Comparison between a phenomenological approach and a morphoelasticity approach regarding the displacement of extracellular matrix

Biomechanics and Modeling in Mechanobiology, vol. 21, pp. 919–935

Abstract

Plastic (permanent) deformations were earlier, modeled by a phenomenological model in Peng and Vermolen (Biomech Model Mechanobiol 19(6):2525-2551, 2020). In this manusctipt, we consider a more physics-based formulation that is based on morphoelasticity. We firstly introduce the morphoelasticity approach and investigate the impact of various input variables on the output parameters by sensitivity analysis. A comparison of both model formulations shows that both models give similar computational results. Furthermore, we carry out Monte Carlo simulations of the skin contraction model containing the morphoelasticity approach. Most statistical correlations from the two models are similar, however, the impact of the collagen density on the severeness of contraction is larger for the morphoelasticity model than for the phenomenological model.

Authors 3

1. Qiyao Peng corresponding Aachen Mathematical Institute

   Leiden University · Delft University of Technology · Hasselt University

   Affiliation as printed

   Computational Mathematics Group, Discipline group Mathematics and statistics, Faculty of Science, Hasselt University, Campus Diepenbeek, Agoralaan Gebouw D, BE 3590, Diepenbeek, Belgium. Q.Peng@math.leidenuniv.nl

   Delft Institute of Applied Mathematics, Delft University of Technology, Mekelweg 4, 2628 CD, Delft, The Netherlands. Q.Peng@math.leidenuniv.nl

   Mathematical Institute, Leiden University, 2333 CA, Niels Bohrweg, The Netherlands. Q.Peng@math.leidenuniv.nl

   Computational Mathematics Group, Discipline group Mathematics and statistics, Faculty of Science, Hasselt University, Diepenbeek, Belgium

   Delft Institute of Applied Mathematics, Delft University of Technology, Delft, The Netherlands

   Mathematical Institute, Leiden University, Niels Bohrweg, The Netherlands

2. W. S. Gorter

   Delft University of Technology

   Affiliation as printed

   Delft Institute of Applied Mathematics, Delft University of Technology, Mekelweg 4, 2628 CD, Delft, The Netherlands

   Delft Institute of Applied Mathematics, Delft University of Technology, Delft, The Netherlands

3. Fred J. Vermolen

   Delft University of Technology · Hasselt University

   Affiliation as printed

   Computational Mathematics Group, Discipline group Mathematics and statistics, Faculty of Science, Hasselt University, Campus Diepenbeek, Agoralaan Gebouw D, BE 3590, Diepenbeek, Belgium

   Delft Institute of Applied Mathematics, Delft University of Technology, Mekelweg 4, 2628 CD, Delft, The Netherlands

   Computational Mathematics Group, Discipline group Mathematics and statistics, Faculty of Science, Hasselt University, Diepenbeek, Belgium

   Delft Institute of Applied Mathematics, Delft University of Technology, Delft, The Netherlands