JOURNAL OF DIALYSIS, 1 ( 4 ) , 333-347 (1977)
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KINETICS OF 1NTERMI”T
AND CONTINUOUS PERITONEAL DIALYSIS
Fernando Villarrcel Artificial Kidney-Chrcnic Uremia Program Natimal Institute of A r t h r i t i s , Metabolism and Digestive Diseases Natimal Institutes of Health Bethesda, Maryland 20014 ABSTRACT
Relatims were developed for clearance mder both intermittent
and continuous flow peritmeal dialysis. The theoretical . prediction was compared w i t h data from other investigators. A mass transfer characteristic of 52 m l / m i n per 1.85 l i t e r s of dialysate was determined for urea from Boen’s single batch experiment. This number was used to calculate the value of clearance for intermittent d i a l y s i s versus rate of dialysate exchange. The calculated clearances are i n good agreement w i t h b e n t s experimental results.
The calculated urea clearances for continuous flow d i a l y s i s were compared w i t h Shinaberger’s data. The predicted curve is in reasmable agreement w i t h the data although there is a rather large scatter of the points. Some possible explanati,ms for the scatter are provided as a caviat for f u t u r e experimental research. A theoretical comparison between intermittent and ccntinuous flow clearances shows that the l a t t e r is more efficient,
particularly a t higher flow rates. INTRODUCTION
Several investigators [ 1-81 have attempted to characterize and compare the intermittent and cmtinuous modes of peritoneal
dialysis.
333 Copyright @ 1977 by Marcel Dekker. Inc. All Rights Reserved. Neither this work nor any part may be reproduced or transmitted in any form or by any means. electronic or mechanical, including photocopying. microfihning. and recording, or by any information storage and retrieval system, without permision in writing from the publisher.
VILLARROEL
334
Although there is no s u b s t i t u t i o n for the experimental measure-
m e n t of physical parameters, it is important t o have a theoret-
ical descriptim of the phenomena t o interrelate the effect of the many independent variables.
Ren Fail Downloaded from informahealthcare.com by University of Otago on 01/06/15 For personal use only.
Analysis o f mathematical rePatims often mcover LrfiSUSpeCtedly large effects of variables which otherwise could be assumed to have no significant importance.
The derivatim of t h e relations presented here are given in detail in the appendix.
The calculated clearances are compared
w i t h data obtained by b e n [ l ] and Shinaberger [ 2 ] and then used
t o compare the two modes of peritmeal dialysis mder equal cmditims. APPROACH
The analysis is based m a cmceptual descripticn of the phenmenm where the fluid in t h e p r i t m e a l cavity is assumed t o be well mixed and the mass transfer across the peritmeal
membrane is defined as the product of a mass transfer coefficient,
Kos the area available for transfer,
A , and
the ccncentratim
difference between the blood pool, CB, and the dialysate pool,CD. The area available for transfer is assumed proportional t o the dialysate volume, VD. Since the ccncentraticn in the blood pool changes slowly in r e l a t i m t o that in the dialysate, the equatims were developed assuming ccnstant plasma ccncentraticn.
This assumptim appears
reasmable for the intemittent mode since the change in plasma
335
INTERMITTENT AND CONTINUOUS PERITONEAL DIALYSIS
In t h e next secticn
c c n q e n t r a t i m during each exchange is small.
it is shown that t h i s assumption introduces an i n s i m i f i c a n t error in t h e clearance calculated f o r t h e ccntinous flow case. The most c l i n i c a l l y meaningful clearance mder i n t e r m i t t e n t
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d i a l y s i s is t h a t measured over each e n t i r e exchange including inflow, residence, and outflow processes.
The clearance,
rI, is
given by equation 14 derived in t h e appendix.
[
-
(14)
KI =
1 1
-
-
exp(-Z
tt
to) 1
-
exp(-Z
ti) exp (-Z tr>
ti
to
1
where tt= tr+ti+to+tp is t o t a l time, tr is resident time, ti
is inflow time, to is outflow t i m e , t is t he pause time between P
inflow and outflow, and Z = K o A p D M . t h a t A and V,
The subscript M indicates
are evaluated a t its maximum value in each exchange.
In the ccntinuous flow mode, the apparent clearance calculated using the output d i a l y s a t e c m c e n t r a t i m differs from t h e real clearance which is based cn the actual s o l u t e removal
from blood.
The apparent clearance increases rapidly w i t h time
a t the beginning o f t h e process while the real clearance decreases during most o f the process.
The difference between t h e two values
is due t o the s o l u t e accumulaticn in the resident volume. The apparent clearance reaches 95% o f its maximum value
after an initial period approximately given by equaticn 20, where
Q, is t h e d i a l y s a t e flow rate.
