to maintain the pH level constant will be done.

Acino><~lrdgnirni-~-~Thi'aurhoi would like t o acknowledge the National Scinice id Engineering Rcrraich Cuuiicil o1 Canadi for support or this research.

I"

i ".-. met the requirements of high common-mode rrjecti<rn - large differential input impedance. The only design.

er than that of the authors, that was considered suit-

transistois in a differential-amplifier configuration at the t o an instrumentation amplifier cir~uit. While i t sins the etfsiive input impedance of the operational ;p, enerally true that dirrcte tm.nsistoi~ have lower noise amplifier itself is ven' large. At high frequencies, the & 11 operational amplilias, it was felt that the increased reactive component of Z," is almost zcro, so that

~culty ofexactly matching the two sides of the discrete Z,. E Rim. However, R,. is physically limited by the avail- düTercntial pair outweigtvd the slight improvement in ability of highquality. stable resistances which can be +se expgted. There would also be a slight increme in matched lo the requ!red degree. We require at Imt Q iiponent cost. Hmnts and MARHEWS (1978) dewribe -eral hundred megohms, and metal-film resistances are _ne specifications for the type of circuit considered, in not a v a i l a k in such values. Funher, an emor of even

ahich a pair of field-ctT& transistors (í.e,t,s) are used 0-27- in rhsrance matching would rerult in a 1 mV in the input stage. They give a noise specification oí differential input signal beingproduced bya I \'common-

pV 1.m.s. ( I O kll input impedance: I O &-IO kHz mode signal. A signal oí this magnitude would cause i idwidth). However, it ir difficult to compare their amplifier wuration. Similar comments apply to the i-se specifications with ours in that they do not include matching oí C,. values, where phase-shift errors similar +L we did the misy d.c.-lOM band. Still lower noise to those d i m r e d earlier could occur. {auld be achicved by-- bipolar tIansiston in this .bother option for B.C. coupling is shorn in Fig. lb.

~ ,figuration, since they have lower internal noise than This i s more acceptable than the first, bur the large 1,s in the bandwidth of interest (On, 1977). However, capacitanes (C, and CL) needed to meet the low- &-' mncluded during the design o í the present system frqquency pole requirements would makc tantalum

:e cntiemely high qualify oí the bipolar transistors capacitors lor clectrolytics) essential. Again, this presents ,A- , P?41 OP-10 offered sufficiently low noise while ilre prohlern of component matching, as even a slight

~ admg the difficulty and expense of using a discrete error would show up as a phase difference between the Lrerentiai input pair. two inputs ro the second stage oí this preamplifier, and

Two options. orher han that actually implemented, errors wouid result. re available for a.c. coupling the preamplifier stage. For the m o m given, both these options were rejected

pie was to feed the signal input directly into a high-pass in favour of a single capacitor design in which no addi- et and then into the operational amplifiers. as shown tional component matching is required. Sufñcient reduc- L Fig. 70. This would aertainly simplify the amplifier tion in d.,:. gain is made in the first stage to permit

ilciign. but L an unacceptable alternative for it eve rely subsequent high-pars tiltenng at a point where mput ,?its the input impedan- of the circuit at signal Ire- irnpedanas need not be very large.

quencier. Fm one input. referred to earth. the input impdance in this Case IS appioximately k involved thc intrwJuaion of a pair of discrete I,. K.- . {G"- '

I . _

ii *-

P

c

Analysis of a tubular haemodialyser-eff ect of ultrafiltration and dialysate concentration R. Jagannathan U. R. Shettigar Dspaifmeni of Chsmical Engineering, Indian InsIif~le of T e c h n o b y . Mad,- 600036. India

Abstisct--A rlieorerical amIys>s has been made of mas^ iiansfci in d ho l low~f ib re aiiificizl kidney will, ~,ll,,7/illr~~!,o~', 1,s; . ( dialysatii concer:lialion and (ii: s vaiable dialysate c o ~ : c ~ ~ ~ : r a l ~ o n alii,ig iiri l d i l e r i s a coniugaied boundaari-value problem. The sohi ion is obramsd I o / srparaiion o í variables U J ~ Y an i n í m l e series expansion considering llie / h i d 10 be ddule and Newroiiiaii. firsui:.? indicale ihar the ullrafiliraiion ,die. iuiiiieabilily o/ rhe rnimbraiic a i i d :he nonzeio ~'miyiaie conienfialio,n ail have a siynificunl effecr on rhe clearance oirhe solure. The tubulaf d,ameler análcnyrli ha.'i veiy Iilile rffecr ('r, rhe clearance of rhe solute for a consranf membrane surface area. ulfrafrhrafion m e and a IVW

membrane permeability. Al high ulirafiltmion m e s , the effecr of fhe solufe concenrrarlon in ihe dialysafe phase on the clearance become negligible. This analysis I S compared wirh those o/ Popovicheral. (1971). Ross (1974) andCooneyeta1. (19741.

Keywords-Artiíiclal organ, Boundary-value problems, Mass rraansfer

in the dialysate phase. Recently, COOUFY er u/ . (19746) have considered the problem oí a nonzero Y a" \La< 1 Introductiw

THE conieot of a nortable. wear ble haemodialvsis I~ ~

machine !nvoives. the d k g n of recirculating dialysate iystem and reseneration modules (STEPHFSS

I uI!rnii!tmtion rate and a nonzero dialysate-concen- troiiiiii, which accounts for the mass-transfer rcsist:8ncT or ;he dialysate phase. The design analysis: , :if the ieimeratiori module will be dealt niih in n

dialysate Concentration. However, they assumed a zero ultrafiltration rate. This uork considers the effects of both a varying dial>-sate concentration along the length of the dialyser and the ultrafiltration rate on the clearance of a solute in a tubular haemo- dialyser. ultrafiltrarion rate is assumed to be

iw&LsaklG ' ' t l i - o .

16nlpmA uJ:+loOn,~ @\n.o&o, I sb.b\e- cu- ee;i

2 Analysis

2 . I co\<.-i. rr,,,A,t:t:r ,I:~;I> W. I ,:<.<,,,rr

hc sol\cd for thc velocity components of Us aiid b'B.

With boundary conditions

Boundary condition I :

.Y < o; all J. c-' =. 1

Boundary condition 2 :

<IC' <JS

all s. .Y '= o, - = o

ihUnddl-y condition 3 :

and Pc. = c..,RID.. the wail-oemeation Pcclet By separation of variables. the soiution of eqn. I may be written as

r- 1-

?-With the following recurrence formula for II 5 8

I

F,(2n-4-L2)a . . ,+ F i (12-n+4)un~, ir

.-

r-and with

1 Re,

2 9

. . . . (13)

Mass-transfer coeficienrs: For a constant dialysate concentration. the mass-transier rate over a dilier- entia1 transfer area is given by

di+r = ( P i c , TE)(CBW.-Cd

where Ceu = Cs at s = I .

If the dialysate concentration Co is assumed to be ?- 6 = Ic.,/ú(O)lh~(O) negligible compared with Csvi the differential

mass-transfer rate becomes I- The eigenvalues A, can be obtained from boundary condition-3. Thus A. are the roots of the equation . . . . . . (14)

p-The A, codficients in eqn. 9 are determined from t boundary condition-I and the orthogonality dril = (hd+h,)CBddA . . . . . . (15) :,-principle to yield

and in terms of the overall mass-transfer cwfficient, h. i s given by

di+, = h.C,dA (16) P- I

y-.

( I -k ) 5 o.s"d(s).ds

,,- i 5 a.9 0"s" d(s)ds

! i- u,here

"=u . . . . . . . . . . (11) A m = ,

Eqns. 14, 15 and 16 yield

. .?O "=o h, = h,+h, . . . . . . . . . (17)

tid = PCBT,!CB (18) . . . . . . . .

h, = ur TR CewiC~ . . . . . . . (19) 1

k The mixingsup concentration is defined by

(121

The mer311 m3r,-iranrfer codiicieni of the dial)\er & clmpuied from eqns I 3 and 17 I O IY a. a function of the hvdrodniamic conditions,zem~bTze permeability, membrane transmittance factor. ultra-

rhc lrngrh of rhe dialyser Blood containing the toxic metabolic waste Pro-

ducts Rows through the semipermeable hollow fibre tubes and the dialysate flows on the shell side of the 1- Th e dialysate concentration I S assumed to v a n alonq the length of the dial>s-r. This i5 more *r

r- .,... ca+ '(.Y) = <: i~

.. ,... ..--- J-'d e (SB 1 0 cf&

M ith houndai~y conditions Boundai). condition-I:

.Y 6 o, all 3, cs+ = o

ail x, s = o; acB+jas = o ihiiuidary condition-2:

&>undary condition-3:

be writter a i

If the a x d diffusion term is very small compared t V & - (20) with the axial convective term, and the u l Ü ~ X w

arsumptim is also made, then the aboveceqwjop becomes

ac.+ .JS

__-.

or in a dimensionless form

ail X , s = 1, Cs+ = Ca+.++(x) Eqn. 25 is subjecied to the following boundary conditions Eqn. 20 is first solved for a constant surface c o x e n -

generatised to vaqing Surface wncentratlons using Vuhamelp theorem.

1Tie solution to eqn. U) tor the constant surface ccncentration is

x s O, C , = O for all Y

Y = o, co = C d X ) and Y + T, CD is finite for all X.

Then the S n e r a l solution for the variable dialysate concentrimon at the wall becomes

q = z,'i40 ( P e l i .Y-B>t)dfl

and zm are the roots of the equation

. . , - i : P 1 : 1 < 1 - # l d p , . , ( 2 7 , b. are @ven by eqn. 10 with i, replaced by u-. Using Duhamel's theorem. the general SOIUtiOn for the We now wive for the unknown variables Co,l.YJ variable surface concentration k o m e s and C.,i 1 ~ 1 using the ilux conditions a: the neni-

brane sud;Le. i.e.

<?C.i .\ I

dS

a A I S = 1. C.+(S. .Y) = \ C2"(8) j':

= Sh,, CD.! Yi-Sh., 1, Cn,,íX) !?SI x (1 +wsfs . .Y-J>)dB (24)

W e no\\ consider the dialysate phase. Because o f the cornpirx~ry ot rhe dialysate tlow field on rhe 'shelly

at '' = o. * ,,c:,, , ~

-_I-

i

Shwx S/iw2 k, (281 / ,G+ SA,, k, - . ~ ~. ~~~~~~~

I- x i r i q + l ) - y i q + ~ , -/J/z)) (31)

yíq. -p:2di is the-incomplete gamma function. S h . . , + x , í p . f e 2 ) which can be expressed in terms of the confluent

SEGCS, 19681. -hypergeometric function M ( A e n a ~ o v i r z and Tdking the Laplace transform of eqn. 35. i n

dimensional form, we get j_

I I -

Since J is of the order of 10- s. pi28 may be taken Io be very large. in which case we get

Laplace inversion of CJs. p) in esn. 39 is obtained by the numerical method of ZAKIAN (19691.

I-

r L i ,

Substituting eqn. 32 into eqn. 31. and assuming that p 3 is very large, we get

,-

'The form ofeqn. 33 suggests that the t e r m ( I - - 2 ñ X ) u n eqn. 21 can bc approximared as unity. I f i r e ~ incorporate this approximation in the axiiil velocity Ipwpression. eqr. ? I hecomes

3 Results and discussion

The cornDutation.. were cerformed on our IRM

factor is not available. we a s u m e to he it: the rangéof0 .8 to I ~PUPOVICH e1 al.. 1971) for haenio- dialysis mcmbranei. Wherea5 lor the reverse

I! t h Monsxnl@ hollo\v fibre n:iemudial>ser ( S a ~ i r x l p d hence the zener¿¡ solution to eqn. 20 becomes ,,I., 1971 , I< ~ 0-0125cni. .\, = 8ooO. L = 5cni.

.A == 0.314m'l. Ttie results arc expressed in terms of I

rhe clearance of solute, which i s delincd by the l a rl Y qm"

T h P i r k i n r l i r r t < a l h o t h k F I .

. .

ultrafiltration rate along the length oí the dialyser

a i d douhlc asymptotic expansiorij. His iaults are not directly compared here owing to the noiiilvail- ahility of his data on the ultraíilimion Tale. t l ic total surface area and the blood Roiu rate.

. _ . concentration) is shown in Fig. I . Shown here ase the axial mixing cup and the interfacial fluir!. membrane concentration profiles in the dialysate a @ the blood phases. It i s clear that there is decrease in the diffusive mass-transfer driving force alore the lenglh of thz djalyser and i t is much niore iñ

I

1 7 i

Fig 1 Variation of solute concentration as a function of dimens,onless length X

c c

I 1-

care-) than i n care-I, due I O the cieady huild-up of predicted hy caw-? is lei5 by about 6 mt/min than the dialysate concentvation alung lhe Icngtli o1 the that predictcd by case-I 2nd th!s dilkrcncc remains dialyser. However, the mixing-cup conccntration almost constant uith the increase in Xi.. i n the blood phase is seen to be little añected by the X L = O corresponds to the care of zero ultra- varying dial!siite concentration. This m a y be due to filrrarion, which is directly comparable with the the fact that the overall mass-transfer rate is con- work of COONEY eI al. í1974), as pointed out trolled by the ultraiütratiori rate. This i s more before. It should be noted that at zero ultrafiltration,

17 clear from Fig. 2 where the clearance of solute is the clearance for case-2 is nearly 20;: less than that shown as a function of the fraction of the feed for case-I. When the franion of the feed ultrafiltered - ultrafiltered A', for both cases. The clearance is increased to 0.125. the clearznce predicted by

I-.

-

O 0.090 0.180 0,270 0.3 60 0.450 2

Dimensionless length, Z = X D I ~ , , ~ R

Frg. 3 Variation of bulk concentration with dimension- D = 1.8 x 10 -5 cm21r P Te = 0.9

i P = 0-0101 cmlmin L = 5 c m

less length Z, for constant PRID and various ultmfimation rates OB = 150m//min

R = 0.0725cm N T = 8000 c e= .o 1 2 6 e

b* ~ . ~ c o - S & Z &

&& L- 5cu Al,= em.

I

wax I

~ r Fig. 4 Variation of bulk concentration with dimension- 1 8 less length Z for diffetenf pe,nieabilities with

T, 0 - 9 t i a = 750mllmin , L-.

zero ultrafiltration 4 --1- . _ _ -

e\lKik& fClV htfer-4. ph hOa b:l;ky 7 - . O r o / ,awe3 0 . 0 6 0 6 r ~ * f 2 f ~ ~ h ~ A ,

case-2 is only 1, y; leSS than that predicted by case-l. increases with the increase in ultrafiltration rate This hmre shows that the effect OS a nonzero (see Fig. 3). This is due to the variation in the dialysate concentration can he ignored at high relative removal rates of solvent and solute with ultrafiltration rates. I n other words, the results of the increase i n ultrafiltration. The increase in solute the p r w n t work imply that the models OS Pow~n.1~~ concentration at any axial position in the blood PI rrl. (1971) and ROSS (1974) predict the dialywr phase with the ultrafiltration rate could oñset the perSormani:e satirí~~ctorily at large ultrafiltration effect of a nomero dialysate concentration in rates and the model oi' CCX~SEY ci o/. (1974) holds decreasing the diffusive mass-transport driving good at small !iltrafiltration rates. force. This figure again serves to indicate that at high

It may be further noted that the solute concen- ultrafiltration rates, the nonzero disly,ite coiicen- trafion in the blood phase at any axial position tr-d!ion has little cffecl on the overall Clearance.

I I I

0 09

0-87 *u

2 0 8 5

2 - -

0.83 u c o " 0-81

0.79

O 0.2 0.4 0.6 0.8 0.77

Reduced radius. r l R

Frg. 5 Radial concentration profile at the exit of T8 = 0.9 diafilter for various ultrafiltration rates P = 0-0101 cmlmin, R = 0.0125cm. D = 1 . 8 ~ 1 0 - ~ c m ~ / s NT =8OW

Q g = 150mlimin L = 5 c m

Fig. 6 Radial concentration profiles at the exir of d i a ~ htrer with oltralilrration and , . . . without ultra-

R = f f . 0 1 2 5 c m . D = l ~ 8 x l f f - i ~ m 2 / r

T, = 0-9, Os = 150rnl/rnin. L = 5 c m

, - I I -

!- almost linear since the" are obtained Sor a smd1 in uliriiiiliiai,«ii iate. 1 . k effect i,r m mhwne ~ ~~ I ~~ 1- permeability ( P R I D , = 0.12). When the perinea-

bility is increased ( P R I D , = 2.80). the solute concentration decreases very steeply at the inlct

1- region and this is then followed hy a gradual decrease , as shown i n Fig. 4.

