Farshid Guilak, Mansoor A. Haider, Lori A. Setton, Tod A. Laursen, and Frank P.T. Baaijens

ABSTRACT: Cells are highly complex structures whose physiology and biomechanical properties depend on the interactions among the varying concentrations of water, charged or uncharged macromolecules, ions, and other molecular components contained within the cytoplasm. To further investigate the mechanistic basis of the mechanical behaviors of cells, recent studies have developed models of single cells and cell matrix interactions that use multiphasic constitutive laws to represent the interactions among solid, fluid, and in some cases, ionic phases of cells. The goals of such studies have been to characterize the relative contributions of different physical mechanisms responsible for empirically observed phenomena such as cell viscoelasticity or volume change under mechanical or osmotic loading, and to account for the coupling of mechanical, chemical, and electrical events within living cells. This chapter describes several two-phase (fluid-solid) or three-phase (fluid-solid-ion) models, originally developed for studying soft hydrated tissues, that have been extended to describe the biomechanical behavior of individual cells or cell matrix interactions in various tissue systems. The application of such biphasic or triphasic continuum-based approaches can be combined with other structurally based models to study the interactions of the different constitutive phases in governing cell mechanical behavior.