Comparative performance of artificial kidneys

I

C O M P A R A T I V E P E R F O R M A N C E OF

A R T I F I C I A L K I D N E Y S

PROEFSCHRIFT

TER VERKRIJGING VAN DE GRAAD VAN DCXTOR IN DE TECHNISCHE WETENSCHAPPEN AAN DE TECHNISCHE HOGESCHOOL DELFT. OP GEZAG VAN DE RECTOR MAPNIFICUS IR H R. VAN NAUTA LEMKE, HOOGLERAAR TN DE AFDELING DER ELEKTROTECHNIEK, VOOR EEN COMMISSI UIT DE SENAAT TE VERDEDIGEN OP ^ ° WOENSDAG 20 OKTOBER 1971 TE 14.00 UUR

DOOR

JAN MAARTEN KOOUMAN

NATUURKUNDIG INGENIEUR GEBOREN TE ROTTERDAM

Bi:LI01H££;<

DER

TECHHiSCHt HOGtSCHOOI

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DIT PROEFSCHRIFT IS GOEDGEKEURD DOOR DE PROMOTOR PROF.DR.IR. N.W.F. KOSSEN

Het onderzoek, dat uiteindelijk in dit proefschrift resulteerde, vormt de bijdrage van het Laboratorium voor Fysische Technologie van de Technische Hogeschool te Delft aan het onderzoek programma van de werk-groep "Rationalisering kunstnier", die door initiatieven van Dr.J.de Boer in 1968 werd opgericht. Financiële steun werd verleend door de

Gezondheidsorganisatie van het T.N.O.

Een deel van het onderzoek werd door B.Metz, D.C.van Zanten en m i j , buiten de Technische Hogeschool uitgevoerd. Door ons in te wijden in de problematiek van de hemodialyse behandeling en door te proberen ons te behoeden voor misstappen op medisch gebied, zijn wij vooral Dr.J.M. Wilmink van het Wilhelmina Gasthuis te Amsterdam en Dr.E.E.Twiss van het St. Clara Ziekenhuis te Rotterdam dank verschuldigd. De reologische experimenten werden mogelijk gemaakt door medewerking van de staf van de Hemodialyse afdeling van het Academisch Ziekenhuis Dijkzicht te Rotterdam. Dr.M.R.Esseveld van het zelfde ziekenhuis heeft ons hierbij

terzijde gestaan en ons voorgelicht over de gecompliceerde aard van de toch zeer veel voorkomende vloeistof "bloed".

Aan het onderzoek, dat op het Laboratorium voor Fysische Technologie werd uitgevoerd,hebben velen meegewerkt. Met name de studenten wil ik hier bedanken: E. Eggers H. Goslings B. Metz A.C. Pronk K. van 't Riet W.T. Slager A. Smit J.S. Stapersma B. Stork M.M. Vermeule D.C. van Zanten

ACHTERGROND EN SAMENVATTING VAM DIT ONDERZOEK

Hoewel met het onderzoek naar de technische aspecten van kunstnieren in Nederland nog slechts een pril begin is gemaakt, wordt elders en met name in de Verenigde Staten en in mindere mate ook in Groot-Brittannie en West-Duitsland reeds jarenlang intensief dergelijk onderzoek verricht. Een zeer groot aantal publicaties is hiervan het gevolg, die slechts gedeeltelijk in tijdschriften terecht kwamen, die ook door medici worden gelezen. Dit bemoeilijkt in niet geringe mate de contacten met de

medicus als aanbrenger en beoordelaar van de doelstellingen van eventu-eel te verrichten onderzoek. Uiteindelijk zijn de volgende twee problemen uitgekozen, waarop de aandacht verder werd gericht:

- Een verantwoorde vergelijking maken van de veel gebruikte kunstnier typen, om tot een keus van het meest geslaagde ontwerp te komen. Dit onderdeel van het werk zou vooral de medici van dienst moeten zijn. - Een onderzoek verrichten naar de invloed van niet-newtonse eigenschap-pen van bloed, pulserende bloedstroming en plaatselijke hoogte verschil-len langs het bloedkanaal op de stofoverdrachts theorieën, die werden ontwikkeld voor sterk geïdealiseerde kunstnier modellen. Dit onderdeel van het onderzoek zou de fysisch technologische nieuwsgierigheid moeten bevredigen. De resultaten zijn verwerkt tot een vorm die als uitgangs-punt kan dienen voor een ontwerp van een kunstnier, waarbij door optima-lisatie van stroming en stofoverdracht een meer rationele hemodialyse behandeling mogelijk zal worden.

In deel I van dit proefschrift wordt een korte inleiding tot de hemo-dialyse behandeling gegeven. Enige grootheden, die door fysiologische eisen slechts binnen zekere grenzen kunnen worden gevarieerd, worden toegelicht. Tevens wordt een overzicht gegeven van de verschillende be-schrijvingswijzen van het stof overdrachts proces in de kunstnier.

In deel II wordt een keus gemaakt uit de momenteel veel gebruikte platen en spiraalvormige kunstnier typen. Gebruik makend van literatuur gegevens, die waar nodig werden aangevuld of gecontroleerd met eigen metingen, worden vergelijkende waarden gegeven van de stofoverdrachts grootheden, drukval karakteristieken en volumina van de kunstnieren. De hoeveelheden bloed, die na spoeling met een zout oplossing in de kunstnier achter blijven, worden bepaald uit de verblijfsduur karakteristieken die voor elke kunstnier werden gemeten. Binnen het raamwerk van de fysiologische eisen, die voor de verschillende grootheden slechts een beperkt variatie toestaan, kan het meest geschikte kunstnier type worden geselecteerd.

In deel III wordt de stofoverdrachts theorie uitgewerkt voor drie geïde-aliseerde kunstnier modellen met bloed compartimenten bestaande uit respectivelijk een evenwijdige platen kanaal, een rechthoekig kanaal of een kanaal met ronde doorsnede (de zgn. capillaire kunstnier).

- Voor newtonse stroming van bloed door de evenwijdige platen of capil-laire kunstnier wordt aangetoond door scheiden van de totale Sherwood getallen in een bijdrage van de wand van het bloedkanaal (dus samengeno-men voor membraan en dialysaat) en in een bijdrage van het bloed, dat de

invloed van het wand Sherwood getal op het bloed Sherwood getal klein is. Het blijkt dat de verhouding van de bloed Sherwood getallen bij respectievelijk een bepaalde wand weerstand en bij een verwaarloosbare wand weerstand (randvoorwaarde met constante concentratie) vrijwel onafhankelijk is van de plaats langs het bloed kanaal. De correctie van de verhouding van deze bloed Sherwood getallen wordt gegeven als functie van het Sherwood getal van de wand. Voor veel toepassingen kan de correctie echter worden verwaarloosd.

Voor een kunstnier met rechthoekige doorsnede van het bloed kanaal worden de Sherwood getallen van het bloed vergeleken met die van de evenwijdige platen kunstnier. Grafisch kan de correctie als functie van hoogte/breedte verhouding worden bepaald.

