Spatially varying equilibria of mechanical models: application to dermal wound contraction

Mechanochemical models based on the Oster-Murray continuum framework have been applied to a variety of biological settings to obtain an understanding of the morphogenesis of living tissues. Wound-healing in mammalian skin is an important example, because a complex sequence of biochemical and biomechanical responses are orchestrated to close a wound by a combination of new tissue formation and wound contraction. Mechanical interactions between dermal fibroblastic cells and the collagen-rich extracellular matrix are crucial in the development of a contracted wound state. We and others have previously proposed mechanochemical models for wound repair to gain a greater understanding of both normal and abnormal healing. In the present work, the existence of spatially varying equilibria of these models is investigated by using a small-stain approximation and phase-plane techniques, with numerical simulations to confirm the analytical predictions. These results are sources of novel insight into the roles of key biological parameters in determining the mechanical properties of a contracted wound. These methods may also be relevant to other morphogenetic scenarios for which similar mechanochemical models have been proposed.