The International Journal of Artificial Organs / Vol. 32 / no. 8, 2009 / pp. 482-491
Artificial Kidney and Dialysis
In vitro tests and modelization of bicarbonate kinetics and mass transfers during online hemodiafiltration Hélène Morel, Michel Y. Jaffrin, Patrick Paullier, Cécile Legallais Compiègne University of Technology, UMR CNRS 6600, Dept. of Biological Engineering, Compiègne - France ABSTRACT: This paper proposes an in vitro hemodiafiltration (HDF) model in which the patient is represented by a 2 L bag of fresh heparinized bovine blood circulated by a 4008H monitor through a 0.6 m2 hemodialyzer to investigate kinetics of bicarbonate (HCO3-) during online post-dilution HDF. Five tests were carried out, with three ultrafiltration rates, zero (HD test), 30 and 50 ml/min. Blood gases, pH, HCO3-, hematocrit and electrolytes were measured with an ABL77 (Radiometer) blood gas analyzer, and HCO3- was simultaneously measured with a biochemistry analyzer. The variation over time of plasma HCO3- concentrations was also calculated using mass conservation and the model of Legallais et al (JMS 168, 2000, 3-15). Agreement between theoretical and measured concentrations was good during the first 25 minutes of each test, corresponding to the time necessary to dialyze the blood. In hemodialysis (HD), there was an HCO3- mass transfer into blood through the membrane due to diffusion which vanished after 40 minutes, while in HDF tests, blood lost HCO3- due to ultrafiltration after 10 minutes. With reinjection, the net HCO3- mass flow rate to the “patient” decayed, from 1.8 mmol/min at t=0 to zero at the end of the test (t=60 min), and was higher in HD than in HDF. “Patient” dialysance, taking into account reinjection, was positive in all tests, and decayed from about 110 ml/ min to 40 ml/min at the end of dialysis. These data confirmed that online HDF automatically corrects acidosis without creating alkalosis when HCO3- dialysate concentration is around 30 mmol/L. (Int J Artif Organs 2009; 32: 482-91) Key words: Hemodiafiltration, Acid-base balance, Bicarbonate dialysance
Introduction Blood acidosis needs to be corrected in end-stage renal disease patients as it affects several metabolic processes in the body (1) and could lead to malnutrition. This correction can be achieved by including a buffer such as bicarbonate (HCO3-) in dialysis fluid and the buffer gain should be adjusted so that patients are maintained close to the physiological bicarbonate range. In the case of hemodiafiltration (HDF), with a higher ultrafiltration (UF) rate than standard hemodialysis, there is a significant loss of HCO3from blood through the hemodialyzer membrane. This loss can be corrected by including buffer in the re-infusion fluid, which, in online HDF, has the same composition as dialysis fluid. The kinetics of bicarbonate transfers in HDF has been investigated by Pedrini et al (2) for different infusion modes, pre-, post- and mixed dilution. They observed that, in 0391-3988/482-10$25.00/0
© Wichtig Editore, 2009
HDF, blood always lost HCO3-, which was compensated by re-infusion; and that the patient gain in HCO3- was larger in post-dilution than in pre-dilution. They also computed the instantaneous net HCO3- mass flux to the patient and found that it decreased from 1.8 mmol/min to 0.4 mmol/ min after 175 minutes in HDF post-dilution. Ahrenholz et al (3) also studied the impact of infusion mode on the acidbase status and concluded that acidosis was effectively corrected without excessive compensation by the buffer. They found that, in fact, the HCO3- concentration increase during dialysis was larger when its initial concentration was low, so that the final HCO3- concentration remained generally between 28.3 and 29 mmol/L. Heineken et al (4) developed a method based on Sargent and Gotch’s equation (5) to determine the correct dialysate bicarbonate concentration for dialyzed patients. Dialysis fluid HCO3- concentrations for their 9 patients ranged from 29 to 38 mmol/L. After a 30-week study period, they con-
Morel et al