- De invloed van niet-newtonse eigenschappen van bloed is nagegaan. Daartoe werden eerst enige viscositeitsbepalingen verricht met bloed afkomstig van gezonde donors en van kunstnier patiënten. Het bleek dat een reologisch model voor bloed volgens Casson tot een betere beschrij-ving van het stromingsgedrag bij lage afschuif spanningen moet leiden dan het newtonse model. De stofoverdrachts theorie wordt gecorigeerd voor deze snelheidsverdeling. Het effect van de niet-newtonse eigen-schappen op de stofoverdrachts theorie blijkt echter klein te zijn. - Het effect van pulserende bloed stroming op de snelheidsverdeling in het bloed kanaal is bepaald uit vergelijkende verblijfsduur metingen. De beïnvloeding blijkt verwaarloosbaar klein te zijn.

- Vermindering van de totale stofoverdrachts weerstand die een gevolg kan zijn van een verbeterde membraan-ondersteunings constructie in het dialysaat compartiment, is kwalitatief bepaald uit verblijfsduur metingen en kwantitatief door meting van de stofoverdrachts weerstand in een kunstnier bestaande uit twee identieke dialysaat compartimenten geschei-den door een membraan. Het blijkt dat gebruik van pyramide ondersteunin-gen of plastic gaas in plaats van de driehoekige kanalen als veelal toegepast in de platen kunstnieren tot een aanzienlijk verminderde stof-overdrachts weerstand kan leiden bij beperkte toename van de drukval over het dialysaat compartiment.

In het laatste deel van dit proefschrift wordt de stofoverdrachts theorie die ontwikkeld werd voor geïdealiseerde modellen van kunstnieren, toe-gepast op enkele veel gebruikte platen en spiraalvormige kunstnieren. - Het blijkt dan dat de invloed van de niet-newtonse eigenschappen van het bloed kan worden verwaarloosd bij deze kunstnieren. Het effect zal

echter van meer belang worden bij de sterk verkleinde kunstnieren, die momenteel in diverse laboratoria worden ontwikkeld en beproefd.

- De invloed van de hoogte verschillen in het bloed compartiment van deze kunstnieren op de stofoverdrachts efficiëntie is geschat.

Voor de platen kunstnieren blijkt dat deze variaties, veroozaakt door een niet geheel verantwoorde mechanische constructie van de kunstnier, de oorzaak kunnen zijn van de wisselende stofoverdracht, die veel wordt gevonden bij herhaald gebruik van deze kunstnieren.

Bij de spiraalvormige kunstnieren blijkt de experimenteel bepaalde stof-overdrachts weerstand aanzienlijk lager te zijn dan de berekende. Dit is een gevolg van het plastic gaas dat als membraan ondersteuning wordt gebruikt maar dat ook een plaatselijk vervormen van het bloed comparti-ment en daardoor niet laminaire stromings condities veroorzaakt. Tenslotte kan worden geconcludeerd, dat de wisselende condities die in

alle onderzochte kunstnieren werden gevonden, een diepgaander studie van de stofoverdrachts theorie overbodig maakt.

SUMMARY

The research described in this dissertation has been performed to enable the selection of the most satisfactory dialyser design out of the vast field of commonly used apparatus. Furthermore the effect of conditions such as non-Newtonian and/or pulsatile blood flow and varying geometry of the blood channel (either caused intentionally or due to practical design limitations) on the mass-transfer theory as set forward by many a chemical engineer for idealized dialyser models, has been determined. In part I of this dissertation a short introduction to the haemodialysis procedure is given. The physiological restrictions set to the treatment are indicated. The concepts commonly used to describe the mass-transfer process in the dialysers are summarized.

In part II a number of dialysers as currently used, is selected. From literature data extended where necessary with own measurements, a com-parison is made of the mass-transfer efficiency, the pressure-flow characteristic and the volume of these dialysers. To detexrmine compara-tive blood rests in the dialysers at the end of the treatment, after the perfusion with a salt solution, the residence-time distributions are used. After allowing for the physiological limitations set to the treat-ment, the most satisfactory dialyser design currently available can be

selected.

In part III the mass-transfer theory is given for three idealized models of actual dialyser designs: The parallel-plate, the rectangular

and the capillary dialysers. Some experiments are described,performed to test the assumptions behind these models.

- For Newtonian blood flow in parallel-plate and capillary dialysers it is shown by separating the total Sherwood numbers into a blood and wall Sherwood number,that the influence of the wall resistance on the blood Sherwood number is small. The maximum effect can be estimated from the solution obtained for constant mass-flux boundary condition. For the ratio of the blood Sherwood numbers, calculated at respectively constant wall resistance and constant concentration boundary condition, it is found that the influence of the dimensionless length of the dialyser is also small and can in fact often be neglected. Correlations are pre-sented in section H I E to determine this ratio as function of wall Sherwood number. As the determination of the blood Sherwood number is generally followed by the calculation of the total Sherwood number, the effect of wall resistance on the blood Sherwood number becomes even less important. In fact for many design purposes the total Sherwood numbers can be calculated by simply combining the wall Sherwood number with the blood Sherwood numbers for constant concentration boundary condition. For a rectangular dialyser the influence of height/width ratio on the solution obtained for a parallel-plate dialyser is determined; a correc-tion graph is provided.

- The influence of non-Newtonian properties of the blood on the mass-transfer theory given for Newtonian blood flow is investigated. From experiments with blood it is concluded that a Cassonian model for the

rheological behaviour of blood will be an improved description at low values of the shear stress at the wall. The influence of shear stress on the mass-transfer theory given for Newtonian blood flow can be deter-mined graphically, as shown in section IIIC, but appears to be small. - The effect of pulsatile blood flow has been determined experimentally from the residence-time distributions, and appears to be negligible. - The improvements to be obtained from different membrane support systems

in the dialysate compartments have been determined from mass-transfer measurements and from residence-time distributions. It is found that the pyramid supports and the plastic webbing supports are most promising, as the dialysate mass-transfer resistance can be decreased considerably at a limited increase in pressure drop.

In the final part of this dissertation the mass-transfer theory given in part III for simplified models, is applied to the actual dialysers as selected for the comparison in part II.

- It appears that the influence of the non-Newtonian properties of blood can be neglected for these dialysers. However the effect of non-Newtonian blood properties will become more important for the miniaturized parallel-plate and capillary dialysers which are currently being developed in various research centres.

- The ipfluence of variations in the height of the blood compartment, as found in actual dialysers, on the mass-transfer efficiency is estimated. For the commonly used parallel-plate dialysers it can be concluded that these variations, caused by the mechanical design, account partially for the badly reproducing mass-transfer efficiency. For the coil dialysers a considerably lower mass-transfer resistance than

calculated with the theory based on average blood channel height is found, which is caused by the deformation of the blood channel by the membrane

support system.

