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A morphoelastic model for dermal wound closure

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Abstract

We develop a model of wound healing in the framework of finite elasticity, focussing our attention on the processes of growth and contraction in the dermal layer of the skin. The dermal tissue is treated as a hyperelastic cylinder that surrounds the wound and is subject to symmetric deformations. By considering the initial recoil that is observed upon the application of a circular wound, we estimate the degree of residual tension in the skin and build an evolution law for mechanosensitive growth of the dermal tissue. Contraction of the wound is governed by a phenomenological law in which radial pressure is prescribed at the wound edge. The model reproduces three main phases of the healing process. Initially, the wound recoils due to residual stress in the surrounding tissue; the wound then heals as a result of contraction and growth; and finally, healing slows as contraction and growth decrease. Over a longer time period, the surrounding tissue remodels, returning to the residually stressed state. We identify the steady state growth profile associated with this remodelled state. The model is then used to predict the outcome of rewounding experiments designed to quantify the amount of stress in the tissue, and also to simulate the application of pressure treatments.

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Notes

  1. We note that there is a one-to-one map between all states. Our convention is generally to view all spatially dependent variables as functions of the independent variable \(R_0\). So, for example, we write \(T_{rr}(R)\) as \(T_{rr}(R_0)=T_{rr}(R(R_0))\).

  2. Numerically, we define steady state to be such that each \(\frac{\partial \gamma _i}{\partial t}\) is below a positive threshold value close to zero. For the simulations in Fig. 14, the threshold was taken to be \(10^{-5}\).

  3. To test this, we ran simulations where the axial deformation was not fixed according to \(\lambda (t)=\lambda (T)\), but instead satisfied the spring condition in Eq. (29j). In this case, the sensitivity of the remodelling time to the axial growth parameter was significantly lower than that presented in Fig. 14.

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Acknowledgments

LGB gratefully acknowledges the UK’s Engineering and Physical Sciences Research Council for funding through a studentship at the Systems Biology programme of the University of Oxford’s Doctoral Training Centre. The authors thank Dr. P.Y. Liu and Dr. X.T. Wang (Department of Plastic Surgery, Alpert Medical School of Brown University) for valuable discussions.

Conflict of interest

The authors declare that they have no conflict of interest.

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Authors and Affiliations

  1. Wolfson Centre for Mathematical Biology, Mathematical Institute, University of Oxford, Andrew Wiles Building, Radcliffe Observatory Quarter, Woodstock Road, Oxford, OX2 6GG, UK

    L. G. Bowden, H. M. Byrne, P. K. Maini & D. E. Moulton

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  1. L. G. Bowden
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Correspondence to L. G. Bowden.

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Bowden, L.G., Byrne, H.M., Maini, P.K. et al. A morphoelastic model for dermal wound closure. Biomech Model Mechanobiol 15, 663–681 (2016). https://doi.org/10.1007/s10237-015-0716-7

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