A mathematical model for the simulation of the contraction of burns.
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.
Delft Institute of Applied Mathematics, Delft University of Technology, Delft, The Netherlands. D.C.Koppenol@tudelft.nl.
Daniël C
DC
Koppenol
Delft Institute of Applied Mathematics, Delft University of Technology, Delft, The Netherlands.
Fred J
FJ
Vermolen
Department of Psychology, Education and Child Studies, Erasmus University Rotterdam, Rotterdam, The Netherlands.
Gabriela V
GV
Koppenol-Gonzalez
Department of Plastic, Reconstructive and Hand Surgery, MOVE Research Institute, VU University Medical Centre, Amsterdam, The Netherlands.
Frank B
FB
Niessen
Department of Plastic, Reconstructive and Hand Surgery, MOVE Research Institute, VU University Medical Centre, Amsterdam, The Netherlands.|Burn Centre, Red Cross Hospital, Beverwijk, The Netherlands.|Department of Plastic, Reconstructive and Hand Surgery, Red Cross Hospital, Beverwijk, The Netherlands.
Paul P M
PPM
van Zuijlen
Delft Institute of Applied Mathematics, Delft University of Technology, Delft, The Netherlands.
Kees
K
Vuik
D000465:Algorithms; D002056:Burns; D003094:Collagen / Q000378:metabolism; D003198:Computer Simulation; D006801:Humans; D008954:Models, Biological; D014945:Wound Healing
D003094:Collagen
Burns; Heterogeneous, isotropic, compressible neo-Hookean solid; Moving-grid finite-element method; Multiple linear regression analysis; Probabilistic analysis; Wound contraction