Finally it is concluded that the conditions found in the actual dialysers do not warrant the sophisticated theories brought forward by many

CONTENTS

SAMENVATTING

SUMMARY

INTRODUCTION

A. MOTIVATION AND PURPOSE OF THIS STUDY 1 B. ORGANIZATION OF THIS DISSERTATION 1

C. NOTATION 2 D. LITERATURE SEARCH 2

PART I AN EVALUATION OF SOME ASPECTS OF THE HAEMODIALYSIS TREATMENT

lA. INTRODUCTION 3 IB. PHYSIOLOGICAL ASPECTS OF THE HAEMODIALYSIS

TREATMENT

1. The function of natural and artificial kidney 3

2. The haemodialysis procedure 5 3. Interaction of dialysis with body processes 6

IC. THE MASS-TRANSFER PROCESS IN ARTIFICIAL KIDNEYS

1. Introduction 9 2. The local description of the mass-transfer

process in the dialyser 11 3. The overall description of the mass-transfer

process in the dialyser 12 4. The mass-transfer process in artificial

kidneys 15 ID. CONCLUSIONS FOR FURTHER RESEARCH IS

PART II THE OVERALL PERFORMANCE OF ARTIFICIAL KIDNEYS

H A . INTRODUCTION 21 IIB. A SURVEY OF DIALYSER DESIGNS

1. Constructional details 22 2. Dialysers selected for the comparison 24

l i e . M A S S - T R A N S F E R C H A R A C T E R I S T I C S O F D I A L Y S E R S

1. The solute transfer rate 26 2. The ultrafiltration rate 27 IID. PERFUSION CHARACTERISTICS OF DIALYSERS

1. P r e s s u r e - f l o w c h a r a c t e r i s t i c s of the b l o o d c o m p a r t m e n t

2. F l u i d d i s t r i b u t i o n in the d i a l y s e r 3. V o l u m e of t h e b l o o d c o m p a r t m e n t 4. Blood loss in the dialyser

28 29 31 32 H E . CONCLUSIONS 1. T h e o v e r a l l p e r f o r m a n c e o f d i f f e r e n t d i a l y s e r d e s i g n s 33 2. The comparative performance of artificial

kidneys 35

PART III ASPECTS OF THE LOCAL MASS-TRANSFER PROCESS IN DIALYSERS

IIIA. INTRODUCTION 37

IIIB. THE MASS-TRANSFER PROCESS FOR NEWTONIAN BLOOD FLOW

1. Introduction and literature survey 39 2. T h e p a r a l l e l - p l a t e d i a l y s e r 41 3. The rectangular dialyser 52 4. The capillary dialyser 53 IIIC. THE MASS-TRANSFER PROCESS FOR CASSONIAN BLOOD

FLOW

1. I n t r o d u c t i o n

2. T h e r h e o l o g y o f b l o o d

3. T h e f l o w of a C a s s o n i a n f l u i d b e t w e e n p a r a l l e l p l a t e s and through c a p i l l a r i e s 4. The mass transfer from a Cassonian fluid

for the parallel-plate and the capillary dialyser

56 56 62

66

H I D . EXPERIMENTAL INVESTIGATION OF THE MASS-TRANSFER PROCESS

I . Introduction 73 2. D e t a i l s of e x p e r i m e n t a l m e t h o d a n d set-up 7 4

3. T h e m e m b r a n e p e r m e a b i l i t y 7 7 4. The mass transfer in the dialysate

compartment 79 5. The mass transfer in the blood compartment 82

H I E . CONCLUSIONS

1. C o n c l u s i o n s f r o m m a s s - t r a n s f e r theory 8 5 2 . C o n c l u s i o n s f r o m m a s s - t r a n s f e r e x p e r i m e n t s 8 9

3. General comments

FINAL CONSIDERATIONS AND GENERAL CONCLUSIONS

90

A, APPLICATION OF THE LOCAL MASS-TRANSFER THEORY TO ACTUAL DIALYSERS

1. Conclusions from the flow conditions in

the dialysers 91 2. Conclusions from the mass-transfer

conditions in the dialysers 92

B. GENERAL CONCLUSIONS 95

APPENDICES

App.A. DETAILS OF THE DIALYSERS AND THEIR PERFORMANCE

(on micro-fiche) 97 App.B. RESIDENCE-TIME DISTRIBUTIONS IN THE DIALYSERS

1. Introduction 97 2. Experimental method 98 3. Interpretation of the measurements 98

App.C. DEVELOPED MASS TRANSFER FOR A CASSONIAN FLUID

1. Constant concentration boundary condition 102 2. Constant mass-flux boundary condition 107

REFERENCES ₁₁₁

INTRODUCTION

A. MOTIVATION AND PURPOSE OF THIS STUDY

The early developments of artificial kidneys by medical practitioners was essentially empirical and often haphazard. As a mass-transfer separation process haemodialysis is a natural candidate for the appli-cation of chemical engineering principles and analysis. After incidental attempts by Wolf(26) and Rerikin (27) it has attracted from about 1957 onwards general interest of chemical engineers who have since then con-tributed significantly to the understanding of the mass-transfer process within the artificial kidney. However the theory of mass transfer can only be applied to geometrically idealized haemodialysers, which have not yet been constructed. The more immediate problem for the physician,

the selection of the best artificial kidney out of a vast field of non-ideal apparatus, has not been solved. It was felt that the study as pre-sented in this dissertation should have a twofold aim:

- Comparison of the performance of different existing artificial kidneys and selection of the most satisfactory one. Results should be of immediate value to the medical profession.

- Investigation of the mass-transfer process in the artificial kidney, as is being done in numerous centres outside the Netherlands as well, but with special attention to the non-ideal conditions in the apparatus.

B. ORGANIZATION OF THIS DISSERTATION

This dissertation is divided into three major parts and is concluded with a discussion of the results obtained.

Each of these parts is written as a self-contained entity, where certain aspects are introduced and evaluated . Conclusions which can be drawn within the context of each part will be given.

In part I an introduction to and an evaluation of various aspects of the haemodialysis treatment is given.

In part II the efficiency and the limitations, resulting from the com-plicated mechanical design of some commonly used artificial kidneys are investigated.

Part H I of this study is concerned with a strict description of the mass-transfer process under certain non-ideal conditions.

The scope of this study for artificial kidney design is outlined in the general conclusions given at the end of this dissertation.

The first two parts of this dissertation are aimed at both physicians and chemical engineers. To facilitate the readability of these parts for physicians "clinical units" are used for the quantitative description of the processes. The third part is mainly aimed at chemical engineers and S.I. units could be used.

C. NOTATION

The notation to describe the dialysis process is that conventionally used in haemodialysis applications. It is consequently different from the one used by chemical engineers to describe their unit operation "dialysis".

D. LITERATURE SEARCH

For general information on the progress made in haemodialysis treatment the "Artificial Kidney Bibliography" proved to be extremely useful. This is published by

National Institute of Arthritis and Metabolic Diseases Artificial Kidney Program, U.S. Department of Health Education and Welfare,

Bethesda, Maryland.

Although many articles referred to in this publication can also be found in the "Index Medicus" (also published by the U.S. Department of Health, Education and Welfare), the lists of yearly progress reports describing the research work at universities and industrial laboratories in the United States, are extremely valuable and should be essential reading for any one planning to join the queue of research workers in this field. For systematic search of published work the Science Citation Index

(Institute of Scientific Information, Philadelphia, U.S.A.) was used, which covers both medical and chemical engineering journals.

PART I AN EVALUATION OF SOME ASPECTS OF THE HAEMODIALYSIS TREATMENT

lA. INTRODUCTION

To understand the requirements which an artificial kidney should meet some knowledge of what functions the natural kidney performs is nec-essary. These functions and the extent to which an artificial kidney can replace them are discussed in section IB. In this section some physiological aspects of the haemodialysis procedure are also summa-rized. In particular the interaction with the circulatory system of the body will be discussed.

The different concepts which are used to describe the mass-transfer process quantitatively will be recapitulated in section IC.

In section ID problems which remain to be solved are mentioned. An outline of the work undertaken to solve some of these problems is given as well; the outcome is reported in part II and H I of this dissertation.

A list of selected additional references on the different subjects discussed is given at the end of this dissertation.

IB. PHYSIOLOGICAL ASPECTS OF THE HAEMODIALYSIS TREATMENT

IB.l. The function of natural and artificial kidney.

