Mathematical modeling of dermal wound healing: A numerical solution

Though wound healing process is well-researched, this area is poorly known. One reason is that all interactions have not been discovered, the main reason, though, is that the involved processes interact in a very complicated manner with nonlinear feedback. Such complex feedback mechanisms can be easily addressed by mathematical modeling. This paper contains a review of the mathematical modeling of cell interaction with extracellular matrix components during the process of dermal wound healing with focusing on remodeling phase. The models are of partial differential equation type and solved by numerical method.

[1]  Jennifer L. West,et al.  Tethered-TGF-β increases extracellular matrix production of vascular smooth muscle cells , 2001 .

[2]  D. Birk,et al.  Extracellular compartments in tendon morphogenesis: collagen fibril, bundle, and macroaggregate formation , 1986, The Journal of cell biology.

[3]  J. Xu,et al.  Extracellular matrix alters PDGF regulation of fibroblast integrins , 1996, The Journal of cell biology.

[4]  Jon R. Cohen The Molecular and Cellular Biology of Wound Repair , 1997, Springer US.

[5]  J L West,et al.  Tethered-TGF-beta increases extracellular matrix production of vascular smooth muscle cells. , 2001, Biomaterials.

[6]  T M Krummel,et al.  Regulation of wound healing from a connective tissue perspective , 1996, Wound repair and regeneration : official publication of the Wound Healing Society [and] the European Tissue Repair Society.

[7]  A Curtis,et al.  Topographical control of cells. , 1997, Biomaterials.

[8]  C. Wilkinson,et al.  Topographical control of cell behaviour: II. Multiple grooved substrata. , 1990, Development.

[9]  P. Hsieh,et al.  Behavior of cells seeded in isolated fibronectin matrices , 1983, The Journal of cell biology.

[10]  R T Tranquillo,et al.  A methodology for the systematic and quantitative study of cell contact guidance in oriented collagen gels. Correlation of fibroblast orientation and gel birefringence. , 1993, Journal of cell science.

[11]  M. Denyer,et al.  Adhesion, orientation, and movement of cells cultured on ultrathin fibronectin fibers , 1997, In Vitro Cellular & Developmental Biology - Animal.

[12]  C. Streuli,et al.  Extracellular matrix remodelling and cellular differentiation. , 1999, Current opinion in cell biology.

[13]  W. Parks,et al.  Role of Matrix Metalloproteinases and Their Inhibition in Cutaneous Wound Healing and Allergic Contact Hypersensitivity , 1999, Annals of the New York Academy of Sciences.

[14]  W. Eaglstein,et al.  Inhibition of cell proliferation by chronic wound fluid , 1993, Wound repair and regeneration : official publication of the Wound Healing Society [and] the European Tissue Repair Society.

[15]  Martin Raff,et al.  Cell Junctions, Cell Adhesion, and the Extracellular Matrix , 2002 .

[16]  K Hayashi,et al.  Biomechanical studies of the remodeling of knee joint tendons and ligaments. , 1996, Journal of biomechanics.

[17]  M. P. Welch,et al.  Collagen matrices attenuate the collagen-synthetic response of cultured fibroblasts to TGF-beta. , 1995, Journal of cell science.