Radial concentration profiles as a function of wall-permtation Peclet number at the exit of the - diafilter are shown in Fig. 5. It may be noted that the zero Peclet number corresponds to the work of - COONFVFI a/. (1974). The concentration profile shifts

1-

rs is t ince (fc:r tt2c sanie R and Lfl? ii is wers:I? proportional I<> the nicrnbreiie Sticrwood num'xr P R I L ) , ) e n ihc iadi;il ci>ncentrótion pi. 6le (Or both case5 o1 x r o and nonxro ul:rafiltrat xi rilles are shown iii Fig. 6. I t i s clear that t t e radial conwiltration profile breames flat Sor s m : l vdues o f P(= 0.0101 cinlminl and is explained p'iysically by the fact that the rnei:ibr;ine is not able tc rern<we the solute as f i s t as i t is brought :o the mcnibrmr interface. W!ien the permeability is incrased to

c

Li

r ! I

Ua-L 0.025 0.050 @C75 0.100 o. 125 2

X L i (F)(vw/ü(o)) L

F,y. 7 Variarion of clearance with dimensionless axial lengrh for different permeabilities

P = 0.0707, 0.0303. 0-0606, 0~ 7272 cm:min. R = 0 . 0 7 2 5 c m . L = 5 c m . N T = 8 0 0 0

r-

;mall. This figure suggests that the clearance of large m o l m ~ l a r weight components ('middle molecules') i n most of the existing dialyrcrs can he improved by

r?ncrcising the ultraliltration rate. 'This has considrr- j ablc ;linical significance smce many nephrologists "-believe that an insufficient removal of 'middle

molecules' may he responsible for the development iaf secondary complications such as polyneuropathy I and hone disease of the dialysed patients. For &xanple, the blood serum of uraemic patients

contains middle-molecule peptides, but not in the naonuremic patients (BERGSTROM ei o/., 1975). Its

niagnitiide appears to be related to the severity of u-uiaemii. There is an upper limit on the filtration

flux uiiich i\ governed by the initiation o f concen- ,-aration polarisarion ar,d gel formation.

The effect of the membrane-transmittance factor the clearance is shown in Fig. 8. It is clearly

seen that the e l k t of Te is insignificant over the +yges of 7, for +aeniodialysis reported in the

~ ,itcratuie ( P o m v i o i ef al., 1971). The clearance of a J-.niute is more sensitive to the changes in the ultra-

.tion rate than to thechanges in the transmittance

The Shewood-number variation with the fraction G f % I o r ' the feed ultrafiltered is shown in Fig. 9. The overall Sherwood number for X, = O corresponds fo the case o f zero ultrafiltration (COONEY ef o/., 1 1974). The diffusive Sherwood number ternains

L i m o s t constant, since the membrane transport pruperties have been assumed to remain the same rrespective of the ultrafiltration rate. The convective Y. ,herwood number increases almost linearly with the

L_iitrafiitrntion rate. For example, the rnass-transfer rate I S doubled when the fraction or the feed ultra- filtered is increased from O to O - l l . The slope o f the

r w e r a l l Sherwood-number curve shown in Fig. Y 1 iepcnds u p n the permeability of the membrane. p i g . 10 shows the effect of permeability on the

overall Shewood number. The diffusive Sherwood iumbsr Nrra increases with tlie permeability, The lope of the con\,ective Shenvood-number hi,,, curve L ecreases \vith the increase in permeability. That is,

at a high permeability (e.g. PRID, = 0-7014) the ~-onvective transpoit becomes negligible compared

1 o thi. diffusive transport. The convective transport a s c o m e s more important when the permeability o i ! the solute is smGl (e& PRID, = 0.1169). For

xample, nhcn XL i> increased from0 to 0.125. ;ysb,, ncreases h> about liO:,: at PRID, = O.lihY, L hereas at P K l D , = 0.7014, the corresponding

, increase in .hrxhc, is cmiy 33%. The computation\ show that the radius and length

~f th? tubular membrane have very little effect on L e cleiiance of the solute for a constant rnmihrane 1 surS.ice a r a ana ultrufiltration rate for l o w ~?rrmiiihiliry nienihrmcs. Results indicate that , :e.!rxiice decrease> by about 2 9 , when the radius i.-nas doubled, keeping the surface area and ultra-

I...

.

filtration rate constant, whereas hoss reported that the clearance increased markedly as the radius is increased while holding all the parameters c o i ~ t a n t . AS the radius R increases, the surface arca increases as R, and the residence time i i i c r e a as K'. l h i s should causean increase in the clearance with an in- creascin R as reported by Ross. i n the present study, the effect of surface area on clearance is eliminated by keeping it a constant while R i s varied. The residence time in this case is proportional to R. Since the compumtions show very l i t t le effect of R on the clearance while holding the surface area and ail the other parameters constant, the residence time has a negligibleeñect on theclearanceat a low permeability. In the absence of ultrafiltration, at high pennea- bility, the clearance decreases with an increase i n radius since the solute transfer becomes controlled by the diffusion in the hulk fluid.

4 CORdMiOl7S

A solution for tlie concentration profile in a iubxlar h e m o d i a l ~ s e r operdling uiih a ,ignifi;ant ultrahltraiion rate and a nonzero solute concentra- tioniKtG diai>SaC phak has&noTkined~iñbth bloog.. and dial-ysaLy phases by- I!IC method oí s e p e - n , of barisbles u i n a an-infinite ai= expansion. Results-indicate that at large u l t ~ ~ -

filtration rateX-Tfie of a nonzero dialysate concenmtion on the. overall mass-transier rate !s . negligible, ..__~..___ whereas at low ultrafiltration rates i t is quite significant.

