Wound healing, a multidisciplinary approach: combining mathematical models and biological experiments

Cutaneous wound repair occurs as a continuous process in both space and time; however, studies of healing mechanisms and outcomes frequently generate spatially and temporally sparse datasets. We propose a range of techniques that allow the size, cellular processes and scar tissue properties of wounds to be measured and predicted at high spatial and temporal resolution. A non-invasive wound imaging system is shown to provide reliable measurements of wound diameter, perimeter and surface area, but is less reliable in producing 3D metrics such as volume and depth. Wound size and time post healing have a combined effect on reliability, with more reliable measurements obtained at earlier timepoints. A semi-automated pipeline is found to be appropriate for determining the cellular composition of the wound space, but cannot be applied to areas of healthy epidermis due to the close packing of keratinocytes. A range of mathematical models are employed to predict cell numbers within the wound space. An extended domain, partial differential equation model with spatial control of cell proliferation and migration is found to best recapitulate the cellular dynamics observed in vivo. However, if epidermal stratification is to be incorporated, an agent-based description may be preferable. Finally, we formulate a model system that can predict the alignment of collagen fibres and fibroblasts over continuous orientation space. Parameter sets that include large shear forces (which may result from elongated wound geometries or interventions such as suturing) can produce skewed distributions of orientation that cannot be established using discontinuous approaches. Together, this suite of computational approaches provides a powerful set of tools with which the mechanisms of cutaneous wound healing can be investigated, quantified and elucidated.