Abstract
We review several of our mathematical models that we constructed for the simulation of contractures and morpho-elastic scars that are typically associated with deep dermal (burn) injuries. The models are based on partial differential equations, which are solved by the use of finite-element methods. The models contain elements of non-isotropy, morpho-elasticity for the treatment of the mechanics of the skin. Furthermore, we take into account the balances of fibroblasts, myofibroblasts, collagen and a generic growth factor. Using the models, we are able to simulate permanent contractions using physically sound principles.
Introduction
Over the globe, about eleven million individuals are affected by burn injuries. In about six hundred thousand cases, the injury is so serious that the patient dies. After serious burns or incisions, hypertrophic scars may arise among patients, who need plastic surgery. Another side effect of burn injuries is the formation of contractures, which lead to permanent deformations and stresses in the skin of the patient. This causes a reduction of the mobility of the patient. This reduction is a consequence of the pulling forces that are exerted by the fibroblasts and myo-fibroblasts.
Discussion
The models that we have shown in this manuscript are all based on cell densities and they have a fully continuum-scale character. In order to consider the processes on a very small scale, it could be worth to consider small-scale models like the cellular Potts formulations or semi-continuous cell-based models. However, for larger scales, it is appropriate to use the current partial differential equations-based continuum-scale models since cell-based models would require too many computational resources. Research of interest could be directed to the upscaling of small-scale models to larger scales. The current models further miss the link to the immune system. This link could be investigated more in clinical experiments so that models that couple wound contraction and hypertrophy can be formulated.
