Search

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-ormicroparticles) within fluid as blood. And we employ transport equations, coupling fluid flow and diffusion, for transport of distributed matter as biological proteins within blood.

Diffusion in nanospace does not strictly obey to Fick's law generally used in macroenvironment. Deviation from this law is due to surface effects, i.e. due to interaction between transported molecules and bounding surfaces. A hierarchical modeling approach which accounts for interface effects on the diffusion coefficient was introduced in Ziemys et al. (2011). The model employs molecular dynamics (MD) for calculation scaling functions to reduce the diffusion coefficient corresponding to 'bulk' values. With this reduced diffusion coefficient, modeling is performed using the finite element method (FE) within an incremental iterative scheme. In this paper we summarize this hierarchical (multiscale) model and present its generalization to include adsorption at the walls. Also, we briefly discuss further possible applications of the multiscale modeling of diffusion through complex media with distributed solid constituents, as in case of polymers or biological fluids.

A 32-year-old man with thoracic vertebral osteomyelitis and with no predisposing factors is reported. Vertebral osteomyelitis (VO) was caused by E. Coli which was confirmed by blood culture. Diagnosis of vertebral osteomyelitis is usually difficult and can be easily misdiagnosed. the patient developed acute cholecystitis (AAC) probably caused by ceftriaxone antibiotic treatment. Diagnostic and treatment possibilities of acute acalculous cholecystitis are discussed.