arXiv subjects

Paul van Zuijlen

Publications and source records attributed to Paul van Zuijlen.

2 recordsLinked to original sources

arXiv2021

A one-dimensional morphoelastic model for burn injuries: sensitivity analysis and a feasibility study

We consider a one-dimensional morphoelastic model describing post-burn scar contraction. This model describes the displacement of the dermal layer of the skin and the development of the effective Eulerian strain in the tissue. Besides these components, the model also contains components that play a major role in skin repair after trauma. These components are signaling molecules, fibroblasts, myofibroblasts, and collagen. We perform a sensitivity analysis for many parameters of the model and use the results for a feasibility study. In this study, we test whether the model is suitable for predicting the extent of contraction in different age groups. To this end, we conduct an extensive literature review to find parameter values. From the sensitivity analysis, we conclude that the most sensitive parameters are the equilibrium collagen concentration in the dermal layer, the apoptosis rate of fibroblasts and myofibroblasts, and the secretion rate of signaling molecules. Further, although we can use the model to simulate distinct contraction densities in different age groups, our results differ from what is seen in the clinic.

math.NA↗

arXiv2021

A one-dimensional morphoelastic model for burn injuries: stability analysis, numerical validation and biological interpretation

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.

math.NA↗