Homogenization approach to the multi-compartment model of perfusion

The paper deals with modelling of the coupled diffusion-deformation processes in biological tissues with potential applications in describing the blood perfusion, or fluid filtration phenomena in general. The micromodel to be homogenized is based on the Biot type model for the incompressible medium. Due to the strong heterogeneity in the permeability coefficients associated with three compartments of the representative microstructural cell (RMC), the homogenization of the model leads to the double diffusion phenomena. The resulting homogenized equations, involving the stress-equilibrium equation and other two equations governing the mass redistribution, describe the parallel diffusion in two high-conducting compartments (arterial and venous sectors) separated by the low conducting matrix which represents the perfused tissue. To obtain the homogenized model, the method of two scale convergence is applied. The homogenized coefficients are defined in terms of the characteristic response of the RMC. It is possible to identify the instantaneous and fading memory viscoelastic coefficients; other effective parameters, controlling the fluid redistribution between the compartments, are involved also in time convolutions. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)