-
336
VILLARROEL
The apparent and real ccntinuous flow clearances are given by e q u a t i o n s 18 and 23 in t h e appendix. clearance
The , m i m u m apparent
KCM, is given by equation 21. 1
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(*I)
KcM
-E +-
1
QD Ko% The real c l e a r a n c e is h i g h e r than Km during most of t h e d i a l y s i s
process except a t its i n i t i a t i o n , w h i l e t h e p e r i t o n e a l c a v i t y
is being f i l l e d . After an i n i t i a l period of t h e same o r d e r of magnitude of
tg5, the real c l e a r a n c e approaches KCM, which is t h e e f f e c t i v e
clearance d u r i n g most of t h e ccntinuous flow d i a l y s i s . RESULTS AND CONCLUSIONS
The classical paper published by Boen [ 11 in 1961 provides a complete s o u r c e of experimental d a t a f o r i n t e r m i t t e n t d i a l y s i s . The perfusi.cn technique employed by k e n occupied about seven m h u t e s f o r inflow and t h i r t e e n minutes for outflow using a d i a l y -
sate voPume o f 1.85 liters. of d a t a :
He measured two independent sets
D i a l y s a t e ccncentrati.cn in t h e p e r i t o n e a l f l u i d v e r s u s
time and clearance v e r s u s d i a l y s a t e rate of exchange.
In a d d i t i c n t o o t h e r measurable parameters, t h e d i a l y s i s prac e s s is governed by t h e mass t r a n s f e r characteristic, KoAM.
The
value of t h e mass t r a n s f e r c h a r a c t e r i s t i c must be determined exper-imentally and is a f m c t i c n of t h e d i a l y s a t e r e s i d e n t volume, VDMa The v a l u e o f KO%
f o r u r e a was determined u s i n g Boen's ccncen-
t r a t i o n ratio d a t a for 1.85 liters r e s i d e n t volume.
F i g u r e ? shows
INTERMITTENT AND CONTINUOUS PERITONEAL DIALYSIS
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x
(I ,A'[
-;!;
I / L
-I
T
I
,
I
, , ' ,; TIME
OO
337
1.0
40
1
,; :
- Minutes 60
80
loo
120
FIGURE 1
Boen's c c n c e n t r a t i m r a t i o d a t a versus time and a curve calculated using equation 8 f o r an inflow time of seven minutes and r e s i d e n t
time ranging frm 0 t o 120 minutes.
KO%
of 52 ml/min.
The best f i t is obtained f o r a
The v e r t i c a l line shorn a t each point i n d i c a t e s
the range o f v a r i a t i m of t h e d a t a , n o t t h e standard deviaticn.
Figure 2 shows Boen's data f o r urea clearance v e m w rate of d i a l y s a t e exchange.
It also shows t h e t h e o r e t i c a l curve f o r a
K A of 52 rnl/min assuming a me minute pause time. O M
The remrk-
able agreement of t h i s group of d a t a w i t h t he calculated values
is a good indication of t h e self ccnsistency o f t h e theory. The clearance values obtained by Wen, however, are somewhat h i g h e r than those obtained by o t h e r investigators.
Shinaberger's
(21 i n t e r m i t t e n t urea clearance a t a d i a l y s a t e rate of exchange o f
two l i t e r s per hour averaged 17.4 ml/min with a maximum of about 23 ml/min.
Lhfortmately, Shinaberger does not describe h i s inflow-
VILLARROEL
338
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L
I
i
FIGURE 2
outflow protocol in h i s paper.
The d i a l y s a t e rate of exchange as
well as the inflow and outflow process have a s i m i f i c a n t effect on t h e o v e r a l l clearance.
If Shinaberger had f i f t e e n minutes inflow
and outflow times, t h e calculated clearance a t two liters per hour would
be 22.6 m l / m i n , which is within Shinaberger's range of
experimental data. %he urea data published by Shinaberger f o r cmtinuous peri-
tcmeal d i a l y s i s nas compared w i t h the curve calculated using a
KoAn of 52 m l / m i n . in figure 3.
The t h e o r e t i c a l curve and t h e d a t a a r e shown
The d a t a a t each flow show ccnsiderable s c a t t e r i n g .
This s c a t t e r i n g might be due to s e v e r a l factors:
( a > D a t a where
obtained before the clearance reached its maximum value (tg5) ; this effect would be p a r t i c u l a r l y large a t low flow rates.
(b) Exces-
s i v e l y large values of clearances might be due t o measurement of a high l o c a l c c n c e n t r a t i m n o t representative of the average ccncen-
t p a t i a a in t h e resident volume i n s i d e the peritcnedl cavity.
INTERMITTENT AND CONTINUOUS PERITONEAL DTALYSIS
loo] .-C
2:
E
I
I
I
.
I
I
I
Shinaberger (2)
- Theory lKcM)
*J
a a a
so20-
4
ax::-
, ita
1
-
a
60
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1
339
3 +
-
-
a 4
-
a4
DIALYSATE FLOW RATE - mltmin
4 .
FIGURE 3
(c)
It is possible t h a t a t higher flow t h e value of the mass
transfer c o e f f i c i e n t increases due t o additimal mixing; t h i s could explain t h e l a r g e number of points above t h e t h e o r e t i c a l l i n e f o r KO%
o f 52 ml/min a t the d i a l y s a t e flow rate of 300 ml/min.
the of Shinaberger's points a t 300 m l / m i n is n o t indicated in f i g u r e
3.
