Cell proliferation, apoptosis, and myosin-dependent contraction can generate elastic stress and strain in living tissues, which may be dissipated by tissue rearrangement through cell topological transition and cytoskeletal reorganization. The present work demonstrates significant nonlinear effects in macroscopic tissue mechanics arising from the competition between force-generating and dissipating processes. We develop a mathematical model to describe the coupled dynamics of tissue activities and mechanics in the nonlinear regime. The model exhibits multi-timescale behavior when the timescale of rearrangement is much shorter than that of growth and constriction. Under this condition, tissue behaves like an active viscoelastic solid at the shorter timescale and like an active viscous fluid at the longer timescale. The accumulated prestrain due to growth and constriction can regulate its viscosity. We solve the full nonlinear system considering the local growth rate coupled with a chemical gradient within a 2D radially symmetric tissue region. We find that the elastic properties and rearrangement rate can regulate tissue size as a higher-order effect due to advection in tissue flow. Furthermore, we show that tissue mechanics nonlinear effects can increase tissue size control sensitivity via mechanical feedback mechanisms.
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