Parametric analvsir shows that the d- ~ _ _ _ _ _ _ _ ~ ~ ~

Iui1?th of the tubular membrdne have ver+ liii& e&ui on the d u r a n c e o f the solutc. for the comtan:

~~~~~~~~~~ . . membrane surfdce area dnd u I t r ~ r . i t z ffw

ah an incrcav in diameter for h i g h - r x r m e w Ion --s

m..ml.rin-r

___._... Clearance of .... hkher molecular weight components iihirb are less nermedble throuah tlie mcnibra!Jn.;an

tilinlion. This k in5asd-n ultra Jus _imMTfanl cltm ?dl simiticansi ;!KC larger

. .

Zotatioo

A = membrane area C = concentration; C' = C/C,; C + + =~ C ' k k

C;+ = mixing-cup concentration, (C C,)jC, C+ = dimensionless concentrttion, (C- C,)/C, Ck = clearance B = dlffusivity

.

(1 i ~ i ? < t ~ > ~ r n ~ n IPRj/>, .~ I .41J2ñ1. ii rnaikcd r.~ú:di ~~inrini~ilt i i , l i gradicnt ii X X I I . T ~ C nomero ultr.i- 6ltiaiioi shific the rad)ai concenlraiioll profile< in the direcrian a l increasing concentration.

The clearance of the solute is shawn in Fig. 7 ac a function of X,,, the fraction of the feed ultra- filicicd. I t is clearly seen that at a low permeability, the ultrafiltration contributes significantly to the

~ ~ I c i r a ~ i w (>¡ the roliite. For exampk, when ihc fr. . , ~ i t < w d ilic feed iillratiltered i\ inzrc~pcd irmi film IO O 125, ihc clearance of the salute for P = O-üI0I cmimin í P R I D , = 0,1169) increased by mnrr than thrce times its value at zero ultra- filtration. On the other hand. the carreinonding increase in clearance for P = 0.1212 cmlmin ( P R I D , = 1,4028) due to the ullrafiltration is very

Fig. 9 Variation of overall Shemood number wifh dimensionless axiai length ( = half the fraction of the feed ultrafiltered)

P = 0-0101 cmlmin, R = 0.0125 cm D = 1 ~ 8 ~ l O ~ ~ c n ~ ~ l s . T ~ =0.9

= r50rn//mh, L = 5 c m NT = Bwo

c-

h = m;iss-[ransfer cozfficient. h. overall value. h, Conveciion, and I,, diffusion coefficients

AcIn~ ,wl<~~ l~meni -The authors would like to [hank ihz rouncii of Scimiific & Industrial Reiesrch (India) io: auarding senior r e ~ a r c h fcllouihip to R. Jagann;ith;ln

.._ h.íO\ = I 2 Ko./lX+X1Re.'/5400 . . , ~ .~. " , ~ ~ ~. I .

k = (Co/Cen)/(I + c r í T R - I ) I P ) k, = I +.r,JTR- l ) /P ki = 1 + L ' ~ TRIP L = length of the tube rn = mass-transfer rate

N , = number of lubes, N s M = h. R I D , , h-s,, = h, R I D , , N S M = h, RID,

P = permeability Pe = prmeatiun Peclet number, Pe, = u , R I D , ;

A P = pressure drop p ~ z = (U, R / D d ( O x d W ) )

p = iaplaceian parameter Q = blood flow rate

R = radius of tube q = a,zi46

Re, = permeation Reynolds number, uv R / y Sh, = wall Shewood number,

íPRID, ) í l + iow/P)(Tx- 1)) SA,, = P R I D , , Sh,, = P R I D I ,

s = reduccd radius, r j n T, = transniittance factor U , = dimensionless axial velocity in the blood

phase, u./U(O) u = axial velocity, ug axial velocity in the blood

phase, itsD axial velocity o f the dialysate phase, üx0 average u.vD: uyo transverse velocity component in the dialysate phase

ü(0) = average inlet velocity of blood phase V. = dimensionless radial velocity, osio, c. = radial velority in the blood phase. u, = wall permeation velocity X = dimens:onless axial length,

x = axial length Y = ? i R y = transverse distance from the wall in the

Z = reduced axial length, xD,lu..,R*

d = c,h,iO)ia(O) 7 = kinematic viscosity /< = viscosity

S = íx/R)(c,/!i(O)), XL = X at x = L

dialysate phase

2.: 1 = cigeri value

Subscripts E = b l w d phase D = dialysate phase i = inlet

IV = wall I = blood phase , ? = dialysate phase i A = diniensionlcss

References

ABRAWOVITZ. M. and SEGUN, 1. A. (1968) Hmdbook o/ niorhenioricril/r<ncrions, Dover Publications, New York.

BERGS~KOM, 1.. FURST, P. and Conmu, A. (1975) A study of uremic toxicology. 8th Annual Contractor's Conference of the Artificial Kidney Program of NIAMDD.44

COLTON, C. K., SMITH, K. A,, STROEVE, P. and M ~ n n i ~ r , E. W. (1971) laminar flow mass transfer in a flat duct ducl with permeable walls, Anrer. Imi. Chcnt. Eng. 17,773-780.

CWXEY, D. O., KIM, S. S. arid Davrs, E. J. (19740) Analp% of mars transfer in hemodialyscrs for laminar blood tlow and homogeneous dialysate. Chcm. Eiig. J. Sci. 29,1731L1738.

COOYEY, D. O., DAVIS, E. J. and KIM, S. S. (19746) Mass transfer in parallel-plale dialysers-A conjugated boundary value problem. CI~PIII. Eng. J. 8, 213-222.

Gmrwnr:D, L. and BABE, A. L. (1966) Velaity and concentralioo profiles Tor laminar flow of a Newtonian fluid in a dialyser. Chrrn. Ew. Proc. Synzp. Ser. 62, 20-31.

POUNICH, R ~ , CHRISTOFIER, G. and Baan, 4. L. (1971) i h e eKect ai membrane diffusion and ulirafil1ru;ion properties on hernodialyser design and pdormancc. Chmi. Lw. Pmg. Syntp. Srr. 67, 105-115.

Ros. S. M. (1974) A nwtheinarical rnodcl of nuass tramport in a long permeable tube with radial convec- tion. J. Fluid Mrrh. 63, 157-175.

SALYER, I. O., BALI., G. L. and BEEMETERBOCER, C. L. (1971) ~Wen~brnne p m c c ~ s e s in i n d ~ s r i onri biontedicine. M. Uilr (Ed.). Plenuni Press, 33.

Sii€rric.m U . R.. PRABHU, H. J. and GHIST.~ . D. N. (in press) Biood ultrafiltration: Design analysi:. n f d ir B i d Enn.

1

I-

This gave 'b

- rn = -0.53 (005)

- b = 4 0 (0.1)

From analogous calculations as given lor R, (see Fig. 41, it lollows that the total variation in a prediction of A, Irom logli.,,,) or IogíZ, at IOOHz) amounts to a

So notwithstanding the fact that log(v-,J and IogíZ, at 100Hr) are chosen on purely empirical grounds. i t may be stated in conclusion that these parameters can be used as predictors for the permeability olcmunel. Furthe? research is carried on in our laboratory about the mechanisms that give rise to these correlations, not only to resolve the lack o l a solid theoretical foundation per SE, but also expecting :<> find along that p d t h parameters that will show tidedl 1 b l correlation.

rilcior 20.

- -Ii.knoirl~dg>,irnt--~The authors would like to thank B. H. M. Kok and Dr. A. 1'. J. van IXurvn (Labaratoryfor Sola-State Physics1 and W. %hui 1Ektronics Research and Development Department) lor providing the ncceisary measuring-equipment. R. üorirren for his skilíul tchntcal

.. ~

c

I

Rderrncn

R<>YO<,YFVFF'~ .I M. P. M . V A \ Dllr I W 1. ani! D F ~ r s t \ \ . F C bl. r 6V771 Aquantitativerrd,ochemicalsiud? ofiimic and rnokmiar triin%porl in b . i i n c denial enamel. Ar<hr. Oral Biiri. 2L 461 ~ 4 7 2 .

B o u i z ~ ~ r ~ . . I. M. 1'. 51. i~r, Dub, J W. E. and DBIILSSF\C. F. C . M. 61981) Elfo-1 oí mono- and divalent ions on diBurion aod binding in bovine tooth enamel. .4rrh\. Oro1 Bioi.. U, 663-669.

BUCK. R. P 11968) Transient elmrical khaviaur oí glass m e m b r m . Part 11: The impedance t r p u r i m ~ n r a l J . Elecrroonul Chem., 18, 3XI-3R6.

BL-CY. R. P and KPLLI.. I. 119681 Transient c l a r i ~ a l khaviour of ~ l a n s membrana. Part 111. trpurime'nral J. Elecrrood Chem., 18. 387-39 -

Cv1.c. K. S ilY2XI Electric impedance oí susp;n~ion oí sphcrcs. i Geii. Pb>i,oi.. 12, 29 ~ 3L.

COI.E. K. S. * 19321 Electnc p h a x angle ofcell membranes J. Gen. Phpwsl.. 15. Ml&MY.

Cole. K. j. and COLL K H. 119111 Diipcriion and abroiptm; in dieleci"cs. J . C'brm. P h i i . 9. ,341~ .XI.

D a a o t ~ . N. K. and SMITH, H . 11YhhI Ipplird rrgrunioii < m d j . m John Wile) and Sons Inc. S e w York.

VAX Diir. J. U. E., BVR~UREVEV,I. .M. P. M. and D H i w c s . F. C. M. I :Y791 Chemical and mathematical riniuiaiion of caries. C i r : i r Res., 13, 169 180.

G c ~ s 119Xi Scientific Tahlci 1-th edition). Cibzt-Gc~g? Ciirporatisln. New York.

Monmv. E~ C. and ZAHRALMK. R. T. !I9741 Chcmair) oí enamel rubwrface dernincra:iratiori. J. Dc.iir. Rem- 53.226- 236.

SIL\IOsToNt. L M. IlY7.7l struc,ure oí carious enamel. i"d"diii&. r i c early ;<,ion 11,'ii s,i R..,.. 2. I*) IN)

II- ' I L

I- C. ;I- +

h: c s c b...~

, . .

Series-elastic properties of strips of smooth muscle from pig urinary bladder

A. van Mastrigt E. A. Tauecchio Depanmeni of Urologv, Erasmur UniVeiSitv Ronerdam. PO. Box 1738. 3000 DR Rot!erdam. The Netherlands

Depanment o1 Biological & Medical Phyriw. Eiajrnus Unwemiy Ronerdam.P.0. Box 1730.3000 DR Rotterdam. The Nerherbnds

Abstract-The seres elas1,ciIy Ofsmps o fsmmln muscle from prg urinary bladder was investigated by meam of d series of computerised qwck-release and qwck-stretch measuremenre wiih and wñhiout st,molalion of the muscle. and at ditlerenl shorrenrngs and force levels. ihhe iesultr cannot be interpretedm terms o l a drscrelppassiveseries-elastic element. The; Can. however. be inlerpretedin trims of Ihe sliding~f,lammls model / D I conrra~liny musclc

Kevwords--Quick-r~lease iechn,oue. Series elaslmr;. Sliding fiiamenrs model, Smooth muscle. Urinai; bladder

List of s?mbols a = constant iactor representing geometry of

A = coefficient oí exponential crnssbridge

fi = exponent ni exponential crossbridge

!< I,, = inponent i n cI:,s11c chaiactericiic ufdiwctr. elastic element

= c o p t i e d force decrease during stimulation and quick rcledse ( i n the rising phase i>l the contractionl

1F,. = corrected force incrensc during 4mi i !a t ion and quick stretcli ( i n the ririnp phase (if the ciwtraction I

m"Xk

elasticity

elasticity

AFl

F,.,, = preset force-trigger levci g(X I = force as a function of lrngth of a crossbridge

/I = upper limit of crossbridge lengths 1 = length of muscle strip

isometric contiaction

I; = tissue vulunie oi strip .Y = Icngth u i crossbridse .Y = macroscopic eqiiivalent oí S obtained by

addition oiiengths ofcrossbridges w h i c h are in scrics

<í, = force measured during a quick rcIc:ix or quick stretch. norrnaliscd b) di\idm? h! the cTuss-scc1m:II are3 oí thc strip

n.irl = number of actire crossbridges during an

niXI = spectrum oí lengths of crossbridges

t t i n po-+cok* 4hekíce -ueLAj Q'.QCR".c.4.\ d a c r i ingt ~selem~ntI&m an isonletric címlc_ti(>n.

1-odo thiswe-nced a m~thcmaticaidcss~iritiirn c~W scric<&t!c~ eiemrnJuFRG llYh7). AI 1 Xa\I>I:H (1976). P A R M I . ~ . Y and COXZI-NXLICK Il9671, blE1SS [19íK) and H A ~ ~ T H N Y/ al fIY7X)descrihe ihc.wrics ciasiicity ?[..-~mooih muscle as ajproxim+& exponential. I r we interpret this In term5 o í a n rlast~c

-nine :, stress which depends exponentially <in strain. the calculation becomes very simple I V A N C > L ~ L ',I id/.. 19781, hut results in an infinitely high maximum contraction velocity orthc musclc. which is unrealistic (VAN MASTRIGT and üRlFFi ' iHS, 1979U). An interpretation i n terms oí an clement having an exponential elastic modulus yields more realistic rcsultr I V A N M A S T R I G T ~ ~ ~ GRIFFITHS, i979a)and is also in accordance with measurements of the passive properties ofurinary bladder strips ( V A N M A S T R I G T P ~ oí.. iY78uI. Otherauthors iike &AN& el o/. llY72!, CHAPMAN and HARROWER (1977) and JULIAIi ci '11. (1978). howe\.er. present measurements indicating that the serirr clzsiicity of muscle cannot be deicribed in wm5 of a ciiiciete passive series element, but depends ,I the actiwion of the muscle, or on the force the

muscle exerts (RRESSLER and CI.INCH, 1974; FORD et <,I.. 1977 HALPERN and MULVANY. 1976). This is in agreement with the sliding-filaments modcl for contractins muscle, introduced by HUXLEY 11957) íor modelling striated muscle. if the series elasticity is assumed IO he located in the crossbridges.

Although the muscle structure on which the sliding- filaments model is based cannot be seen in smooth musclc. the model is very olten also applied to. or

round to beapplicableio.t l i istypofmu~lel~i i I I M H <,I al. I 9 7 6 Gc>HBo\i and S J i . L V A > , l Y 7 1 : J ~ L X I U ~ . 19571. tl<iue\cr. many authors convder that the rcries rlarticity in smooth muscle cannot he ascribed solcly I O ihe crosshridses btit must be íound at least partially e~terrialtri them (GRoar) and MA^ FS, 1975;SIKMAN L,i 01.. 1976: HALI'EKY ct ai.. 197X: M m s , 1Y7X; HELLSTRAK'D and JOHANSSON. 19791. in view 01 the possible clinical value oí a method of determining contractiic properties From isometric contractions of the urinary bladder ( V A N MASTRET Y I ai., 1979h) the present stud) was undertaken io investigale the possibility o¡ quantitative mcdelling of the series elasticity oíunnary-bladder smooth muscle in terms of a discrete. passive elastic element.

Measurements were perlormed by means of the quick-relcsie icchnique, because this metliod tests the serics elarriciiy directly.

2 Methods Experiments were períoormed on strips oípig urinary

bladder wall measuring approximately 10 x 27mm. The bladders were obtained from the local slaughterhouse. The strips were submerged in a physiological solution at a temperature of 37°C Contractions were e\oked by ekclrical stimulation.

Four insulated silver wires were inserted into the strips. parallel to the short side. and a mass electrode was placed into the immersion fluid. Rectangular pulses 01 Xi\.', lasting 7ms 2nd at a repetition rate oí 2 0 H r (GRIFFITHS et al.. 1979). Kere applied. One of

u-- - length T

I I

the.amplit;de'ofthe length change ofthe musrie could hi adjusted with micrometers. I ~ h e electrical stimulation and the movement of the pneumatic c?ltndei were controlled by the minicomputer.

The stnps uei-e adjusted to an initial length where t k i u e i ~ ,u<! taut. Prior to each stirnulation. ih> force vaiue u;%> cmsidered t o be duc l o pasri\e, paral!el elastic properties olthe strip. and was subtracted from al! forces measured during contraction One mcaasiircnxnt consisted oí thc íollowing sequence (see Fie. 1 I Stimulation IS iurncd on: when u preset trigger lebe1 ( d e n o i d by F,,J is reached. the muscle strip is reieaird for 250ms and then reset to the original length. Next. stimulation is turned oil as soon as t h e foris starts to decrease. indicated by E:,, in F-ip. I . When the decreasing force again r e a c h ihe trigger Ie\el. a second quick. release is performed. After a r w i n g period oí 7min. R control measuremenf is carned out. starting w i t h a release. After the stimulation has heen turned on, two quick stretches arc measurcd in the some way as during the first stimulation. and. finall). thc musclc is reset to the oesinal length.

411 releases and srreiches during one measurement sequence imply the same preset amount of shortening or elongation. A typical íorce:time recording for one rsieasc puke prolonged to 500ms is shoun ifi Fig. 1~ During each release o r stretch pulse. 10 íorce samples are read h! t he computer at inferials of 25ms. The niinimuni or maximum in this sequence was taken to tx repixwntitivc the hrce during the release or stretch

The íorce change thus measured is assumed to he - composed oca chanss in act!\c rime and i change in pai\ive force The latter force is due to the stretching oí

!&:I>! .! . ' p:,,\,,c fort ell:,. ;trc

I ~ V I L : N ~ at !ES hc:inniii- and ihc end o í ihc x n t r o i nieawrinicnt . as hhoun in Fig. I . Thii.. each rncü\orei:ieni >ielilcd four corrcctcd isltiei in ilie rising and falling pliiiw oí a contraction. a n d dui tng r e l e i r e a n d s t r e t c h d e n n i c d h ) AF* .Ax,. , AF,+. AF*+, rerpectiwl). The maximum isomaric iorcc which the strip yielded uiuall) dccreaicd during the course of the measuremenis. The first íeu ciintractions measured on each strip >ielded an f,-. between 0.4 and 1.6 N . This yields an isomeiric iictiw i t r w k t w e n 1 x 10' and 2 r IO'Nm-:

smooth musclcs 12.5-35~ 1 0 " N m ~ ~ ' ~ H A L P L R S 01.. 19-8: I ~ L L . L S T R A N ~ . 1979: MURPHY. 197611. bot i t corrslaies well aith the maximum pressures measured i n the normal urinar) bladder i v . 4 ~ M isr!ii<,i and

Measuremenis \rere cmtinued until F,,,, u a s hwer than Cr,,. Generally 10 to 20 contractions cozid be nicamred on one strip. This rapid deterioration is at least partly due to the fact that quick stretchsj were alsoaonlicd.uhich orobahlv damaged thesirini FORD

his IS Inu compared with d u e s rouiid for other

C i K I F C I I H S . 197VUl

.. " cf 01.. 19771. However. a maximum posíible number oí nboui 20 contractions has been found before for strim p r e p a r d in this uaj . even without quick stretches (GRIFFITHsc~ U!., 19791.Thereleaseandstretchspeeds ofthe pneumaticdevicearein theorderoí200mms ~' This is uell above the maximum speed of contraction. which was estimated at 5mms." for these strips IGRIFFITHS ei d. 1979: VAK MASTR~GT and GRIFFITHS, 1979ul. This tmOx (normalised 0-1 strip length, per srcunJ which agrees very uell with 5aIiic1 found for other smooth muscles ~ML'RPHY. IY7hi l i s a factor of 20- IW lower than values found for itriated muscle ~MLKPHY. 19761. This justifies the use oí a relati\cl) s l o u ~ force transducer and low sampling rate.

3 Rewlts of measurements with steps oí equal lrnerh and constant trigger l o e l

Wc consider the four measured AFs thc dzpendmt \ariahies in our experiment. Thereare three

7

,n clpLl,mc.n/ dcin9 w ~ c / r 0- /y llso bid independent variablcs, cz0, AI and t;,<<. in this Section wcdeszribethe,relation between the AFs and F,.,.The

deviations for all measurements arc shown in Table 1 A significant (student's 1 test. VYq. ihouph rather .. . ~~

latter varies considerably during each experiment. Measurements were performed on fiYe strips. F,,j, wa.. fixed at D 3 N and Al was 0 1 mm for two strips and 0 3 m m for the other three. The results of one measurement are shown in Fig. 3. Two values of 6- were obtained :íor.sach measurement. The higher plottai value~was always mcasured in the first of the two contractions

Although some common pattern can be seen in the A F and F, curves, the dependence is so slight

ation, wecan regard the AFsai T h e averages and standard

' , . . .

smaii, difference between the four APs is a l iays seen. The AFs measured without stimulation ( i r . in the lallingphase ofthecontrac1ion)arc lS%preater on the average than thosc measured with stimulation (in the rising phase ofwntraction). This holds p o d For quick- release as well as for quick-stretch measurements. Furthermore, when we omit the signs, the responses to quick stretches are 14% smaller on the average than those to quick releases. This wili be discussed in the rollowing Section. Apart from ,these second-order &ts we conclude that, to a first approximation, the measured d a r e a x or increase in force is independent rrf F

. - . . ,

. . . . < < .

. .

4 Results of mmurements with steps of varying length Next, we investigated the depndence ofthe AFs on

Aiat a constant FWnis of03 N. Eleven experiments were performed. A typical plot of the active force Fu exerted by the strip dming shortening or elongation, as a function ofAl;isshown in Fig. 4. F~iscalculated from the AFs byaddmg to i/,,with theapproprialeseiise, as foliows: 1 , .

Fbl = &-A&. and ,FA( = &-AF0-

Fu = t&+Ac+ and FA! = F,,,+AF,,

, . . , .

. \~ for I Ai > O , (shortening) t ,

for. 'Ai c O i (elongation)

Thus, for each value of Ai. two force va!ues are plotted, the tipper one representing the lore change measured in the failing phase of a contraction and the lower one the force change measured in ihe rising phase uf the Contraction. Ascan be seen, the results obtained with quick releases and quick stretches are consistent in that they yield a continuous curve. The dwrease in the slope of the curve for high Ai cau be understood frorn the fact that the force during the quick stretch then exceeds the maximum force which causes the

0-1 --@OX5 --o1 tlX

(1.096 o 086

14 I S Y

I?

;o 30 29 29

~~tractile'machiner)'io'süp' (HILL. 1938; L.EYIN and WYYAN. 1927: 1uLw.x YI u!.. 1978). The curve shown in Fig. 4 cartbe understood as the

clastic charmeristic 0i;g discrete passive series-elastlc element We plotted the 'stilTness' of this hypothetical elastic element (the derivative dFJdAl normalised with respect to the cross-scctiooal area of the strip to yieldda.JdAi)asaíunctim olainFig . 5.Theresultsof

. , . . . . .. , .. ~. .

35co i I Table 2. Acerages and standard decinriansoJparomrrers 6th hypothetical. dimere. passive soies-elarric e h n i , d&d from rhe dafa of Fig. 5

RelPtive otandard Numberd

Parameter Average deviation measurernear

%

Bil, 674 (m- ') 31 9 E J . 475xiO3Nm-' ' 10 9

the best cight out o¡ the 11 measured curves are displayed. As ?he plotted curves are not straight line>. ihe measured quick-release curves (Fig. 4) are not directly cxponenrial (see Introduction). I t was concluded from measurements performed un whok bladders ( V A N MASTRIGT and GKiFFtlnS, L1)79a) and bladder-wall strips (VAN MASTRIGT er o!., 1Y78a) thai !he series elasticity of urinary bladder-wnll muscle can he adcquatrly dcscnbid by ¡.he íunctlon

i: is the tissue volume of the strip

I is the lerigih oí the stnp

and Ax is the elongation of the series-elastic element.

This formula can be fitted to the measured Fbl curves byputtingAs = h-AI,wherehisthevalueofAlwhm FA, = O. The fitting was performed by estimating h. at FA, = O , by estimating h from the Fa against AI p b t (see Fig. 4). dividing FA, by (h-AO and plotting the result semilogarithmically. Nine out of the I I c u m measured could be described in this way.

Averages and standard deviations of the resultsig parameters are shown in Table 2. The average vdws can be compared with thchwmeasmcd on a d i e bladder (VAN MASTR~GT apd G K F ~ S , 1979ut by applying a correstion factor fa the diierent geomáry ( V A N MASTRICT, unpublished data). The hiph standard deviations found in Table 2 show that this modelling of the series elasticity ofthe urinary h l a w r wall is not very successful.

represented by ihe'open circles shown in Fig. 4. Starting from the point along !he curvecorrespondkg with thelower valueof F.... (o~ncircle),theamplilnde

wiii t~ presented in Siction 6.

5 Results of measurcmenis with varying (rigger lomes where

t h i s increased the reprodiicihilitj. This, howcvcr. \\.as not the CLISC. as can be Secn in lahlc 3. The riroportionality found ktween force change and E,(" nccessitates a number of remarks.

r' 4- First. u e I now have a method for correcting

