A detailed analysis of sodium removal by peritoneal dialysis: comparison with predictions from the three-pore model of membrane function

Marissa C. Aanen1, Daniele Venturoli2 and Simon J. Davies3

1 Department of Nephrology, Academic Medical Center, University of Amsterdam, Amsterdam, The Netherlands, 2 Department of Nephrology, Lund University Hospital, Lund, Sweden and 3 Department of Nephrology, University Hospital of North Staffordshire and Institute of Science and Technology in Medicine, Keele University, UK

Correspondence and offprint requests to: Professor Simon J. Davies, Department of Nephrology, University Hospital of North Staffordshire, Princes Road, Hartshill, Stoke-on-Trent, ST4 7LN, UK. Email: SimonDavies1{at}compuserve.com



   Abstract
 Top
 Abstract
 Introduction
 Subjects and methods
 Results
 Discussion
 References
 
Background. The development of fluid and salt retention is a potential problem for all peritoneal dialysis (PD) patients. Sodium removal by the peritoneum is predominantly determined by convective fluid loss but influenced by diffusion and sieving due to free water transport as predicted by the three-pore model (TPM). The aim of the study was to establish the effect of transport status, dwell length and glucose concentration on observed ultrafiltration (UF), dialysate sodium concentration ([Na+]D) and removal, and compare this with that predicted by a computer program based on the principles of the TPM.

Methods. This was a cross-sectional study of UF and [Na+]D collected prospectively from dwells classified by length, glucose concentration and membrane transport characteristics. Solute transport, converted to area parameter and UF capacity, was measured on each occasion by the peritoneal equilibration test. These parameters, along with plasma [Na+], were entered into the computer model. Fixed values for other parameters, e.g. hydraulic conductance and lymphatic absorption and sump volume, were used.

Results. A total of 1853 dwells from 182 patients [10% were on automated PD (APD)] were analysed. There was a high degree of correlation (r = 0.83–95, P<0.001) between the observed and predicted values for UF, [Na+]D and sodium removal across the full range of dwell categories. The model overpredicted UF as the net volume increased with increasing glucose concentration, independently of solute transport. This bias was not fully explained by the preferential use of hypertonic dialysate by patients with reduced UF capacity. The prediction of [Na+]D described sodium sieving, which was overestimated in a small number of patients with UF failure. There were no discrepancies between continous ambulatory PD (CAPD) and APD patients.

Conclusion. This analysis endorses the TPM as a description of membrane function, particularly in relation to sodium sieving and removal. The relationship between dialysate glucose concentration and achieved UF appears to be more complex; even accounting for extended time on treatment and reduction in the osmotic conductance in patients preferentially using hypertonic exchanges, further adjustments may be needed to account for the tendency to overestimate UF.

Keywords: automated peritoneal dialysis (APD); computer modelling; continuous ambulatory peritoneal dialysis (CAPD); hydraulic conductance; peritoneal membrane; sodium sieving



   Introduction
 Top
 Abstract
 Introduction
 Subjects and methods
 Results
 Discussion
 References
 
Adequate water and sodium balance is crucial in the management of patients on peritoneal dialysis (PD) especially when the patient is anuric. In at least one prospective cohort study, the removal of sodium and fluid has been identified as a predictor of mortality in PD patients independent of residual renal function [1], and failure to achieve >750 ml of daily ultrafiltration (UF) in anuric patients was associated with increased mortality in the European Automated Peritoneal Dialysis Outcome Study (EAPOS) [2]. The combination of fluid overload along with hypertension can be a major factor for developing cardiovascular disease, the leading cause of death in PD patients [3].

