Thanks to their softness, biocompatibility, porosity, and ready availability, hydrogels are commonly used in microfluidic assays and organ-on-chip devices as a matrix for cells. They not only provide a supporting scaffold for the differentiating cells and the developing organoids, but also serve as the medium for transmitting oxygen, nutrients, various chemical factors, and mechanical stimuli to the cells. From a bioengineering viewpoint, the transmission of forces from fluid perfusion to the cells through the hydrogel is critical to the proper function and development of the cell colony. In this paper, we develop a poroelastic model to represent the fluid flow through a hydrogel containing a biological cell modeled as a hyperelastic inclusion. In geometries representing shear and normal flows that occur frequently in microfluidic experiments, we use finite-element simulations to examine how the perfusion engenders interstitial flow in the gel and displaces and deforms the embedded cell. The results show that pressure is the most important stress component in moving and deforming the cell, and the model predicts the velocity in the gel and stress transmitted to the cell that is comparable to in vitro and in vivo data. This work provides a computational tool to design the geometry and flow conditions to achieve optimal flow and stress fields inside the hydrogels and around the cell.
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