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Dialysis & Kinetics

Dialyzer Clearances and Mass Transfer-Area Coefficients for Small Solutes at Low Dialysate Flow Rates

Leypoldt, John K.*†; Kamerath, Craig D.; Gilson, Janice F.; Friederichs, Goetz

Author Information
doi: 10.1097/01.mat.0000227687.88929.08
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Abstract

Dialyzer clearances for small solutes during hemodialysis are determined by the flow conditions (blood, dialysate, and ultrafiltration flow rates) and the mass transfer-area coefficient for the solute of interest. Conventionally, the mass transfer-area coefficient has been assumed to be relatively constant; therefore, solute clearances under given flow conditions are routinely estimated by using standard equations describing diffusive and convective transfer within the dialyzer.1,2 Several recent in vitro studies have shown that the mass transfer-area coefficient for urea was independent of blood flow rate but increased with increasing dialysate flow rate.3–6 In one study on 22 different dialyzer models, the urea mass transfer-area coefficient increased by an average of 14% when the dialysate flow rate increased from 500 to 800 ml/min.4 The clinical significance of these findings was subsequently demonstrated in studies of patients on chronic hemodialysis.7,8

There is recent interest in novel hemodialysis therapies that use dialysate flow rates lower than the conventional rate of 500 ml/min to optimize the use of dialysate, both for treatment of acute9–13 and chronic14–17 renal failure. There are, however, few studies describing the impact of low dialysate flow rate on dialyzer clearances of small solutes. We have previously shown5 that decreasing dialysate flow rate below the conventional rate of 500 ml/min decreased mass transfer-area coefficients of urea and creatinine; however, confidence in those results was tempered because solute mass balance errors in some of those experiments were inexplicably high.

The current study describes a detailed investigation of dialyzer clearances for urea and creatinine at low dialysate flow rates, using a new dialyzer containing PUREMA membranes (NxStage Medical, Lawrence, MA). Dialyzer mass transfer-area coefficients for both urea and creatinine were also calculated and compared with values reported by the dialyzer manufacturer under conventional test conditions.

Methods

Experimental Procedures

Evaluation of dialyzer clearances for urea and creatinine was performed in vitro. The System One dialysis delivery system (NxStage Medical) was used to perfuse the test dialyzer, using bovine blood, with the hematocrit adjusted to 33 ± 2% and total protein concentration to 6.0 ± 0.5 g/dl (Lampire Biological Laboratories, Piperville, PA). Each batch of blood was used in experiments within 48 hours of collection. Approximately 4 liters of blood was placed in a reservoir maintained at 37°C, and 3.0 g of urea and 0.4 g of creatinine were added to the blood to obtain concentrations of approximately 75 mg/dl (urea nitrogen) and 10 mg/dl, respectively. Twenty thousand International Units of heparin (Baxter Healthcare Corporation, Deerfield, IL) was also added to the blood to prevent clotting. The dialyzer blood-side circuit was primed with saline, which was then replaced with blood. The dialysate (PureFlow Solution, NxStage Medical) contained 140 mEq/l sodium, 3 mEq/l calcium, 1 mEq/l potassium, 1 mEq/l magnesium, 105 mEq/l chloride, and 40 mEq/l lactate and was warmed to 37°C by the dialysis delivery system. The blood in the reservoir was first recirculated through the dialyzer without dialysate flow for at least 10 minutes to attain thorough mixing. To begin a clearance determination, the blood and dialysate were perfused in countercurrent directions (single pass with no recirculation) through the test dialyzer at the desired blood, dialysate, and ultrafiltration flow rates until approximate steady-state conditions were reached. During this time, the inlet or arterial blood flow rate was measured by a calibrated ultrasound flowmeter (HD01 monitor, Transonic Systems, Ithaca, NY). After 8 minutes, samples were then taken in rapid succession from the blood outlet, dialysate outlet, blood inlet, and dialysate inlet, in that order. The effluent blood was collected and supplemented with additional urea, creatinine, and heparin for additional dialyzer clearance determinations on the same day. If necessary, the hematocrit was adjusted to 33 ± 2% by adding saline.

