A mathematical model for the simulation of the contraction of burns

Daniël C. Koppenol, Fred Vermolen, Gabriela V. Koppenol-Gonzalez, Frank B. Niessen, Paul P.M. van Zuijlen, Kees Vuik

Research output: Contribution to journalArticleScientificpeer-review

4 Citations (Scopus)
31 Downloads (Pure)

Abstract

A continuum hypothesis-based model is developed for the simulation of the contraction of burns in order to gain new insights into which elements of the healing response might have a substantial influence on this process. Tissue is modeled as a neo-Hookean solid. Furthermore, (myo)fibroblasts, collagen molecules, and a generic signaling molecule are selected as model components. An overview of the custom-made numerical algorithm is presented. Subsequently, good agreement is demonstrated with respect to variability in the evolution of the surface area of burns over time between the outcomes of computer simulations and measurements obtained in an experimental study. In the model this variability is caused by varying the values for some of its parameters simultaneously. A factorial design combined with a regression analysis are used to quantify the individual contributions of these parameter value variations to the dispersion in the surface area of healing burns. The analysis shows that almost all variability in the surface area can be explained by variability in the value for the myofibroblast apoptosis rate and, to a lesser extent, the value for the collagen molecule secretion rate. This suggests that most of the variability in the evolution of the surface area of burns over time in the experimental study might be attributed to variability in these two rates. Finally, a probabilistic analysis is used in order to investigate in more detail the effect of variability in the values for the two rates on the healing process. Results of this analysis are presented and discussed.
Original languageEnglish
Pages (from-to)1-31
Number of pages31
JournalJournal of Mathematical Biology
Volume75
Issue number1
DOIs
Publication statusPublished - 8 Nov 2016

Keywords

  • Burns
  • Wound contraction
  • Heterogeneous, isotropic, compressible neo-Hookean solid
  • Multiple linear regression analysis
  • Probabilistic analysis
  • Moving-grid finite-element method

Fingerprint

Dive into the research topics of 'A mathematical model for the simulation of the contraction of burns'. Together they form a unique fingerprint.

Cite this