A Mathematical Model of Local Stimulation of Perfusion by Vasoactive Agent Diffusing from Tissue Surface

Abstract

The delivery or removal of solutes to/from the tissue through its surface is a key process of some medical treatments, as peritoneal dialysis, local chemotherapy, and others. The rate of blood flow and the active capillary surface area in the tissue contribute to the rate of the solute transport, and these factors may be regulated by vasoactive components of or additives to the media that carry the solutes outside the tissue. Peritoneal dialysis fluids per se are known to induce transient vasodilation and increased diffusive transport of small solutes. Using the existing data on the kinetics of the diffusive mass transport parameters during peritoneal dialysis after infusion of fresh dialysis fluid, different hypotheses about the kinetics of the capillary surface area behind the observed changes are investigated. A distributed mathematical model describes a vasoactive agent that diffuses from the tissue surface, induces vasodilation, and is absorbed in blood. The model is applied for the prediction of the transport parameters of the agent and other, passive solutes. It is shown that the initial increase in the capillary surface area by 2.75 times, induced by a suprathreshold concentration of the agent, and the subsequent decrease in the capillary surface area with a fixed time constant and independently of the actual concentration of the agent, may explain the clinical data. In contrast, the vasoactivity that changes according to the actual level of the agent yields wrong prediction.