Dialyzers and Flow Conditions

The majority of experiments were performed with the use of a dialyzer containing PUREMA membranes (1.46 m2 of membrane surface area). Clearances were determined at a nominal blood flow rate of 400 ml/min, dialysate flow rates of 40, 80, 120, 160, and 200 ml/min, and ultrafiltration flow rates of 0, 1, and 2 l/h. Additional experiments using this same dialyzer were performed at a nominal blood flow rate of 200 ml/min, dialysate flow rates of 40 and 80 ml/min, and ultrafiltration flow rates of 0, 0.25 and 0.50 l/h. The lower ultrafiltration flow rates in these latter studies were to simulate typical conditions during long hemodialysis treatments. Additional studies were performed with the use of the Optiflux 160NR dialyzer, containing polysulfone membranes (1.6 m2 of membrane surface area, Fresenius Medical Care North America, Ogden, UT), and a dialyzer containing Synphan membranes (1.46 m2 of membrane surface area, NxStage Medical). The latter studies were performed only at a nominal blood flow rate of 400 ml/min, a dialysate flow rate of 160 ml/min, and an ultrafiltration flow rate of 1 l/h. Therefore, all dialysate flow rates used were low, less than or equal to 200 ml/min, and considerably less than a conventional dialysate flow rate of 500 ml/min. Each experiment was performed with a new dialyzer and was repeated 3 times under each set of conditions.

Analytical Analyses

All samples were collected and then immediately centrifuged to obtain plasma for assay. Each plasma sample was aliquoted into two separate tubes to allow measurements in duplicate. Urea nitrogen and creatinine concentrations were determined through the use of an autoanalyzer (Dimension RX-L, Dade-Behring, Deerfield, IL). Blood hematocrit was measured by centrifugation.

Calculations

Data reliability was assessed by calculating the urea mass balance error (MBE), which determines the net loss of urea within the dialyzer expressed as a percentage, and is defined by the following equation.

where Cd and Cbw denote concentrations in dialysate and blood (or plasma) water and Qd and Qbw denote the flow rate of dialysate and blood water, respectively. The additional subscripts i and o denote parameter values in the inlet and outlet flow streams to the dialyzer. Plasma water concentrations were calculated from the measured plasma concentrations by dividing by 0.93. The inlet blood water flow rate was calculated from the inlet blood flow rate (Qbi) measured by the ultrasound flowmeter, using the following equation18:

where H denotes the hematocrit. The outlet blood water flow rate was calculated as the inlet value minus the ultrafiltration flow rate.

Dialyzer clearance (K) for urea and creatinine was calculated from both the blood-side and the dialysate-side, using the following equations:

This equation assumes that both small solutes, urea and creatinine, are distributed equally throughout the water space in blood, an assumption that is more accurate for urea than creatinine.19 The dialysate saturation (S), a term describing the extent of equilibration of dialysate with blood water, was defined as the ratio of dialysate outlet concentration to the blood water inlet concentration, or

The mass transfer-area coefficient (KoA) was calculated from the measured dialysate saturation under the given flow conditions. Since dialyzer clearance is equal to dialysate saturation multiplied by the dialysate outlet flow rate (see Equation 3), KoA can be calculated exactly from S when there was zero ultrafiltration, using the following equation1,4:

where ln denotes the natural logarithm. Since S was observed experimentally to be independent of the ultrafiltration flow rate (see results below), KoA was calculated by using Equation 5 at nonzero ultrafiltration flow rates as an approximation by substituting Qbwi and Qdo for Qbw and Qd, respectively, into Equation 5. A second approach for calculating KoA under conditions of nonzero ultrafiltration flow rate was to use the analytical solution derived by Vincent et al.,20 which assumes that the solute sieving coefficient across the membrane is unity (or the solute reflection coefficient is zero). Assuming that convective solute transport across the dialysis membrane is determined by the volume flux times the average of the solute concentration in blood water and dialysate, KoA can be calculated from the following equation20:

where Qf denotes the ultrafiltration flow rate. We compare below the calculated values of KoA under nonzero ultrafiltration flow conditions when using both Equation 5 and Equation 6.

Statistics

All values are reported as mean ± standard deviation. The significance of urea mass balance errors with respect to the expected value of zero was tested by using a Student's t test. The significance of differences in dialyzer clearances, dialysate saturation, and mass transfer-area coefficients as a function of blood, dialysate, and ultrafiltration flow rates was determined by using analysis of variance.

Results

Sixty-nine separate experiments were completed in total. The urea mass balance error for all of these experiments was 0.87 ± 5.72%, a value not statistically different from zero. Based on this result, dialyzer clearances for urea and creatinine for all experiments were calculated as the average value of that determined from both the blood and dialysate sides.

