On growth and morphogenesis in mechanobiology

Abstract: Morphoelasticity represents a foundational theory for tracing back growth, remodelling, and morphogenesis, yet crucial challenges persist. A unified growth law, -- independent of a priori assumptions about constitutive relations or specified structures of the growth tensor -- remains in fact elusive, as does an intimate connection between local anisotropic growth, morphogenesis dynamics, diffusion phenomena and mechanics. When anisotropy of growth is not prescribed arbitrarily, current frameworks mainly attribute shape emergence to growth-induced global configurational switches, somehow neglecting the existence of local drivers of spontaneous patterning or distorsions also in stress-free conditions. To overcome these limitations, in this work we propose a theoretical approach that reformulates anisotropic growth, remodeling, and morphogenesis starting from first principles, grounded in mass balance. In particular, by positing mass conservation as the sole dynamic constraint for the growth problem, we generalize the mass balance equation to derive evolution laws for mass distribution and geometric reconfiguration. This reveals how mass transport and associated microstructural evolution of the tissue fabric synergistically guide biological, geometric, and constitutive changes of living matter, with the isochoric component of growth orchestrating local anisotropy and, at the macroscale, even spontaneous shape development. The proposed fully coupled modelling approach integrates chemo-mechanical and biological interactions inherent to living systems, offering a pathway to investigate complex scenarios in growth and morphogenesis, redefining the latter in a Continuum Mechanics framework. It is felt that this strategy could help to take a step forward a unified perspective for biomechanical and mechanobiological problems, bridging scales from local drivers to emergent tissue forms and shapes.