i-

1-

-600 4-.

-200 L O

r L-

. . squares1 when corrected for the lower e,,, value by the simple factor c,Le E,,* j .

In four out of the five experiments from Section 4 i n which measurements at lower E,.. values were available, these could be fitted to the measured curves by applying this correction lactor. Secondly the observation ihat the measured force change is proportional 10 the force level at which the length change is imposed has been made by many authors

J U L I A S ci 01.. 1976; M f m . 1978; HELLSTRAND, 19791. Most of them conclude that this means that the loru: length characteristic is exponential. We found thisnot to be thrcase (secSection 4). Furthcrniorc. the proportionality was also found for large length changes IAI = 1 mm. which i s 38",n o1 h. the length -change for uhich Fb: = O), which, in terms ola passive discrete serieseiasticity, can only be understood from a linear force, kngth characteristic parallel to the íorce axis.

Finally, these findings have to be compared with those of Section 4. I f we model the series elasticity of this type of smooth muscle by a discrete, passive series element. this comparison can be made in terms of stillness. as explained in Fig. 7.

The stillness data of Fig. 5 are replotied i n Fig. Y. Two straight lines have been inserted representing the measurements presented in this Section for AI = O-2mm. I t can be seen that especially at high lorceir the srilínesses measured in the two dillcrent ways do not agree. We must thus abandon the idea oí one discrete passive series element representing the elasticity ofurinary bladder smooth muscle. as has also been concluded by other authors for other muscle iypcs I B L A X E Yi o.. 1972: CIIAPMN and HARROWLQ 19771.

(BRESSLER 2nd CLINCH. 1974: FORD PI ai.. 1977:

ni ~' variahie I x Ab,. AI N 9

11 l , < , xgxAFo . AI -14 l i

I8 7

21 20

6 lntmpretstiv reide in terms 01 sliding filaments model

In the prcr;eding Sections w e described three findings which cannot hr interpreted in terms O l the model of HILL 11938) using a discrete passive series elastic demeni. namely

(i) the proporuonalitg oirtillness and iorce lor large

lill the dillercxes in stiffness Found by varying AI and

( i i i ) the fact tbai measurements made ai a lower t& (Section 4 1 must be corrected by a lactor e,, >IF,,,, , (Seciion 51

We nil1 nom ;ionsider these findings in terms a l the slidin~-filamer!is model proposed by HUxLEi (1957. 10741. ll we asunie that there is no elasticity apart from that in :.he crossbridges IBLANGÉ et u!:. 1972; HUXLEY, 195-1 íhe force the musclc exens dt any moment can k expressed as the integral oí the forces exened bg t h e crossbridges over a spectrum of cross- bridge lengths I H U X L E I . 197):

length ckanpes (Section 5, Table 31

K,;# (Fig- ñi

-I

F = ~1 1 n ( X ) g ( X l d X . . . . .(2) i

- c

where

F = Foryv exerted by muscle X = lengh of crossbridge

ni> i = s p x u m of k n g h s of crossbridges y l X ) = force as funaion of length of crossbridge

(I = ccnstant lactor representing geometry etc.

A real mucle. or muscle strip consiFts of a lot oí

contractile units [sarcomeres) in serics. taken intn account by replacing the parameter X by Y . i t \ macroscopic equivalent. i t is assumed that in the mmetr ic ciisc rhe crossbridge length is alas?\ disiribuird uniíormly within acerlain range 1Hixi.r i 19571.

ni.rl = OJor x > h and -< < O

n ( s l = >io lor O < x < h . . . .13i

o b

*- I-

Ein Kopplungssystem für die Longenforschong durch die Realzeitb~andlung von durch transthorakische lrnpedanz erhaitenen Kurven

1-

r- *-

apparaf gebaut- ' in P a t i e n t - ~ o m p u l e r - K o p p l u n ~ ~ ~ ~ l e m . Mil diesern Gerat werden sofort alle wichtigen Pararnzr der r sh l en und linken Ventilationrkurven aufgezcichnef. wie L B. Amplitude, Pcriodc, Ausatmungs- und Einatmungszeil. Verschiebung zwiwhen der Brurtkarkxtension und den Venlilatianskurven. Weiterhin kalkvlieren wir die Durch~nittsperfusionikuNe durch eine Srimmelmethodc. Dicws ermoglichl uns. Perfusions- und Ventilationrkurven ohne K unstprodukte herzustcllen.

c

i-

r

.Med. & BmI. Enp. &cunpiii.. I Y 7 8 . 16. d?l 482

Passive properties of the urínary bladder in the collection phase R. van Mastrigt 8. L. R. A. Coolsaet W. A. van Duyl Depammmt of Urolagy. Gasmui University Romrdom. PO BOX 1738. Ra-dam. The Netherlands

Abstract-A model is presented lhar describes the passwe properlies of the urinary bladder in the collection phase. A black-box approach is used. The sysrem under inistigalion. which is défihed in [ e m s of a pressure-voiume reiarionship. 1s divided inro four subsystems or biocks. namely fwo geometry blocks. a block describing the time~dependenl properlies of the bladder wall. and a block describing 11s length-dependeni pmperries. Models have been developed and lest;d io, each block separarely. wirh regard lo geomevy, the bladder is described as d

thick-wailed sphere of Constdnt tissue volume. The rime-dependence of the propenies of the wall can be explained using a visco-elastic model. and the length dependence 01 the wall properlies is shown to yielddastic moduli which depend biexponeniially on strain. Esrimares of rhe value of the parameters involved were obtained from experiments on strips of urinary bladder. obrained from the local slaughterhouse. Combination of the blocks yielded an overall model of rhe passive propenies of the urinary bladder in rhe collection phase. The model contains 74 paramelem The classical way of investigating the urinary bladder. by filling ir slowly and measuring rhe pressure produced, yields a preudostaric pressure-volume relalion- ship called a cy~t~metrogiam. The model predicts the form of the cysromeuogram accvrarely. However. analysis o f a classical cystomer~ogram enables us to determine on& rhree parameters of our model. A better measuremenr method is based on srepwise (or almost stepwisej sfraining of the urinary bladder. One stepwise siraining yields eight parameters. provided the initial volume of the bladder is known, and several measurements on one bladder ar differen1 strains enabte us ro delemine ten parameters. The results obtained with stepwise straining are compatible with the model.

KeywordP--Eiomechanifs. Modelling. Urinary bladder

List of symbols a,, = consiani in niultieirponential model. N a. = coeffrcient of nrh exponential (initial height

of exponential decay curve). N e = base of natural logarithms

e. = relativr elastic modulus E.iE(lc!i E. -= elastic modulus of iith spring. Nlm'

E('ci) = sum of elastic moduli as a function of

,€l. = elastic coefficient, N:m' amplitude of applied strdin, Nlm*

k = nurnher of iyponeii t ial teriiir used 1 = length of bladder-wall strip, :n , o -~ ~~ iengh , of bladder-wall strip rinsirained, m

= index n u r n k r . I> == pressure in the bladder above barometric

t = time, s pressure. '- m'

I ' == \olume contained by bladder, ni' C, = unstrained volume of bladder. rn' i; = xolurnc of bladder-wali fissue. m' /in :-: siastii e\FOnent

: ,, = relaxation constant i n irth exponential term, c - 1

((I - l o ) / l o ~

I O E = strain

i: = amplitude of applied strain vS = viscosity modulus of the dashpot. Ns:m' ~i = Poisson's ratio

= strecs in bladder wall m u , = standard deviation of parameter u. relative

to ll o = sum of least sqiiares. N'

1 Inrroduction 'Two phases can be disiinguished in the uorking cycle of the urinary bladder: the colleciion phase (in xhic l i the urine produced by the kidneys i s colbxted i n the bladder) and the evacaiion phase ( in rihicti ilic urine collected i i expelled .¡a the urethrd). The bladder is dominated hy diffrreni propriies (,brxli passive and ac;i\s) in these tno piia'ss. B y passi\e prnperiies is uiidersrood to ~:iiliiv tIii,-c pisper t i i s \v!~ich do nos invoI\e energy

LIUCiV. ---, ~ $?ofi?!ion ih? nictahul~wi. ivhi.c i idl ic pii>p<'1 \ ~ w o i i \ elcmcnt n: a step%,,e straining is a niono- "'I<>. c \ p w m i ~ a l l > decaying \trew ( C w > t . s a ~ ~ er al..

quantitatively, in physical termí, tile ]passive pro- Since one cxponential terni does not Fit the penies of the urinary bladder i n the m!lection phare. inediuied curves adequately, tlie mechanical modcl

r" These properties can he described i n terms or a is expanded with extra elements in parallel. each volume-pressure relationship. Thc volume and clement consisting oí a viscous and an clastic

9- pressure interact via the hiadder wall. A certain element in series (CHRISTENSEN, 1971). A non- voltme V of fluid in the bladder strains the bladder decaying component represented by a single spring

*- wall 10 a certain degree. in parallel with the above must also be introduced. The stress resulting from a strain step can then be described as:

Thc purpose id t h i o invcstigaliiiti i\ clc\criht. 197-h!. i s -

The strain CIS defined as: u_

1-1, lo

6 = - m-

a = a.r'-'"'+a,, . , . . . . i?) " - 1

*'- where ID is the original length ( I ) and I i s the strained ! length of an imaginary piece of bladder wall. A- The straining &he wall caUYS a s,,ess ~ in Generally we will UY a model with three exponential ! i wall, which, in turn, determines a pressure depending and a as shown in 2; the argu- + on the geometry (,f the bladder. hi^ of caUSai ments for this are discussed in Section 2.3.

, relations is illustrated in the model o í Fig. I . We i f we measure the step response of a strip of - Chal1 investigate the functions of the various blwks bladder wall and fil the results with a sum of a 9 o. c this model in separate sections. number of exponential terms plus a constant, we 4- Since bladder-wall tissue is a nonlinear visco- obtain the coefficients a. and relaxation constants

fi- ,ignal of the wall block depends on time as well as Introducing the tissue volume V,. we can relatc a. !I

'.,(tic material. which means that the output 7" as parameters.

I U- I

"t t l- geometry wall gemetry

1 1 4- I

on strain or length (JAMISON ef al., 1968). the wall block is split up into two subblocks describing these dependencies separately.

In Section 5 the properties of all blocks wi l l be combined to yield one cumplete model.

~

c c C' 1 2. Time-dependent behaviour of the bladder wall

2.1 Theory The time-dependent behdviour of the urinar!

bladder wall can be investigated by expcriments on isolated strips of hladder wail (COOLSAET <I 01..

The total time-dependent khavioiir can hc 1 determined in one measurement. and at one strain I ieicl, by straining these stripsstepwise and observing C thc stress resnonse lCimLS.&ET er al. . 1976). It i s

1 1975h).

1 I "

-4- I io

to the elastic inoduli t. a i follows tC<x>i.snil PI ul., i975a)

a, I E. = Tv; (31

The virosity moduli >I. can be obtained írom the relaxation constants y". However, in order not to combine the standard deviations of coefficients and relaxation constants in our calculations, we will use the elastic moduli and relaxation constants as fundamental parameters. For our description of the fundamental time-dependence of the stress-strain relationship, only the relaxation constants are relevant.

2.2. Mcrhods I>

DOK- and Die-bladder strim measurinz about

0-30 maintained for loo0 s followed by 20min rest at zero strain. About 10 measurements were taken from each strip. The C U N ~ measured were fitted with a muliiexponential model using the stepwise approximation method described by van M~srnior (1977b) and discussed by KUIK (1976) and VAW MASTRIGT (1977~).

The separation of a signal into exponentials is a very awkward problem (LANCZOS, 1956). A number of models and methods were tested (VAN MASTRIGT. 19770) as alternatives to the computational method used here, but none u í them turned out tu bc succr55íu1.

2.3 Rcs~rlrr The basic shape oi the force-rime curve obtained

resembles that of Fig. 3. Pig-bladder strips and sometimes also dog-bladder strius when investigated . . _ - - -

10 x 20 nini ucre strained sternisc using il pncumaii; in ihc natural solution shou a spontaneous rh)thmic itririn dc\iic ~ C W I . S A ~ T ,>I., 1976,. The sirips a:i.vii) uhlch IS rimpl) added tu the cume Mere irnmerwd in a physiologic31 wlution which Wnen I> 600 or E G T A wh:. uwJ, spontaneous U J > conrtantly pcriured, aerated uith Y5:. O 2 and actibii) not obserbed To determine expcri- So., <'O> and kept ai 37 C The measured iorsc mentally the or& of the r)stem under in\cstigation. ud\ .iigitiad and fed dirmly into a 'Texas Instru- ¡.e. the number of exponentials which should ix rnrnts 9806 minicomputer. uwd or, [lie value of k in eqn. 2, the EGTA group

tAperimciiir ueie performed using a number or o i curra uas rirred uiih an increasing nuinhsr of uitlercnt ptiysiologul solution) (CcoL,&ti <.I u/ . . exponeniial iernis. Thc results can bc srpn in Fis. 4. 1977,. hut onl) tun of these are releiant here: From ihe flattening OR of the abcrage sum of t i ) A modined Krebs sulatiun (Antmc, and AXLLS- least squares ai k = 4 He can concludc that thc

(o%. 19ASl. uhich %e used as standard solution; order of the system is four. This has been ionfirmed thii IS callcd ihe 'naiural' sdlution below uith the aid of an F-test Houcier. somr curtes

i i i ) A soldiim Jsed tu reduse ihc influence 111 the can oh\iousl) be fitteJ adequately aith three :+c i~\c ?rorerim ;>i tlic tissue For pig blddder, Ckponentds lye Fig. 4. curhe StQO) *h~Ic oiherr EGT.4 ud, used I ( ' r rnc \c i . 1977). for dog require ai least five exponentialo (Fig. 4. cunc hladjerc D a 1 ( I n > FH +I al . . 1972,. S W). I n fact. we shall use ihric exponential$ and a

111 311 ca..cs, the time thai elapsed hei.\ren the constant to avoid 'merfitting' of curva like S6M). Jeiih 01 the dhimd an.( the C I X t oí the experiment lahle I shuus thc aterage relaxation constant, nar dhout iwe hour and standsrd debiatiom determined for a number

l !x t~ ie ina l length i uas dcierniine.! h) allouIrig uf meaurement$ \'ariaiic: analysis uitr c i i ~ ~ l :'3

ihc. <tr!p I.\ \tretch uiidcr the uedgi I ui t lw !<>wcr ap!t$ the \arisn;e ,If ihc relaxation con~iint, into .limp I n n \ < = 13 tuo .ompunenis. The h i :omponeni I ) re1aic.l 1 0 :<v dhnLt I \ Thc niedsurcnicnt q c l e son<:\le; nt a srcp .+ doníidnt r iray of the dilTcren.n betueen 011 one \trip.

7:3 J

r- h n d is called the physiologi~ni sprciid 1 iic sicond

c<wiponciif c i > n i c r n \ JiITc:ciwc\ hci\\stii itrips +ind is caílid thc h o l o g ~ ~ l \prciid 1 !ir orre\-

iwndiny *taridad de\iativm ar t ' ~ I U U ! I i n l~ahlc I ,lor the grcups 'dogs. naluiai' aii., 'p"& E t i l A ' .

The 1o~e r standard deviations in the lattcr group are clearly caused by a lower biological spread.

r" We can concliide tentatively from thi?. that large 1, difiereiices between strips are probably caused by u-active properties only. The group 'pigs, EGTA,

increasing strain' contains measurements at in- ?-creasing strains between 0 . 2 and 1.6. From the i' fact that the standard deviations in this group are

E

u-

, . , , . ,

not significant!) larger than those in thc corrc- > a m d i n g g i i i z nicaiiired at constant strain, we . ~ . . ! : : d ~ . : t ic , i.cia~.8iion constante are in- depndent oi -:rain. i n order to test for homogeneity And i ~ u i i m p > . wries o¡ measurements were per- Soimed on pairs ol strips taken from the same urinary bladder, hut uiih their longitudinal axes at right angles. These measurements are shown i n the last two rows of Table I . No significant differ- ences between the \,alun measured could be found by Student's I test or a Wilcoxon symmetry lest.

3 Lengihdependent hehaviour of the bladder wall 3. I . P u i x ~ I J P ~ S I ~ ~ C I I I C I ~ ~ S

3.1 . I Thheorv: in contrast to the relaxation constants, the elastic moduli do depend on the amplitude of

1 I

i

7 '"

Fig 5 Modihed mechanical model with in,lial-ltngth dashpot endactwe elemenf

- F ig 4 Average sum of least squares as a function of niimberofexponenri~ltermsfilfed

1-

~

iablc I Rc1,wat;on conslams f rom the various gmups of memuremenis ,-

Number of

rnents Group yr(S-') r(;..) :'i(S-') g(j',) ;.'z(SY') G ( j ' : ) measure-

I

, ~ _ _ _ _ _ ~ __ ~ _ _ ~ _ _ I F % %> %

1 biological spread 46 40 15

Dogs, nafura! 0.47 66 0.045 7i o 0050 50 1 18 physiologml spread 50 5Y 46

1 D O ~ S , D m 0 82 33 0.062 37 0-0037 30 26

(5.32) (99) 0.14 28 0.0090 A6 99 8- l Pigs, natural 0.23 66 0.033 45 0.0044 64 1 9

J- Pigs, EGTA 1-05 23 o 077 Fl 0.0061 62 1 o4 l physiological spread 21 49 60 ,- bio lo~ica l spread E 13 16 , Pigs. CCTA.,ncrearingstrn:n 0.36 27 52 0.0052 *y 98

55 0,0063 E5 45 47 O 005A 52 48 1 ' Pigs. EGTA. venical strip 0 .97 26 L 4Dil

Pigs, k G T A horirontal stiip 1 -OE 25

.. I ~ ~ " s _ _ _ _ _ ~

tlie stepwise straining

E. = E.1 E’) . .

3.1.2 Methods: Strips were repeatedly strained for 625 ms at intervals of 62 .5 s, usins the pneumatic

14) strain device mentioned in Section 2.1. During where I C / is the amplitude of the applied strain. I t turned out that when the eiastic modu:i were rereatedly determined at one strain level, they generally decreased: this was axribed to a gradual increase in the rest lerimh I, ( C ~ U A E T el al.. 1976).

To incorporate this tehaviour in our niechanical model, we addcd a plastic eleirrnt qo in series with tlie parallel combination of F= 2. The resetting of the plastic element is thou& to be an active process, symholised by an e l e m n t C (see Fig. 51. Since the observed trends i n the elastic moduli werc always Similar, R e assume that the relative elastic moduli (the elastic moduli divided by tlie sum of the elactic moduli) are constant.

where

We call e. the relative elastic moduli and Elel the elastic modulus function. The relative elastic moduli are independeni of strain and can thus be determined from stepvise measurements. Table 2 contains average values of the measured relative elastic moduli and their standard deviations. The strain varied batween 0 - 2 and 1 .6 The rewits o f meaxremeats perfonnrrl on SG+~S cut al dilfercnt a n g l o from tiir urinary bladdsr are shown i n the hoimm two r o u i of l~ahle 2.

Here student’s f test showed significant diñerences (17 <: 0.05); but the W4coxon symmetry test did not. We iionclude that there is a marginal luck of isotropy and homogereity. Tbe el~stic inodulus function cannot be reliably dnermined from the stepresponse me%suremeiits si ni;^ here the,increase i n I,, affccts the resulis.

Hov.ever. since we only need io knos the initial hc:@ o í the step-rcwoiises I O determine this Siinction, ue can restrict cur stmining to very short prriods, so that !he increase in I, u i l l be insigniticnni.

each strain pulse the resulting i<>,rce va\ %in:lc.o four times. The average was taken as a rneiiure d the resronsc to the strain l ewl in que5tion. and will be called the ‘average peak Force. from now on. Strips from the wsterior wall of pig bladdcrs were used i n an ECX.4 soliltion and the initial length was determined as dexribed in Scction 2 . 2 .

3.1.3. Rerrilrs: The reproducibility of our method was tested hy applying a series of w a i n pulres oí aniplilude 0.30. Sincc succcssi\e nicaiurcmcnt~ tended to yield significantly lower responses. v e concluded that the influence of the tio element was still too larec. When D U ~ S ~ S at two different - strain levels were alteriiarcd, we found chat the absolute diferenres bctweeii these peak forces were very repralucible as long as the two %train levels were not too far apart i s O . 3 1 .

Using this information, a measurement ser¡=

0 0.2 C.d 0.6 0.8 1.2 1.2 1.4 ’,.: IC1

Fig. 6 Measured @/astic modulus function H-• andfitfedmono-ex~onenrialfoncrion

% ’i. a; % Pigs EGTA. in:reas!ng s:!Jlri O q : 32 0.50 19 0.20 1 5 0 I 4 72 Y8 Pir~s.EGTA,hr;irontal;:::? 0 ’ : 51 O 5 5 19 U 1 3 :2 O 1 3 12. 68 Pigs. EGTA. vertir,al S t r i U U ‘5 36 O 50 15 0.75 28 0.20 11 .! i:

1 -~--*

1-f 2- 2? TO e 5-?4 Z b

J-25Nh2 8 c e eo 66 0 2 ? ' -' ' Q -

r'involving increasing strain pulses with added Unless otheruiu ipeci:ieZ. iiie speed u s d r correction pulses was designed. The elastic modulus 1-66 x I O - ' "1,s. This meal. that lull citemion +function was computed as a function of strain of the strip 150 inm) was reached in about 5Dmin.

according to eqn. 3 from the average peak forces Force was plotted against l e n s h and elastic modulus c-measured in this way. in Fig. 6 thc dots represent against strain using a Hewlett Packard point [ the values thus calculated. plotter, while both curves werc also plotted semi- 4- A nioiioexponentiai function: logarithmically.

I Parts o f the curves could be fitted with a mono- 4- E i l e l ) = \EL exp ( 8 , I E I ) . . . . . (" exponential curve using a ksi-squares criterion.

turned out to fit the measured data very well (Fig. 6, Strips from the posterior wall of pig bladders were Y- full line). We shall call (El, the elastic coefficient, again uscd in an E G T A solution, and initial length

1 and /I, the elastic exponent. was determined as described in Section 2.2. Tcn nieasurements were performed on strips of 1' bladder wall fro," seven diRerent bladders. The 3.2.3 Resdls: In the first experiments Strips were

1- parameters determined are shown in Table 3.

1-

extended up to 5Omm once at constant speed. The force-length plot shoued sudden drops after an initial smooth rise and an irregular pattern of -

j-aable 3. average7znd standard dev;ai;on for the paramerers def;n;ng the elasric modulus funcrion ai low mains

increasing ana decreasing force at high strains. These high-strain phenomena were ascribed to the 'flow' of the plastic element q0. T o obtain reliable measurements o f the elasticity involved, a series of quick-release experiments was performed. in which the strip was extended at constant speed up to a value certain force, quickly relcased to force zero, and

1.28 19 10 then extended again at the original speed up to a 43 10 higher force. The resulting lore-length plot is

shown in Fig. 7.

Number Of

Parameter Average standard measure- deviation ment*