Figure 1 and Figure 2 show urea and creatinine clearances, respectively, at a blood flow rate of 400 ml/min and various dialysate and ultrafiltration flow rates during experiments using dialyzers containing PUREMA membranes. Both urea and creatinine clearances increased with increasing dialysate flow rate (p < 0.001) and with increasing ultrafiltration flow rate (p < 0.001). At these low dialysate flow rates, both urea and creatinine clearances approximate the sum of the dialysate and ultrafiltration flow rates. These results are expected because clearances under these conditions are limited largely by the low dialysate flow rate.

Figure 1.
Figure 1.:
Dependence of urea clearance for dialyzers containing PUREMA membranes on dialysate flow rate at a blood flow rate of 400 ml/min for ultrafiltration flow rates of 0 (white bars), 1 (black bars), and 2 (striped bars) l/h. Standard deviations for all conditions studied were consistently small (individual values not shown) and ranged from 1.7 to 14.0 ml/min. Analysis of variance demonstrated that urea clearance was significantly dependent on both dialysate flow rate (p < 0.001) and ultrafiltration flow rate (p < 0.001).
Figure 2.
Figure 2.:
Dependence of creatinine clearance for dialyzers containing PUREMA membranes on dialysate flow rate at a blood flow rate of 400 ml/min for ultrafiltration flow rates of 0 (white bars), 1 (black bars), and 2 (striped bars) l/h. Standard deviations for all conditions studied were consistently small (individual values not shown) and ranged from 0.7 to 15.7 ml/min. Analysis of variance demonstrated that creatinine clearance was significantly dependent on dialysate flow rate (p < 0.001) and ultrafiltration flow rate (p < 0.001).

To illustrate potential limitations of low dialysate flow rates on solute clearances, dialysate saturation or S was determined by calculating the ratio of the dialysate outlet concentration to the blood water inlet concentration. Analysis of variance showed that S was independent of both blood and ultrafiltration flow rates but decreased (p < 0.001) with increasing dialysate flow rate. As plotted in Figure 3, S for all experiments using dialyzers containing PUREMA membranes was combined for all blood and ultrafiltration flow rates. The decrease in S with increasing dialysate flow rate was greater for creatinine than for urea, as expected for the larger solute whose rate of diffusion across the membrane is expected to be lower.

Figure 3.
Figure 3.:
Dependence of dialysate saturation (S) of urea (white squares) and creatinine (black circles) for dialyzers containing PUREMA membranes on dialysate flow rate at blood flow rates of 200 and 400 ml/min and ultrafiltration flow rates of 0 to 2 l/h. Error bars denote 1 standard deviation. Analysis of variance demonstrated that urea and creatinine S was independent of blood flow rate and ultrafiltration flow rate but significantly dependent on dialysate flow rate for both urea (p < 0.001) and creatinine (p < 0.001). Data are shown as averaged values at a given dialysate flow rate.

Mass transfer-area coefficients for both urea and creatinine were first calculated by using Equation 5; the resulting calculated values were independent of blood and ultrafiltration flow rate but increased (p < 0.001) with increasing dialysate flow rate. These calculated KoA values are shown in Figure 4, plotted as a function of dialysate flow rate, with results at all blood and ultrafiltration flow rates combined together. As observed in this figure, the calculated mass transfer-area coefficients were approximately linearly related to the dialysate flow rate. The best-fit linear regression equation for urea was determined as KoA = 62 + 2.40 × Qd, r2 = 0.86, p < 0.001 and for creatinine as KoA = 89 + 1.42 × Qd, r2 = 0.61, p < 0.001. Further, the mean ratio of KoA values for urea to creatinine of approximately 0.8 is as expected for the dependence of solute diffusion on molecular size.

Figure 4.
Figure 4.:
Dependence of mass transfer-area coefficients for urea (white bars) and creatinine (black bars) using dialyzers containing PUREMA membranes on dialysate flow rate at blood flow rates of 200 and 400 ml/min and ultrafiltration flow rates of 0 to 2 l/h. Values under all conditions were calculated by using Equation 5. Error bars denote 1 standard deviation. Analysis of variance demonstrated that the calculated mass transfer-area coefficients for both urea and creatinine was independent of blood and ultrafiltration flow rate but decreased with decreasing dialysate flow rate (p < 0.001).