Pvinoiple of the kidney.

The kidney is in combination with the other excretory organs responsible for maintaining the constancy of the internal environment of the body. It has the following functions

a. A waste excretion function: metabolic non-volatile products are removed from the blood, hence from the body as a whole. These products include e.g. water produced by oxidation processes, urea and other nitrogenous material from the various protein and nucleic acid metab-olic cycles, pigment derivatives, drugs, etc.

b. A regulating function: the pH and electrolyte balance of the body fluids is regulated by selective processes within the kidney.

c. A hormone producing function: the healthy kidney produces a hormone renin, which exerts effects upon extra-cellular volume and blood pressure and it produces or activates the production of another hormone erythropoeisis, which regulates the production of red blood cells in the bone marrow.

To perform the variety of functions described above the kidney has an aggregate of about 10" nephrons, each capable of producing urine by itself. A schematic diagram of a single nephron is shown in figure I-I.

«fftrtnt arUrxMc glomcrutu» 'jS aH«r«nt orUriol* ) v«in ^.^^^ Bowman 's capsule / glomtrulor m«mbron« •J- /'\-'-~-~^ proximol tubult ^p?^l \ /^^^^-^--^ dpstfll tubult

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Blood enters the glome-rulus of the nephron through the arteriole, then flows through the peritubular capillaries surrounding the tubules of the nephron and final-ly back to the vein. The glomerulus is a network of parallel capillaries encased in the Bowman's capsule. Ultrafiltration occurs across these cap-illaries due to the dif-ference in the hydrostat-ic pressure in the arte-riole and the sum of hydrostatic and osmotic pressure in the proximal tubule. In this ultra-filtrate only lower molecule weights are collected, the largest mole-cules such as proteins are retained in the blood. The ultrafiltrate from each channel then passes through a tubular passage, the loop of Henle, and comes via cells lining the tubules into contact with the blood flowing through the peritubular capillaries. During passage through these capillaries and tubules selective reabsorption and secre-tion takes place involving both passive and active transport, the latter occuring against the concentration gradient. Most of the water ultra-filtrated in the proximal tube is transported back to the blood again. Finally the residue of the ultrafiltrate, the urine, passes from the kidney to the bladder.

F I G U I E 1 - 1 : THE ll(l>l<ltOH.

Prinoiple of the artificial kidney.

The dialysis treatment at present involves directing a fraction of the total circulatory blood flow from the patient to an apparatus, the dia-lyser, containing a semi-permeable membrane which separates the blood from a dilute aqueous solution, the dialysate. This procedure is known as haemodialysis and it is used intermittently for periods of about

10-12 hours every 2-3 days or longer depending on the clinical status of the patient.

The processes occuring within the dialyser are

a. Waste excretion: metabolic products are removed from the blood by using dialysate compositions from which urea, creatinine, etc. are absent. Surplus water is removed by ultrafiltration due to the pressure difference between blood and dialysate fluid. Dextrose is used to adjust the osmolarity of the dialysate.

b. Regulation by equiliberation of blood and dialysate composition: the sodium and potassium content of the dialysis fluid is maintained just below normal plasma level to facilitate control of the blood

pressure. Low levels of calcium and magnesium are used to hold acceptable ionic plasma levels, see table I-l .

TABLE I - l : THE COMPOSITION OF Concentration mEq/1 calcium magnesium potassium sodium c h l o r i d e a c e t a t e u r e a c r e a t i n i n e p r o t e i n s glucose

DIALYSATE COHPAHEn WITH BLOOD PLASMA ( S ) , ( h } , ( 1 1 ) .

D i a l y s a t e 2 . 5 1.5 2 . 0 132 100 35 Blood plasma 5 3 4 142 103 1.0 0 . 2 1.2 5 . 6

Comparison of natural and artificial kidney.

From an engineering point of view the separation process in the natural kidney is extremely sophisticated compared with that of the artificial kidney. The essential difference is the capability of the cells in the tubules to recognize solutes required by the body and to transfer them back into the blood stream. The rate at which water and solutes enter the extra-cellular compartments of the body will vary with changes in dietary intake and with alterations in the rates of various metabolic processes. The kidney by means of built-in feedback loops compensates for these variations by regulating the ultrafiltrate rate with the variable permeability of the glomerular nembrane. The artificial kidneys used at present supplement or replace to some extent the excretory and regulatory functions. The regulation according to food intake and the hormone production is not replaced in any way. The feedback loops of the natural kidney are to some extent replaced by the physician who from observation of long term trends in the patient has a form of manual control, with diet and intensity of haemodialysis treatment as the reg-ulating mechanism.

IB.2. The haemodialysis procedure.

In conventional artificial kidney systems the patient's blood flows from the connection placed in a peripheral artery of the arm or leg through suitable plastic tubing to the dialyser as shown in figure 1-2. To prevent clotting of the blood an anti-coagulant, heparin, is injected into the blood circuit. The blood is led into the dialyser where trans-port of solutes across a semi-permeable cellophane membrane takes place from the blood to the dialysate. The dialysed blood is returned via a bubble catcher to the connection in the vein. The heparin can be neutral-ized by injection of protamine. The connections of the extracorporeal blood circuit to the circulatory system of the patient are made either through cannulas permanently implanted in artery and vein or by vene-puncture of artery and vein. In the latter case artery and vein are connected with a subcutaneous shunt ^^(hich causes the vein to extend.

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Blood flow rates of around 150-350 ml/min can be ob-tained depending on the design of the dialyser and shunt. A blood pump is re-quired to achieve adequate flows during short dialysis periods with a high resis-tance apparatus. The pump may be omitted if dialysis

time is prolonged and a low resistance dialyser with multiple parallel paths is used. The dia-lysate is a buffered elec-trolyte solution containing approximately physiological concentrations of a number of important diffusible solutes. It is prepared either manually in a rap-idly recirculating batch of large volume (150 litres) or in case of single-pass systems, as shown in fig-ure 1-2, by diluting with proportioning pumps a con-centrated dialysate fluid with filtered tap water. In the latter case dialysate flow is reduced to about 500 ml/min to avoid fluid wastage. In centres where many patients are treated simultaneously^centralized systems for preparation and distribution of dialysate are used. The dialysate is heated to 38°C, monitored and led to the di'alyser. The concentration and the temperature of the dialysate is measured with monitors. In the dialysate leaving the dialyser, another monitor registers a blood leak caused by incidental membrane ruptures.

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FIGURE 1 - 2 ; THE A R T I F I C I A L KIOHEY SYSTEM.

IB.3. Interaction of dialysis with body processes.

By selecting an appropriate membrane and increasing the membrane area any component can be removed from the blood stream. There are however physiological limitations to the accompanying increase in dialyser volume and efficiency: It should be realized that the patient with the disease uraemia is in an equilibrium condition. This equilibrium is disturbed by the dialysis procedure, where part of the circulating blood is removed from the body dialysed and returned with a different composition. The fluid-dynamic and mass-transfer conditions in the dialyser should be chosen in such a way that the equilibrium is not too severely disturbed. The physiological considerations behind this choice will be listed in the following paragraphs.

Fluid-dynamia conditions.

There is a limit to the amount of blood which can be removed from the circulatory system as homoeostatic mechanisms will fail to maintain blood pressure and circulatory performance. The maximum flow rate which can be obtained is determined by internal conditions of the circulatory system and external conditions, which depend on the artificial kidney system used.

