(522e) A General Solution for Equations of Poroelasticity

Mechanical properties of the cell, controlled by its cytoskeleton, are important biomarkers for probing its architectural changes caused by cellular processes and/or pathologies. Previous studies suggest that the cytoskeleton can be modeled in the continuum limit as a viscoelastic network permeated by the cytoplasmic fluid. We use a two-phase formulation for the poroelastic material and assume general linear viscoelastic constitutive equations for computing the fluid and the network stresses. After taking Laplace transform in time, the momentum and mass conservation equations of the fluid and the network phases are assembled into a set of linear non-homogenous Navier-like equations for the fluid and the network displacement vectors that are solved analytically in spherical coordinates. We, then, use this solution to compute the displacement fields induced by a rigid sphere moving under a constant velocity in a poroelastic material, and discuss the implications of our findings in analyzing the results of single particle and two-point microrheology of cellular materials.