The use of Equation 5 to calculate mass transfer-area coefficients under nonzero ultrafiltration conditions is an approximation that is expected to be valid only when the ultrafiltration rate is relatively low. Mass transfer-area coefficients under nonzero ultrafiltration conditions were therefore also calculated by using Equation 6, one that is valid for higher ultrafiltration flow rates as long as the solute sieving coefficient across the dialysis membrane is unity. Example calculated mass transfer-area coefficients for urea determined at a blood flow rate of 400 ml/min and dialysate flow rates of 40 and 160 ml/min, using Equations 5 and 6, are compared in Figure 5. Calculated KoA values were higher when using Equation 6, but these differences were relatively small and do not substantially alter our results or conclusions. When all values under all nonzero ultrafiltration conditions were averaged together for dialyzers containing PUREMA membranes, urea KoA was 7.2% and creatinine KoA was 1.1% higher when using Equation 6 than when using Equation 5.

Figure 5.
Figure 5.:
Example urea mass transfer-area coefficients for dialyzers containing PUREMA membranes at a blood flow rate of 400 ml/min and at dialysate flow rates of 40 (black squares) and 160 (white squares) ml/min for nonzero ultrafiltration flow rates, using Equations 5 and 6.

A comparison of clearances and dialysate saturation for urea and creatinine when using dialyzers containing different dialysis membranes under identical flow conditions are shown in Figure 6 and Figure 7, respectively. Clearances and dialysate saturation for both urea and creatinine when using dialyzers containing PUREMA membranes were higher (p < 0.05) than measured for dialyzers containing Synphan membranes but were not different from those measured for dialyzers containing polysulfone membranes.

Figure 6.
Figure 6.:
Clearances of urea (white bars) and creatinine (black bars) for dialyzers containing different dialysis membranes at a blood flow rate of 400 ml/min, a dialysate flow rate of 160 ml/min, and an ultrafiltration flow rate of 1 l/h. Error bars denote 1 standard deviation. Urea and creatinine clearances were higher (p < 0.05) for dialyzers containing PUREMA membranes than those containing Synphan membranes but were not different from those containing polysulfone membranes.
Figure 7.
Figure 7.:
Dialysate saturation of urea (white bars) and creatinine (black bars) for dialyzers containing different dialysis membranes at a blood flow rate of 400 ml/min, a dialysate flow rate of 160 ml/min, and an ultrafiltration flow rate of 1 l/h. Error bars denote 1 standard deviation. Dialysate saturation for urea and creatinine was higher (p < 0.05) for dialyzers containing PUREMA membranes than those containing Synphan membranes but were not different from those containing polysulfone membranes.

Discussion

Mass transfer-area coefficients for hemodialyzers are frequently reported for a given solute only under limited conditions. Increasing the dialysate flow rate from the conventional 500 ml/min to 800 to 1000 ml/min has been shown to increase urea KoA values from both the dialyzer3,4 and the patient.7,8 The effect of lowering dialysate flow rate below the conventional rate of 500 ml/min has not been studied extensively because high dialysate flow rates are commonly used to decrease treatment times during thrice-weekly therapy in the dialysis unit.

There is recent interest in new, daily hemodialysis therapies that operate at low dialysate flow rates to optimize the use of dialysate. When these therapies have been used to treat chronic renal failure, little work has been performed to assess the effect of the low dialysate flow rates on solute clearances. Instead, clinical studies have been directed to understand the many advantages of such intensive therapies that achieve a very high dose of dialysis such as nocturnal hemodialysis17 or during therapies that use sterile dialysis solutions and minimize inflammation.15,16 When such therapies have been used to treat acute renal failure, certain clinical investigations, especially the pioneering study by Marshall et al.,13 have suggested that urea clearances and urea mass transfer-area coefficients were lower than expected at low dialysate flow rates. Those investigators, however, did not perform a systematic study of the effect of low dialysate flow rates on dialyzer clearances as performed here.

The current studies extend the work of Vincent et al., published over a decade ago,20–22 which demonstrated that small solute mass transfer-area coefficients decreased with decreasing dialysate flow rate during continuous arteriovenous hemodiafiltration. They determined mass transfer-area coefficients of small surface area hemofilters under conditions of high ultrafiltration flow rates but low dialysate flow rates. Their results using conventional hemodialyzers22 were not, however, entirely consistent with their studies using small surface area hemofilters. The current findings determined mass transfer-area coefficients of conventional, large surface area hemodialyzers under conditions of low dialysate and ultrafiltration flow rates, and we observed that the dependence of mass transfer-area coefficients on dialysate flow rate was similar to that reported by Vincent et al.20–22 for hemofilters.