cluded that individually prescribed HCO3- concentrations resulted in a more normal acid-base status. Since the acidic state is related to CO2 blood concentration, and bicarbonate can form when CO2 released by cells combines with H2O in the presence of an enzyme from red cells, the acid-base status may also be monitored from partial CO2 pressure (pCO2). Sombolos et al (6) investigated the pCO2 and pO2 increments observed in blood after its passage through the hemodialyzer. They measured a blood pCO2 increase from 38.3 to 62.8 mmHg after 5 minutes of high-flux dialysis, while dialysate pCO2 fell from 79.8 to 53.3 mmHg. Blood pO2 also rose from 86.8 to 100.6 mmHg while dialysate pO2 dropped from 134 to 125.8 mmHg. They concluded that gas transfers from dialysate were responsible for these changes and measured mean dialysances for CO2, O2 and HCO3- of 0.45, 0.12 and 0.134 l/min, respectively. Canaud et al (7) published a 12-month study on 55 patients treated with online HDF. Mean plasma HCO3- concentrations were 22.8 mmol/L pre-dialysis and 29.9 mmol/L post-dialysis. To avoid overcompensation resulting in postdialysis alkalosis, dialysate HCO3- concentration had to be reduced from 39 to 35 mmol/L after a six-month period. Due to the large number of parameters governing HDF, such as blood, UF and dialysate flow rates, HCO3- concentration, pCO2, pH, and so forth, and the necessity of collecting many blood samples for a thorough analysis, a complete study of the effects of these parameters is difficult to carry out in dialyzed patients. It is thus legitimate to check whether an in vitro HDF model using fresh bovine blood can provide useful information with better control of different parameters by varying a single parameter at a time. To this effect, in vitro tests were conducted on an extracorporeal circuit filled with two liters of heparinized bovine blood using a Fresenius Medical Care 4008H dialysis monitor and FX40 hemodialyzers.
inlet dialysate HCO3- concentration and α the Donnan factor, equal to 1.05 (8). The numerator of Eq. 1 represents the bicarbonate mass transfer Mbh per unit time from blood to dialysate through the membrane Mbh=QbiCbi-QboCbo
This mass transfer can also be calculated in the dialysate by Mdh= QdoCdo- QdiCdi
Dialysances and mass transfers calculations The hemodialyzer bicarbonate dialysance Dh was calculated using:
[1]
where Qbi and Qbo denote inlet and outlet blood flows, Cbi and Cbo represent corresponding bicarbonate blood concentrations at hemodialyzer inlet and outlet, Cdi the
[2b]
In hemodialysis without reinfusion, the hemodialyzer dialysance is equal to the patient dialysance, as QboCbo is equal to mass flow rate returning to the reservoir representing the patient. In HDF with a reinfusion flow rate Qr, the HCO3- mass flow rate returning to the patient is QboCbo + QrCdi, so that HCO3- concentration in blood returning to the patient C’bo is given by (Qbo+Qr)C’bo = QboCbo+QrCdi
[3a]
With the help of Eq. 3a, the “patient” dialysance Dp, which is the clinically significant one, is given by
[3b]
Thus, the net HCO3- mass transfer gained by the “patient” per unit time (Mbp) is: Mbp= QboCbo + QrCdi –QbiCbi = QrCdi- Mbh
[4]
Since flow rates Qbi, Qf, Qr are known because they are controlled by the generator and Qbo= Qbi-Qf
methods
[2a]
[5]
experimental mass flow rates and dialysances can be calculated as a function of time from measurements of Cbi and Cbo in blood samples. HCO3- can only be measured in plasma, but it is also present in red cells. HCO3- is distributed in plasma and red cells according to: Crc = KCp
[6]
where Cp and Crc denote HCO3- concentrations in plasma and in red cells, respectively. The partition coefficient K has been taken as equal to 0.57, according to Pellet (9). 483
Bicarbonate kinetics in hemodiafiltration
Consequently, blood and plasma concentrations are related, from mass flux conservation, by QbCb= HQbCrc + (1-H)QbCp
[7]
where H denotes the local hematocrit. With the help of Eq. 6 and dividing Eq. 7 by Qb Cb = (1 - H + 0.57H)Cp= (1-0.43H)Cp
[8]
Applying Eq. 8 at inlet and outlet and substituting Cpi and Cpo to Cbi and Cbo respectively into Eqs 1-.3 yields [9] Mbh=QbiCpi(1-0.43Hi)-QboCpo(1-0.43Ho)
[10]
Fig. 1 - Schematic of one compartment model and extracorporeal circuit (with Qf = Qr = 0, 30, or 50 ml/min and Cdi (HCO3-) = 32 mmol/L).