The three-pore model (TPM), developed by Rippe, provides a quantitative description of sodium and water removal across the peritoneal membrane [4]. In particular, this approach is able to account for the phenomenon of solute sieving that results in an early fall in the dialysate sodium concentration, due to its dilution by osmotically driven free water transport [5], occurring via aquaporins [6,7]. This dissociation between UF of water and sodium transport is, therefore, of greatest clinical relevance to patients using automated PD (APD) during short dwells [8] that might have clinical consequences [9]. Prediction of time-dependent UF profiles by the TPM has been validated previously in a small number of patients [10]. It also forms the theoretical basis of the personal dialysis capacity (PDC) test [11], which is rather better at predicting daily UF volume than PD Adequest [12]; whereas PDC utilizes individual data from dwells of differing length and glucose concentrations, the latter relies on a single peritoneal equilibration test (PET) and overnight fluid volume to determine UF capacity. The ability of the TPM to describe dialysate sodium concentration and, in combination with UF volume, the net sodium removal under differing conditions of dwell length, peritoneal solute transport characteristics and strength of the glucose exchange, has not, so far, been evaluated. The purpose of this study was to compare observed UF dialysate sodium concentration, and thus sodium removal, with that predicted by the TPM, under differing conditions (glucose concentration and dwell length) using computer simulations individualized for peritoneal transport status and plasma sodium concentration.



   Subjects and methods
 Top
 Abstract
 Introduction
 Subjects and methods
 Results
 Discussion
 References
 
Study design
A cross-sectional analysis was performed using prospectively collected data from dialysis dwells of PD patients undergoing their routine treatment. For each dwell, the net UF, dialysate sodium concentration and thus calculated sodium removal was measured and categorized according to dwell length, solute transport and glucose concentration. These empirical data were then compared with that derived from the TPM using grouped median measures of peritoneal solute transport and plasma sodium concentrations in the modelling process. Comparisons were also made between the APD and continuous ambulatory PD (CAPD) patients where the same length exchanges were performed, again comparing these with values predicted by the TPM computer simulations.

Sample collection
Data for the present analysis were collected between January 1998 and May 2001. Dialysate and blood samples were analysed for sodium content when patients were undergoing routine tests for dialysis adequacy and peritoneal membrane function. This procedure was performed every 6 months, unless the patient developed peritonitis in the preceding month. Each assessment involved the patient collecting each dialysate drain for a 24 h period followed the next day by a standardized PET. In CAPD patients, all the exchanges were brought to the hospital and analysed separately, the net UF being corrected for the overfill of dialysis bags, typically found to be 200 ml, which bypasses the peritoneal cavity as part of the flush before fill procedure, but is collected in the drainage bag. This amount was derived from regular monitoring of overfill performed following completion of this study, corroborated independently by another study [13], and from personal communications with senior Baxter personnel confirming that the overfill volume has been stable for at least the duration of this study. For APD patients, long day dwells were treated in a similar fashion, except that there is no overfill flush volume; exchanges using icodextrin were excluded, and all the patients performed a 9 h dwell. This was because use of APD during the study period was confined to anuric patients who required an additional fill volume. The overnight exchanges were collected into a single drainage bag, sampled by the patient to determine the mean sodium concentration. Net overnight UF was determined from the APD device and divided by the number of exchanges. Information, including dialysate fluid type (glucose 1.36, 2.27 and 3.86%) and dwell length, was collected for each exchange. Dwell lengths were defined and categorized as follows: short, ~90 min, typical for overnight exchange in APD patients; medium, ~300 min, typical for daytime dwells in CAPD patients; and long, ~540 min, being either overnight dwells in CAPD or daytime dwells in APD patients.

Peritoneal equilibration test (PET)
The PET, performed as the first exchange of the day in all patients, was utilized to measure solute transport and UF capacity, and this was performed as described previously [14]. Briefly, a standard 4 h dwell period was used (first exchange of the day), using a 2.27% glucose concentration 2 l volume exchange. The patients used their usual overnight dialysis regime, and both the overnight and test drainage volumes were measured. The dialysate:plasma ratio of creatinine at the completion of the 4 h dwell period (D/Pcreat) was used as the estimate of low molecular weight solute transport. As glucose interferes with the assay for creatinine in a linear fashion, concentrations for both these solutes are measured at 4 h and the true value for creatinine obtained by subtracting the glucose concentration multiplied by a correction factor derived locally by our laboratory (0.00047).

