论文标题
燃烧损伤的一维形态弹性模型：稳定性分析，数值验证和生物学解释
A one-dimensional morphoelastic model for burn injuries: stability analysis, numerical validation and biological interpretation
论文作者
论文摘要
为了处理永久性变形和残留应力，我们考虑了皮肤创伤后伤口愈合的疤痕形成的形态弹性模型。在机械成分（例如应变和位移）旁边，该模型说明了生物学成分，例如信号分子的浓度，成纤维细胞和肌纤维细胞的细胞密度以及胶原蛋白的密度。在这里，我们为该形态弹性模型的一维对应物提出了稳定性约束，即连续和（半）离散问题。我们表明，与连续和半混凝土问题关联的这些特征值之间的截断误差是$ \ MATHCAL {O}（H^2）$的顺序。接下来，我们对这些约束进行数值验证，并对（在）稳定性方面提供生物学解释。对于模型的机械部分，结果表明该组件以（非）单调方式达到平衡，具体取决于粘度的值。结果表明，模型的化学部分的参数需要根据信号分子的衰减速率来满足稳定性约束，以避免结果不切实际。
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 $\mathcal{O}(h^2)$. 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.