Due to fragility, blood will be damaged during the transport through the extracorporeal circuit. Reactions of blood molecules with foreign sur-faces will cause denaturation and clotting of the blood. High shear rates in the dialyser and especially in the blood pump will cause the destruc-tion of blood cells. This destructive process (haemolysis) has been

extensively investigated by Bernstein and Blackshear (14), (IS). It appears

to be of minor importance in the dialysers and blood pumps currently used. To conclude it should be emphasized that no firm guideline for the flow conditions in the dialyser can be given, but the following conditions should be fulfilled:

- Blood volume which is circulating outside the body should be less than 500 ml.

- Blood flow rate should be less than 350 ml/min.

- Turbulence, stagnation and boundary layer separation should be avoided in the external blood circuit. (In all dialysers flow con-ditions in the blood compartment with Reynolds number considerably less than 100 are found).

- Clotting of blood on the surfaces of the external circuit should be prevented (for example, by adding large doses of heparin).

Mass-transfer conditions.

The efficiency of a dialyser in removing solutes such as urea from the blood stream should not be increased beyond certain limits: Too rapid removal of urea causes various physiological and mental disturbances which have been related to the mechanism controlling the concentration gradient between the brain and the surrounding environment. The diffusion rate of urea out of the central nervous system is slow compared with that of the adjacent parts of the body. The osmotic pressure gradient causes excessive water transport into the central nervous system to maintain equilibrium and causes an unfavourable condition in the patient known as the "desequilibrium syndrome".In general with present dialyser efficiency and by choosing blood flow rates below 250 ml/min this situ-ation will not be reached.

The general question, which solutes should be removed and which should be retained, how much of each is to be removed and how fast, and physio-logical effects of intermittent removal, is still far from being answered. It is customary to compare the performance of different dialyser designs on their efficiency in removing urea from the blood stream through the dialyser. However urea is the symbolic rather than the demonstrable con-trolling solute. Other substances, such as creatinine or even larger molecules,are less easily excreted. Another complication, as mentioned

above for urea, is that although the solutes might be removed from the blood stream they can still be retained in other parts of the body. To illustrate this a simplified diagram of the human body is given in figure I-3a.

three pool model; b. one poot model :

r'

I

T T

F I G U R E I-Ï: S I M P L I F I E D M O D E L S OF THE D I S T R I B U T I O N OF THE B O D Y F L U I D S .

The body fluids can be divided into three broad categories: intracellular, interstitial + transcellular and blood plasma. These fluids are normally distributed throughout the body in a heterogeneous manner, but the concept of three separate homogeneous pools is more convenient from the math-ematical point of view. Production of the solute is assumed to take place only in the intracellular compartment. The solute is then transported by diffusion through biological membranes into the interstitial pool and then transferred to the blood plasma. Via the blood plasma the solute comes into contact with the dialyser where it can be removed from the blood circulation.

The solute excretion from such a system with internal and external mass-transfer resistances has been extensively investigated by Vadot (16)

and others (17) to (19). Their results showed that for many solutes even more simplified models can be used e.g. as shown in figure I-3b. One mixed blood reservoir is assumed into which a supply of solutes is led.

Calculation of the actual solute concentration changes in the body caused by the dialysis procedure is complicated, as transport rates between the different compartments are not always known.

During each dialysis treatment water should be removed from the patient as well. The amount which has to be removed varies: From observation of the patient's weight over longer periods of treatment an average loss of approximately 1.5 to 3 kg per week was found. For twice weekly treatments of ten hours each this would mean a minimum ultrafiltration rate of 75 to 150 ml/hour. In some dialysis centres the ultrafiltration rate is mainly limited to the last three hours of the treatment. This would make a minimum ultrafiltration rate of 200 to 300 ml/hour essential.

Additional conditions.

At each dialysis treatment a certain amount of blood is lost - when connecting the patient to the artificial kidney;

- in the blood samples, necessary to determine the composition of the dialysed blood;

- at the end of the treatment during the disconnection of the patient, and in the dialyser, blood lines and bubble trap.

Membrane ruptures can cause additional but occasional severe blood losses. The blood loss occuring when connecting and disconnecting the patient and when taking blood samples is entirely related to the efficiency of the medical staff. The other blood losses depend on the design of the dialyser and blood lines. The accumulative effect of the blood losses for chronic kidney patients can be severe. The hormone which activates the blood production is not released and regular transfusions have to be given to compensate for these losses. The blood losses should there-fore be kept to a minimum.

An additional hazard for the patient is a serum hepatitis infection. Due to the repeated access to the circulatory system of the patient, the medical staff runs the risk of contacting the infection as well by accidentally handling the blood. Disposable dialysers would diminish this risk.

IC. THE MASS-TRANSFER PROCESS IN ARTIFICIAL KIDNEYS

IC.l. Introduction.

The actual mass-transfer rate which can be obtained with different artificial kidney systems depends on the construction of the dialyser and on the way the dialyser is connected to the dialysate reservoir. A dialyser is shox^m schematically in figure I-4a. Two fluids, the blood and the dialysate, are separated by a membrane. Depending on the con-struction of the artificial kidney system as a whole,the flow of dialy-sate can be in co- or countercurrent direction with the blood flow, or the dialysate can be considered to be well mixed during its passage through the dialyser. In these conventional dialysers the driving force for the transport of solutes through the semi-permeable membrane is the concentration difference between the blood and the dialysate stream. This concentration difference changes continuously during the passage of the fluids through the dialyser. The mass transport from blood to dialysate depends furthermore on the resistance against solute transport from the one flow to the other. This mass-transfer resistance is a function of membrane properties, membrane area, fluid channel geometry and local

fluid velocities.

Due to ultrafiltration in the dialyser the in- and outgoing blood or dia-lysate flows will not remain equal. With this water transport a certain amount of solute will be taken along. The total effect of ultrafiltration on the mass-transfer process has been estimated and is under normal con-ditions less than 3%. In the further description it will be assumed that the contribution of ultrafiltration to the mass transport is negligible and that blood and dialysate flow remain constant during transport through

FIGURE ! - > » : MASS SAIAIICE OVER THE DIALYSER, OVERALL APPROACH:

dialysatg in : ^ , C. dialysata out ^^ . C^^

FIGURE l-fcb: MASS BALANCE OVER THE DIALYSER, LOCAL

the dialyser. However the amount of water which is removed during the total dialysis treatment is extremely important as the careful dieting of chronic kidney patients and the remaining water excretion functions through transpiration and lungs, cannot fully compensate for the absence of the water excretion function of the kidney.

The mass-transfer process in the dialyser can now be described in two different ways, based upon local and overall approach:

- For the local description the transfer process at a certain location along the blood channel is considered first, as shown in figure I-4b. The change in concentration difference between blood and dialysate over this element of the dialyser can be calculated, within certain restricting conditions, from fluid dynamics at this point along the channel. From these local concentration differences the concentrations of the outgoing fluids are calculated.

For comparison of dialysers now regularly used this method is only of limited value. The integration step to calculate the total amount of solute transported through the membrane can not accurately be made: From measurements of volume and from pressure-flow characteristics only average values of channel height can be determined; the variation along the channels cannot be measured. Furthermore some of the

assumptions made to calculate the local mass-transfer coefficients from fluid-dynamic conditions need verification. For the designer however, these local mass-transfer calculations are extremely impor-tant as they enable him to determine for idealized models of haemo-dialysers, the optimal channel height and the improvement to be

ob-tained from different membranes.

