Transport in biological systems

Transport of matter in biological systems represents the vital and most important process. The transport occurs in different scales, spanning from the atomic to macroscale. It is very complex since it involves both biochemical and mechanical sources. Modeling remains a challenge due to this complexity. In this report we refer to the following specific topics: diffusion in complex media, transport of solid bodies by fluid, and transport of distributed matter by fluid. Those are the topics on which the research has been performed at The Methodist Hospital Research Institute, Houston; and at Metropolitan University, Belgrade R & D Center for Bioengineering, Kragujevac. The methodology for diffusion relies on a hierarchical modeling approach introduced in [Ziemys et al. 2011] which accounts for interface effects between solid phase and transported molecules. Here, a generalization of the hierarchical approach is proposed for diffusion in composite media. We employ a remeshing concept to model transport of deformable bodies (biological cells, as red blood cells) or rigid bodies (nano-or micro particles) within fluid as blood. And we employ transport equations, coupling fluid flow and diffusion, for transport of distributed matter as biological proteins within blood.