title: An ordinary differential equation model for full thickness wounds and the effects of diabetes.
abstract: Wound healing is a complex process in which a sequence of interrelated phases contributes to a reduction in wound size. For diabetic patients, many of these processes are compromised, so that wound healing slows down. In this paper we present a simple ordinary differential equation model for wound healing in which attention focusses on the dominant processes that contribute to closure of a full thickness wound. Asymptotic analysis of the resulting model reveals that normal healing occurs in stages: the initial and rapid elastic recoil of the wound is followed by a longer proliferative phase during which growth in the dermis dominates healing. At longer times, fibroblasts exert contractile forces on the dermal tissue, the resulting tension stimulating further dermal tissue growth and enhancing wound closure. By fitting the model to experimental data we find that the major difference between normal and diabetic healing is a marked reduction in the rate of dermal tissue growth for diabetic patients. The model is used to estimate the breakdown of dermal healing into two processes: tissue growth and contraction, the proportions of which provide information about the quality of the healed wound. We show further that increasing dermal tissue growth in the diabetic wound produces closure times similar to those associated with normal healing and we discuss the clinical implications of this hypothesised treatment.
authors.affiliation: Wolfson Centre for Mathematical Biology, Mathematical Institute, University of Oxford, Andrew Wiles Building, Radcliffe Observatory Quarter, Woodstock Road, Oxford OX2 6GG, UK. Electronic address: bowden@maths.ox.ac.uk.
authors.forename: L G
authors.initials: LG
authors.lastname: Bowden
authors.affiliation: Wolfson Centre for Mathematical Biology, Mathematical Institute, University of Oxford, Andrew Wiles Building, Radcliffe Observatory Quarter, Woodstock Road, Oxford OX2 6GG, UK.
authors.forename: P K
authors.initials: PK
authors.lastname: Maini
authors.affiliation: Wolfson Centre for Mathematical Biology, Mathematical Institute, University of Oxford, Andrew Wiles Building, Radcliffe Observatory Quarter, Woodstock Road, Oxford OX2 6GG, UK.
authors.forename: D E
authors.initials: DE
authors.lastname: Moulton
authors.affiliation: Department of Plastic Surgery, Rhode Island Hospital, Alpert Medical School of Brown University, Providence, RI, USA.
authors.forename: J B
authors.initials: JB
authors.lastname: Tang
authors.affiliation: Department of Plastic Surgery, Rhode Island Hospital, Alpert Medical School of Brown University, Providence, RI, USA.
authors.forename: X T
authors.initials: XT
authors.lastname: Wang
authors.affiliation: Department of Plastic Surgery, Rhode Island Hospital, Alpert Medical School of Brown University, Providence, RI, USA.
authors.forename: P Y
authors.initials: PY
authors.lastname: Liu
authors.affiliation: Department of Computer Science, University of Oxford, Wolfson Building, Parks Road, Oxford OX1 3QD, UK.
authors.forename: H M
authors.initials: HM
authors.lastname: Byrne
mesh_terms: D003920:Diabetes Mellitus / Q000378:metabolism / Q000473:pathology / Q000503:physiopathology; D006801:Humans; D008954:Models, Biological; D014945:Wound Healing; D014947:Wounds and Injuries / Q000378:metabolism / Q000473:pathology / Q000503:physiopathology
keywords: Asymptotic analysis; Contraction; Dermis; Epidermis; Tissue growth