- For the overall description, which is essentially empirical, less details have to be considered. Concentrations in the in- and out-going fluids are measured for each dialyser. By comparing the amounts of material removed with different dialysers the most efficient design can be selected. Unfortunately it is not apparent from the overall description how the efficiency of a given dialyser depends on geometry, fluid velocities and membrane properties.

In the following paragraphs of this section the local and overall mass-transfer process in the dialyser will be considered in more detail to illustrate the differences in approach.

In paragraph IC.4 the actual dialysis function of the artificial kidney system as a whole, consisting of dialyser and dialysate reservoir, will be examined to determine the effect of different blood and dialysate connections on the efficiency of the dialyser.

IC.2. The local description of the mass-transfer process in the dialyser. In figure I-4b this transport process has been shown schematically. The mass transfer per unit area of a solute from the blood stream to the

dialysate at a location x along the channel is formally described as a

product of two quantities, the local mass-transfer coefficient k and the

local concentration difference.

For the local transport density (|i^' through a unit area of the membrane

a total local mass-transfer coefficient k^Q-j^ is c'efined, based upon the

difference in average concentration of blood <cfc> and dialysate <C(^>.

't'm ^ '«tot (<ob> - <o^>) (I-I)

The reciprocal value of this mass-transfer coefficient fe^ot is a measure for the resistance against mass transfer between blood and dialysate. This resistance is caused by the limited permeation of the solute through the membrane and by diffusional resistance in blood and dialysate fluids. To compare the contributions of these three layers additional local transfer coefficients are defined. For the liquid layers the local mass-transfer coefficient is based upon the difference between the average

concentration <a> and the concentration at the membrane surface Cy,

for blood:

for dialysate:

K - ^d '°wd - <v^ ^"-'^^

The complicated physical process of intra-membrane transport of the sol-ute can be adequately described by application of irreversible thermody-namics and defining phenomenological quantities to characterize the system. However for haemodialysis applications, where balanced osmotic pressures and zero (volume) flow through the membrane are found, these general equations can be considerably reduced to

An alternative expression results from the application of Fick's law:

where U ^ is the diffusion coefficient of membrane-solute system based

upon intra-membrane concentrations c^}^ and c^^, and tm is the thickness

of the membrane.

By using the solute distribution coefficient m between membrane substance

and solute, defined with respectively c^j, = m a^^ and c^i - m c^j,

equation (I-5a) can be written analogous to equation (1-4) as

^^meff^^rn^ ^'^b ' <^wd> (I-5b)

A." —

Eliminating the concentrations from equations (I-l) to (1-5) gives for the relationship between total and individual coefficients:

1__ _ 1 ^m 7

T<tot = fefc ^ IDmeff ' "^T ^'^^

total local local blood membrane local dialysate resistance resistance resistance resistance

The membrane resistance tm/IUmeff ^^''^ ^^ written alternatively as

At every location along the channel fc^ot now has to be calculated from the three individual coefficients before the total amount of material removed from the blood stream can be determined: The membrane permeability is known for a number of solute-membrane systems. The local coefficients of blood and dialysate are not constant along the channel and only for a very limited number of cases their magnitude as a function of location along the channel is known. These solutions will be more extensively discussed in part III. They lead to the determination of a total overall

mass-transfer coefficient ^^tot- "^^^ total amount of solute '^rn removed

from the blood stream can be determined with

V = Hot ^ ''''log <I-7)

where ha%Qq is the logarithmic averaged concentration difference between

blood and dialysate compartment and A the total membrane area of the

dialyser.

However t h e n o n - i d e a l c o n d i t i o n s , such as non-Newtonijin blood flow and varying dimensions along the blood and dialysate channels, which are found in all dialysers now regularly used, make the integration of the total local mass-transfer coefficient impossible for other than ideal situations.

IC.3. The overall description of the mass-transfer process in the dialyser. A mass balance over the dialyser, as shown in figure I-4a, for the transfer

of an amount ^^n °^ ^ solute from the blood stream to the dialysate will

give

Analogous to equation (1-7) the mass-tranfer rate is now described with

<'<-tot^ = (1-9)

A l^aiog

where <K-t^Q-f> is the average total overall mass-transfer coefficient,

de-termined under non-ideal conditions, and A is the total membrane area of

the dialyser. For ideal conditions the two mass-transfer coefficients <K-f^Q-f^> and K^^j^ will become equal.

In medical articles a different quantity, the dialysance, is used to

describe the mass-transfer rate. In 1951 Wolf^in his pioneering studies

of the physiology of the artificial kidney (28), rather wishfully tried

to treat the mass-transfer process in the artificial kidney as similar to that in the natural kidney. In the latter case the separation process

is described with the clearance CI, which is the hypothetical blood flow

rate from which the solute is completely removed:

CI = *^ fcfc^ - a^^)/(c^.) (I-10)

Wolf extended this definition, as he found experimentally that the rate

of excretion was proportional to the concentration difference between blood entering the dialyser and dialysate. The blood compartment of the artificial kidney used in his experiments was suspended in a mixed

dia-lysate reservoir with volume V^. Dialysance D at a time t was then

defined by him analogous to clearance as

^d t=d^*^ - «d^ö;} *^ {a^^(t) - c^^(t)]

D = (I-l la)

t {c-^i(t) - c^(t)} a^^(t) - a^(t)

Later investigators used this approach to describe the mass-transfer process in other types of dialysers as well, but used a slightly modified dialysance definition:

•^b (°bi - %o^

D = (I-llb)

%i

~ °di

For single-pass dialysate flow systems with initial zero dialysate con-centration, this equation reduces to the clearance definition.

Dialysance is useful clinically for comparison of artificial with natural kidney function but it is otherwise difficult to use as it depends on a large number of parameters. Unfortunately nearly all mass-transfer mea-surements available in literature are expressed in dialysance values. By eliminating the concentrations from the equations (1-8), (1-9) and (I-llb) the dialysance as a function of overall mass-transfer coefficients can be determined.

for aocurrent blood and dialysate:

<Hoe ^ C't'fc + ^d^

r r " t o t - " "Tb * d ' 1 -i

.[/-exp{- _ } ]

for countercurrent blood and dialysate:

7 - exp j \ — - »b ^d ' tó *fc <Ktoe A c-t-fc - ^d^ -I exp|- j '^d *b *d (1-13)

for mixed dialysate:

1 - exp J

7 + — 7 - exp J [ I

(1-14)

The case for cocurrent blood and dialysate flow was originally presented by Leonard and Bluemle (20), while equations (1-13) and (1-14) were derived by Michaels (24). For increasing values of ^^/<i:b a^- three equations can be approximated by

Ö <Ktot> A

—~ =

7 - exp ] I

h ^ ^b '

(1-15)

A similar equation was derived by Renkin (27) although he assumed that the mass-transfer resistance was concentrated in the membrane.

Dialysance as a function of the flow ratio and mass-transfer properties was calculated from the above equations by Michaels (24). These results have been reproduced in figure 1-5. With these graphs the total overall mass-transfer coefficients can easily be determined from the published dialysance measurements.

. » limit —^ e Q ( I - 1 S ) / cocurrent 1

kNvv

PMeoX^

fe

V

$

^

^^-^5^

FIGURE 1-5: DIALYSANCE AS FUNCTION OF BLOOD AND DIALYSATE FLOW qATE FOR THREE FLOW CONOITIOMS.

