A Mechanochemical Model for Adult Dermal Wound Contraction and the Permanence of the Contracted Tissue Displacement Profile

Abstract

The healing of adult mammalian skin wounds involves a complex sequence of spatially and temporally coordinated processes. Wound contraction, by reducing the size of the injury, is an intrinsic component of full-thickness excisional dermal wound healing. The underlying biomechanics of wound contraction, however, are not fully understood, and little is known about the pathogenesis of severe medical conditions known as fibrocontractive diseases. The aim of this work is to investigate a deterministic mathematical model in order to obtain insight into the mechanistic relationships between wound contraction and associated normal and pathological healing processes. The model describes the essential roles of fibroblast and myofibroblast cells, a chemical growth factor and the extracellular matrix which includes type I collagen. The model results are qualitatively consistent with the biology of fibroplasia and wound contraction. It is shown that a contracted state evolves during a (long) transient phase of healing known as ''proliferation'', while collagen kinetics are fundamental to the considerably longer ''remodelling'' phase. Some quantitative results, notably on the evolution of wound contraction, compare favourably with experimental data. Application of the model to adult human dermal wound healing in vivo, with a greater understanding of the underlying biological mechanisms involved, may suggest strategies for controlling contraction and fibrocontractive diseases.

Mathematical Modelling of Juxtacrine Patterning

“…Mechanochemical models have been applied to a variety of patterning problems, such as feather germ primordia (Murray et al, 1983) and cartilage formation in the vertebrate limb (Oster et al, 1985). Recent work on wound-healing in mammalian skin is an important example of how the models can be adapted to obtain an understanding of morphogenesis in living tissue (Murray et al, 1988;Olsen et al, 1995).…”

A mathematical model for fibro-proliferative wound healing disorders

“…The fill model framework. We have recently proposed a continuum model for fibroplasia and wound contraction in adult mammalian dermis (Olsen et al, 1995). This "full" model is briefly summarized here since it will be used to investigate abnormal healing.…”

“…Governing equations, boundary and initial conditions. With some further detail on the mathematical representations of these processes (Olsen et al, 1995) the non-dimensional model equations are derived from conservation laws for the fibroblast density n(x, t), myofibroblast density 111(x, t), chemical concentration c(x, t) and collagen concentration p(x, t), where x is the spatial position vector and t denotes time.…”

“…These are investigated within the framework of a mathematical model recently proposed for fibroplasia and wound contraction (Olsen et al, 1995) with the aim of an improved understanding of the pathogenic mechanisms of such conditions and their relationships to normal healing.…”

Semi-stochastic cell-level computational modelling of cellular forces: application to contractures in burns and cyclic loading

“…In this study, we present a simplified framework for the modelling of contractures, which can be used in more realistic mathematical models to actually predict the likelihood for the occurrence of contractures, as well as the likelihood for the occurrence of excessive scar formation. Mathematical models for wound contraction can be found in the papers by Olsen et al (1995), Murray (2004) and Vermolen and Javierre (2012) and most recently in Valero et al (2014), where the last mentioned paper provides a breakthrough in modelling regarding the relation between myofibroblasts and local dilatations. A second application involves modelling cyclic loading where the present model allows to quantify the impact of phase perturbations in the cycles of individual cells on heart performance.…”