An Eulerian Nonlinear Elastic Model for Compressible and Fluidic Tissue with Radially Symmetric Growth

Cell proliferation, apoptosis, and myosin-dependent contraction can generate elastic stress strain in living tissues, which may be dissipated by internal rearrangement through cell topological transition cytoskeletal reorganization. Moreover, cells tissues change their sizes response to mechanical cues. The present work demonstrates the role of tissue compressibility rearranging activities on its size mechanics regulation context differential growth induced a field growth-promoting chemical factors. We develop mathematical model based finite elasticity theory reference map techniques describe coupled Eulerian frame. incorporate introducing rate evolution, leading elastic-energy dissipation when deformation are radial symmetry. By linearizing model, we show that follows Maxwell-type viscoelastic relaxation. rate, call fluidity, sets relaxation time, ratio between shear modulus fluidity viscosity. nonlinear simulation growing spheroids discs with graded rates along radius, find influence equilibrium size. comparing simulations linear analytical solutions, as effect due advection density flow, only occurs both small. apply study tumor spheroid epithelial disc reaction-diffusion process determines factor field.