Abstract

The biological systems are tied to the molecular transport across the living tissues which in turn highly depend on kinetic and thermal energy exchanges. For various applications ranging from artery modeling to very sensitive tissue modeling such as the brain, porous media modeling accurately predicts biological behavior. This article elaborately addresses the fundamentals of porous media and provides a comprehensive synthesis of the theory development from the primary methods available in the literature to the modern mathematical formulations. Specifically, this paper concentrates on two remarkable biological applications including (1) blood flow interactions with the porous tissue and (2) hydrodynamic impacts of particle-particle interactions in the microscale modeling that requires a Lagrangian frame.

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