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Bioengineering Research of Chronic Wounds pp 127–168Cite as

A Suite of Continuum Models for Different Aspects in Wound Healing

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Part of the book series: Studies in Mechanobiology, Tissue Engineering and Biomaterials ((SMTEB,volume 1))

Abstract

Wound healing proceeds through a sequence of partly overlapping processes that can be classified into three phases: inflammation, proliferation and remodeling. Among them, wound closure, angiogenesis and wound contraction play a significant role. First, the connective tissue that is present initially is replaced with fibrous tissue. The production of fibrous tissue by fibroblasts is initiated by fibroblast migration into the wound region and enhanced by the proliferation of these cells. Since the fibroblasts start pulling on the surrounding tissue, the wound starts contracting. Mathematically, the visco-elastic equations are solved in combination with a set of diffusion-convection-reaction equations. Once connective tissue has been replaced with fibrous tissue, a capillary network is established. The capillary network formation is enhanced by a macrophage derived growth factor, of which its production is initiated by a lack of oxygen. Several models exist and are discussed here for this partial process. For the wound re-epithelialization, in which the wound is actually closed by a layer of epidermal cells, several models are used. In this work, we will consider a simplified mathematical model that tracks the epidermal cell density and a generic growth factor that either inhibits or activates this process. Further, an alternative model is discussed, which contains a discontinuous switch mechanism, based on the assumption that the wound edge moves as a result of its curvature and of the concentration of a generic growth factor. In this work, finite element results will be presented, as well as parts of the performed mathematical analysis.

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Authors and Affiliations

  1. Delft Institute of Applied Mathematics, Delft University of Technology, Mekelweg 4, Delft, 2628, CD, The Netherlands

    F. J. Vermolen

  2. CIBER-BBN Centro de Investigación Biomédica en Red en Bioingeniería, Biomateriales y Nanomedicina, Zaragoza, Spain

    E. Javierre

  3. Group of Structural Mechanics and Materials Modelling, Aragón Institute of Engineering Research (I3A), University of Zaragoza, 50018, Zaragoza, Spain

    E. Javierre

  4. Aragón Health Sciences Institute, Zaragoza, Spain

    E. Javierre

Authors
  1. F. J. Vermolen
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  2. E. Javierre
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Editors and Affiliations

  1. Fac. Engineering, Dept. Biomedical Engineering, Tel Aviv University, 69978, Ramat Aviv, Israel

    Amit Gefen

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Vermolen, F.J., Javierre, E. (2009). A Suite of Continuum Models for Different Aspects in Wound Healing. In: Gefen, A. (eds) Bioengineering Research of Chronic Wounds. Studies in Mechanobiology, Tissue Engineering and Biomaterials, vol 1. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-00534-3_6

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  • DOI: https://doi.org/10.1007/978-3-642-00534-3_6

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-00533-6

  • Online ISBN: 978-3-642-00534-3

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