A poroelastic immersed boundary method with applications to cell biology

The immersed boundary method is a widely used mixed Eulerian/Lagrangian framework for simulating the motion of elastic structures immersed in viscous fluids. In the traditional immersed boundary method, the fluid and structure move with the same velocity field. In this work, a model based on the immersed boundary method is presented for simulating poroelastic media in which the fluid permeates a porous, elastic structure of small volume fraction that moves with its own velocity field. Two distinct methods for calculating elastic stresses are presented and compared. The method is validated on a radially symmetric test problem by comparing with a finite difference solution of the classical equations of poroelasticity. Finally, two applications of the modeling framework to cell biology are provided: cellular blebbing and cell crawling. It is shown that in both examples, poroelastic effects are necessary to explain the relevant mechanics.