Mathematical modelling of fluid and solute transport though the muscle tissue – a spatially distributed approach
Fluid transport through the tissue plays crucial role in keeping local body homeostasis. Water bulk flow works not only as a vehicle for transport of solutes that are necessary for proper functioning of cells but it also can be used as a drug delivery mean. Local properties of the tissue (in particular interstitium) are not constant but rather change dynamically in reaction to the fluid and solute transport though the tissue. The importance of fluid transport and complexity of the observed phenomenon creates a need for mathematical modeling. During my talk I will focus on so called “distributed approach” in which tissue is treated as a porous medium and its properties such as compliance, hydration or hydraulic conductance change in response for fluid flow resulting in the system of nonlinear PDE with Neumann boundary condition at one side and a system of ODEs describing evolution of solution on the other side. Chosen numerical simulation as well as theoretical results will be presented to illustrate particular clinical problems and model applications with special focus to the transport processes occurring during peritoneal dialysis.