Oscillatory Pressurization of an Animal Cell as a Poroelastic Spherical Body

Abstract

The analytical solution of a spherical poroelastic body under an oscillatory hydrostatic pressurization is obtained. This solution is then parameterized and interpreted in terms of a spherical animal cell with the cytoskeleton serving as the solid phase. It is found that for a cell with free or nearly free membrane leakage (such as in the case of an osteocytic cell body), the induced pore fluid pressure amplitude near the center of the cell exceeds the amplitude of the applied pressure by 50% if the loading frequency falls near that of normal human gait (1 Hz). A parametric analysis shows that the leakage coefficient is proportional to the intrinsic permeability ratio between the boundary and the bulk matrix. The physiological implication of the solution is further interpreted and discussed through an anatomical analysis of two representative cellular entities under compression: a chondrocyte and an osteocytic cell body. Finally, through a comparison between the characteristic time of gait and the characteristic pore fluid pressure relaxation times of various fluid-saturated entities in the body (such as a tumor, the brain, the cortical bone, the trabecular bone, and the cartilage, etc.), it is found that the gait-induced pore fluid transport seems to be important only in deeply buried cells and the mineralized cartilage.

Boning up on Wolff's Law: Mechanical regulation of the cells that make and maintain bone

“…The effects of hydrostatic pressure on individual cells are complicated by spatial heterogeneity in local cell stiffness; for example, the cell body will deform more than cellular processes under hydrostatic loads, since the cell's body is more compliant than its processes (Docheva et al, 2008). Poroelastic cell models with idealized geometries have been developed to estimate local deformation of a cell under cyclic hydrostatic pressure (Zhang, 2005). Physiological loading also causes strains in whole bone in vivo which are typically in the range of 0.04-0.3% for animal and human locomotion, but seldom exceed 0.1% (Rubin and Lanyon, 1984;Fritton et al, 2000).…”

Nonlinear Elastic and Inelastic Properties of Cells

“…Poroelasticity has been a popular model to describe the resistance of soft tissues to compression. Only recently, the poroelasticity model was applied to explain various cellular behaviors, such as cell migration [160,161], cell responses to an oscillatory pressure [162], and bleb formation [163][164][165]. It was also suggested that poroelastic parameters may serve as biomarkers for cancer diagnosis and therapies [166].…”

Multiscale Modelling of the Poroviscoelastic Rheology of Cell Cytoplasm

“…One possible approach to modelling such flows is to use poroelasticity theory (e.g. Zhang, 2005;Kimpton et al, 2015;Copos and Guy, 2018), which has been well validated against experiments (Moeendarbary et al, 2013). We incorporate poroelastic effects into the model constructed below.…”