This point shows an extremely high clearance of 125 rnl/min. The t h e o r e t i c a l descripticn may be used t o compare t h e
two modes o f peritmeal d i a l y s i s mder i d e n t i c a l c c n d i t i m s . Table I w a s calculated taking a typical case i n which t h e in-
flow time is ten minutes, t h e outflow time is f i f t e e n minutes, t h e pause time is me minute, and the resident volume is two
liters.
The value of KO%
f o r urea was set at 52 ml/min and
f o r a middle molecule of the s i z e of Vitamin B,* was estimated t o be 12 ml/min [81.
The values for Km calculated as show be-
f o r e were compared t o those obtained using equaticns 31 and
VILLARROEL
340
32 developed for maximum plasma concentration decay. The body volume of d i s t r i b u t i o n for urea and the middle molecule for t h i s l a s t case were estimated to be 35 and 20 l i t e r s respectThe real and apparent clearances calculated w i t h equations
ively.
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31 and 32 were within 2 3% of that calculated w i t h the simple
theory assuming canstant plasma concentration.
The values of tg5
calculated by iteration of equations 31 and 32 were not significantly different from those calculated using equation 20 shown earlier. Table 1 shows that t h e r e is a very small change in intermittent clearance within the normal range of dialysate exchange of It also shows that the time needed
two t o four l i t e r s per hour.
to reach 95% of the maximum apparent clearance is approximately m e hour for urea and even larger for middle molecules.
The
calculated clearances show that ccntinuous flow peritoneal dialysis is more efficient than the intermittent made, particularly a t
higher flow rates.
TABLE I
Comparison of Intermittent and Continuous Peritoneal Dialysis Flow Rate or Rate of Exhange
Middle Molecule
Urea fT I
K
m
a
t
95
E/hr
ml/min
ml/min
& u
4.00 3.00
22.9 24.7 23.3
30.4 26.4 20.9
51 59 70
2OOQ
I
t
R
CM ml/min
95
6.3
10.2
76
7.3
9.7
8.1
97
8.8
132
ml/min -
1NTERMI"T
AND CONTINUOUS PERITONEAL DLUYSIS
341
The clearance of middle molecules shows a decrease with flow i n t h e i n t e r m i t t e n t case in c c n t r a s t with the increase show i n t h e ccntinuous mode.
The r e l a t i v e inefficiency of i n t e r m i t t e n t
peritoneal d i a l y s i s is the r e s u l t o f t h e inflow and outflow
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processes which take a l a r g e part o f the d i a l y s i s time.
In t h e
hypothetical case in which both t r a n s i e n t processes are eliminated leaving m l y t h e c m s t a n t volume resident process, t h e i n t e r m i t t e n t
mode of d i a l y s i s would be more e f f i c i e n t than t h e ccntinuous mode. Theoretically, i f cmtinuous flow rates of 130
- 200 ml/min
are achieved [71, the clearance o f urea could increase 50 t o 70%
over that obtained using n o m l i n t e r m i t t e n t mode of d i a l y s i s . The clearance of middle molecules could cmceivably be increased by about 40%.
h e should be aware, however, that the mass transfer coeffic i e n t , KO, assumed ccnstant for t h i s a n a l y s i s , is a parameter which is affected by t h e d i a l y s a t e side resistance. The value of KO f o r ccntinuous flow d i a l y s i s may be higher o r lower than that f o r i n t e r m i t t e n t mode depending cn t h e positicm and design
o f the catheters.
If the cmtinuous flow produces a d d i t i m a l
mixing, KO could be higher;
but i f flow channeling o r by-pass
occurs between the input and output catheters then Ko.could be s i g n i f i c a n t l y reduced and t h e advantages of using ccntinuous flow d i a l y s i s cancelled.
It is q u i t e possible that a compromise
between ccntinuous and intermittent peritoneal d i a l y s i s could
be achieved by using a s i n g l e c a t h e t e r and a l t e r n a t i n g t h e inflow and outflow process with an average resident volume of about two
342
VILLARROEL
liters.
If an a lt e rna t ing input-output flow of 200 m l / m i n is
obtained at i n t e r v a l s of me minute, the resident volume could be maintained between 1.8 and 2.2 l i t e r s w i t h an equivalent
cmtinuous flow of 100 m l / m i n .
'his process is ccnceptually more
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e f f i c i e n t than the present intermittent peritmeal d i a l y s i s mode and has t h e advantage of using cnPy me catheter.
ACKNOWLEDGMENT
The views expressed here are the a ut hor 's own. No o f f i c i a l support o r endorsement by t he National I n s t i t u t e s of Health i s intended nor should be inferred. However, the author wishes to thank DT. Robert P. Popovich of the University of Texas f o r h i s cooperation and invaluable exchange of ideas. REFERENCES
"0:
1.
Boen, S. T. Medicine,
2.
Shinaberger, J. H. Shear, L., and Earry, K. G . Soc. Artif. Int . Organs, 2:76, 1965.
3.