~~~ .~ ____ #I IEI, 16 084 Nim'

3.2 Ramp meosurements

3.2.1 Theory: ~l-he dynamic measurenients described in Section 3.1.3. could not be performed at strains higher than 1.6 because the forces involved would damage the strip.

Since the elastic moduli may deviate from a mono. exponential function at high strains (VAN MASTRIUT pr al., 1977d). we investigated the elastic moduli or modulus at high strains by quasi-static measure- ments, which yield lower forces. The error ill- volved due to the influence o f the dashpots can be estimated from the relaxation constants, which yields about IO",; using the data o f Section 3.2.2.

\Vhen the \~iscous effects can be ignored and the influence of the active element is reduced by EGTA. the model reduces to the Eo spring in series with rhc >lo eicment. D

F ~ N ) 8946 ,//

,

io s i (mm)

3.2.: Merhods: The pneumatic strain device inen- tioned in Section 2.2 was modified so that the strip F;~. 7 ~ ~ ~ ~ ~ . ~ ~ ~ g t h pior of a strip of bladder wali could be strained at a constant speed by slowly S1ra;ned at constanr speed with repeated

Table 4.

paying out a steel wire, using an infusion pump. quick ,&?ases

Relative standard deviation Parameter Average Physiological Biological N u r n ~ r of Number of

value Total spread spread curves measwemenis

.,i,-rg ::.<:: thc cn..4<ip? oí iiicsc cwveb mc\\ t i i pressure, is conicrneti, LAM; 11852, p. 2121 ,h , )w, I!-!.: ,u,,,c paiicrii ,I. ~ ~ x n t i ~ a : d a h ~ i c ; gibe. a relatiowhip for a linearised thick-walled h<i*e,cr, i n j i ; i i i l Ja l cur\e. ri,ing to :!K envelope sphere. which can be siniplified (va% MASTRIC;- . are quite smooth ;<nd reprcducihie. We iilterpret 197'70) to: ih1.i by asjumiiig t h i the plasciic element 11" imlilies some thrc-holti force. When the threshold force

which the elerrierit last ceased to Row) is exceeded. plastic flew begins. The repeated ascending curves This relationship can also te obtained by simply up to the enveloping 'plastic Row' curve would thus calculating the balance of force over two hemi- seem to reprcsenr elastic properties at different spheres (MATSUMOTO and LA GRANGE, 1973; strains. The las! two or three ascending curves C ~ L S A E T p i 01.. 1975a). If we take V, < 0. i x C'. from ex!-, se: of mcasuremi?ts (&pending ori ho\v which i s generally a fairly realistic assumption, close tog-iher the curves were) were ñtted with a the total error introduced by simplifying the ori- monoexponential. 'The results can be rerii in Table 4. ginal relation is a b u r io;.;, Now the very high standard deviation of the elastic coefficient. which is caused by the elongation of the 4.2 ,ifei/rod.r t iu clement. Variance analysis applied to the data Eqn, 9-for the first block,.aiid showed that the differences between strips ibio- eqn, IO-for the second.-can both be teted by logical spread) was significantly greater by m e s t measuring the pressure.volume relationship of a than the differences within S l r lQS tphysiobical bladder, quasistatically calculating the srress-strain spread). Note furthermore the significant difference relationship of block from the reSUlrS, and beween the vdue of rhe elastic exponent found then measuring this stress.strain relationship directly here and that found in Section 3- 1. We conclude on a strip of bladder wa~, that at high strains the elastic modulus function Since quasistatic meaSurementS on bladder wall shows a different slope than at low strains; thus we are rather t;me-consuming, we perconned the represent the elastic modulus function by a 2- measurements on a rubber balloon which showed exponential expression: negligible viscosity.

The balloon was connected to the catheter and to

3pY (which in these experiments equals the force at 2 I;

0 -= - , . . . . . . . . t l i l l

E ( ¡ C i l = ! E l , eXP ( f i t \ E ¡ l A ! E ! l exP ( f121ri ) (8i the rest of the apparatus described in 'Section 5, Finally, it should te noted that although we ex- pected a ~ircoelastic relaxation of about IO>; upon ?topping the straining of the strip at there low siram s p e d s , . a mentioned i n Section 3.Z.I. in fact a relaxation oí about 50:; was seen. This might be an indication that the time-dependent behaviour of the strip is nonlinear. This unexpected hehaviour c a n probably be described more ade- quately using a continuous relaxation model instead of a discrete modcl. Future research on this topic is called for.

4 Geometry of the urinary bladder 4.1 Theory

In this Section \\e will consider the two geometry blocks of Fig. I . Our basic assuniption will be that the urinan hladder i s a thick-walled hollow sphere ~ O S B O R ~ E and SLTHERI.A>D. 1909: MA~SCMUTU and LA G n a w r . 1973). The hrst eeonietry block. relating voltinie lo

strain. can then be described as follows:

and was submerged in water. We calculated the stress and strain for each measured set of volume and pressure values, and hence the elastic modulus. using the relationship:

d = 2EE . . . . , . . . . . (11)

The reason for the factor 2 here is that we strain the material in o// directions in the surface and not only in one as is the case with strips. It c a n easily be shown (see FRAXK, 19%. or BROOY and QUIGLEY. 1948) that in ihe linear case this yields a rnulti- plicative factor of ( / / / - p ) , where /i equals Poisson's ratio which we a s u m e to be 0.5 IV, is constant). The elastic modulus was also obtained from mea- surements on a strip from the wall of the balloon. using the equipment described in Section 2. In both cases ilota1 balloon and strip) measurements were first made for a small increment in strain and then for a similar decrease. and the average of the ino nieasiiied values was uyed.

3.) RP.Tl,l tX

Measurements were made on three balloons.

for the balloon as a \\hole. Thc areraerl \slues v i Fig. x il,o$\s 11,s preisiire as il fiincii"" of YOlLl"lC

r- L ? i- deb-iation oí ihe elastic moduli ic significantly largci

iuur ihe measurements on strip, i h u n rirr i h r i x o11 ihe - haiiooii its ic u h ~ k which ~mcilm illill ilir i i i i . ; isuid curie ior sirips shows a trcnd. Tlic rc!iitiic!y small diíierences &tween the elastic modiiii cal- culated from strip measureinenis and whole hdlloon mmurements indicate that our geometry models

I- r- are reasonably accurate.

5 tirsirntiun inial bladdcr model

? I 'I Ii."r-?

O u r overall bladder md?! can be obiained b:. combining all the blocks considered above: see Fig. 9. I n this section we uil! test the entire model by comparing the results oí measurements on whole bladders with the predicted responses.

Ffg 8 Pdssore as a function of voiume for

-- a rubber balloon

ww

- .- o 20 40 60 80 100 120 140 160 180 200-

V X l O d ím3!

time dependence

. ~ 1- VJ gxmet r y b 3 le"gth L ...*

dependence IEll,IE$, PI, P, -

L

i

r Table 5. Average elastic moduli, relative standard deviation and difference befween avezape moduli for measure-

Fig. 9 Overall model of rhe passive properties of the urinary bladder in the collection phase

i menrs an rubber balloons and sfrips of balloon ~L -

I I balloon Difference 1 r Measurement Elastic Relative Number of Elastic Relative Number of between

~t deviation menti deviation men15 moduli

Result of measurements on whole Result of measurements an strip

number modulus standard measure- modulus standard measure- average elastic

-. i ____ __ -__-

, 2 427 375

N/"?2 %, 4 520 284 10 22 1

6 20 434 841 22 20 2 ' 0 455 7?'1 23 11

- c NI+ ?a 1 51 7 662 3

3 507 359 k 3 %

I

, i - -. ~~.

First, we consider cystometry. which in\,olves quasistatic filling of the bladder yielding a pressiire- volume plot called a cystometrogram. With a very slow ramp as input (strain) signal. the niodel (see Fig. 5) reduces to the E , spring in combination with the !lo element. Assuming that the qo element cannot follow the ramp at the low stress caused by the Eo spring alone, we c a n write for the time-dependent properties of the wall

n = ZCE, . . . . . . . . . (121

(see eqn. I I). inserting the relation for the other blocks, we

obtain:

Fig. 10 shows the result of fitting this function to a cystometrogram measured on a pig bladder in riiro, using a least-squares criterion. The five independent parameters were determined as follows:

We see that especially the second elastic exponent agrees very well with the value measured in Section 3. A far more important conclusion is that the usual

clinical cystometrogram gives only five parameters

, ap.i&,w-L ~ ~ * p J , a k a - r p (of which 1x0 are even comhinati<ms) out of the 14 paramaers which define our bladder model f V 0 , I ; . cy>. e: .e i . r i .7 , , ; I * , 7,. :F;l,. E 1i P,. íi2, ver.

However. if we apply a stepwise iiilume change to the urinap hladder (CWLSAET ci al.. 1973) me obtain from one measurement the relayation con- stants 7,. and the relative elastjc moduli Y " , e , . e , . ea. To e\aluate these values we have to know the tissue volume 6,. So eight paramete? are needed to describe om stepwise measurement using our model. I f we measure the initial volume V , and if we jxríorm se\'eral measurenients on one bladder at convenient strain levels. a correnion as was used in Section 4 for pulse inrzssurenients can be applied. W e can then also determine the elastic modulus frinction--only a i low strains. however (because at high strains the fay1 straining would yield too high a pressure): this yields [ E ! , and p i . This means 1 1 paramcrers are needed 1 0 describe the results of more than one stepwise nieasurement. In practice, since displacement of a volume oí fluid always takes time, the volume change cannot he considered as stepwise e w n at very high fding rates.

l h e calculated coefficients o f the multirxponential decay function will thus be too low. The coefficicnts of slower exponentials can be corrected, but for high strains the coefficient o f the fastest exponential becomes w small that our model reduces to a 2-exponential one.

5.2 M',thOdf5

txperimsnts were performed on female mongrel dogs under continuous intravenous pentobarbital anaesthcsia. Do@ were used because dog bladders show less spontaneous activity (sx Section 2). Most experiments uere performed with an open abdomen in order to avoid the influence of the abdominal wall, A double lumen catheter Uas introduced into the

bladder. Tbt bladder was filled with physiological saline at 37 'C. at a rate of 10 cm'is. via one channel. Tlic przssurr in the bladder was measured via the other c h a r m 4 The electrical pressure signal w i s punched on v a p r tape at intervals of Is for I 5 tiiin. The initial wli me ofrhe bladder was determined by slowly íiili:ie i t with a syringe. Aboui 10 measurc- inienis were $xrt»rnied on each animal at'@iervais o f tifteen Piinules. The results xcrc ana!>sed as ilescribed !L S'rctior. 2.2. After the end of the niea<uremen:3 the bladder was extirpated Sor dctcrmina~~,.w of ihc iicsue volume.

i..! R<~r , i l : l

A s cxpecrcd. ihc doe hla&lc;s shou,ed \ t r y l i t t ic spontanco~ii acti\it?. Table h s h o s i the a\'erasc rch\ztioii ' r w x i i i i i t b and their siandard dei i a t i o i i i C!, dclcrn,,::<2 rr<.i,i m Y ~ S I I r ~ n l e n t b i," sc\c,i doss.

