Mechanobiological modeling of viscoelasticity in soft tissue growth and morphogenesis

•A multiscale mechano-chemo-biological model is proposed for the growth and morphogenesis of soft tissues.•Viscoelasticity significantly modulates the stress accumulation and growth of soft tissues and organs.•Viscoelastic effects on the surface instability and morphogenesis of growing organoids are revealed. Most soft biological tissues feature distinct mechanical properties of viscoelasticity, which play a significant role in their growth, development, and morphogenesis. In this paper, we propose a mechanobiological viscoelastic model in the framework of thermodynamics. The multiscale mechanisms underlying the viscoelasticity of tissues are clarified, such as extracellular matrix composition and organization, cell types and states, dynamic cell–matrix and cell–cell interactions, and active cytoskeleton evolution. This model enables us to elucidate how viscoelastic effects modulate the growth and surface instability of soft tissues via coupled mechano-chemo-biological regulatory mechanisms. The proposed constitutive model is implemented into the finite element method, to explore the growth, stability, and morphological evolution of tissues. Illustrative examples, including tumor growth and organoid development, demonstrate that viscoelasticity can facilitate sustained tissue growth, and significantly influences the critical conditions of surface wrinkling and the morphological evolution of tissues. The results are consistent with relevant experimental observations. This study provides a theoretical model for growing soft tissues with viscoelastic effects, and holds promise for potential applications in clinical diagnosis and treatment of some diseases. A multiscale mechano-chemo-biological model is proposed to reveal the influences of viscoelasticity on the growth and morphogenesis of soft biological tissues and organs. [Display omitted]