Miller, J. H., Cipstein, R . , Margules, R., Schwarts, M . , and Rubini, M. E. Trans. h e r . Soc. A rtif. I n t . Organs, '12: 98, 1966.
4.
243, 1961. Trans. h e r .
Gross, M. arid M c h a l d , H. P. J. h e r . Med. Ass. 363, 1967.
202:
5.
h g e , K. and Tresser, G. Organs. 3:164, 1967.
6.
Cordan, A . , Lewin, A. J . , Maxwell, M. H., and Morales, N . D. T m s . h e r . Soc. Artif. I n t . Organs, 2: 599, 7976.
Trans. Amer. Soc. Artif. Int.
7.. Stephen, R. E , , Atkin-Thor, E . , and Kolff, W. J. Amer. Soc. Artif. I n t . Organs, 2:575, 1976.
8,
Popovich, R. P., Mcncrief, J. W. and Decherd, 9. F. Proc. 9th Annual Ccntractors' Ccnference of the Artificial Kidney Chrcnic Uremia Program, NIH 77-1 167. 2: 126, 1975.
-
INTERMITTENT AND CONTINUOUS PERITONEAL DIALYSIS APPENDIX
INTERMITTENT FLOW DIALYSIS Inflow Process
(1)
dt
(2)
d(CDVD) Z +
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d(CDVD)
- cD)
K A(CB 0
-(C
dVD
v
D D
) =
Qi
B' vD Qi
where the inflow rate, Qi, is constant, and
(3)
2 =
-- "D
"DM 1
(4)
CD1 = CB [1
= constant
-
-
exp(-Z ti) ti
1
where C is the dialysate concentration at the end of the inflow D1process. Constant Volume Process
(5)
VD = VDM = constant
is the dialysate concentration at the end of the where C constan?2volume process.
343
VILLARROEL
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Outflow Process
where the outflow rate, Qo9 is constant and is equal to - d V D/dt. Then
(10)
-
dCD
= Z(C,
- CD)
dt
During the outflow process, the dialysate concentration is given by the following expression:
where t ranges from 0 to to.
-
where ED is the concentration of the dialysate collected at the end of the exchange. The intermittent clearance is defined by
(13)
-KI
-
- -QD
cD a
cB
-
Where QD equals VDM/tt
Then
345
INTERMITTENT AM) CONTINUOUS PERITONEAL DLALYSIS
( 14)
-KI
[
vDM t
CONTINUOUS
-
1
1
- exp(-Z
-
1
exp(-2 t i )
exp (-2 t r > to
t
now
to) 1
ti
DIALYSIS
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Apparent C l e a r a n c e Neglecting t h e inflow process
(15)
VDM
dCD
Ko%(CB
-
- QDCD
CD)
dt where Q
D
is t h e d i a l y s a t e flow.
where t is t h e t i m e l a p s e d s i n c e t h e b e g i n n i n g of t h e p r o c e s s . The a p p a r e n t c l e a r a n c e measured on t h e o u t f l o w i n g d i a l y s a t e is g i v e n by:
-cD
KCA
QD
cB
eA KCA
1
-+-
KO%
Q,
BA=l-exp
(-
QD
.)
KCA r e a c h e s 95% of i t s maximum v a l u e , Km,
(20)
tg5 =
'DM Ko%l
+
QD
when
eA
5
0.95 a t
346 The maximum a p p a r e n t c l e a r a n c e i s g i v e n by: 1
1 +A QD
KoAM
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Real C l e a r a n c e The r e a l c l e a r a n c e i s g i v e n by:
S u b s t i t u t i n g e q u a t i o n 15 i n t o 2 1 y i e l d s :
(24)
eR=
1
+
-
KoPk exP
(- ":Dl
QD
.>
QD The w a l u e of KCR p r e d i c t e d by e q u a t i o n 2 3 i s always h i g h e r t h a n KCM E f f e c t of C, Decay k
Maximum CB d e c a y OCCUKS when t h e g e n e r a t i o n r a t e of t h e s o l u t e i s assumed t o be z e r o . Then
deB
(25) vB
dt
a
-
Ko%(CB
-
CD)
where V g i s t h e volume o f d i s t r i b u t i o n of t h e s o l u t e i n t h e body. S o l v i n g e q u a t i o n s 15 and 25 s i m u l t a n e o u s l y r e s u l t s i n :
INTERMITTENT AND CONTINUOUS PERITONEAL DIALYSIS 1 - exp(-2Bt) cD cB +a? 1 + 6 e x p ( - Z @ t ) 1
(26)
=
1
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Where
(28)
BxK
(29)
Y =
A
O M
V
(30)
6 =
(1 + a )
B VDM +
v p
+a)
'DM 'B VB VDM + v ( 1 + * ; 2
v~~
+
B
Substituting equation 26 i n t o 17 y i e l d s :
1 (31)
1
-
1
+
KCA =
-1+ QD
Y '0%
exp(-2
fit)
exp(-2Bt)
347
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KINETICS OF 1NTERMI”T
AND CONTINUOUS PERITONEAL DIALYSIS
Fernando Villarrcel Artificial Kidney-Chrcnic Uremia Program Natimal Institute of A r t h r i t i s , Metabolism and Digestive Diseases Natimal Institutes of Health Bethesda, Maryland 20014 ABSTRACT
Relatims were developed for clearance mder both intermittent
and continuous flow peritmeal dialysis. The theoretical . prediction was compared w i t h data from other investigators. A mass transfer characteristic of 52 m l / m i n per 1.85 l i t e r s of dialysate was determined for urea from Boen’s single batch experiment. This number was used to calculate the value of clearance for intermittent d i a l y s i s versus rate of dialysate exchange. The calculated clearances are i n good agreement w i t h b e n t s experimental results.