The total overall mass-transfer coefficient depends on the resistance to mass-transfer offered in the three layers through which transport has to take place. For this resistance can be written, analogous to equation (1-6) 7 <Hof> t o t a l o v e r a l l r e s i s t a n c e 7 <^fc> blood o v e r a l l r e s i s t a n c e 7 ^m membrane r e s i s t a n c e + 7 <Kd> d i a l y s a t e o v e r a l l r e s i s t a n c e (1-16)

The membrane permeability P„ of the commonly used cellophane membranes and hence the resistance has been experimentally determined for a number of solutes. From equation (1-16) the average resistance of blood and dialy-sate layer can then be estimated.For some types of dialysers the dialydialy-sate resistance forms a negligible part of the total fluid resistance and hence the blood resistance is found. In general however, the blood resistance cannot be determined from the overall description.

IC.4. The mass-transfer process in artificial kidneys.

pre-vious paragraphs to characterize the mass-transfer process in the dia-lyser. It has been found that the actual mass-transfer rate, which can be obtained with a certain dialyser, depends on the way the dialyser is con-nected to the dialysate supply; the cases of cocurrent and countercurrent blood and dialysate were mentioned. The actual mass-transfer rate which can be obtained with the artificial kidney system as a whole then still depends on whether a recirculating dialysate supply or a single-pass dialysate fluid is used.

To illustrate the effect of these different connections on the perfor-mance of each artificial kidney system it will now be assumed that the dialysers are used to remove a solute from a mixed blood reservoir. This blood reservoir can be seen as a hypothetical patient to which the artifi-cial kidneys are connected. By comparing the changes in concentration in this reservoir obtained with each dialyser the most efficient unit can be found.

In figure 1-6 different artificial kidney systems are listed. The figure has been extended to cover also some models used in earlier attempts to describe the overall mass-transfer process in artificial kidneys. In figure I-6a it is assumed that the exchange of a component from a mixed blood reservoir with volume V^ takes place through a membrane to a

mixed dialysate reservoir with volume V^, The dialysate concentration

increases from the initial concentration assumed to be zero, to a limit which depends on the volume of both reservoirs. This simple model is

important as it figured in the earliest attempts by Wolf (26) to clarify

the mass-transfer process in the artificial kidney.

In figure I-6b to I-6e recirculating blood streams from the mixed blood reservoir are assumed.

In figure I-6b the dialysate reservoir is considered to be fully mixed. This flow situation occurred in the original artificial kidney system, as

designed by Kolff and described in e.g. reference (1), where the blood

compartment was suspended in the dialysate reservoir.

In figure I-6c and I-6d the fluid from the dialysate compartment is return-ed to the dialysate reservoir or the dialysate is discardreturn-ed after perfusion of the dialyser. These connections are found in the commonly used artifi-cial kidney systems,

In figure I-6e both blood and dialysate are discarded after flowing through the dialyser. This situation covers the "in vitro" mass-transfer measurements.

For recirculating dialysate supply systems the concentration decrease in the blood reservoir as a function of time will be

cy,(t) = 0^,(0) \ exp r- e t ; + \ ( i - i 7 ) ^ y^ + y^ Vb + Vd ^

For single-pass systems a higher efficiency of the artificial kidney system is found; the exponential decrease will be

Cb(t) = 0^(0) exp (- 6 t) (1-18)

The coefficients B are given in figure 1-6 for each different case; the initial dialysate concentration is assumed to be zero. By comparison with

Figure a : Mined ttöóó Oftfl d l a l y t e t e

-t:

» ° P Cb'"

i i i , , A i v „ . V a l

r i g u r a b Bccirculoting blood ond m i « « a d i o t y t q f

^

C , ( t ) ^

_ 3 _ * 2

VfcV-" t o t * * ^

RaclrcukHinfl biqod ono d t o l y i g t » . c a u n t « r c u r r « n 1 :

'

'

'

=*>

1 ^

JC

!

1

- l L ^ „

| r ^

\ ^

c o c u r r e n t : c o u n t a r c u r r c n t :

^

'.

h V

1

-._..vjj.

1^1

I

r^

i and Kfgf A o> darinad in f i g u r a C

F i g u r a a : S i n g t a - p o » btood ond d i o l y t o t a , c o c u r r a n t : c o u n t a r c u r r a n t : D S ~

[riT^"

= s

-±

\\.*'...:^'

equations (1-12) to (1-14) it appears that the coefficients as given in figure I-6c and 6d can be written as

8 ^-D/Vj^ (1-19)

By comparing the respective times t' and t " needed by two artificial kidney systems to reach a prescribed blood concentration, it follows that

t>/t" ^ D"/D' (1-20)

Hence the dialysis time of an artificial kidney system is inversely pro-portional to the dialysance of the dialyser connected as shown in figure I-6c and 6d.

The equations describing the concentration changes in the artificial kidney systems from figure 1-6 can be extended to cover cases where the initial dialysate concentration is not equal to zero. The real dialysis situation can be better approximated by using a one-pool model of the body with solute inflow, as discussed in paragraph IB.2, instead of the mixed blood reservoir. However this paragraph was only intended to give an interpretation of the dialysance of an artificial kidney system. The step to cover the actual solute transport from the body itself is out-side the scope of this study and will not be made.

ID. CONCLUSIONS FOR FURTHER RESEARCH

It has been shown that the dialysance or the mass-transfer coefficient of a dialyser can be used to describe the overall mass-transfer process of an artificial kidney.

Although the results of numerous investigations of mass-transfer prop-erties of artificial kidneys have been published, several problems were repeatedly encountered in the initial and planning stage of this study:

- A direct comparison of dialyser designs, with emphasis on both mass-transfer and physiological conditions, from which the most promising design could have been selected was not available. Such specific dialyser design could then have been.used for a detailed study of the actual flow and mass-transfer conditions.

- The application of local mass-transfer theories, as schematically outlined in section ID, was found to be questionable as the influence of non-ideal conditions such as non-Newtonian and pulsatile blood flow and varying geometry due to practical design limitations had received only very little attention in the literature. This made differences between theory and measurements difficult to interpret. - The improvement of the haemodialysis efficiency by using better

membranes was difficult to determine as an enormous research effort in laboratories all over the world has resulted in a continuing output of new membranes with either improved or more selective permeability.

- Accurate values of the effective diffusion coefficients in blood of solutes as urea, creatinine and sodium chloride were not available.

It was decided to limit our own research to the first two problems: In the next two parts of this dissertation the results of the indepen-dent but coordinated studies of mass and momentum transfer in dialysers, undertaken to solve these problems are reported.

Measurements have been done with some commonly used dialysers to achieve insight in the practical design limitations. From these measurements, extended with published data, an overall comparison of the performance of artificial kidneys has been made. This work is reported in part H . In specially designed apparatus in which certain variables can be exam-ined under carefully prescribed conditions, some aspects of the local mass-transfer process of a solute under the influence of a concentration difference and for dominant fluid resistances have been investigated. The theory is given for blood flow between two semi-permeable membranes and for flow through circular channels with semi-permeable wall. To facilitate the experimental problems the theory has been extended to cover the case of blood flow between a semi-permeable and an imperme-able parallel membrane and was compared with measurements. This work is reported in part H I .

For all experiments cuprophan membranes have been used for which

PART II THE OVERALL PERFORl'lANCE OF ARTIFICIAL KIDNEYS

H A . INTRODUCTION

With an artificial kidney system a certain amount of waste products have to be removed from the circulatory system of the patient within a certain time and concentrations of other components have to be main-tained within prescribed limits.

