Computational systems mechanobiology of wound healing

Achieving perfect skin regeneration after wounding remains challenging because of the lack of fundamental understanding of the harmonious interplay among different cell types, complex cell signaling networks and mechanical feedback loops evolving in space and time during healing. Here we show a novel computational framework to simulate the healing of wounds that brings together knowledge from continuum mechanics, growth and remodeling, and systems biology regulatory networks. At the tissue scale we consider a field of displacements that satisfies linear momentum balance, and continuous fields for cells and chemical signal concentrations which obey reaction-diffusion equations. At the cell scale a set of ordinary differential equations describe the dynamics of remodeling. Our major contribution is the modeling and simulation of the coupling of cellular and chemical fields to tissue-level mechanics via local changes in fiber alignment, dispersion, collagen content, permanent area change, elastic deformation, and active contraction. Numerically, the constitutive equations for remodeling are solved at the integration points while the displacements and biological fields are solved monolithically with a finite element formulation. The method presented here is at the junction of applied mechanics and systems biology, two exciting fields that continue to approach each other as we seek to unravel the basic principles of mechanical adaptation in living materials with the aid of computational simulations.