The calculated urea clearances for continuous flow d i a l y s i s were compared w i t h Shinaberger’s data. The predicted curve is in reasmable agreement w i t h the data although there is a rather large scatter of the points. Some possible explanati,ms for the scatter are provided as a caviat for f u t u r e experimental research. A theoretical comparison between intermittent and ccntinuous flow clearances shows that the l a t t e r is more efficient,
particularly a t higher flow rates. INTRODUCTION
Several investigators [ 1-81 have attempted to characterize and compare the intermittent and cmtinuous modes of peritoneal
dialysis.
333 Copyright @ 1977 by Marcel Dekker. Inc. All Rights Reserved. Neither this work nor any part may be reproduced or transmitted in any form or by any means. electronic or mechanical, including photocopying. microfihning. and recording, or by any information storage and retrieval system, without permision in writing from the publisher.
VILLARROEL
334
Although there is no s u b s t i t u t i o n for the experimental measure-
m e n t of physical parameters, it is important t o have a theoret-
ical descriptim of the phenomena t o interrelate the effect of the many independent variables.
Ren Fail Downloaded from informahealthcare.com by University of Otago on 01/06/15 For personal use only.
Analysis o f mathematical rePatims often mcover LrfiSUSpeCtedly large effects of variables which otherwise could be assumed to have no significant importance.
The derivatim of t h e relations presented here are given in detail in the appendix.
The calculated clearances are compared
w i t h data obtained by b e n [ l ] and Shinaberger [ 2 ] and then used
t o compare the two modes of peritmeal dialysis mder equal cmditims. APPROACH
The analysis is based m a cmceptual descripticn of the phenmenm where the fluid in t h e p r i t m e a l cavity is assumed t o be well mixed and the mass transfer across the peritmeal
membrane is defined as the product of a mass transfer coefficient,
Kos the area available for transfer,
A , and
the ccncentratim
difference between the blood pool, CB, and the dialysate pool,CD. The area available for transfer is assumed proportional t o the dialysate volume, VD. Since the ccncentraticn in the blood pool changes slowly in r e l a t i m t o that in the dialysate, the equatims were developed assuming ccnstant plasma ccncentraticn.
This assumptim appears
reasmable for the intemittent mode since the change in plasma
335
INTERMITTENT AND CONTINUOUS PERITONEAL DIALYSIS
In t h e next secticn
c c n q e n t r a t i m during each exchange is small.
it is shown that t h i s assumption introduces an i n s i m i f i c a n t error in t h e clearance calculated f o r t h e ccntinous flow case. The most c l i n i c a l l y meaningful clearance mder i n t e r m i t t e n t
Ren Fail Downloaded from informahealthcare.com by University of Otago on 01/06/15 For personal use only.
d i a l y s i s is t h a t measured over each e n t i r e exchange including inflow, residence, and outflow processes.
The clearance,
rI, is
given by equation 14 derived in t h e appendix.
[
-
(14)
KI =
1 1
-
-
exp(-Z
tt
to) 1
-
exp(-Z
ti) exp (-Z tr>
ti
to
1
where tt= tr+ti+to+tp is t o t a l time, tr is resident time, ti
is inflow time, to is outflow t i m e , t is t he pause time between P
inflow and outflow, and Z = K o A p D M . t h a t A and V,
The subscript M indicates
are evaluated a t its maximum value in each exchange.
In the ccntinuous flow mode, the apparent clearance calculated using the output d i a l y s a t e c m c e n t r a t i m differs from t h e real clearance which is based cn the actual s o l u t e removal
from blood.
The apparent clearance increases rapidly w i t h time
a t the beginning o f t h e process while the real clearance decreases during most o f the process.
The difference between t h e two values
is due t o the s o l u t e accumulaticn in the resident volume. The apparent clearance reaches 95% o f its maximum value
after an initial period approximately given by equaticn 20, where
Q, is t h e d i a l y s a t e flow rate.