[11]
Mbp is still given by Eq. 4. If Vb denotes the total blood volume, the HCO3- mass balance in the total extracorporeal circuit of Figure 1 is expressed as: d(VbCbi)/dt= Mbp = QboCbo + QrCdi –QbiCbi
[12]
In the case of a weight loss rate Qp = Qf- Qr, we have dVb/dt = -Qp
te transport across the membrane by both diffusive and convective mechanisms. It computes local concentration, flow rate and pressure variations along the membrane in both the blood and dialysate compartments and was modified in order to use it for bicarbonate at any dialysate inlet concentration Cdi. Inserting values of Cpo as a function of Cpi for each experimental condition made it possible to numerically integrate Eq. 15 using Matlab software.
[13]
Experimental set-up leading to Vb=Vbin- Qpt
[14]
if Qp is constant and Vbin is the initial blood volume. Using Eqs 8, 13 and 14, Eq. 12 becomes (Vbin- Qpt)(1-0.43Hi) dCpi/dt = QboCpo(1-0.43Ho)+ QrCdi–Cpi(1-0.43Hi) (Qbi –Qp) [15] where Ho = Hi (Qbi/Qbo) = Hi (Qbi/(Qbi –Qf))
[16]
Modelization of time variation of HCO3- concentration and mass fluxes Cpo was expressed in terms of Cpi using the model from Legallais et al (10), developed in Turbo Pascal, which calculates solute removal in a hemodialyzer as a function of module geometry, membrane characteristics and operating conditions. This model accounts for solu484
In vitro experiments were carried out using a 4008H hemodialysis monitor (Fresenius Medical Care, Bad Homburg, Germany). The FX40 module parameters were L=23 cm, 4490 fibers of 185 µm inner diameter, a 35 µm membrane thickness and a membrane hydraulic permeability of 34 ml/h/mmHg/m². The “patient” was represented by a 2 L bag of heparinized bovine blood, collected at the Laon (Aisne) slaughterhouse with one volume of anticoagulant (1 L PBS + 5 mL of heparin at 5000 U.L./ mL), for eight volumes of blood. This low volume permitted each test to be repeated under the same conditions using a second blood bag from the same animal, in order to check the repeatability of the tests. Blood was transported from the slaughter house to our laboratory in an ice box and kept at 4°C. The first blood bag was used 24 hours after collection at the slaughterhouse and the second blood bag at 48 hours. Only small changes were observed in pH, pCO2 and pO2 as shown in Table I. FMC FX40 hemodialyzers with a membrane area of 0.6m² were selected because of the small blood volume.
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Test protocol Five tests were carried out at an inlet blood flow (Qbi) of 200 ml/min (due to the small hemodialyzer area and the small blood volume), a dialysate inlet flow rate Qdi of 500 ml/min and Qp=0. Composition of dialysis fluid in mmol/L was: Na: 142; K:3; Ca: 1.75; Mg: 0.5; HCO3-: 32; Cl: 114.5; H+: 3; and glucose: 1 g/L. The first test (HD) was done at Qf=Qr=0. Two tests, HDF1 and HDF2, were carried out with the same blood at Qf=Qr=30 ml/min and tests HDF3 and HDF4, also with same blood, at Qf=Qr=50 ml/min. The duration of each test was about 1 hour. It will be shown later that the equivalent dialysis time was about 20 minutes, based on a Kt/V = 1.4. Blood temperature was maintained at 37±1°C. Three 1 mL samples in the extracorporeal circuit were collected simultaneously at the blood inlet and outlet of the hemodialyzer and at the dialysate outlet, every 5 minutes in the first 30 minutes and then every 10 minutes. Only one sample in the dialysate inlet was taken at the beginning of the experiment in order to check the bicarbonate concentration. Blood samples were immediately analyzed by a blood gas analyzer ABL77 (Radiometer, Copenhagen, Denmark). Plasma samples of 0.3 mL obtained after centrifugation were also analyzed by a biochemistry automate Konelab 20 (Thermo Fisher Scientific, Waltham, MA, USA) together with dialysate samples.
[17]
where pKp is an empirical constant which takes into account the various forms of bound CO2. Eq. 17 becomes:
[18a]
with
[18b]
where αCO2 = 0.0307 mmol/(LmmHg), and pCO2 is in mmHg (11). Total CO2 concentration in plasma ([tCO2]) is given by [19] tCO2= αCO2 pCO2 + [HCO3-(P)] Bicarbonate concentration in plasma was also measured by a colorimetric enzymatic method using the Konelab 20. The plasma CO2 (in the form of bicarbonate ions) reacts with phosphoenolpyruvate (PEP) to form oxaloacetate and phosphate. The resulting decrease in absorbance at 380 nm was proportional to the amount of bicarbonate present in the sample (12). All measurements were done in triplicate and average values and SD were recorded.