For the artificial kidney system as a whole the following additional conditions can be formulated:

- The disturbance of the circulatory system of the patient should be minimal.

- The system should allow a relatively easy treatment at an accept-able cost level and it should have repeataccept-able performance. - The system should be safe for patient and medical staff.

To judge a complete artificial kidney system, including the monitors and pumping systems on these grounds is beyond the scope of this study. The further discussion will be limited to mass- and momentum-transfer aspects of artificial kidney systems.

A comparison of different dialyser designs, as currently in use, is made with emphasis on both mass-transfer requirements and the physiological restrictions set to the dialysis treatment. The flow condition in the dialyser itself depends completely on the construction of blood and dialysate compartment of the dialyser. Therefore first the constructional details of different dialysers will be compared before their performance will be judged on each of the following points:

- The quantity of solutes and water removed from the blood stream to the dialysate during the passage of the blood through the dialyser.

- The pressure difference necessary to maintain a certain blood flow through the dialyser.

- The fluid distribution through both the blood and the dialysate compartment of the dialyser.

- The volume of the dialyser at the beginning of and during the treatment.

- The blood loss in the dialyser.

These points will be further evaluated in the following sections. In section IIB the construction of dialysers, currently in use, is reviewed and the flow conditions for each design are indicated. In section IIC the measured mass-transfer rates for urea, creatinine and water which can be found with these dialysers at different blood flow rates are compared.

In section IID the flow characteristics of each dialyser are given and compared with those based on idealized models of the different dialyser designs.

design are compared and a method to. select the most efficient artificial kidney system is proposed.

IIB. A SURVEY OF DIALYSER DESIGNS

IIB.1. Constructional details.

The historical developments in dialyser designs were reviewed by Kolff (1) and Colton (2). In this section more recent dialysers will also be included. The majority of the commonly used dialysers can be divided into two groups, the coil dialysers and the parallel-plate dialysers. A third group the capillary dialysers, is still under development and not much clinical experience has been obtained with these apparatus so far. The design of these dialysers will now shortly be described.

The coil dialyser.

The blood compartment is formed by a tubular membrane which is wound around a coil as shown in figure II-1 . The wind-ings are kept apart by a plastic mesh webbing. It is claimed that the obstructions in the blood channel, due to the web-bing, cause some mixing of the blood. In some designs parallel blood channels are used to ob-tain the necessary mass-transfer area at a limit-ed pressure drop over the dialyser.

The dialysate is thorough-ly mixed as it is pumped through the plastic web-bing. After use the coil dialyser is discarded. Recent examples of this design are the Travenol Uf-lOO and Uf-145 which have two parallel blood channels. A single coil as shown in figure II-l IS manufactured by Extracorporeal as the Ex-Ol.

FIGURE M - I : THE EX-01 COIL DIALYSER. (FROM EXTRACORPOREAL MEO.SPEC.

The parallel-plate dialyser.

- The blood and dialysate compartments are identical and they are formed by a great number of parallel grooves with triangular cross-section, cut out in plastic plates. In the original design

by Skeggs and Leonards (20) rubber plates were used which caused extensive blood clot-ting, but in later de-signs such as the Dia-lung as shown in figure II-2, plastic plates ate used which prevent •clotting. Blood and

dialysate are separated by a membrane clamped between two plates. In the Dialung dialyser a cross flow of blood and dialysate is found and up to 65 plastic plates can be stacked together to achieve the required exchange area. After use the dialyser is returned to the factory to be reloaded with membranes.

- The blood compartment is enclosed between two membranes clamped at the sides between two plates as shown in figure II-3.

• ^ » « ( » « » t - C O rmiL amsmc riuio n » r ( ZAf P L i T C • IHSIHS F i ü r B pLkJt

FinutlE 11-2: THE DIALUNG PARALLEL-PLATE DIALYSER. (FROM CARDIOVASCULAR ELECTROVN.CORP.CATALORUE).

DiALTSU CLAMP BLOOD P W T CtHTRt DlALYStR H M D O U I T S A T I PORT OUKX n S O M N E C T M T T O H DUU.TXR

FIGURE 11-5; THE K M L PARALLEL-PLATE DIALYSER. (FROM WATSON-MARLOW CATALOGUE).

Parallel channels have again been cut into the plates. Through these channels dialysate can flow in co- or countercurrent manner with the blood. The first dialyser of this kind was a modification by Skeggs

and Leonards of their original rubber plate design described above. It has between four and twelve parallel blood compartments. The rubber plates can be compressed to reduce the blood volume of the dialyser. Unfortunately this generally causes uneven distribution of blood over the various parallel compartments and unpredictable performance. In a later modification by Kiil (22) plastic plates were recommended. Dialysers of this design are still widely used. The Kiil dialyser has two parallel blood channels and dialysate grooves with triangular cross-section and is shown in figure II-3. Cocurrent blood and dialysate flows have to be used to ensure a more even perfusion of the dialyser.

Recently dialysers with a more rigid construction and with improved dialysate compartments have been marketed: The triangular channels have been cut in two perpendicular directions, forming a pyramid type of membrane support. In these dialysers countercurrent blood and dialysate can be used. The pyramid supports cover less membrane area than the triangular grooves of the Kiil dialysers. It is claimed that the dialysate is somewhat mixed while flowing around the pyramids, thereby further improving the mass-transfer rate. Before use these parallel-plate dialysers have to be loaded with either presoaked membranes, requiring formalin sterilization afterwards, or with dry sterile mem-brane packages. The latter are more convenient but due to stretching the blood volume is increased and the mass-transfer rate is reduced by about 10-15%.

To eliminate the tricky membrane loading procedure of the Kiil dialyser, many further modifications to make the parallel-plate dialyser dis-posable have been suggested by among others Flower (25), Nose (22) and

Dasco (24).Only two are marketed so far, the Rhone-Poulenc and the Gambro dialyser. The Rhone-Poulenc is a parallel-plate package with eight parallel blood compartments which are clamped between a metal frame.The Gambro dialyser as shown in figure II-4 is completely disposable; after use the whole dialyser including the metal clamping frame is discarded. This latter design has eight parallel blood and dialysate compartments but has pyramid supports for the membrane as well which again should cause some mixing of the dialysate.

The capillary dialyser.

Dialysers very similar to tube heat exchangers and incorporating polymer tubing as blood compartment have been in use for some time now in the U.S.A. Although a tremendous increase in the ratio of area and volume could be achieved with these dialysers, the problem of distributing the blood stream equally over the parallel capillaries and of preventing damage to the blood components,resul ting in clotting and blocking of the dialyser,is still far from being solved. From articles giving details of these capillary dialysers no consistent data could be extracted and as no such unit was available for testing, this dialyser could not be included in the following comparison.

IIB.2. Dialysers selected for the comparison.

FIGURE ll-li: THE GAHSRO PARALLEL-PLATE DIALYSER. (FROM AS GAMBRO CATALOGUE).

the following units are considered to be representative of the many different makes:

Coil type

Farallel-plate type

early designs: Travenol Tc-145, improved designs: Travenol Uf-145 and

Travenol Uf-lOO, Extracorporeal Ex-Ol. Kiil design: Watson and Marlow, Meltec,

Sweden-Seattle, improved design: Western-Kiil, different design: Gambro, Dialung.