Distributed modeling of diffusive solute transport in peritoneal dialysis

The diffusive transport between blood and an ex-tissue medium (dialysis fluid) is evaluated using a mathematical model that,takes into account the (quasicontinuous) distribution of capillaries within the tissue at various distances from the tissue surface, and includes diffusive-convective transport through the capillary wall and lymphatic absorption from the tissue. General formulas for solute penetration depth, Lambda, and for the diffusive mass. transport coefficient for the transport between blood and dialysis fluid, K-BD, are provided in terms of local transport coefficients for capillary wall, tissue, and lymphatic absorption. For pure diffusive transport between blood and dialysis fluid and thick tissue layers (i.e., if the solute penetration depth is much lower than the tissue thickness) these formulas yield previously known expressions. It is shown that apparent tissue layers, with widths Lambda(TBL) and Lambda(T), respectively, may be defined according to the values of local transport parameters in such a way that K-BD is equal to the solute clearance K-TBL from the tissue by blood and lymph for a layer with width Lambda(TBL) or-to the solute clearance K-T from blood to dialysate by diffusion through the tissue layer with width Lambda(T). For tissue layers with width much higher than the penetration depth: Lambda(T)approximate toLambda(TBL)approximate toLambda. These characteristic width lengths depend on the transport parameters (and thus on the size) of solutes. Effective blood flow, which may be related to the exchange of the solute between blood and dialysate, is defined using an analogy to the extraction/absorption coefficients for blood-tissue exchange. Various approximations for the distributed model formula for diffusive mass transport coefficient (K-BD) are possible. The appropriate range for their application is obtained from the general formula. (C) 2002 Biomedical Engineering Society.