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.
Olsen
L
L
Centre of Mathematical Biology, Mathematical Institute, Oxford, United Kingdom.
Maini
P K
PK
Sherratt
J A
JA
D000818:Animals; D001696:Biomechanical Phenomena; D002465:Cell Movement; D003094:Collagen / Q000096:biosynthesis; D005109:Extracellular Matrix / Q000473:pathology / Q000502:physiology; D005347:Fibroblasts / Q000473:pathology / Q000502:physiology; D006801:Humans; D008433:Mathematics; D008954:Models, Biological; D012867:Skin / Q000293:injuries / Q000473:pathology / Q000503:physiopathology; D014945:Wound Healing / Q000502:physiology*
D003094:Collagen