A mathematical analysis of physiological and morphological aspects of wound closure

Javierre, E.; Vermolen, F.J.; Vuik, C.; Zwaag, Sybrand van der

doi:10.1007/s00285-008-0242-7

Cited by 56 publications

(38 citation statements)

References 46 publications

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“…Simulations are in agreement with available lung tissue data of human patients [163]. Javierre et al [164] analyzed the roles of diffusion, closure rate, and wound geometry on healing kinetics and concluded that healing is always initiated at regions with high curvatures.…”

Section: Models With Internal Structuresupporting

confidence: 66%

Towards a unified approach in the modeling of fibrosis: A review with research perspectives

Amar

Bianca

2016

Physics of Life Reviews

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Pathological fibrosis is the result of a failure in the wound healing process. The comprehension and the related modeling of the different mechanisms that trigger fibrosis is a challenge of many researchers that work in the field of medicine and biology. The modern scientific analysis of a phenomenon generally consists of three major approaches: theoretical, experimental, and computational. Different theoretical tools coming from mathematics and physics have been proposed for the modeling of the physiological and pathological fibrosis. However a complete framework is missing and the development of a general theory is required. This review aims at finding a unified approach in the modeling of fibrosis diseases that takes into account the different phenomena occurring at each level: molecular, cellular and tissue. Specifically by means of a critical analysis of the different models that have been proposed in the mathematical, computational and physical biology, from molecular to tissue scales, a multiscale approach is proposed, an approach that has been strongly recommended by top level biologists in the past decades.

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Section: Models With Internal Structuresupporting

confidence: 66%

Towards a unified approach in the modeling of fibrosis: A review with research perspectives

Amar

Bianca

2016

Physics of Life Reviews

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“…The first model describes a traveling wave analysis, whereas the second paper assesses fundamental mathematical questions on existence, uniqueness of solutions, and the mathematical nature of the moving boundary separating the wound from the undamaged tissue. Javierre et al (2009) presents a numerical solution method for the moving boundary problem.…”

Section: Introductionmentioning

confidence: 99%

A semi-stochastic cell-based formalism to model the dynamics of migration of cells in colonies

Vermolen

Gefen

2011

Biomech Model Mechanobiol

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We consider the movement and viability of individual cells in cell colonies. Cell movement is assumed to take place as a result of sensing the strain energy density as a mechanical stimulus. The model is based on tracking the displacement and viability of each individual cell in a cell colony. Several applications are shown, such as the dynamics of filling a gap within a fibroblast colony and the invasion of a cell colony. Though based on simple principles, the model is qualitatively validated by experiments on living fibroblasts on a flat substrate.

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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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A mathematical analysis of physiological and morphological aspects of wound closure

Cited by 56 publications

References 46 publications

Towards a unified approach in the modeling of fibrosis: A review with research perspectives

Towards a unified approach in the modeling of fibrosis: A review with research perspectives

A semi-stochastic cell-based formalism to model the dynamics of migration of cells in colonies

Mathematical modeling of collagen turnover in biological tissue

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