Mathematical modeling of fluid and solute transport in peritoneal dialysis

Abstract

Optimization of peritoneal dialysis schedule and dialysis fluid composition needs, among others, methods for quantitative assessment of fluid and solute transport. Furthermore, an integrative quantitative description of physiological processes within the tissue, which contribute to the net transfer of fluid and solutes, is necessary for interpretation of the data and for predictions of the outcome of possible intervention into the peritoneal transport system.

The current project includes the investigations of 1) the effectiveness of crystalloid osmotic agents in evoking ultrafiltration from blood, 2) the impact of ultrafiltration on protein transport, 3) the evaluation of the role of perfusion in the peritoneal transport, and 4) the integration of the physiological data about transport characteristics of the capillary wall, the tissue, and lymphatic absorption for the description of the net peritoneal transport, using the methods of mathematical modeling.

Three different methods were tested for the estimation of fluid transport parameters. All three provided good description of the data, however some differences were found, especially in time dependence of the parameters during a single dwell study. The effectiveness of glucose as an osmotic agent, evaluated as osmotic conductance, were much lower in the patients with permanent ultrafiltration capacity (UFC) loss related to the increased transport of small solutes than in stable patients on continuous ambulatory peritoneal dialysis (CAPD). In contrast, patients with permanent UFC loss related to the increased absorption of fluid from the peritoneal cavity bad similar osmotic conductance as stable patients.

A discriminative impact of ultrafiltration on peritoneal transport of albumin, [beta]2-microglobulin, and total protein, was found in stable patients on CAPD: in some patients sieving coefficients for the proteins were high and the initial increase of the protein concentration in dialysate was fast; in another group, with low sieving coefficients for the proteins, and the increase of the protein concentration in dialysate was slow. No difference in the diffusive mass transport coefficients for the proteins and small solutes, neither for fluid transport, between these two groups of patients was found.

The perfusion rate of the tissue with blood was included into the distributed model of peritoneal transport. It was shown that changes of perfusion rate during a single dwell study, which might be induced by vasodilatory effect of dialysate, could explain the time-dependence of the diffusive mass transport coefficients (described previously). The model could also explain why the estimations of the effective peritoneal blood flow yielded much different values for gases and then for small solutes.

Transport characteristics for the capillary wall, the tissue, and the rate of lymphatic absorption from the tissue, were incorporated into the distributed model, to provide an integrated mathematical description of diffusive and convective transport of solutes of any size. The phenomenological transport parameters, diffusive mass transport parameter and sieving coefficient, the solute penetration depth, and effective peritoneal blood flow, were described as functions of the local, physiological parameters of the peritoneal transport system.