Biochemical analysis
Results
The pH, pCO2, pO2, hematocrit and electrolytes (Ca2+, Na+, K+, Cl-) were measured in whole blood using the ABL77 and HCO3- concentrations in plasma ([HCO3-(P)]) were calculated using the Henderson-Hasselbalch Eq. 11:
Tests characteristics and pre- and post-dialysis plasma and blood concentrations are listed in Table I. Cdi was set to 32 mmol/l in the dialysis machine for each test, but measured values ranged from 29.1 to 31.3 mmol/L as seen in Table
TABLE I - BOVINE BLOOD CHARACTERISTICS IN THE TESTS MEASURED WITH ABL77 AND KONELAB 20 FOR TPROT Mode Qb (ml/min) Qf (ml/min) pH pCO2 (mmHg) pO2 (mmHg) Hi (%) Na (mmol/L) K (mmol/L) Ca (mmol/L) Cl (mmol/L) HCO3-(P) (mmol/L) tCO2(P) (mmol/L) Cdi HCO3-(mmol/L) TProt (g/dL)
HD Pre
7.17 35 53 34 146 4.9 0.89 113 12.3 13.4 6.6
Post HD 200 0 7.12 91 58 35 139 2.9 1.55 106 28.3 30 29.9 6.7
HDF1 Pre
7.26 45 30 34 143 5.2 0.95 111 19.5 20.9 5.7
Post HDF 200 30 7.14 88 40 36 139 2.9 1.6 106 28.7 31.4 29.1 5.7
HDF2 Pre
Post
HDF 200 30 7.2 7.14 57 89 20 27 35 37 141 138 6.7 2.9 0.96 1.57 111 105 21.4 29 23.1 31.7 30.8 5.9 6.3
HDF3 Pre
7.27 46 35 31 147 4.1 0.97 119 19 20.4 5.5
Post HDF 200 50 7.15 85 45 33 140 2.9 1.62 108 28.4 31 29.6 5.5
HDF4 Pre
Post HDF 200 50
7.14 56 39 30 146 5.4 1.01 119 18.3 20
7.13 91 45 31 140 2.91 1.61 108 29 31.8 31.3
5.5
5.4
485
Bicarbonate kinetics in hemodiafiltration
I. This is due to the fact that the generator measures Cdi from fluid conductivity before mixing with the rest of dialysate. It can be seen that blood pH, hematocrit (H), pCO2 as well as ion concentrations are comparable to those of dialyzed patients, but as expected, since the blood was collected from a vein, values of pO2 are much lower than for in vivo arterial blood. The initial HCO3concentration was unrealistically low in the HD test, but it is interesting to see that the final value was similar to those in other tests. Another difference is the high pCO2 increase post-dialysis, due to the fact that the CO2 transfer from the dialysate described in (6) was confined into 2 L of blood, which is much less than in vivo under breathing conditions. The pO2 also increased post-dialysis, but less than pCO2, due to the smaller pO2 in dialysate. Table II gives the increase in HCO3- concentration measured by ABL and the increase in total CO2 measured by ABL during the tests. Unlike the in vivo case, the pH did not increase as expected after in vitro dialysis, due to absence of breathing which would have reduced CO2. Application of the Legallais et al model (10) to the FX40 hemodialyzer for experimental conditions of each test resulted in the following relations between Cpo and Cpi in g/L, using the mean measured value of Cdi=30 mmol/L Test HD1, Qf=0 Cpo=0.1179Cpi +1.6143 [20a] Tests HDF1 and HDF2, Qf=Qr=30 ml/min Cpo=0.1015Cpi +1.6462 [20b] Tests HDF3 and HDFD4, Qf=Qr=50 ml/min Cpo=0.0871Cpi +1.6722 [20c] By substituting Cpo from Eqs. 20 in Eq. 15 and integrating with time from initial conditions by Matlab, we have obtained theoretical curves for the HCO3- concentration shown in Figures 2 and 3. Initial conditions for HCO3- concentration and hematocrit used in the Matlab model for the tests are given in Table I.