. .. C83

*-

i-

i

c

L

f- L I

IC

li 1-

.A\ is!¡ nwsurmicnt~ \\ere i?i;idi. iii rx ihcr to,.<

> i t & i i ~ . the cnpcrincntal curre:, could be fiiicd tk11h

three exponential funriions. I t was not possible to draw any c~nclusions about the elastic modulus function, as the measurements were not perlormed in an order which permitted correction for the increase in rest length. However, the relative elastic moduli were still reproducible. These are shown in Table 7, and compare well with the values measured i,, cirro.

As in the case of strips. we see that the relative ciastis moduii are more reproducible than the relaxation constancs. The average initial volume was found to be 30 ml with a relative standard deviation of 67:i and the average tissue volume was 26 mi, with a rrintive standard deviation of 5 4 X for the SCVCLI bladders. ksthel-e is a high correlation between these two quantities (correlation coefiicient: 0.87). it would probably be sufficient to measure only one in practice.

., . ., ~.

Ti.-: m x k l h\ol\c\ the folhwing I4 paramrter~: , . ~ I he tiswe \vlitms i ,

(%,* l h e initial holiimr 1'" i i i t t The relaxation constants :',. y*, i r (ir¡ Four relative elastic moduli eo. E , . cl, (v3 The elastic coeñicients IEI,. /E/>

( v i l The elastic exponents J,. b'> ( i i i ) One (or more?) parameters describing the

behaviour of the qo element. For all parameters except qo, average values and standard deviations have been determined for dog a i d pig bladders. The values were obtained by various measurement fechniques. The model des- cñbes tice form of a 'quasistatic cystometrogram' adquarely. An alternative method for testing the w i v e properties of the urinary bladder in the collection phase is proposed.

.4ri<mu~iedgme~-Wc would like IO thank D. J. Griffithr ínr his help in interpmting the ramp measuremcnts.

werences &RO, A. K. G. and AxEIsco';, 1. (1965) Same niechan-

ical aspects of intestinal smooth muscle. Aria PhJ'sbI. sCOnd.64.L5-27.

urinary bladder. Am. J. Physid. 220-5. 1413-1421. A,PIER. 1. T.. M*soi, P. and LANO, G. (1972) Urinary

,, (1970) Mgbnical propertis of sma>th muscle. In Búrsnrsc. E. (1970) Smooth nioscle h o l d .

BnoDu, D. A. and QL'IGLEI. 1. P. (1948) Some mechanical

bladder fn~lors in the dynamics of the thin-walled. spherical viscus. Bull. Murh. Biopl?y.s. IO, 25-30.

the 'lace and the in which lhey CHRtsTEsSE>, R. hl. 0971, Tlir0r.r of circo.rlorricir,-. tin are measured (isotropy and homogeneity) i n r r ~ r h ~ h n . Academic Press. Ncw York. ih) The relaxation constants, and elastic nioduli C ~ U A E T . B. L. R. A,. VA\ ni!^'^. W. A , , Y & V h'íasriuu-i,

relative to their sun1 are constant, which implies R. and VAS DER ZWART. A. (1973) Stepwizecysromlry a linear time-dependence of urina- bladder. L : r d U-3.255-251.

Cm~snrr , B. L. R. A.. VAS D u n , W. A. VAN M~STiucr, K. and VAS DER Z w m r . A. (197Sol Visco-elartic properties of the bladder wall. Uini. I n r . 30. Ih 3.

6 Conclusions I t may be concluded that dog urinary bladders show mainly passive progerties in the collection phase. Pig bladders show more active,properties, but the R. s. M~hanical passive can be described adequately in terms of the model =presented by Figs. 5 and 9 and eqns. 9. 10,8 and I I . The iollowing assumptions were made in establishing this model: ( u ) All parameters which reflect properties of the

in our model are indeyiendenl of

b,adder wall dynamics. ,ncc,rig, (I,ol, -, 520-526.

i c ) The tiisue volume of the wall is constant

( d ) The urinary bladder is spherical

Table 6. Average relaxation constants and standard devia:ions measured on doy bladders

9L % 0 .45 69 0.059 54 0 . W 3 42 44

%

Table 7. Average relarive elastic moduli and standard deriarions measured on dog bladders in vivo

% "^ n 7 2 7R 44

% %

R. and S w r n x m , J. \V. fIY75bl Viifo-elastic pro- perties of hiadder wall strips. hre.rii#. U d 12-5, 351--3Sh.

COOLSALT. n. L. R. A, . VAS MASTIIGT, R.. VAX i l c r ~ W. 4. and Hwom. R. F. F. fl97h) Yisco-ela6lic properties of bladder wall strips a i cnnslant elongation. chid. 134,425-440.

Cmi.srrr, B. L. R. A. (1977) Srepuiv cyscomctry. A new method to awestigate properim of rhe urinary hladdcr , Thesis, Erasmus Univmity Rotterdam. The Netherlands.

die Elastizitit U.C.W. Amid. Ph.v"k.. M)2-608.

rmuoth muscle. Proc. Roj . Soc. 100. 108-l I S .

FRANK, O. (1936) Die Analysc Endlichcr Dchnuirg und

H~tt., A. V. (1926) The viscous clastic properties of

J n ~ i s o ~ , C . E., MARANGONI, R. D. and úussn, A. A. (1968) Viscoelastic properties of soft tissue hy dir- mete model characterization. J. Bionicih. 1, 33- 46

KUIK, A. J . 11976) Estimation of the parametus of a multi-exponential signal. Afstudeerverslag d e l 1. Laboratoriiirn wor Technixhe Naiuuikiinde. Delft, 1 he Netherlands.

LAM<, hl. G. ( I 852) Lqonr sur la theorie rnatheniaiique de Ilelasticité der corps rolida. Paris, Bachclier, Imprmeur-libiaire du Bureau der Longitudes et de L'ecole Polytechnique.

i'ork M n i r ~ i t i r , R. \AV ( 1 9 7 7 ~ ) 4 \ystems approach ! o thi:

parsive properties oi the ur imry hiadder in the collection phase. The5iq. Erarmus liniversity Roller- dam. Rotterdam.

Masrni<;r. R. VAS ( l Y 7 7 h ) Conrtant step appíoximaiiori of multi-ei;ponential signals using a least square criterion. Compul. B i d M P J 7, 231-247.

Masrnicr. R. VAN (1977~) A short note on the pcrfor- minrroft~ocompvrerpro~~arns for the estimation of the parameters of a multi-cxpoiicntial model. ¡hid. 7. 249.

MAS~R~GHT, K. VAW. CWLSAET, B. L. R . A. and DuYL. W. A. VAN (1977d) The passive properti- of the uriniry bladder in the collection phase. U r d /ni. to be published.

MATSUMOTO, Y . and LA GRAYGE, R. (1973) Dog hiadder pressure-volume relation determined from isolated strip of wall muscle. force-length ciiiie J~&G i<i 12.

MAYER. C. J., BUIEMFN, C. \'AN and C6rtei.s. R . (1972) The action o f lanthanum and D600 oii the calcium exchange in the smooth rnus~lc cells of the guinea-pig Torniocoli.PflÜgrrs Archic. 337.

OSBORNE, W. A. and SUTHEKI.ANO. W. (1909) The elasticity of rubber balloons and hollow viscera. Proc. Roy. Soc. E 81,485499,

Les propriétés passives de la vessie durant la phase de coliecte Sommaire-Cer anide &me un modele dicrivant les propriétér passives de la vessie durant cetie p k

de collste. Une tahnique genre " b i t e noire" est iitilirCe. Le syrteme btudié, quint défini en teme &une relation prcrrionjvolume. est divisé en quatre sous-sysiemes out blocs i savoir deux blon. g6omérrique$,, un bloc décrivant les propriétk des par~is de la vessie en fonction du temps et un bloc décrivanr les proprieiér en fonction de sa longueur. Les modeles onf Et6 mis au pointel testés pour chaque bloc répa&neiit. En ce qui cuncerne la géométrie, la vessie est dicriie comme une sphere 6 paruis Epaisser don1 les tisms on! un Y D I U ~ P consfant. La dCpendance des propriétés de ces parois en fonction du temp peut Ctre expliquée avec un modele visco-+lastique, tandis qu'on ut monfrer que la relation e n i ~ les propiiétis de ces parois et leur longueur correspond i des modules elastiques qui dependent da- remions de maniere biexponentielle. Les valeurs estimCer des parametres en question om été obtenues i la suite d'expériences r&lis&s sur der bands de vessies obtenues aup& de I'ubattoir Inal. La curnhinaiwn der blocs a domé un modele global des propriétes passives de la vessie d a m la p h i c de ~ I I P C I E . Ce modelo cmtienf quatorre parametres. La maniere classique d'éiudier la vesse. qui consim A la remplir lentemeni et A mesurer la pression obtenue, donne une relation pression volume pseudo-siatque appelée un cyrtométrogramme. Le modele prédir précisi- men1 la forme du tq srometmgramme. Cependani, i'analyse d'un te1 cystometrogramme clasrique ne nous permet de dcterniiner que trois parametres dc notre modele. IJne meilleure mérhode de m e s u i i consiste A mefire s u s tension de maniere graduelle ("u preique) la vcssie. Cela permet d'ohienir hui: parameties. pounu que le volume inicial de la vessie soil connu, ct plusieurs mesures sur mr vessic .i diHérenre\ iensioai m u s per~;ettent de déterminer di\ parametres. Les résultars obtenus avti Cclic rnrthode de mi% .oui irosion par Crape sont cornpatihies avec le modele.

Med. Diol. 6-8. d Comwc. 197'1. 17. LXI 90

A , L Q

Active mechanical properties of the smooth muscle of the urinary bladder D. J. Griffiths' R. van Mastrigt W. A. van Duyl 6. L. R. A. Cooisaet Dopartmmnts 01 B w i c a i 6 Mdicai Physic. EM of Uiolopi. E r a m u i University. Ratterdim. The Nakrlands

Abstrect.-SIlipi o fp ig bladder have been maximally slimulaled in v i l o ar 37'C via electroderplaced in ~~ - ~ - - - t ñ e m u r c l e . i n order, parliculariy. to measure rhe dependence o f l h e resoiling aclive force on rhe

velocify of shorrenmg and on lengrh changes. The acrive lsomerm force a~nd rhe~passwe viscoelasric force are a p p r o x i r n ~ u u a n recisely. addilive. The acZGZ~E~omeiiic force. like h e sreaay (equilibrium) passive lotce. is a funif ion of rhe exrension o i ihe strip above irs msr~ lengrh. which is~inoeased afler siibjecrion ro a high passive force. The steady paj5ive force inmeares quasiexponenlially wilh lhis exrewon. of which ir is rherefore a measure The aciive isometric force f,.o increaser approximalely Iineaiiy wirh lhe errension unlil ir appcosches a maximum in fhe region where il and tbe sreaúv passive force are comparablF%F~,-+~~Tiie rnaximumlspa~lyobscureabyresr-lenglh changes. T b dmendence ofrhe aclivefwce Fon rhe speed of shorieping~che-zglp has been measuredin a new way. wi lh a correclion for&; viscoelaslic effects. For a given srnp rhe r m o (5. approxtrnarely. d luncrian o i rhe co^nfraclmn velociif only. The function ir similar lo lhar of rhe classical Hill equarion bur no1 identical, possibly for geomelrical reasons. The resolls imply lbal a velociry parameier Y*.

analogous lo Hill's parameler b. is approximalely consfanr for each slrip, independen1 of changes of lengrh and -si length.

Keywords-Forcellengrh relarionship, Foxcelveioory relalionship. Plarricify. Smoorh-muscle nrips. vi~coelaslicil"

List of symbols length. What is required is a series of simple approxi- a = force parameter in Hill equation, N S E n s that can be used in a mathematical model b = Velocil?i i n ill of micturition (GRIFFITHS and ROLLEYA. 1979).

USCle behaves like a q i v e ~ ~ \ : i s o e I & g i - substance. It &o exhibits plasticiry: itsrest length k r ~ d - a f te rg - sAEi er <;rr;W:We31aii réíer t d a r ~ ~ s a x d b y uoimulated muscle>lG&h'e'.7~

When the muscle is stimulated ;o cotnmckan- extra active iorce is deieiopea. ;Rich-presumably depends on thelength oí !he musc e and on the speed o ~ s l i o r t e n i n g as in other smooth and str!a?ed m ~ m G o ~ ~ ~ ' . and SIEC\;;\. !9fli:TTís ác%? forcQ-eases with increasing swed of &=I-

1 introduction The act ive force ai canqtani length (zerc speed of DunI& micturi:i«n the ":!nary bladder coytracts sliorreningl is caTlebiTic~ETTEtr¡cfQr&'& In order to

f ~ m a_voL\[iÜ<-üJ i e r a i htlndred~ ii3lilitres~ (iñ make reliahls measuremcn!s of the veIw¡ty depeii- man) i t s :$gKa& :erLactiuelv expelling its dence ofihe acti\e iorce. horh ihe passiie \Iscw!aslic cpn!gn!.s. C o ~ ~ n d i t g f ? . the--the m ñ i force. u hicli also i s \e lo<i i> 6eepeiident. and possible t$Ue thanges-grcrcTb tC<üFEY?ER. 1968). Therefore, changes i n the rest lcngrh ~ U S I be taken inlo axount . l n ~ l o @erstand ihe course of miciuriiion,- 1" the cspcriments reporicd here !hz iollouing i t is necessary t.>+?o,w hou~ the mechanical properties ha,,e ken inVestigBtCd: the cIependsnce ,>f ilie

r a t !cnpih of the m u ~ ! ; . I!K rrla!imi iziv+i.i.ri t he I S O ~ C ~ T I C a l id pactiie :L. ,ra5: the iorni c > r I ~ C r c l : ~ r t s ~ n

P = a c t i ~ ~ e force during shortening, N pnstimulated. noncommc- ~ __ Ftso = acthe isometric force, N ,c pqx -- .. steady (equilibrium) passire force, N

f, -&() = functions of variables in parentheses

I, = rest length of muscle strip, mm I = length of muwle strip, mm

I ' = speed oi shortening. mmk = physiological maximum speed of shorten-

I.* :: velucil? parameter for muscle strip. mm:s

~ __ -.- ing, mm.'r

OT tñe~E5ñrraQxs mus&- n change\ m i f 3 jS<>metric acliyc forc? ~ r i i,hangcr i~ l I ~ C icn$:ti : ~ n t i

Received 23m Maw .?le

'O" k a r e <,om I -$ 2 C P 8 , I m ~ - 01 Ph>.STS, Y - i . F l i i , y Of Fxreicr 1, , De""". &.,ana h e t w c n ! t ic acti \r . tcr ie .:mi the c p d i ~ f ~ l ~ < x c n 8--

rnd its dependence on changes o f the length and rest ! :ngth of the muscle. For the majority of the eweri- % e n s strips of pig bladder were used. A few

libservations were made on human bladder. The were stiniulated electrically by electrodes

iserted in the muscle.

n-

l'j

A-

i

1 Bladder svip (S). stimulating electrodes (E) and clamps (C) . T E force transducer, I = indifferent elecuode. The strip is abour 9 mm

iL-'

l a d i 5tr ip was about 15 niiii long by 9 m n i broad and has cut From the posterior wall. running longitudinally. The strip was fixed vertically between two toothed clamps (see Ca>l.snEr PI al., 1975) under very little tension 0.01 N), so that ahout 8 mm of free length remained between the clamps. Thus the rest length o f the portion of strip under ihvesti~ation was initially about 8 mm. This represented about 1/20 oí the total circumference of the bladder.

Electrodes made o í silver wire, diameter 0. I nim. insulated except within the muscle, were threaded through the strip using a hypodermic needle as an inserter. They were approximately equally spaced and usually four in number, as shown in Fig. I. The strip was then submerged in modified Krebs solution at 37~C, oxygenated b.y bubbling with a 95%. 0,/5% CO, gas mixture. During most experiments the bath was slowly perfused with fresh Krebs solution.