Sodium analysis
Plasma and dialysate sodium, glucose and creatinine were determined on an automated discrete random access analyser (DAX 72, Bayer Instruments, Basingstoke, UK). This employs an indirect electrode method to measure sodium concentration, using pre-dilution of the sample, thus minimizing the influence of sodium binding to protein and inorganic ions. Because concerns have been raised as to the accuracy of direct electrode methodology [15], the indirect electrode measurements were cross-checked using the flame photometry technique. In this comparison of methods, the results were always within 1 mmol/l of each other.

Modelling
For the modelling of the data, three transport groups (low average, high average and high) were formed according to their D/P creatinine ratio obtained from the 4 h 2.27% PET data. Each transport group was divided further according to the dwell lengths (90, 240, 300 and 540 min, see above for definitions) and glucose strength concentrations (1.36, 2.27 and 3.86%). For each of these groups, the median of the estimate of solute transport made in the PET (D/P creatinine ratio) was converted into a value for area parameter, having first established the relationship between these parameters as defined by the model.

The computer simulations were performed on a personal computer using a specifically designed Excel® worksheet (Microsoft, Bellevue, WA), developed by one of us (D.V.), according to the principles of the TPM of peritoneal transport [16]. This worksheet enables rapid simulations to be performed whilst allowing the operator to enter both empirical data and alter one or more of the model parameters. For the present analysis, the original parameters were employed as recently published (see Table 1) [16,17]. Notably, the permeability area product (PS) values for glucose and sodium were perturbed, as described; the value for glucose is increased to account for the effects of interstitial and intracapillary glucose concentrations, whereas that for sodium is decreased in keeping with observations that its mass transfer coefficient is much lower than predicted from its molecular weight. The Gibbs–Donnan effect for sodium is also accounted for in the model, employing a dissociation constant of 0.93. In addition, the computer model also enables the operator to use a fixed value for hydraulic conductance (LPS) even when the value for the area parameter is altered, and this is the approach we adopted for this study.


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Table 1. The parameters used for the computer simulation three-pore model

 
Three parameters were altered for the analysis of each dwell, namely the glucose concentration, the median value of sodium plasma concentration and the area parameter. Drained dialysate volume, dialysate sodium concentration and thus derived sodium removal were calculated according to dwell length in each case.

Statistical analysis
All data are expressed as mean values, with error bars denoting SDs. The comparison between observed and predicted data is expressed graphically as a scattergram and statistically using Pearson linear regression, in which each point represents one of the 27 subcategories according to transport category, dwell length and glucose concentration. The agreement and systematic bias of observed and predicted values for these categories were analysed using the Bland and Altman method. Comparisons between solute transport groups or dialysis modalities were made using non-paired t-tests or analysis of variance (ANOVA) where appropriate.



   Results
 Top
 Abstract
 Introduction
 Subjects and methods
 Results
 Discussion
 References
 
Patient demographics of the different dwell groups
A total of 1853 dwells from 182 patients (55% male) were analysed. Ten percent of patients were using APD, and these had been on PD dialysis significantly longer than CAPD patients for each of the glucose and transport categories (Table 2). Generally, the use of higher glucose concentrations was associated with longer time on treatment, especially in CAPD patients (ANOVA, P = 0.001) and higher solute transport. The only exception to this was the APD 3.86% group, where the low average transporters had been on treatment longer than high average and high transporters. No consistent significant differences in body surface area were found between these groups.


