A mathematical analysis of physiological and morphological aspects of wound closure

Fundamentals of Advanced Materials, Delft University of Technology, Delft, The Netherlands.
Journal of Mathematical Biology (Impact Factor: 1.85). 11/2009; 59(5):605-30. DOI: 10.1007/s00285-008-0242-7
Source: PubMed


A computational algorithm to study the evolution of complex wound morphologies is developed based on a model of wound closure by cell mitosis and migration due to Adam [Math Comput Model 30(5-6):23-32, 1999]. A detailed analysis of the model provides estimated values for the incubation and healing times. Furthermore, a set of inequalities are defined which demarcate conditions of complete, partial and non-healing. Numerical results show a significant delay in the healing progress whenever diffusion of the epidermic growth factor responsible for cell mitosis is slower than cell migration. Results for general wound morphologies show that healing is always initiated at regions with high curvatures and that the evolution of the wound is very sensitive to physiological parameters.

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    • "Because wound healing involves so many biological processes, there have been many different types of modeling technique used. Some research is concerned with the geometry of the wound and focused on the formation of the skin matrix (Almeida et al. 2011; Javierre et al. 2009). These models do not implement the effect of inflammation, an important stage of wound healing, particularly for wounds that fail to heal. "
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    ABSTRACT: Wound healing is a complex biological process which involves many cell types and biochemical signals and which progresses through multiple, overlapping phases. In this manuscript, we develop a model of collagen accumulation as a marker of wound healing. The mathematical model is a system of ordinary differential equations which tracks fibroblasts, collagen, inflammation and pathogens. The model was validated by comparison to the normal time course of wound healing where appropriate activity for the inflammatory, proliferative and remodeling phases was recorded. Further validation was made by comparison to collagen accumulation experiments by Madden and Peacock (Ann. Surg. 174(3):511-520, 1971). The model was then used to investigate the impact of local oxygen levels on wound healing. Finally, we present a comparison of two wound healing therapies, antibiotics and increased fibroblast proliferation. This model is a step in developing a comprehensive model of wound healing which can be used to develop and test new therapeutic treatments.
    Bulletin of Mathematical Biology 07/2012; 74(9):2165-82. DOI:10.1007/s11538-012-9751-z · 1.39 Impact Factor
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    • "Note that Eq. (1) is of Fisher– Kolmogorov type, which in the absence of passive convection admits solutions with a traveling wave structure. The mechanism of fibroblast differentiation to myofibroblasts has not yet been taken into account as was done in Olsen et al. (1995) and Javierre et al. (2009a). Biologically, one could interpret our simplified approach as assuming that c f ib models the density of both fibroblasts and myofibroblasts. "
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    ABSTRACT: A simplified finite-element model for wound healing is proposed. The model takes into account the sequential steps of dermal regeneration, wound contraction, angiogenesis and wound closure. An innovation in the present study is the combination of the aforementioned partially overlapping processes, which can be used to deliver novel insights into the process of wound healing, such as geometry related influences, as well as the influence of coupling between the various existing subprocesses on the actual healing behavior. The model confirms the clinical observation that epidermal closure proceeds by a crawling and climbing mechanism at the early stages, and by a stratification process in layers parallel to the skin surface at the later stages. The local epidermal oxygen content may play an important role here. The model can also be used to investigate the influence of local injection of hormones that stimulate partial processes occurring during wound healing. These insights can be used to improve wound healing treatments.
    Journal of Mathematical Biology 11/2011; 65(5):967-96. DOI:10.1007/s00285-011-0487-4 · 1.85 Impact Factor
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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. an upward traction force on the substrate. "
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    ABSTRACT: 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.
    Biomechanics and Modeling in Mechanobiology 03/2011; 11(1-2):183-95. DOI:10.1007/s10237-011-0302-6 · 3.15 Impact Factor
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