-
336
VILLARROEL
The apparent and real ccntinuous flow clearances are given by e q u a t i o n s 18 and 23 in t h e appendix. clearance
The , m i m u m apparent
KCM, is given by equation 21. 1
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(*I)
KcM
-E +-
1
QD Ko% The real c l e a r a n c e is h i g h e r than Km during most of t h e d i a l y s i s
process except a t its i n i t i a t i o n , w h i l e t h e p e r i t o n e a l c a v i t y
is being f i l l e d . After an i n i t i a l period of t h e same o r d e r of magnitude of
tg5, the real c l e a r a n c e approaches KCM, which is t h e e f f e c t i v e
clearance d u r i n g most of t h e ccntinuous flow d i a l y s i s . RESULTS AND CONCLUSIONS
The classical paper published by Boen [ 11 in 1961 provides a complete s o u r c e of experimental d a t a f o r i n t e r m i t t e n t d i a l y s i s . The perfusi.cn technique employed by k e n occupied about seven m h u t e s f o r inflow and t h i r t e e n minutes for outflow using a d i a l y -
sate voPume o f 1.85 liters. of d a t a :
He measured two independent sets
D i a l y s a t e ccncentrati.cn in t h e p e r i t o n e a l f l u i d v e r s u s
time and clearance v e r s u s d i a l y s a t e rate of exchange.
In a d d i t i c n t o o t h e r measurable parameters, t h e d i a l y s i s prac e s s is governed by t h e mass t r a n s f e r characteristic, KoAM.
The
value of t h e mass t r a n s f e r c h a r a c t e r i s t i c must be determined exper-imentally and is a f m c t i c n of t h e d i a l y s a t e r e s i d e n t volume, VDMa The v a l u e o f KO%
f o r u r e a was determined u s i n g Boen's ccncen-
t r a t i o n ratio d a t a for 1.85 liters r e s i d e n t volume.
F i g u r e ? shows
INTERMITTENT AND CONTINUOUS PERITONEAL DIALYSIS
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x
(I ,A'[
-;!;
I / L
-I
T
I
,
I
, , ' ,; TIME
OO
337
1.0
40
1
,; :
- Minutes 60
80
loo
120
FIGURE 1
Boen's c c n c e n t r a t i m r a t i o d a t a versus time and a curve calculated using equation 8 f o r an inflow time of seven minutes and r e s i d e n t
time ranging frm 0 t o 120 minutes.
KO%
of 52 ml/min.
The best f i t is obtained f o r a
The v e r t i c a l line shorn a t each point i n d i c a t e s
the range o f v a r i a t i m of t h e d a t a , n o t t h e standard deviaticn.
Figure 2 shows Boen's data f o r urea clearance v e m w rate of d i a l y s a t e exchange.
It also shows t h e t h e o r e t i c a l curve f o r a
K A of 52 rnl/min assuming a me minute pause time. O M
The remrk-
able agreement of t h i s group of d a t a w i t h t he calculated values
is a good indication of t h e self ccnsistency o f t h e theory. The clearance values obtained by Wen, however, are somewhat h i g h e r than those obtained by o t h e r investigators.
Shinaberger's
(21 i n t e r m i t t e n t urea clearance a t a d i a l y s a t e rate of exchange o f
two l i t e r s per hour averaged 17.4 ml/min with a maximum of about 23 ml/min.
Lhfortmately, Shinaberger does not describe h i s inflow-
VILLARROEL
338
Ren Fail Downloaded from informahealthcare.com by University of Otago on 01/06/15 For personal use only.
L
I
i
FIGURE 2
outflow protocol in h i s paper.
The d i a l y s a t e rate of exchange as
well as the inflow and outflow process have a s i m i f i c a n t effect on t h e o v e r a l l clearance.
If Shinaberger had f i f t e e n minutes inflow
and outflow times, t h e calculated clearance a t two liters per hour would
be 22.6 m l / m i n , which is within Shinaberger's range of
experimental data. %he urea data published by Shinaberger f o r cmtinuous peri-
tcmeal d i a l y s i s nas compared w i t h the curve calculated using a
KoAn of 52 m l / m i n . in figure 3.
The t h e o r e t i c a l curve and t h e d a t a a r e shown
The d a t a a t each flow show ccnsiderable s c a t t e r i n g .
This s c a t t e r i n g might be due to s e v e r a l factors:
( a > D a t a where
obtained before the clearance reached its maximum value (tg5) ; this effect would be p a r t i c u l a r l y large a t low flow rates.
(b) Exces-
s i v e l y large values of clearances might be due t o measurement of a high l o c a l c c n c e n t r a t i m n o t representative of the average ccncen-
t p a t i a a in t h e resident volume i n s i d e the peritcnedl cavity.
INTERMITTENT AND CONTINUOUS PERITONEAL DTALYSIS
loo] .-C
2:
E
I
I
I
.
I
I
I
Shinaberger (2)
- Theory lKcM)
*J
a a a
so20-
4
ax::-
, ita
1
-
a
60
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1
339
3 +
-
-
a 4
-
a4
DIALYSATE FLOW RATE - mltmin
4 .
FIGURE 3
(c)
It is possible t h a t a t higher flow t h e value of the mass
transfer c o e f f i c i e n t increases due t o additimal mixing; t h i s could explain t h e l a r g e number of points above t h e t h e o r e t i c a l l i n e f o r KO%
o f 52 ml/min a t the d i a l y s a t e flow rate of 300 ml/min.
the of Shinaberger's points a t 300 m l / m i n is n o t indicated in f i g u r e
3.