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Table 2. Time on treatment (±SD) of patients in each of the dwell categories, grouped according to glucose concentration (1.36, 2.27 and 3.86%) and membrane transport category (TC)

 
Comparison of observed and predicted data
Ultrafiltration. Figure 1a–c and Table 3 summarize the comparison between observed and predicted UF according to each of the 27 potential categories (three transport, three glucose concentrations and three dwell lengths). Overall, there is a strong and highly significant correlation, r = 0.89, P<0.001. It can also be seen that there is a systematic bias, such that as the net UF increases, there is an increasing tendency for the modelled data to overpredict the observed data (Bland and Altman correlation r = 0.84, P = 0.001). This overprediction is independent of transport category (Figure 1b) and was most marked in the very small number of patients using 3.86% glucose exchanges exclusively for short exchanges as part of their APD regime (Figure 1c). The possibility that this overprediction of UF reflects the selective use of 3.86%, and to a lesser extent 2.27%, glucose exchanges by patients with worse membrane function was tested by comparing the UF capacity achieved in the PET in these different categories. This analysis demonstrated that patients using stronger glucose fluids did indeed tend to have less good UF capacity: 1.36%, 469±221 ml, n = 1150; 2.27%, 426±266 ml, n = 431; 3.86%, 385±329 ml, n = 237, ANOVA P<0.001. These differences were in part attributable to solute transport category, as patients with higher transport were more likely to use hypertonic exchanges, a difference that is taken into account in the modelling. However, if the differences in UF capacity are broken down by transport category (see Table 4), it can be seen that there is a tendency for patients using hypertonic exchanges to have worse UF capacity for a given solute transport.




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Fig. 1. Correlation between observed and predicted net ultrafiltration, r = 0.89, P<0.001. Each point represents one of 27 different combinations of glucose concentration, dwell length and transport category. (a) Groupings according to glucose concentration: 1.36% (open triangles), r = 0.85, P<0.001; 2.27% (filled circles), r = 0.96, P<0.001; and 3.86% (open circles), r = 0.83, P<0.001. (b) Data are grouped according to transport category: low average (open circles), r = 0.85, P<0.001; high average (open triangles) r = 0.92, P<0.001; and high (filled diamonds) r = 0.94, P<0.001. (c) Data are grouped by dwell length, r = 0.85, P<0.001: short (filled diamonds), r = 0.02, NS; medium (open circles) r = 0.94, P<0.001; and long (open triangles) r = 0.98, P<0.001.

 

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Table 3. Comparison between observed and predicted ultrafiltration according to category

 

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Table 4. Association between peritoneal ultrafiltration capacity (derived from PET) and the selection of glucose concentration

 
Dialysate sodium concentration. As with UF, there was a strong and significant correlation between observed and predicted values across the 27 categories of exchange r = 0.815, P<0.001 (Figure 2a). The difference between observed and predicted values was least for high transporters and long dwells, those dwells in which closest equilibration with plasma sodium will have occurred. The process of sodium sieving was consistently predicted, although again, for those few patients using 3.86% glucose in their short APD dwells, this was less than predicted (Figure 2b).



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Fig. 2. Correlation between observed and predicted dialysate sodium concentration, r = 0.82, P<0.001. As in Figure 1, each point represents one of 27 different combinations of glucose concentration, dwell length and transport category. (a) Groupings according to glucose concentration: 1.36% (open triangles), r = 0.97, P<0.001; 2.27% (filled circles), r = 0.90, P<0.001; and 3.86% (open circles), r = 0.85, P<0.001. (b) Data are grouped according to dwell length: short (filled diamonds), r = 0.04, NS; medium (open circles) r = 0.91, P<0.001; and long (open triangles) r = 0.96, P<0.001.

 
Net sodium removal. Again, correlation between observed and predicted sodium removal is high, r = 0.89, P<0.001. As net removal reflects the sum effects of UF and dialysate sodium concentration, the overestimation of UF by the model results in a proportional overestimate in sodium removal (see Figure 3).