Variation of HCO3- and total CO2 concentrations during the tests These variations with time are plotted in Figure 2 for HD, and Figure 3 for HDF1 and HDF4 tests. Measure-
Fig. 2 - Comparison between plasma HCO3- concentrations (Cpi) measured by Konelab and ABL 77 in HD test and calculated by the model.
ments of inlet HCO3- concentration by the ABL77 and by the Konelab are presented for comparison, together with concentrations calculated by the model Eq. 15 from initial values of Cpi. In the HD test (Fig. 2) both HCO3and total CO2 concentrations reach their maximum level in about 30 minutes, due to the small blood volume, which means that the blood has been completely dialyzed in less than 30 minutes. Error bars shown in graphs correspond to HCO3- variation coefficients of the three samples equal to 1.4% and 7% respectively for Konelab and ABL77. The HCO3- concentration measured by the Konelab is higher than that measured by ABL77 by about 1-3 mmol/L, but remains less than the total CO2 of ABL77. The model curve remains between ABL and Konelab data during the first 25 minutes, and slightly overestimates HCO3- concentration at a longer time. In HDF tests (Figs. 3a and 3b), the HCO3- concentrations measured by the Konelab were lower than those measured by ABL77, but the difference was small: 1-2 mmol/L. Here again, the model is close to ABL data during the first 25 minutes, with a slight overestimation after that. Increasing Qf and Qr from 30 to 50 ml/min did not change the final HCO3- concentrations.
TABLE II - BICARBONATE POST (AT 20 MINUTES) AND PRE-DIALYSIS DIFFERENCES IN TESTS MEASURED WITH ABL77
HD
HDF1
HDF2
HDF3
HDF4
Mean HDF
∆HCO3-(P) (mmol/L) HCO3- gained by the patient in mmoL
13.6
7.6
6.2
8.7
9.3
7.95
22.56
12.05
9.54
14.13
15.48
12.8
486
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Fig. 3 - Comparison between measured plasma HCO3- concentrations (Cpi) and data model in HDF1 (a) and HDF4 (b) tests
A
B
Fig. 4 - Variation with time of HCO3- mass flow rate Mbh leaving blood through the membrane in HD (a) and HDF4 (b) tests
Variation of HCO3- mass transfers and dialysances with time We now calculate HCO3- mass transfers (Mbh) from blood across the hemodialyzer membrane calculated from Eq. 10 using Konelab and ABL data, and those using concentrations Cpi and Cpo calculated by the model Eqs. 15 and 20. This transfer, given in Figure 4a for the HD test, is negative as there is, in dialysis without UF, a net gain of
HCO3- by blood, due to diffusion from dialysate. Figure 4a shows that, as expected, there is good agreement between mass transfers from blood (Mbh) measured by ABL and into dialysate (Mdh) measured by Konelab. The model is in very good agreement with ABL data at all times. Results for test HDF4 with Qf=Qr=50 ml/min are given in Figure 4b. The transfer becomes positive after 2 minutes since there is a loss of HCO3- by UF which exceeds the diffusive transfer from dialysate. Here again, there is good agreement 487
Bicarbonate kinetics in hemodiafiltration
Fig. 5 - Comparison between HCO3- Mbh calculated with ABL77 data in HD, HDF1 (Qr = 30 mL/min) and HDF4 (Qr = 50 ml/min) tests with Mbh from the model.
between Mbh mass transfers measured in blood by ABL and those by the model at all times. Figure 5 represents the comparison of mass transfer (Mbh) calculated from ABL data with those given by the model for tests HD, HDF1 and HDF4. The agreement is very good for the three tests, which confirms the validity of the Legallais et al model. The mass transfer into blood increases with the reinjection flow rate. The variations of Mbp, the HCO3- mass transfer to the “patient”, calculated from Mbh and Eq.10 using HCO3concentrations measured by the Konelab and ABL 77 and calculated by the model are represented in Figure 6 for HD, HDF1 and HDF4 tests. These mass transfers decay with time towards zero and are lowest in the HDF1 test and highest in the HD test. The agreement with the model was very good in all tests. HCO3– “patient” dialysances, calculated from Eq.11 using ABL data are shown in Figure 7 for HD, HDF1 and HDF4 tests. These “patient” dialysances remained positive, as observed previously by Petitclerc (13) but decayed from about 110 ml/min to 40 ml/min in 20 minutes, reaching zero at the end of the test (60 minutes). This is a consequence of the decay of Mbp to zero during the test while the denominator of Eq. 11 remains finite as αCpi-Cdi is negative. The model generally overestimates the dialysance, but a reasonable agreement was observed in test HDF1 between 15 and 30 minutes. The final plasma HCO3- concentration measured with ABL is shown in Table I for all tests and remained between 28.3 and 29 mmol/L, although the initial one varied betwe488
Fig. 6 - Comparison between net HCO3- mass flow rate Mbp gained by theî patientî calculated with ABL77 data in HD, HDF1 (Qr = 30 ml/min) and HDF4 (Qr = 50 ml/min) tests with Mbp from the model.
