Mathematical models of wound healing and closure: a comprehensive review

Abstract

Wound healing is a complex process comprised of overlapping phases and events that work to construct a new, functioning tissue. Mathematical models describe these events and yield understanding about the overall process of wound healing. Generally, these models are focused on only one phase (or a few phases) to explain healing for a specific system. A review of the literature reveals insights as reported on herein regarding the variety of overlapping inputs and outputs for any given type of model. Specifically, these models have been characterized with respect to the phases of healing and their mathematical/physical basis in an effort to shed light on new opportunities for model development. Though all phases of wound healing have been modeled, previous work has focused mostly on the proliferation and related contraction phases of healing with fewer results presented regarding other phases. As an example, a gap in the literature has been identified regarding models to describe facilitated wound closure techniques (e.g., suturing and its effect on resultant scarring). Thus, an opportunity exists to create models that tie the transient processes of wound healing, such as cell migration, to resultant scarring when considering tension applied to skin with given suturing techniques.

A mathematical model for the determination of mouse excisional wound healing parameters from photographic data

“…Over 100 different mathematical models of wound healing have been reported in the literature (for a recent review see Jorgensen and Sanders). The vast majority of such models describe only a single phase of healing, and only a small number describe multiple phases (such as hemostasis, inflammatory, and proliferative phases combined).…”

“…Despite the utility of noninvasive photographic analysis in wound healing studies, there is no standardized methodology for either collection or analysis; furthermore, mathematical modeling of wound healing is typically appropriate only for simulation. 17 For example, while data from photographic studies are a metric of wound magnitude (monitored as a function of time) such data are diversely reported as wound area, % wound area, or wound radius. 16,18,19 A key metric of clinical interest is the wound healing rate; however, rate definition is dependent on how the wound magnitude is quantified.…”

Review on experiment-based two- and three-dimensional models for wound healing

“…Tartarini et al [38] present a review on continuous-scale models, as well as models of cell populations with several cell phenotypes with an application to stem cell therapies in wounds. Jorgensen & Sanders [39] present a review about continuum-based mathematical models for consecutive phases during wound healing, where they emphasize that, for instance, models combining wound closure with suturing (stitches for wound closure) techniques are lacking in the present literature.…”

Treatment with low‐level sodium fluoride on wound healing and the osteogenic differentiation of bone marrow mesenchymal stem cells

“…Skin and mucosal wounds are dependent upon several interdependent steps such as epithelial cell proliferation and deposition of the extracellular matrix . Bone marrow mesenchymal stem cells (BMMSCs) are present in bone marrow and possess the ability of self‐renewal, multipotential differentiation, and immune regulation .…”