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Fig. 3. Correlation between observed and predicted sodium removal, r = 0.89, P<0.001. As in Figure 1, each point represents one of 27 different combinations of glucose concentration, dwell length and transport category, grouped according to glucose concentration, 1.36% (open triangles), r = 0.57, P<0.005; 2.27% (filled circles), r = 0.88, P<0.001; and 3.86% (open circles), r = 0.89, P<0.001.

 
Comparison of long overnight CAPD exchanges with daytime APD exchanges
As both CAPD and APD patients undertook long dwells, it was possible to make a direct comparison of the observed and predicted fluid and sodium removal by modality. There was no difference between the two modalities in dialysate sodium concentration, UF or net sodium loss (see Figure 4), in terms of both the absolute observed amounts and the predictive power of the model.



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Fig. 4. Correlation between observed and predicted sodium removal as achieved during the long exchange according to modality, CAPD (open circles), r = 0.95, P<0.001; APD (filled circles), r = 0.90, P<0.001.

 


   Discussion
 Top
 Abstract
 Introduction
 Subjects and methods
 Results
 Discussion
 References
 
This study presents a detailed analysis of UF and sodium removal in a cross-section of CAPD and APD patients, with particular attention to the effects of glucose strength, dwell length and membrane transport characteristics. It is also the first attempt to conduct a comprehensive comparison between the predicted UF and sodium removal by the TPM using computer simulations and that observed empirically. Although the TPM is used in various studies to assess the peritoneal membrane in a mathematical manner, and is the basis for the PDC test, the model has never been validated in such a manner for the factors that determine sodium removal.

In discussing the observational data, it can be seen that the values obtained for net UF, dialysate sodium concentration and thus sodium removal are influenced by glucose strength, dwell length and membrane transport broadly as expected from theoretical considerations [18]. In other words, by increasing the glucose tonicity, there is more UF and sodium sieving, whereas the opposite tendency occurs as membrane transport increases. The literature contains very little comparative data of this sort, especially on a dwell-by-dwell basis. The analysis by Rodriguez-Carmona and Fontan [8] gives similar values for dialysate sodium concentration and removal overall, but does not break these down by glucose concentration and membrane transport characteristics, and does not distinguish between CAPD and APD ‘short’ dwells. It should be emphasized that there is considerable variability, especially in UF, within each of the 27 transport, dwell length and glucose concentration categories, as judged by the relatively large SDs that can be seen in Figures 1a, 2a, 3 and 4. This variability is probably due to several things, including the accuracy of measurement, variability in sump volume (which may be altered by recumbency or variable programming in APD patients), variability in plasma glucose and urea, hydrostatic pressure and real differences in the intrinsic properties of the membrane, such as UF coefficient. As none of these were measured independently in this study, they were treated as constant, fixed variables in the modelling. The use of a single value for plasma urea, chosen in order to simplify the modelling process, will also have resulted in some of this variability as urea is osmotically active, accounting for ~40 ml less UF for an increase in plasma concentration of 20–30 mmol/l in this model. Thus, ~10% of the variability in UF between the observed and predicted values might be accounted for by this oversimplification.

When the observational data were compared with those predicted by the computed values generated by the TPM, a high degree of correlation between UF, dialysate sodium and consequently sodium removal was observed. It is important to emphasize the nature of the comparison between observed and predicted data that we wished to explore in this study. This was not an attempt to determine the reliability with which this version of the TPM could predict UF (as for example has been shown with the PDC) or sodium removal in individual patients, but an attempt to see how well the TPM described patterns of UF and sodium removal in broad terms. Similarities would indicate that the model is generally correct in its mechanistic description of how the membrane works, whereas differences might point to specific parameters that are either wrong or need to be modified for the future. The high degree of correlation between predicted and observed data does support the view that the model is fundamentally correct in its mechanistic description. There were, however, limitations to the accuracy of this description that require further discussion.

