Representations of Peritoneal Tissue – Mathematical Models in Peritoneal Dialysis

2020

Perit Dial Int

Background: Waniewski postulated a transient increase in peritoneal capillary surface area to fit their model predictions to experimental data of Heimburger measured in renal failure (RF) patients undergoing peritoneal dialysis (PD) but with only a 3.86% glucose dialysis fluid. The present aim is to propose a new mathematical model of the patient PD procedure that could closely fit the complete Heimburger measurement set without this postulate. Methods: The three-pore model of Rippe was used to describe transient changes in peritoneal volume and solute concentrations during a PD dwell. The predialysis, RF patient, plasma solute concentrations were assumed to remain constant during the dwell. The model was validated using the 3.86% glucose Heimburger measurements. Permeability surface area product parameters were chosen to match only the end-dwell peritoneal fluid glucose concentration and the end-dwell amounts of urea, creatinine, and Na+ removed from this simulated patient group. Then, this model was used to predict additional measurements by Heimburger on two other patient groups dialyzed with glucose concentrations of 2.27% and 1.36%, respectively. Parameters were unchanged when simulating these other patient groups. Results: To match the shape of the transient changes in drained volume and dialysis fluid glucose concentration for the 3.86% glucose group, it was necessary for only one parameter, the effective radius of glucose, to vary linearly in proportion to the dialysis fluid glucose concentration. This description was unchanged in the other two groups. Conclusion: Postulated transient increases in peritoneal capillary surface area were unnecessary to predict the entire Heimburger measurements.

Section: Discussionmentioning

confidence: 82%

Are transient changes in capillary surface area required to explain peritoneal transport in renal failure patients?

2020

Perit Dial Int

“…It is well known by myself and others 10 that one can obtain increasingly better fits by increasing the number of unknown parameter values in a model. The use of time-varying inflation functions in the Waniewski et al 2,4 models used to generate their improved predictions, even though physiologically based, add many more parameter value changes compared to the 2004 Rippe 5 model and those leading to the excellent Wolf model fits (see Figure 1).…”

Section: Discussionmentioning

confidence: 99%

Peritoneal physicochemical transport mechanisms: Hypotheses, models and controversies

2021

Perit Dial Int

This study answers criticisms by Waniewski et al. of the recent paper by Wolf on peritoneal transport kinetic models. Their criticisms centre on the accuracy of the data used for model fits, the hypothesis presented, which involves changes in glucose membrane parameters at high peritoneal glucose concentration and on the necessary techniques required to achieve accurate model parameter estimation. In response, this article shows that (1) the mean values previously captured from graphical depictions of Heimburger et al. are not different than those captured from the recent Waniewski et al. graphs, (2) a much simpler hypothesis is proposed, which centres on intraperitoneal pressure-induced lymph flow during the dialysis dwell and (3) the finding that the new model predictions, with only two constant parameter values, as estimated by the Powell algorithm, give a closer fit than the Waniewski model, which uses many time-varying parameters. The current findings again bring into question of the validity of their vasodilation hypothesis, leading to transient changes in capillary surface area during the dwell.

“…Mathematical models have played a significant role in increasing understanding of dynamic interchanges of solutes and water across the peritoneal membrane during peritoneal dialysis (PD). [1][2][3] Less well understood are how these interchanges affect peritoneal acid-base changes.…”

mentioning

confidence: 99%

Mechanisms of Peritoneal Acid-Base Kinetics During Peritoneal Dialysis: A Mathematical Model Study

2020

ASAIO Journal

To investigate mechanisms of acid-base changes during peritoneal dialysis (PD), a mathematical model was developed that describes kinetics of peritoneal bicarbonate, CO 2, and pH during the dwell with both high and low lactate-containing dialysis fluids. The model was based on a previous modification of the Rippe 3-Pore model of water and solute kinetic transport across the peritoneal membrane during the PD dwell. A central feature of the present modification is an electroneutrality constraint on peritoneal-fluid ion concentrations, which results in the conclusion that peritoneal bicarbonate-concentration kinetics are entirely dependent on the kinetics of the other ions. This new model was able to closely predict peritoneal bicarbonate-concentration kinetics during the dwell. Predictions of total peritoneal bicarbonate-mass kinetics were greater than those of porous, transmembrane bicarbonate transport, suggesting that a portion of bicarbonate comes from CO 2 transport, both porous and nonporous and then a partial conversion to bicarbonate. Fitting the model to experimental pH data during the dwell, required addition of a peritoneal CO 2 mass-conservation constraint, coupled with the description for peritoneal bicarbonate kinetics. Predicted pH kinetics during the dwell, closely mimicked the experimental data. The conclusion was that the mechanisms describing peritoneal bicarbonate and pH kinetics during PD must include 1) electroneutrality of peritoneal fluid, 2) porous transport of bicarbonate and CO 2 , 3) nonporous transport of CO 2 , and 4) CO 2 conversion to bicarbonate. These mechanisms are quite different and more complex than the bicarbonate-centered, lactate to acid-generation mechanisms previously proposed.