This point shows an extremely high clearance of 125 rnl/min. The t h e o r e t i c a l descripticn may be used t o compare t h e
two modes o f peritmeal d i a l y s i s mder i d e n t i c a l c c n d i t i m s . Table I w a s calculated taking a typical case i n which t h e in-
flow time is ten minutes, t h e outflow time is f i f t e e n minutes, t h e pause time is me minute, and the resident volume is two
liters.
The value of KO%
f o r urea was set at 52 ml/min and
f o r a middle molecule of the s i z e of Vitamin B,* was estimated t o be 12 ml/min [81.
The values for Km calculated as show be-
f o r e were compared t o those obtained using equaticns 31 and
VILLARROEL
340
32 developed for maximum plasma concentration decay. The body volume of d i s t r i b u t i o n for urea and the middle molecule for t h i s l a s t case were estimated to be 35 and 20 l i t e r s respectThe real and apparent clearances calculated w i t h equations
ively.
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31 and 32 were within 2 3% of that calculated w i t h the simple
theory assuming canstant plasma concentration.
The values of tg5
calculated by iteration of equations 31 and 32 were not significantly different from those calculated using equation 20 shown earlier. Table 1 shows that t h e r e is a very small change in intermittent clearance within the normal range of dialysate exchange of It also shows that the time needed
two t o four l i t e r s per hour.
to reach 95% of the maximum apparent clearance is approximately m e hour for urea and even larger for middle molecules.
The
calculated clearances show that ccntinuous flow peritoneal dialysis is more efficient than the intermittent made, particularly a t
higher flow rates.
TABLE I
Comparison of Intermittent and Continuous Peritoneal Dialysis Flow Rate or Rate of Exhange
Middle Molecule
Urea fT I
K
m
a
t
95
E/hr
ml/min
ml/min
& u
4.00 3.00
22.9 24.7 23.3
30.4 26.4 20.9
51 59 70
2OOQ
I
t
R
CM ml/min
95
6.3
10.2
76
7.3
9.7
8.1
97
8.8
132
ml/min -
1NTERMI"T
AND CONTINUOUS PERITONEAL DLUYSIS
341
The clearance of middle molecules shows a decrease with flow i n t h e i n t e r m i t t e n t case in c c n t r a s t with the increase show i n t h e ccntinuous mode.
The r e l a t i v e inefficiency of i n t e r m i t t e n t
peritoneal d i a l y s i s is the r e s u l t o f t h e inflow and outflow
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processes which take a l a r g e part o f the d i a l y s i s time.
In t h e
hypothetical case in which both t r a n s i e n t processes are eliminated leaving m l y t h e c m s t a n t volume resident process, t h e i n t e r m i t t e n t
mode of d i a l y s i s would be more e f f i c i e n t than t h e ccntinuous mode. Theoretically, i f cmtinuous flow rates of 130
- 200 ml/min
are achieved [71, the clearance o f urea could increase 50 t o 70%
over that obtained using n o m l i n t e r m i t t e n t mode of d i a l y s i s . The clearance of middle molecules could cmceivably be increased by about 40%.
h e should be aware, however, that the mass transfer coeffic i e n t , KO, assumed ccnstant for t h i s a n a l y s i s , is a parameter which is affected by t h e d i a l y s a t e side resistance. The value of KO f o r ccntinuous flow d i a l y s i s may be higher o r lower than that f o r i n t e r m i t t e n t mode depending cn t h e positicm and design
o f the catheters.
If the cmtinuous flow produces a d d i t i m a l
mixing, KO could be higher;
but i f flow channeling o r by-pass
occurs between the input and output catheters then Ko.could be s i g n i f i c a n t l y reduced and t h e advantages of using ccntinuous flow d i a l y s i s cancelled.
It is q u i t e possible that a compromise
between ccntinuous and intermittent peritoneal d i a l y s i s could
be achieved by using a s i n g l e c a t h e t e r and a l t e r n a t i n g t h e inflow and outflow process with an average resident volume of about two
342
VILLARROEL
liters.
If an a lt e rna t ing input-output flow of 200 m l / m i n is
obtained at i n t e r v a l s of me minute, the resident volume could be maintained between 1.8 and 2.2 l i t e r s w i t h an equivalent
cmtinuous flow of 100 m l / m i n .
'his process is ccnceptually more
Ren Fail Downloaded from informahealthcare.com by University of Otago on 01/06/15 For personal use only.
e f f i c i e n t than the present intermittent peritmeal d i a l y s i s mode and has t h e advantage of using cnPy me catheter.
ACKNOWLEDGMENT
The views expressed here are the a ut hor 's own. No o f f i c i a l support o r endorsement by t he National I n s t i t u t e s of Health i s intended nor should be inferred. However, the author wishes to thank DT. Robert P. Popovich of the University of Texas f o r h i s cooperation and invaluable exchange of ideas. REFERENCES
"0:
1.
Boen, S. T. Medicine,
2.