It can be seen that there are very significant degrees of systematic bias between the observed and predicted data, in particular the overprediction of UF that increases as the UF volume increases. This could be due to one of two things: either a selection bias in the use of increasingly hypertonic exchanges according to patient need, or a real difference in the osmotic conductance of the membrane associated with increasing glucose concentration. The former of these explanations is a weakness of the cross-sectional nature of the study design in which patients were using their typical dialysis prescription. Patients are more likely to use hypertonic exchanges for one or more of three reasons: to accommodate increased fluid intake, to compensate for lost urine output or because their membranes are less efficient for a given glucose gradient (reduced osmotic conductance). Only the last of these reasons could explain less observed than predicted fluid removal. Certainly these patients had been on dialysis longer, and when we analysed the relative UF capacity obtained from the PET, we did find that for a given solute transport this was less for patients using hypertonic fluids, indicating that selection for reduced peritoneal osmotic conductance did occur in this study, entirely in keeping with the longitudinal observations of membrane function we have observed. This reduction in osmotic conductance is not, however, sufficient and consistent enough to explain all the discrepancy between the observed and predicted data.

An alternative explanation would be that the osmotic conductance, itself determined by the product of the UF coefficient (LpS) and the reflection coefficient to glucose ({sigma}) is influenced by the glucose concentration. It is important to understand that in this version of the TPM, the value for LpS·{sigma} is fixed for all dwells and that the PS for glucose has been perturbed (increased) in such a way as to reduce the driving osmotic gradient. The reason and rationale for this are as follows: early studies validating the TPM, in rather a small number of patients, indicated that the amount of UF was not as great as predicted. The rationalization is that the effects of the interstitium dissipate the actual glucose gradient at the peritoneal capillary wall. Data from this study would suggest that further perturbation is required, perhaps in a non-linear fashion, to improve the agreement between observed and predicted data.

The agreement between observed and predicted dialysate sodium concentration was good, including the effect of sodium sieving, but again showed bias. This could be explained mostly by reduced sodium sieving in a small number of patients using exclusively 3.86% glucose in the overnight short dwells of their APD regime. These patients all had clinical and PET evidence of UF failure resulting in reduced free water transport as described. Again, it should be noted that in this application of the TPM, the PS for sodium was perturbed, on this occasion reduced, to account for the various factors that alter free diffusion of this ion.

Finally, provided appropriate adjustments for the overfill and flush volume for CAPD patients was taken into account, there was no systematic difference in the UF and sodium removal in the long exchanges according to modality. In comparing APD and CAPD patients in this study, care has to be taken due to the relatively small numbers of APD patients, who were also more likely to be anuric, longer on treatment and thus have acquired changes in membrane function; the smaller SDs (see Figure 4) would suggest that this was, if anything, a more homogeneous group, however, possibly reflecting more precise measurements of UF that are possible with APD, and the parallel nature of the regression lines would indicate that the fundamental relationship between UF and glucose concentration is not different.



   Acknowledgments
 
The authors thank Professors Bengt Rippe and Raymond Krediet for their constructive encouragement of this work. M.C.A. was sponsored by a grant from the Dutch National Kidney Research Foundation. D.V. is supported by The European Union, Contract FMRX-CT98-0219.

Conflict of interest statement. None declared.



   References
 Top
 Abstract
 Introduction
 Subjects and methods
 Results
 Discussion
 References
 

  1. Ates K, Nergizoglu G, Keven K et al. Effect of fluid and sodium removal on mortality in peritoneal dialysis patients. Kidney Int 2001; 60: 767–776[CrossRef][ISI][Medline]
  2. Brown EA, Davies SJ, Rutherford P et al. Survival of functionally anuric patients on automated peritoneal dialysis: the European APD Outcome Study. J Am Soc Nephrol 2003; 14: 2948–2957[Abstract/Free Full Text]
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Received for publication: 13. 3.04
Accepted in revised form: 8. 3.05





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