A one-dimensional morphoelastic model for burn injuries: stability, numerical validation, and biological interpretation
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To deal with permanent deformations and residual stresses, we consider a morphoelastic model for the scar formation as the result of wound healing after a skin trauma. Next to the mechanical components such as strain and displacements, the model accounts for biological parameters such as the concentration of chemokines, the cellular densities of fibroblasts and myofibroblasts, and the density of collagen. We present separate stability constraints for the mechanical part of the one-dimensional morphoelastic model and stability constraints for the chemical part of the one-dimensional morphoelastic model. Stability results are developed for both the continuous and (semi-)discrete problems. For the mechanical part, we distinguish between elasticity and plasticity. We perform numerical validation to these constraints and provide a biological interpretation of the (in)stability. For the mechanical model, the results show that the components reach equilibria in a (non) monotonic way, depending on the value of the viscosity. Furthermore, the results show that the parameters of the chemical model need to meet the stability constraint to avoid unrealistic results.
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