A continuum model for tissues with moderate cell density

Cells sense mechanical stimuli to guide tissue growth and remodeling, a process called mechanotransduction, but it has still been challenging to model how forces affect cells in tissues with medium cell density. Common models like rule of mixtures (ROM) work well for cell dense tissues, and Eshelby's inclusion model fits cell sparse ones, but neither handles the in-between densities accurately. This study looks at how cell density, shape, and material properties affect stress in these tissues and suggests a better way to model them. We used finite element modeling (FEM) to test a bank of tissue samples, modeled as representative volume elements (RVEs), stretched uniaxially. We changed cell shapes (spherical, ellipsoidal, cylindrical), volume fraction, percolation, and stiffness ratio compared to the surrounding extracellular matrix (ECM). ROM could not estimate cell stress accurately when cells were sparse within the tissue, and Eshelby struggled as cells population got denser. Furthermore, we introduced a hybrid model that mixes both ideas, adjusting stress with a factor based on cell volume density. It matched FEM results much better across all cases and even worked for complex nonlinear materials using a simpler stiffness measure. This model improves our understanding of cell stress in diseased tissues like cerebral aneurysms, where cell density is not dense or sparse. It is a step toward understanding tissue mechanics better.