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Abstract：
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 constituents such as the concentration of signaling molecules, the cellular densities of fibroblasts and myofibroblasts, and the density of collagen. Here we present stability constraints for the one-dimensional counterpart of this morphoelastic model, for both the continuous and (semi-) discrete problem. We show that the truncation error between these eigenvalues associated with the continuous and semi-discrete problem is of order [Formula: see text]. Next we perform numerical validation to these constraints and provide a biological interpretation of the (in)stability. For the mechanical part of the model, the results show the components reach equilibria in a (non) monotonic way, depending on the value of the viscosity. The results show that the parameters of the chemical part of the model need to meet the stability constraint, depending on the decay rate of the signaling molecules, to avoid unrealistic results.
摘要：
处理永久变形和残余应力，我们认为瘢痕形成的形态弹性模型是皮肤创伤后伤口愈合的结果。除了应变和位移等机械部件，该模型考虑了生物成分，如信号分子的浓度，成纤维细胞和肌成纤维细胞的细胞密度，和胶原蛋白的密度。在这里，我们提出了这种形态弹性模型的一维对应物的稳定性约束，对于连续和(半)离散问题。我们表明，与连续和半离散问题相关的这些特征值之间的截断误差是有序的[公式：见文本]。接下来，我们对这些约束进行数值验证，并提供（in）稳定性的生物学解释。对于模型的机械部分，结果表明，组分以(非)单调的方式达到平衡，取决于粘度的值。结果表明,模型的化学部分参数需要满足稳定性约束,取决于信号分子的衰变速率，避免不切实际的结果。