Shinaberger, J. H. Shear, L., and Earry, K. G . Soc. Artif. Int . Organs, 2:76, 1965.
3.
Miller, J. H., Cipstein, R . , Margules, R., Schwarts, M . , and Rubini, M. E. Trans. h e r . Soc. A rtif. I n t . Organs, '12: 98, 1966.
4.
243, 1961. Trans. h e r .
Gross, M. arid M c h a l d , H. P. J. h e r . Med. Ass. 363, 1967.
202:
5.
h g e , K. and Tresser, G. Organs. 3:164, 1967.
6.
Cordan, A . , Lewin, A. J . , Maxwell, M. H., and Morales, N . D. T m s . h e r . Soc. Artif. I n t . Organs, 2: 599, 7976.
Trans. Amer. Soc. Artif. Int.
7.. Stephen, R. E , , Atkin-Thor, E . , and Kolff, W. J. Amer. Soc. Artif. I n t . Organs, 2:575, 1976.
8,
Popovich, R. P., Mcncrief, J. W. and Decherd, 9. F. Proc. 9th Annual Ccntractors' Ccnference of the Artificial Kidney Chrcnic Uremia Program, NIH 77-1 167. 2: 126, 1975.
-
INTERMITTENT AND CONTINUOUS PERITONEAL DIALYSIS APPENDIX
INTERMITTENT FLOW DIALYSIS Inflow Process
(1)
dt
(2)
d(CDVD) Z +
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d(CDVD)
- cD)
K A(CB 0
-(C
dVD
v
D D
) =
Qi
B' vD Qi
where the inflow rate, Qi, is constant, and
(3)
2 =
-- "D
"DM 1
(4)
CD1 = CB [1
= constant
-
-
exp(-Z ti) ti
1
where C is the dialysate concentration at the end of the inflow D1process. Constant Volume Process
(5)
VD = VDM = constant
is the dialysate concentration at the end of the where C constan?2volume process.
343
VILLARROEL
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Outflow Process
where the outflow rate, Qo9 is constant and is equal to - d V D/dt. Then
(10)
-
dCD
= Z(C,
- CD)
dt
During the outflow process, the dialysate concentration is given by the following expression:
where t ranges from 0 to to.
-
where ED is the concentration of the dialysate collected at the end of the exchange. The intermittent clearance is defined by
(13)
-KI
-
- -QD
cD a
cB
-
Where QD equals VDM/tt
Then
345
INTERMITTENT AM) CONTINUOUS PERITONEAL DLALYSIS
( 14)
-KI
[
vDM t
CONTINUOUS
-
1
1
- exp(-Z
-
1
exp(-2 t i )
exp (-2 t r > to
t
now
to) 1
ti
DIALYSIS
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Apparent C l e a r a n c e Neglecting t h e inflow process
(15)
VDM
dCD
Ko%(CB
-
- QDCD
CD)
dt where Q
D
is t h e d i a l y s a t e flow.
where t is t h e t i m e l a p s e d s i n c e t h e b e g i n n i n g of t h e p r o c e s s . The a p p a r e n t c l e a r a n c e measured on t h e o u t f l o w i n g d i a l y s a t e is g i v e n by:
-cD
KCA
QD
cB
eA KCA
1
-+-
KO%
Q,
BA=l-exp
(-
QD
.)
KCA r e a c h e s 95% of i t s maximum v a l u e , Km,
(20)
tg5 =
'DM Ko%l
+
QD
when
eA
5
0.95 a t
346 The maximum a p p a r e n t c l e a r a n c e i s g i v e n by: 1
1 +A QD
KoAM
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Real C l e a r a n c e The r e a l c l e a r a n c e i s g i v e n by:
S u b s t i t u t i n g e q u a t i o n 15 i n t o 2 1 y i e l d s :
(24)
eR=
1
+
-
KoPk exP
(- ":Dl
QD
.>
QD The w a l u e of KCR p r e d i c t e d by e q u a t i o n 2 3 i s always h i g h e r t h a n KCM E f f e c t of C, Decay k
Maximum CB d e c a y OCCUKS when t h e g e n e r a t i o n r a t e of t h e s o l u t e i s assumed t o be z e r o . Then
deB
(25) vB
dt
a
-
Ko%(CB
-
CD)
where V g i s t h e volume o f d i s t r i b u t i o n of t h e s o l u t e i n t h e body. S o l v i n g e q u a t i o n s 15 and 25 s i m u l t a n e o u s l y r e s u l t s i n :
INTERMITTENT AND CONTINUOUS PERITONEAL DIALYSIS 1 - exp(-2Bt) cD cB +a? 1 + 6 e x p ( - Z @ t ) 1
(26)
=
1
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Where
(28)
BxK
(29)
Y =
A
O M
V
(30)
6 =
(1 + a )
B VDM +
v p
+a)
'DM 'B VB VDM + v ( 1 + * ; 2
v~~
+
B
Substituting equation 26 i n t o 17 y i e l d s :
1 (31)
1
-
1
+
KCA =
-1+ QD
Y '0%
exp(-2
fit)
exp(-2Bt)
347