Fig. 7 - Comparison between HCO3- “patient” dialysance measured in HD, HDF1(Qr = 30 ml/min) and HDF4 (Qr = 50 ml/min) tests by ABL77 with HCO3- “patient” dialysance calculated from the model.
en 12.3 and 21.4 mmol/L, while the spread of final values was a little larger with the Konelab.
Discussion Our results confirm the observation of Ahrenholz et al (3) that, with proper inlet dialysate HCO3- concentration around 32 mmol/L, the final HCO3- concentration remained between 28 and 29 mmol/L for a wide range of initial concentrations. These results also showed that patient HCO3-
Morel et al
Fig. 8 - Differences between initial and final HCO3- plasma concentrations as function of initial HCO3- plasma concentration (measured by ABL) for the 5 in vitro tests. Final HCO3- concentrations have been taken at the equivalent dialysis time (20 minutes).
mass transfer and dialysances were mainly controlled by initial HCO3- concentration and were higher at low Cbi. For this reason, we could not assess the effect of UF flow rate on HCO3- mass transfer as Cbi varied in our tests.
Comparison of in vitro data with corresponding clinical data from the literature Our in vitro model differs from a patient in several respects: there is a smaller blood volume and no extracellular and intracellular water other than in the blood as well as no O2 transfer from the lungs. Because of this, it is important to verify if and how our results differ from those of clinical studies. We first compare variations of plasma HCO3- concentrations with time shown in Figures 2-3 with those given by Pedrini et al (2) in their Figure 1. For a blood flow (Qbi) of 400 ml/min, a reinjection rate (Qr) of 120 ml/min and a dialysate HCO3- concentration of 28.9 mmol/L, these authors found, for post-dilution HDF, an HCO3- concentration rising from 19.6 mmol/L to 24.3 after 60 minutes and to 26.6 after 175 minutes (end of run). In our test HDF1, with Qbi = 200 ml/min, Qr= 30 ml/min and a dialysate HCO3- concentration of 29.1 mmol/L, Table I shows that HCO3- concentration measured by the ABL77 rose from 19.5 to 28.7 mmol/L at the end of test (60 min). In HDF4 test, with Qr=50 ml/min and Cdi= 31.3 mmol/L, HCO3concentration rose from 18.3 to 29 mmol/L. The mean
HCO3- concentration rise in our tests (see Tab. II) was 9.2 mmol /L versus 7.2 for those of Pedrini et al (2). Pedrini et al also found that the HCO3- mass transfer to the patient Mbp decreased from 1.8 mmol/min to 0.4 after 175 minutes while, in our HDF1 test, it decayed from 1.8 mmol/min to 0.3 after 20 minutes, the in vitro dialysis duration (Fig. 6). Ursino et al (8, 14) also investigated HCO3- kinetics using a three-compartment model and compared it with clinical data. They reported rises in HCO3- from 20 to 25 mmol/L in one patient and from 20 to 28 mmol/L in another, with an inlet dialysate concentration of 30 mmol/L. As seen in Figure 8 and Table I, we obtained similar rises in HCO3- concentration from initial concentrations of about 20 mmol/L. Ahrenholz et al (3) have observed in a series of 150 post-dilution and pre-dilution HDF treatments that the increase in HCO3- concentration decreased linearly with increasing initial concentration. Their explanation was that the dialysate/infusate HCO3- concentration determines the maximum plasma HCO3- concentration. Figure 8, which uses the data from Table II, shows that our increases in HCO3- over 20 minutes (corresponding to the equivalent dialysis time) measured by ABL are a little higher than those from Ahrenholz. But their variation at the same initial concentration is the same (the slopes of the curves are very close: we found -0.8 and Ahrenholz -0.75), confirming that acidosis is automatically corrected with a measured dialysate HCO3- concentration of around 30 mmol/L. These data show that our choice of scaled-down blood volumes, blood flow rates and membrane area leads to HCO3- kinetics close to that observed in vivo. A somewhat unexpected result was that both hemodialyzer and “patient” HCO3- dialysances were not constant, but decayed with time towards zero for both HD and HDF. This result does not seem to have been reported in the literature, but it is consistent with the