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A Differential Equation Model of Collagen Accumulation in a Healing Wound

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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.

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Authors and Affiliations

  1. Department of Mathematics, Virginia Commonwealth University, Richmond, VA, 23284-2014, USA

    Rebecca A. Segal & Angela Reynolds

  2. Center for the Study of Biological Complexity, Virginia Commonwealth University, Richmond, VA, 23284-2030, USA

    Rebecca A. Segal & Robert F. Diegelmann

  3. Department of Biochemistry & Molecular Biology, Virginia Commonwealth University Medical Center, Richmond, VA, 23298-0614, USA

    Robert F. Diegelmann

  4. VCURES, Virginia Commonwealth University, Richmond, VA, 23298, USA

    Robert F. Diegelmann & Angela Reynolds

  5. Michigan Critical Injury and Illness Research Center, Department of Emergency Medicine, University of Michigan, Ann Arbor, MI, 48109, USA

    Kevin R. Ward

Authors
  1. Rebecca A. Segal
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  2. Robert F. Diegelmann
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  3. Kevin R. Ward
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  4. Angela Reynolds
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Correspondence to Rebecca A. Segal.

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Segal, R.A., Diegelmann, R.F., Ward, K.R. et al. A Differential Equation Model of Collagen Accumulation in a Healing Wound. Bull Math Biol 74, 2165–2182 (2012). https://doi.org/10.1007/s11538-012-9751-z

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  • DOI: https://doi.org/10.1007/s11538-012-9751-z

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