The two clamps formed part of a pneumatic straining and force-measuring apparatus that has already been described (CmLS&ET el o/., 1976). The upper clamp was fixed to the cantilever of a force transducer, so that the force in the strip c m l d be recorded on a chart recorder. The svsteni was calibrated. and its linearity checked. wi;h weights.

>laterial and apparatus The cbmpliance of the measuring system was

welored high active forces more reliably.

I

- -1 '.. - \I

St/m",al,On LA.--- ..L--LL*--.. ~...-.L-2

bme. rn8R

b --+ 60 5 Fig. 2 Responses to stimulation by a train of electrical

1 1 I .~ 'itlmuialioc pulses 17 ms. 20 s 'i / a ) Response to prolonged siiniulocioo (60 r j 4 - -1

l l i i p l ill, I>. I,: ;>"sitii>". U"d Lk,, , I t ' < icllgl!l /)I Illf qtrip. was alc- xcordrd on the chart rewrtlcr.

For electricdl stimulation of the strip. the stimu- lating electrrrles were connected in parallel to three Grass Só slimuiators also in parallel. The 'earth' terminals of the stimulators were connected only to a large indiñerent electrode, a strip of stainless steel. in the Krebs bath. The stimuliltors were synchronised and adjusted 10 give simultaneous pulses of the same duration and nominal voltage.

3 Stimulation parameters The follouing results were established under

isometric conditions: (o) Stimulation by a train of electrical pulses gave a

forcc that rose Sairly rapidly to a maximum and then decayed slowly (Fig. 20). This m?ximum was taken iis the isometric force.

(b) I f stimulation was continued long after the maximum waslpassed, the responses tosuccceding periods u: stirnulation were reduced, apparently permanently. If, however stimulation ceased as soon as tRe maximum was reached (Fig. Zb), reason;ibl)- reproducible responses to similar successire periods o f stimulation could be "brained. provided that a resting period of several minutes (usually I5 min) was allowed between ctiniulations. The response varied slowly o ~ e r a period of a few hours (Fig. 3). during which about 20 observations could be made.

(c) Thc active force was greater for pukes of negative than for those oi positiie polarity. w i t h respcct to the indifferent electrode. It was rather insen- iitiw to the duration and frequency o f the pulses, bur uas near maximal for a duration of I my and a frequency o f 2 0 s . ' . These values were used in subwqiient e5periments.

(& ,As the romina! \oltnce of the pukes %a! incrcahed !lie respnnsc at firit rule. but becanc.

. .

reia:i;ci> ci>c:tznt a b - c a certain witaye. who\i value varied from itrip 10 strip. This constant response was taken to be maximal. With four electrodes and three stimulators in parallel i t appeared in experiments on several strips that a maximal rerpnse could always he expected if rhe nominal voltage was 50 V. This \,slue was used in subsequent experiments. I f the nominal voltage was increased much above 50 V the strips were damaged. as evidenced by a rapid decrease in the response to successive stimulations. Since the stiniulators "ere heavily loaded by the low- impedance electrodes. the true voltage was only about 8 V, corresponding to a stimulating current ofabour 250 m.4.

( e ) Spontaneous rhythmic contractions (period e 30s) were superimposed on the 'pasbive' force exerted without stimulation. Their peak-peak amplitude never exceeded IO:,;; of the active isometric force. They did not intersere with the measurements. Thus. under the conditions described, it was possible to make reasonably reproducible measurements of an actwe force that was maximal: ¡.e. was developed by contrac- tion of the whole strip. or all of it that could be electrically stimulated.

4 iMeasurements of active isometric force nod passive force 4.1 Ourline

The passive viscoelastic force is velocity dependent. and. ekrn at constant length, time dependent (TrmLsaEr r r d. 1975. 1976). Therefore, I O obtain reproducible results it is simplest to make nirasure- ments at a given strip length when the passive Sorce has &come stead?. after the time dependent part has decayed. The time dependent pan is much smaller. and so d ~ c a y i tu a negligible value more quickly. i l the ~ t n p lcnqtii is reduced rather than iimca'ie4

-1

r". 3 4 I

' Reiauu the TCSI length of ii strip 15 dirriciiit I O I n v m i e r.s?erimcnti tu11 cr more rnrai~irements .rasure. ditiercrit , ~ u i h o r i Ihavc dclincil d-,d 0 1 ihc i w n w ~ ~ c l'i>rcc ucrc rnadc at one length. ,easured i t in different ways ( A % . n i ~ a , h PJ oi.. Since the d i B r r ~ c c s wcre small. in most experiments

4668; GOROON and SIEGMAN, 1971: CCOLSAET el d. imly one measurement uas made at each length, f p. 1.5-

Fig. 4 Active isornerric (black symbols] endneady passive (open symbols) forces as functions of length lor one strip. Circles, triangles and squarer = respectively first. second and rhifd series of measuremenis at decreasing lengths. Where a range is shown ir indicatesfhe differ- ence between two success- ive measurements. Other- wise Ihe difference was smaller than the size o1 the symbol. Curves linking the points are drawn purely to guide rhe eye

p.. 1.0-

I-

LO

r-5

- < _

35

n- !I j y- i -aL

I ' 5 20 25 30 ri- length, mm ! I !I-976). However, changes in the rest length are because of the limited number of mcasuretnents

possible on one strip (see Section 3 pan b).

4.2 R~JU"~ ~ u i di 'c~nion at increasing strip lengths, successively (a) Forcelieiigrh measuremenis. Fig. 4 shows

typical results from a strip from a pig bladder. 'rii. is lengthened and there is no means of con- i\.liing the increases in rest length. i n a series of ,easurements at decreasing strip lengths, the passive

Similar results were obtained from five other strips of pig bladder and from one human bladder strip.

The sets of points representing tho active and

Measurements were therefore made a3 follows. series. over 10 min. Since the initial r a t length is

substantial passive force (14 N) developed, which as then allmwed to decay viscoelastically. Measure-

1 ments oí the steady passive force and of the

The dependence of the steady passive force F,,, on the strip length in any one series. ¡.e. ai constant rest length, is similar for each series, as shown in

timuhiion were made at a series of decreasing k e n supenmpos-id by shiftin3 Them along the length anis. Thus, as far as ien.gth dep-ndence is concerned. and as a reasonable approxiniation. the

isometric tensioi, developed during Fig. 5, where these passive forcc'length curves have

ngths. The strip was again extended. and further l series of similar measurements made.

10

Fig. 5 Sresdy pasive force F@,< as function o1 extension (I-ioJ above rest length far one strip.

I 7hme series of meawrernenrs at rhree differenr rest lengths have been superimposed by taking res1 lemgrhs oí respec!-

. a - c&&& c[-l0), ively 25 i'c!rcieri. 32.5 rrian- gles) and 35 (squares) mm

.. - M 5 m , -

r' L,.

r' I L.

c: e-

Y..

*-

u..

r t I

i- c I 'r IC

steady passive force depends only on the extension (1-1") relative to the rest length, and not on the rest length l o itself: Le.

F p , , = f , ( I - l o ) . . . . . . . . ( 1 )

'The function f,(l-l,,) has the expsted quasi- exponentially increasing form (AA-D~RSON ef 01.. 1968: VAN M ~ I G T el 01.. 1978).

At constant rest length, the relation between the active isometric force F , ,o and the strip length I is quite different in form, gee Fig. 4. It is nearly linear at small I. and possibly approaches a maximum at larger I , in the region where the passive force is high and comparable with the active force. This relation roo is shifted along the length axis in different series of measurements, again suggesting a dependence on ( l - l o ) . In addition, however. the overall magnitude o f the active forces appears to dccreasr with in- creasing 1,. Iherefore. provisionaliy

F',<, = ~ { l l - L A l " ; . . . . . . ( 2 U j

(b) Relationship berwwi acriue rind parrice forcrs. An important consequence of eqn. 1 is that the steady passive force, which is easy to determine, is a measure o f the extension íl-lol. which is difficult to ascertain directly because o f changes in I,. To test eqn. 2u. then, the isometric force may be plotted against the steady passive force. as in Fig. 6 . Each series o f measurements (at a giren 1,) yields one curve. The curves for the different Series are qualitativeiy similar in shape, although quantifa- tively the isometric forces become a little smaller in each succeeding series. as one would expect from eqn. 20 and Fig. 4. However. because of the time sequence of the measurements, these reductions in the isometric force could well be an artefact due to

Fig. 6 Active isometric force as a 1unct;on o1 steady passive force lor one strip. Orcles. triangles and squares = respectidy first. second and ihird se,ies o1 rnessurementS al decreasing lengths. Range given lo, one pclril shows dii/t bewee , , two measwemenfs due !o resr-ienolh ~~

change yi h i g h passive g c e E"""' are purely

Ihe time dependence of the active propertier (Fig. 3). rarher than a true dependence of the isomelric force on thc rest length.

In order io eliminate any such artelact. measure- ments were made on fresh strips as follows. The isometric force was measured at a given steady passive force. The strip was stretched to increase its rest length, shortened IO regain approximately the same steady passive force. and the isometric force measured again. This was repeated several times. The result of such an experiment is shown in Fig. 7. Within experimental error the isometric forces are equal in íive measurements at similar steady passive forces, although the s:rip length. and therefore the rest length, has increased by 16-5 mm. Therefore. the apparent rest-length dependence of the active force in Fig. 6 is an artefact i n this force range. Since in addition all !he curves have a similar form

F, ,o=f,(Fp, , j . . . . . . . . iil

independent o f changes in the rest length, to a reasonable approximation. The form o f this fundon is shown in Fig. 6.

Since Fp,, is a measure of (¡-lo) (eqn. I). eqn. 20 can be rewritten as

F,,u =f2(l- ia) . . . . . . . . (2bi

i.e. to a first approximation the active isometric force, like the steady passive force, depends only on the extension (l-lo) and not directly on the rest length 1. of the strip.

I-, ---L

30 35 40 1 5 Irngth I , mm

Fig. 7 Acrive isometric lorce (black crclesi and steady passive force (open circles) as functions ollenglh. for one strip Passive force ;s approri- matefy constant. bur rerf lengrh has been mcreared between successive measurements. so that /total) length continually increases l y r n e t m lorce also iemarns approxrmarely -

$-(c) Exirrrnce of', mrrximum in the isomrlrk .force, lw&rrh r&tio~?.~I~ip. Previous authors, reeking a qaxinium in the active Force/length relation for nooth muscle similiir to that in siriated muscle.

g v e Found that it occurs at high extcnsions where the passive and active forces are comparahle

~ n u a u > s ~ t a l . . 196X;Gonoouand SIE~~MAX. 1971), x&stent with Figs. 4 and 6. However, i t is difficult

irest lenglh. If measurements are made at increasing istrip lengths, any increase in the res: length as the

resumed maximum is approached reduces the ;tive force (see Fig. 4). and so can yield a spurious

maximum. Indeed, the presumed maximum is ,difficult 10 reach at ail by increasing the length o1

?-Te strip, since increase of the rest length causes i t I ' ontinually to recede to greater lengths. U- , !:!) Plorrica-. Increases in rest length, as observed

I . , e and b> VA^ M.~STRIGT (1977) appear 10 occur f * , \ e a certain pa& yield stress (VAN MASTRIGT !I i 01.. 1918). They are not easily reversible. Oc- ~ a ~ i o n a l l ~ what appeared to he a very slow, partial reversal was seen during these experiments. pre-

d-oimably either viscoelastic or metabolic in origin. COOLSET et al. (1976) have suggested that ihe

<st length might decrease during active contraction. I Neither the brief contractions produced by electrical

>y the addition of acetylcholine (2 l.gg/ml) to the

e i'" I this region to carry out measurements at constant 3-

r-

./-

1 I

nor a sustained contraction produced

any significant change in rest length in i .!,ese eiwriments.

(c) Adfilivily of pa.rs¡v< alid arrive /brces. The sometric forcc and the steady passive force are dditi\e hy hypotlieris, but the passive force is

I S I 1, . _.__I_ L.-d----" (--o 5 O 0.5 1.0

I

I - F ; ~ 8 tie e//elecr of passive visscoe/astic relaxation on 6. the aclive isometric force I reruits for two srws 1- !circles and stars]. The ordinate shows Ihe i isometric force during relaxation as a percentage

of the isometric force after relaxation has I: ceased. The abscissa shows the difference between fhe passive force &ring relaxation and rhe steady passive force after reiaxaiion ! e the time dependenr part of the passive force. Positive valoes were obtained after

if t l ie a c w e and passive forces were exactly

sime-dependent part of pa5s.ve force. N

I

1- , extension. ncyaiive "dues after shortcnii>? 1 ,

-1 -~ .-.,&diti,,re the ardiiate woidd a b s y s be 700% I 3

viskaelastic in origin and in general var ie~ in time. Experiments were done to we wherher the i\iometric fmcc was merely added i o r5c time-dcpenrlcnt passive force. or whetner i f u a i alt?icd nhen thc passibe iorce \arird in rime. .Ths\c e ~ p e r i r n c n t ~ were not conducicd at large extensions, uhcrc w e n the 'steady' passive force changes with t ime hecdu% oí the gradual increme of the rect Iciigtli.

After a rapid increasz in length. the isometric force was measured just a f t a the increase, when the time dependent part u a s large and rapidly changing. and again considerably later when the time dependent part was negligible. The íormer measurement was smaller than the latter when the time-varying part of thc passive force %ill large. .vz Fig. Y. Therifore the active and passive forces were not strictly additive, altliough the lack of additiL,ity is not likely to he significant under most experimental circum- StBIICCS.

After a rapid decrease in icngtli thc viscoelastic effects are much snialler and i t was not possible to drtec! a significani aiteration in the isometric force. as sho\vn by the points a i negative values of rhe abscissa in Fig. 8.

5 Measurements o í tbe active force developed during shortening of the strip 5 . I O n r f h ,

The active force developed by a muscle depends not only on its length but also on its speed or shortening. In the past the speed of shortening was usually measured under a constant force. To reduce the length dependence and isolate the velocity dependence. tlie measurements were often made near the niaximiini of the isoinetric force: length relatioil. With bladder inuscle. difficulties arise: (a) The maximum cdnnoi easily he reached (Section

4.2) (b) If one ne;.ertheiess u,orks near the :riaximum. t h e

passkr force in large. velociiy dependen! and very sensitive to changes in lsnpth (see Fig. 51: thus. even i f the total liorce on the muscle is constant. the passite part of i t decreases rapidly as the niuscle shortens and the active force col-reqxmding.!) increases.

For these reasons the speed o f shortening is not at all constant in such experiments, and if is ditiicult to obtain reliable rriiults (GoRt>os and S t ~ t i ~ 4 3 .

1971). The belocity dependence han iherefore heen

rncasured in a different way. The bladder strip was stinxilared while ir was shortening at a constant speed. determined by the Harvard pump (see Section 2). After the force had reached a maximum the shortening was 5lOppd and the force rose further to its isunietric \due cxe ]Fig. Y). The ~timi!latiiin i v a i then %)\itched off so that the actiie force I_

i

L L , . >"",,,g ?ah ><e:iiu, ,..>:.:,.' .illLL. I &"it:

thc% i 11~a i~~ement~ anc knous. fnr a given length

< I ! th<: i\ometric IOTC; .ind the rm\i\c '~cxrcc. and t h r

US shortening. One could thus cskulaie the active and passive forces separately ~ncep t for one difiiculty: kcause of viscosiasticity, the passive force just after shortening is not equal to the steady v¿Iue. However, after shortening the active and passive forces are essentially additive (Fig. 8). There- fore it is necessary, before or after these measure- ments, to shorten the strip in (ideally) a similar manner but wittiour stimuiation, and io record the subsequent \iscuelas:ic relaxation. The steady passive force can then be corrected to yield its ~¿Iues just after shortening. so that the isometric force and the active force during shortening can be calculated. as shown in Fig. 9. Usually the viscoelasiic correction is small compared to the actibe forces. so tho1 higli aLcurac) is not needed.

