Theoretical modeling of fluid flow in cellular biological media: an overview

Fluid-structure interactions strongly affect, in multiple ways, the structure and function of cellular biological media, such as tissues, biofilms, and cell-entrapping gels. Mathematical models and computer simulation are important tools in advancing our understanding of these interactions, interpreting experimental observations, and designing novel processes and biomaterials. In this paper, we present a comprehensive survey and highlight promising directions of future research on theoretical modeling of momentum transport in cellular biological media with focus on the formulation of governing equations and the calculation of material properties both theoretically and experimentally. With regard to the governing equations, significant work has been done with single-scale approaches (e.g. mixture theory), whereas traditional upscaling methods (e.g. homogenization, volume averaging) or multiscale equation-free approaches have received limited attention. The underlying concepts, strengths, and limitations of each approach, as well as examples of use in the field of biomaterials are presented. The current status of knowledge regarding the dependence of macroscopic material properties on the volume fractions, geometry, and intrinsic material properties of the constituent phases (cells, extracellular matrix and fluid) is also presented. The observation of conformational changes that occur at finer levels of the structural hierarchy during momentum transport, the correlation of macro-properties with geometrical and topological features of materials with heterogeneous and anisotropic microstructure, as well as the determination of dynamic material properties are among important challenges for future research.