Transport of protein in the abdominal wall during intraperitoneal therapy. I. Theoretical approach

Intraperitoneal therapies such as peritoneal dialysis or regional chemotherapy use large volumes of solution within the peritoneal cavity. These volumes increase intraperitoneal hydrostatic pressure (P(ip)), which causes flow of the solution into tissues that surround the cavity. The goal of this paper is to integrate new experimental findings in a rigorous mathematical model to predict protein transport from the cavity into tissue. The model describes non-steady-state diffusion and convection of protein through a deformable porous medium with simultaneous exchange with the microcirculation and local tissue binding. Model parameters are dependent on local tissue pressure, which varies with P(ip). Solute interactions with the tissue in terms of local distribution volume (solute void space), local binding, and retardation relative to solvent flow are demonstrated to be major determinants of tissue concentration profiles and protein penetration from the peritoneal cavity. The model predicts the rate of fluid loss from the cavity to the abdominal wall in dialysis patients to be 94 ml/h, within the observed range of 60-100 ml/h. The model is fitted to published transport data of IgG, and the retardation coefficient f is estimated to be 0.3, which markedly reduces the rate of protein penetration and is far lower than previously published estimates. With the value of f = 0.3, model calculations predict that P(ip) of 4.4 mmHg and dialysis duration of 24 h result in several millimeters of protein penetration into the tissue.