In some experiments the isometric Force was nicasured again at the same length, after a few minutes, without shortening. Comparison of thc two rnea~ureriients confirmed that the nicthod of correcting Sor ihe viscoelasticity was satisfactory.

a n d rc\t lh>gti,: the .IC.iii) +\>;\e 'uric. thc \ill1i

\un, 0itliL. pau;,, and X t i l C íiucr, hl a y iw , spccd

L.L,,L,,%,3C,,L, vi AI',., ! i . , i i i i ;Y . ; i <>pis ".C?I: C'!ii,tU

out. In the first type rnearurements were made at a f iwd s/-cc<l ni \lmi~tenin?. in order tu dererminc the i.lv .rl? .... rciaiion kiween :he iiiiive force and the velocit). o í shortening. This is of imwrrance not only clinicaliy, because the length oí the biadder muscle changes so much during rnicturilion, hut also expcrinientally, because a set of nieasurenicnts on one strip IF made at various extensions and rest lengths. In the second type of experimenl the actual Forni of the ac!ive forcelvelocity relationship was determined, by measurements at diRerent speeds of shortening.

5.2 .M~<~asiw<~»ie=nrs at o single speed o / s / z o r ~ m i n ~ The strip was extended at 0.6 mm/s without

stimulation. After the time dependent part of the force had decayed, there foilowed a series of shorten- ing\ at a fixed speed. These were mode alternately w i t h stimulation (in order to observe the active force during shortening and the isometric force in the way just described. Fig. 9) and without stiniii- lation (in order to observe viscoelastic rciaxsiion), until the active force kcamc loo small to bc measured accurately. For such a series the rest length

ut chanpci o1 Iwei!i and rcst lcngth on the

,....

F,: ." 1 2 3 L o : 2 3 & 5 6 7 8

lime, m l r ,

Fig. 9 Method of measuring of the vel3cily-dependence u/ fhe actwd force. A ' The lola1 force 1s measured during simultaneour srimulation andshorfenmg at constan1 speed. at a cerlain lengfh. Shortening is $lopped and ihe issomezric force IS recorded a f rhe same length. Sl~rnulalion is stopped and lhe steady passive force FG,s, is measured a1 this length: 8 : Ideally. a precisely similar slionening wilhoor stmilation ytelds a passive uiscoeladic relax.~oori curve. wh;ch nnabies corrreclion o/ ihe p a ~ s i v e / o r e lrom its steady value fo the values appi0p~;ate to the tim mu la lion period. Thus lhe aclwe iorce F during shcrfening and the is0me:ric active force f , s o iit the same length can be calculared and compared. V: periods of shortening. S : period of sr imi la l ion Delred ciiive 8 ' . passive re1axat;on curve 8 disiiloced t o coincide w t h stimulaoon nwasureineiit n.b changes tn rime scale

L ts a m x b a i i y consimi. ~ k he strip waq then ehteinueu c.a@in and a second series of shortenings made, a? a

greater rest length, and so o n Since the viscncla5ii~ relaxations and thr iicliic íorce, w r c nhvried 31

ydjfferent lengths, thc corrections for tlic pdwic 4 , v i y e l a s t i c i t y were est imaid by interpola!ion, and

the isometric force f:,,o and the active force I-during shoncning calculated as shown in Fig. 9. The results

f'for one strip are shown as functions of its length ; I in Fig. IO. 3-

' O r P-

lenqth , inm

Fig. 70 isometric force (black symbols) and active force during shorienhg (open svmbols) at a fixed sp2ed v = 0.64 mrnls, as funclions of length for one strip. Circles, triangles. squares. invwled tnbngles = respectively first, second, third and fowth series of measurements al decreasing lengrhs. Lines linking points are drawn purely to guide lhe eye

6-

_.

... i- I- I

In order to make sense of these results, it i s I iseful to express F as a percentage of Fi,,,. Further-

more, since rizo is a function not of i but of the xtension f i - í o ) above the rest length, i t is sensible

, 133;

i Fig. 7 7 Aclive force F during shortening at a fixed speed Y = 0.76 mm/s expressed as a percenrage of the corresponding isometric force F,50, plotteo as a funclion of the steady passive force FDsc in one strip. Circles.

m d iliiidse!ies of I ~ P ~ S L I I S ~ C ~ ~ S at drciras:ng 1- 1 , l j l-~... irrip Ienghs

triangles. Souales = respectively first. secono P

io E:uJy tlic C i l i i ' o, i ,<'*," i>ii : l - - l " , ~ UT

1 &~>,,. the stead: wssive force. uhich i\ il incaiiiic nf i~-l-.l. 5eecyn. I

!rip arc iiov," lr. f ". I I . Sirnilar resdts hatc beer; ohiainsd with four other strips from pig bladders and for one human bladder strip. at speeds of shortening so that. in different strips, F/F,so ranged from 40 to 8ú"D. A s shown in Fig. I I . the values of FÍF,,, were very nearly the same in different series of shortenings, ¡.e. at different rest lerisths. In most strips some dependence of FIF,,, (ebressed as a percentage) on F,., was observed, ranging from about + 10O;</N to - 2 W % / N , with a mean of -70y;iN for the pig-bladder strips (graphical estirnaies). Since the decendence was relarively slight, and varied in sign from strip to strip, it is reasonable to take F,IF,,o as constant for a given v, independent of F,,r and of changes in the rest length.

Usually, after some hours o f measurement, inconsistent resulls began to be obtained. These were ascribed to muscle damage and no further measurements were niade.

Taken together. these results imply that, 1 0 a reasonable approximation

FÍF,," Z f X C ) . . . . . . . . (4)

wherc the function.Mu) is. for a given strip, approxi- mately independent of i and I , . Thus the velocity scaling o f the force/velocity relation is unaffected by changes oí length or rest length. In particular vmmz, the physiological maximum speed of shortening, attained when FIF,," = O. should be approximately constant. independent of length changes, for a given strip. I n fact. howe\er, we shall see that t!mnx

Fig. 12 Active force F during shortenmg ar speed v. expressedas a percentage of the corresponding isometric force F,,,. plotted as a funclion of v. Poinls show erperimenlalresults for one strip. Curve shows classical Hill equation. eqn. 5, wilh aIF,,, = 0.25 and b = 0.6 mmls. Dofted line ,s E straight line fitted by eye to the experinienlal points for which FIF,,, > 60%. irs emapolation to F i r I v = o yreid.? {he veloiciiy Panmeter Y . . wh;ch here i s equal too.7m.i i ;s

is not a good vel&ty parameter. A better parameter k proposed below: it 100 is approximately ~onstal l t , independent of kn@h change>.

5.3 7hr f o r m o,íihc aciii-e fiwceicrlociiy relaiiortship Given eqn. 4, the form o f the function f4ici can

bedetermined by measuring at different L< on one strip. Such measurements have k e n made on six strips. The most reproducible results were obtained by use o f the following method and by ensuring that the total number of stimulations of one strip did not exceed 12.

l h e strip was extended at 0 .6mmis until the paiclve force war I N. After the time depecdent part had decayed, the strip was shortened ai a given speed, with stimulation, as described in Section 5 . I . to ohserw the force during shortening and the isometric force. The whole cycle of extension and shoi-tcning with stimulation was then re,xated, with a diflereni speed of shortcriing, and so un. I-inally. a number of similar shortenings was niade at the various : ;peds, but without stimulation. i n order io correcf for the visc~elastic effects (see Fig. 9). 'The values oiF(F,,,, obtained in this way lor one strip are plotted against P in Fig. 12. The reproducibility is SatisfactoTy and the form o¡ the function f4io) (eqn. 41 can be seen.

The active iorceivelocity relationship for striated muscle is given by the aell known Him 119381 equation

(I .+olc = lF+.o- t i b

¡.e.

l F ; F , $ " + u ; t , , " w = ( I - F.fF ,,a)h. . . I S )

where u and h are parameters characteristic o f the muscle. * I t r y a is t3pically 0.25 for striated muscle. The maximum speed of shortening is attaincd wlhen F / t , , o = O and is given by rmOr = Fi,,b/o i = 4h. !ypicallyl. Thus h is a characteristic ielocity paranicter.

Eqn. 5. with e F , > = O 25. is also plotted in Fig. I? . The value of b has k e n chosen so that the experimental por-tc lie c l o y 10 the curie in the region t /ky0 > 50"". Although at tirst sight eqn. 5 i\ a reasonable f i t to the points. one difference :onsi<tent;y found is that the experimental points lie on a c u r w uith a long tail. extending to,vrrr high \pee& of shortening at !ow nonzero valucLi of t ' FT , " . Therefore rmnx. the spied of shortenine uhcri

bladder strips. A betier parameter ír* l is provided h y thc errrapoluiion to t í ,," = O of a straight line fitted IO the cxwrimsnral points in the regio:, F!l-,,,> > 50:u, as shown in Fig. I ? . J V * is compar- able. although nor identical, with the paramcler h in the Hill eqn. 5 . For fibe different strips the valua o f I .* lay w i t h i n 2jse of 0-8mmis . For a cunipleie pig bladder. where the speed of circumferential shortening is of importance, I* should be some 20xlarger (see Smion ? J . ¡.e. Iíb2Omm:s.

The principal conclusion oi this section is that the 9;-forc+elocity relationship leqn. 4 ) and the vclociiy parameter I.* describing i t are approximately constant for a given strip. independent o f changes in the length and rest length.

6 Conclusions The steady passibe force exerted by a strip o f

bladder muscle is a u d u l measure of tlie extension i I - i0 ) abovc thc mi length I,. I t is otherwise approximately indepndsni of changci in thc rest length

Thc active isometric force i ir<i which is added IO the steady passive force on maximal stimlilation is a l w to a first approximation, dependent only on 11- 1"). F,,o rises approximately linearly from zero for smal! ( l& lo ) , but approaches a maximum at large í / - l o l , where it and the steady passive force are comparable in size.

.The isometric active force arid the steady passive force are by definition additive. I f the passive force, which is ~iscoelastic. \arks in time, small departures from additivity occur.

The increases in rrsi length [hat occur under high passive forces are not easil? re\srsed. They make 1 1 difficult to observc rhc presumed maximum in the isometric forccilength relationship.

The relationship &-tween the active force F and thc sped o f shoi~tening I ' is given by

,,<, mi F.11.

where the function r; lr-> is approximately un- añected by changes in ( l L I , i snd I,. Although a decreasing function i. i t ditycn in detail from that characteristic of striated niuscls (the Hill equation:, possiI>Iy for geometricdl ,cax>ns. Neverthclesr. a velocity paraiiietcl-comi>~rab!e io [he Hill paramstcr b c3n be delined. that is approximately independent ofchanscs in the leng!h and ri-I lengh of rhe.stiili.

.' Coinbination of eqns. 8 and 9 yields

What happens during. a quick releuse depends On whether the crossbridges can exen a negative force or m i . Some ;iuthorsconcludethattheycannot IBLANGÉ an,lr) cr 'ti.. 1972). though HUXLEY (1957) stales that they im. because a quick-release curve approaches the AI.:txis shorply. This claim is not falsified hy our data (11 meansihatdir,~dAl = Ofarn,, = OinFig. S!hiit we beliwe that this can he understood by assuming

A . . . . . . (101 g(x) = ~ ~ . - - e * . hi

1;,! = ~ [ p - 8 A i L p - O h ] . ~ . . i l l 1 B

not a constant but will probably depend on

A

crosbridgcs which do not exert nqative force but do exeri force i t zero extension ícf. eqn. 101. We will thus

H~~~ A . - B n,(r) in some way. The validity oí cqn. I I can he checked by estimating h from a quick-release cuwe as

415) = o for r < o . . . . . . ( 5 , the point where FA, = O (see Fig. 4. h = 2-6mm). nex l

assume that -~ .4

estimating - from íwhere Ai = O) by inserting the I h r i n i i a quick release. the length distribiition of the R - . . crossbridges shifts lo the origin:

h - 4 ,

Fsj = ano(t! j g1.xid.y . . . . . . ( 6 )

At this stage olour argument, wecan understand why the re~ults of measurements a1 dilyerent forces (presented in Section 51 yielded a constant quotient of AF and F,,,,. Since í&i~simplyequal 10 F(rlar agiven ( r ) . ue l i d

I AF 1 c,te - FAr ~. = ~ ~~

L , A l E,l8 A1

F estimated h. arid then plotting -5 + semi-

logariihmicaliy as a function of AI. T h i s should (and does) yield a straight line.

A s a result of these calculations bared on the sliding- filaments model, and some rather restrictive assumprions, we see that the findings presented in the beginning of this Section can e.asily he explained The proportionality of stillness and force íollou~s from eqn. 7 . The dilierences in stiiiness obtained b) varying AI and ti,8g are esplained by the k t that in ;tic first type Of

A B

iooo 1 -533 ".

f' 4.

r' 1 i.

r'

U.

f.-

t: 4-

I

mcaiuremcnts eqn 1 I holdc. and in the s o n d ca.% eqn. 7.

ViIueS Thouid be correcid according to eqn. 7. and not according to cqn. I1

7 Conclusions and diwnsion The quick-re lax and quick-stretch measurements

w e performed cannot be described in terms of one discrete passive xnes elastic element. They con however be described in terms of the sliding-filaments theory. assuming that

i i ) thLserirs eiasticitv re$jdes in the crosshridses ( i i j the crosshridges cannot push, only p u l l

¡¡,I1 the leneihsolrhecrosshridgesdurin%an i s o m e i n r -action are d i s t r i h u t e d o r m i ? within a piven range. 2.

Especiallb lor the 5rsi assumption. the parameter Ii is oí crucial importance. This is the value of AI which makes tile force during a quick release zero. see eqn. i 1 In the first place. this value is independent oí the force level from which release starts. However large the COnlrdCllk force ir it can always he made exactly zero h> the same amount of release This deduction is confirmed by rhe measurements of Section 5, and is in complete contradiction io the predictions made on the basis of a discrete passive series elastic dement. Secondly. the parameter h varied from 1.2 to 5-5 mm in our me3surenicnli with an average of 2-6mm. Since o u r average strip length amounted to 27mm. we see that il quick sho:i;nin- hy about 10'; oí rhe muylle Iengtli is ai.i.c~!,x) !o icmo\r a l l tension. Tnis is a not uncommon %atlie hr smooth muscle (values found i n Iitifiaturc range ircm 5 to ?O",. M I ' R P I ~ Y í 1976)). It is houcver w r y iaíg: i n comparison with values found ¡or striated muscle. u hich range from 0.4 !O ?",, I FORD ei t i l . . I'J77: R R F S S L ~ R and CLIXC", 1974: B L . ~ P ; ~ ~ E ei .,/.. V1721. \torr uutliori thercforc conclude that ii large p i i t U S the w i e s ebiticit! 31 smooth muscie must he found ou!de thc axsshridgcs [ I ~ I ~ L L S T R ~ \ D . 1479: H . $ L F E R l .>I.. I Y ? : S i E G \ t i \ <'I u!.. 1976. S1I:Ki'Hi. iY7hl. I'ci\i.lp? a large r a i l oíthe smies n i i t iesids i n t h e rii)shridpcs. bot in ~ C I U w t h A n u m h of ci-cis<hrid-ci. Sen.:i ckisticity might h i m$tiincs be iiiiind 31, thc lilmxui~,l~~ this CN !!,c dep<rndenc: <.f i i i i fucs c m force a i d ih' othcr ohsewition< niini:rwetl in Section 6 can siill tie ,in<ii.is!<ii.r! in mii;.. th imc uu!. The oricnt:i:ion oí cell, aithir! I h C I;>> IS also relcvini in t h i , ciinnectiun. I\ I S not ccrt:iin uhrthri these arc ir: wries or lil p:mlleI I M t . R ! ~ t l \ . 19-61 ;*lllioiigh there is .ame c,,dencc I l l :* , cell i?iigii is prc,p<v!i,>n\,l 1,) tot:1! !i,>"C

Finally. measurements made at lower

ci <w rwnilniiitiiin cio ! l t!,,,, 1!1-2!I,~UC t 3 k c , pt:ii.< I t i i i l l hc C l C i l l lh31 l i l i 7 i i l

fiOully, *-&Id mcufzotía p7ltnanC o6 a e v v a k o q

not covered by the theory presented. We noted that the iorcc response both to quick relcaces and in quick stretches was always larger during the declining pari uí a contraction than during the rising part. The same eflect was found hy M E l Z i19lXI in rabhit mesoiuharium smooth muscle. The reverse oí this ellect. ¡.e. a greater stiflness in the rising phase oi contraction. was predicted by GKOOD and M A T E S I 1975) on the basis of a model with the series elasticity partially in t h . crosshridges and partially external to these. HFLLSTKAND and JOHNSTOS (1979) iound this reverse eíícct in the rabbit urinary bladder.