findings reported by Pedrini et al (2) that plasma HCO3concentration leveled off after two hours in a threehour session. In view of the small blood volume, the dialysance Dp decay towards zero is in fact due to the long duration of our tests. A normal duration T for dialysis is such that the ratio DpT/V is around 1.4. Assuming a “patient” dialysance Dp =100 ml/min from Figure 7 and V=2 L, gives a duration T of 20 minutes, which corresponds to a final value of dialysance of about 20 ml/min. It can be noted that the denominator of Eq. 3b becomes very small as t>30 min and the accuracy on Dp which is the ratio of two small numbers may be low. 489
Bicarbonate kinetics in hemodiafiltration
Comparison between Konelab and ABL HCO3measurements Except in the HD test, ABL values were slightly higher than those of the Konelab. We felt that ABL gave more consistent results than the Konelab. In addition, the ABL is more versatile as it also measures blood gases, total CO2, etc., and most authors (2, 3) use blood gas analyzers to measure HCO3-. Engelhardt et al (15) have compared acidbase parameters in blood and dialysate by three techniques: titrimetric method, equilibration technique (ET) and blood gas analyzer. For blood, an acceptable agreement was obtained for pH, pCO2 and HCO3- between the blood gas analyzer and ET, but for dialysate, HCO3-, values obtained by titrimetric method were 3-4 mmol/L higher than those determined by the gas analyzer and ET. This difference may be due to the choice of constants in the Henderson-Hasselbalch equation.
Sensitivity of the model to the partition coefficient K We made calculations with our model using first K=0 (no HCO3- in red cells) and then K=1 (same concentration in plasma and red cells), and the differences between concentrations and mass transfers calculated with these two assumptions were small. So the exact value of K, which has been also reported to be 0.4 (16) is not overly important.
Conclusions Our in vitro model, although it represents the “patient” using a small blood volume, seems to adequately reproduce the kinetics and mass transfers of HCO3- and the acid-base balance in a dialyzed patient. The time to reach equilibrium was much smaller (30 min), than in a patient, but this time could have been increased by using a smaller hemodialyzer and smaller blood flow to reduce dialysance. This model can thus be a convenient tool to compare efficiencies of various HDF strategies or various hemodialyzers. Another interesting result was that HCO3- dialysance seems to behave very differently from urea clearance, even though both solutes have a similar molecular weight. HCO3“patient dialysance” decayed with time from about 110 to 40 ml/min during dialysis, while urea clearance, which we also measured, dropped by only 10% due to membrane fouling. These in vitro and mathematical models will be compa490
red with measurements of HCO3- concentrations and dialysances made in dialyzed patients during HD and HDF runs in a subsequent paper. List of symbols Cb (Cp) Blood (plasma) bicarbonate concentration (mmol/L) Cdi
Inlet dialysis fluid HCO3- concentration (mmol/L)
Dh (Dp) Hemodialyzer (patient) HCO3- dialysance (ml/min) H
Hematocrit
Mbh
HCO3- mass transfer from blood to dialysate per
unit time (mmol/min)
Mbp
HCO3- mass transfer gained by the patient per unit time
(mmol/min)
Qb (Qd) Blood (dialysate) flow rate (ml/min) Qf (Qr) Ultrafiltration (reinjection) flow rate (ml/min) Qp
Weight loss rate (ml/min)
Vb
Blood volume (L)
ACKNOWLEDGEMENTS The authors acknowledge the support of Fresenius Medical Care (FMC), Bad Homburg, Germany, and the technical assistance of the Laon slaughter house for bovine blood collection. They wish to thank Prof. J Vienken and Dr. V. Nier from FMC for stimulating discussions.
Conflict of interest statement: This work was supported by a grant from Fresenius Medical Care Company (Biosciences Dept), 15 Daimlerstr, D61352, Bad Homburg, Germany. The authors have no proprietary interest in this work.
Address for correspondence: Professor Michel Jaffrin UTC Dept GB, BP 20529, 60205 Compiègne, France e-mail:
[email protected]
Morel et al
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