Simple membrane models for peritoneal dialysis. Evaluation of diffusive and convective solute transport

Currently used mathematical models to estimate parameters describing diffusive (diffusive mass transport coefficient, KBD) and convective (sieving coefficient, S) solute transport during peritoneal dialysis, as proposed by Pyle, Popovich, and Moncrief (PPM model) and Babb, Randerson, and Farrell (BRF model), require nonlinear regression and advanced numerical methods for parameter estimation. In this study, a simplified approach to the evaluation of KBD and S, using the same transport equation used in the PPM and BRF models but based on two-dimensional linear regression, is proposed. This new approach can be extended to generate a family of membrane models that differ in assumption concerning the average solute concentration (c) inside the peritoneal membrane. In particular, c was assumed to be equal to the arithmetic mean value of the dialysate and blood concentrations (PPM model), the blood concentration (BRF model), or the dialysate concentration (D model). The investigated family of models was used to study the transport of urea, creatinine, glucose, sodium, potassium, and total protein in 20 single, 6 hr dwell studies carried out in 20 nondiabetic patients in stable clinical condition using hypertonic (3.86%) glucose solution. For the PPM model, the linear and nonlinear regressions were able to provide almost identical values of KBD and S. The theoretical dialysate to plasma concentration ratio (D/P) was adequately fitted to experimental D/P for both the PPM and BRF models, but the fit was worse for the D model. However, unphysiologic (i.e., out of the 0-1 range) values of S were found for urea, potassium, and glucose independent of the version of the model used.