A mathematical model of wound healing and subsequent scarring

Cumming, B. D.; McElwain, D. L. S.; Upton, Zee

doi:10.1098/rsif.2008.0536

Cited by 110 publications

(125 citation statements)

References 22 publications

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“…A key contribution is the work of Fung & Liu (1989), amongst many others, which demonstrates that the volumetric growth of blood vessels induces a change in the natural configuration of the tissue, and induces residual stresses. Diffusion and cells migration models (Javierre et al, 2009;Cumming et al, 2010;Boyle et al, 2011) are other interesting approaches to the problem of biological tissue adaptation.…”

Section: Motivationmentioning

confidence: 99%

Mathematical modeling of collagen turnover in biological tissue

et al. 2012

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We present a theoretical and computational model for collagen turnover in soft biological tissues. Driven by alterations in the mechanical environment, collagen fiber bundles may undergo important chronic changes, characterized primarily by alterations in collagen synthesis and degradation rates. In particular, hypertension triggers an increase in tropocollagen synthesis and a decrease in collagen degradation, which lead to the well-documented overall increase in collagen content. These changes are the result of a cascade of events, initiated mainly by the endothelial and smooth muscle cells. Here, we represent these events collectively in terms of two internal variables, the concentration of growth factor TGF-β and tissue inhibitors of metalloproteinases TIMP. While the upregulation of the former increases the collagen density, the upregulation of the latter increases the collagen density through decreasing matrix metalloproteinase MMP. We establish a mathematical theory for mechanically-induced collagen turnover and introduce a computational algorithm for its robust and efficient solution. We demonstrate that our model can accurately predict the experimentally observed collagen increase in response to hypertension reported in literature. Ultimately, the model can serve as a valuable tool to predict the chronic adaptation of collagen content to restore the homeostatic equilibrium state in vessels with arbitrary micro-structure and geometry.

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Section: Motivationmentioning

confidence: 99%

Mathematical modeling of collagen turnover in biological tissue

et al. 2012

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“…They present one-dimensional simulations as well as a rigorous mathematical analysis of the well-posedness (existence, uniqueness and continuity) of solutions to the PDEs. Recently, Koppenol et al [35] have considered the formation of excess scar tissue (hypertrophic scar) after the occurrence of a burn, where the dynamics of fibroblasts and myofibroblasts has been taken into account. In that work, the tissue is mechanically represented as a neoHookean material, and the migration of cells is obtained by solving Keller-Segel-like equations with reactive terms, and hence these equations fall within the category of transport (predominantly convective-like and diffusion-type)-reaction equations.…”

Section: Models Based On Partial Differential Equationsmentioning

confidence: 99%

Review on experiment-based two- and three-dimensional models for wound healing

2016

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Traumatic and chronic wounds are a considerable medical challenge that affects many populations and their treatment is a monetary and timeconsuming burden in an ageing society to the medical systems. Because wounds are very common and their treatment is so costly, approaches to reveal the responses of a specific wound type to different medical procedures and treatments could accelerate healing and reduce patient suffering. The effects of treatments can be forecast using mathematical modelling that has the predictive power to quantify the effects of induced changes to the wound-healing process. Wound healing involves a diverse and complex combination of biophysical and biomechanical processes. We review a wide variety of contemporary approaches of mathematical modelling of gap closure and wound-healing-related processes, such as angiogenesis. We provide examples of the understanding and insights that may be garnered using those models, and how those relate to experimental evidence. Mathematical modellingbased simulations can provide an important visualization tool that can be used for illustrational purposes for physicians, patients and researchers.

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“…Hybrid approaches have been formulated, for example, to investigate wound healing [236][237][238], interaction of cells (CBM) and the basal membrane and ECM [52], angiogenesis [233,239], and multicellular spheroids with invasion [233,235].…”

Section: Hybrid Discrete-continuum Modelsmentioning

confidence: 99%

Simulating tissue mechanics with agent-based models: concepts, perspectives and some novel results

et al. 2015

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In this paper we present an overview of agentbased models that are used to simulate mechanical and physiological phenomena in cells and tissues, and we discuss underlying concepts, limitations, and future perspectives of these models. As the interest in cell and tissue mechanics increase, agent-based models are becoming more common the modeling community. We overview the physical aspects, complexity, shortcomings, and capabilities of the major agent-based model categories: lattice-based models (cellular automata, lattice gas cellular automata, cellular Potts models), off-lattice models (center-based models, deformable cell models, vertex models), and hybrid discrete-continuum models. In this way, we hope to assist future researchers in choosing a model for the phenomenon they want to model and understand. The article also contains some novel results.

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A mathematical model of wound healing and subsequent scarring

Cited by 110 publications

References 22 publications

Mathematical modeling of collagen turnover in biological tissue

Mathematical modeling of collagen turnover in biological tissue

Review on experiment-based two- and three-dimensional models for wound healing

Simulating tissue mechanics with agent-based models: concepts, perspectives and some novel results

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