The current findings demonstrate that the dependence of small solute clearances on blood and dialysate flow rates differs when operated at lower dialysate flow rates than during conventional three-times-a-week hemodialysis. During conventional hemodialysis using large surface area hemodialyzers with blood flow rates of 200 to 500 ml/min and high dialysate flow rates of 500 to 800 ml/min, small solute clearance are highly dependent on blood flow rate and less so on dialysate flow rate.19,23,24 In contrast, the current findings at low dialysate flow rates (<200 ml/min) demonstrate that small solute clearances are relatively independent of blood flow rate but highly dependent on the dialysate and ultrafiltration flow rate. More precisely, small solute clearances will be relatively independent of blood flow rate but highly dependent on dialysate flow rate only when the dialysate flow rate is much less than both the blood flow rate and the mass transfer-area coefficient for the solute of interest.25 Thus, it should be emphasized that the current findings may not apply outside the conditions used during this study. Indeed, the independence of small solute clearance on blood flow rate may not apply at low dialysate flow rates if the blood flow rate is decreased significantly below 200 ml/min.

The mass transfer-area coefficients for urea determined in this study for dialyzers containing PUREMA and polysulfone membranes are substantially less than those reported for these dialyzers in the literature from the manufacturer (1200 and 1100 ml/min, respectively). The reported urea KoA values are lower partially because our experiments were performed with the use of bovine blood, not protein-free solutions. More importantly, however, we evaluated dialysate flow rates that were considerably below the conventional rate of 500 ml/min. A unique explanation for these low KoA values for small solutes at low dialysate flow rates cannot be determined from the current data. It is possible that the low KoA values reflect unequal distribution of dialysate flow within the dialysate compartment when perfusing the external surface area of the fiber bundle at low dialysate flow rates.26 Alternatively, the low KoA values may be due to thick unstirred layers at the membrane-dialysate interface at low dialysate flow rates. The importance of the latter phenomenon can be examined by plotting 1/KoA versus (1/Qd)n, where n is an empirical coefficient that is expected to be 0.4 to 0.5 for laminar flows and 0.8 to 0.9 for turbulent flows.19 The value of n is often empirically chosen to give the best straight line in a so-called Wilson plot, and the y-intercept provides an estimate of the mass transfer resistance due to just the membrane and the blood-side unstirred layer. We performed such analyses on both urea and creatinine KoA values by using n values of 0.3, 0.5, 0.8, and 1.0. In each case, a significant linear relation was obtained, with r2 values of approximately 0.81 for urea and 0.54 for creatinine; these statistics were relatively independent of the chosen value of n. When n was assumed as 0.3 or 0.5, the y-intercepts for the urea and creatinine data were negative, and when n was 0.8, the y-intercepts were not significantly different from zero. Only when n was assumed as 1.0 was a positive y-intercept obtained for both urea and creatinine. The Wilson plot for urea, assuming n is 1.0, is shown in Figure 8. These analyses suggest that low KoA values for urea and creatinine at low dialysate flow rate may be the result of thick unstirred layers at the membrane-dialysate interface.

Figure 8.
Figure 8.:
Wilson plot of the dependence of urea mass transfer-area coefficient (KoA) on dialysate flow rate (Qd) for all data obtained from dialyzers containing PUREMA membranes. This linear regression was significant (r 2 = 0.82, p < 0.001) with a y-intercept consistent with a urea KoA value (the multiplicative inverse of the y-intercept) at very high dialysate flow rates of 1720 ml/min.

The practical consequences of decreased mass transfer-area coefficients for urea and creatinine at low dialysate flow rates are that clearances of these solutes will be less than expected when calculated by using literature from the dialyzer manufacturer, and such differences must be accounted for when prescribing therapies at low dialysate flow rates. The current observations emphasize that dialyzers require specific characterization under relevant conditions if they are to be used in novel, daily hemodialysis therapies using low dialysate flow rates.

Acknowledgments

This research was supported by NxStage Medical, Lawrence, Massachusetts, and by the Office of Research and Development, Medical Research Service, Department of Veterans Affairs.

References

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