TY - JOUR

T1 - A mathematical model for the simulation of the contraction of burns

AU - Koppenol, Daniël C.

AU - Vermolen, Fred J.

AU - Koppenol-Gonzalez, Gabriela V.

AU - Niessen, Frank B.

AU - van Zuijlen, Paul P M

AU - Vuik, Kees

PY - 2016

Y1 - 2016

N2 - 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.

AB - 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.

KW - Burns

KW - Heterogeneous, isotropic, compressible neo-Hookean solid

KW - Moving-grid finite-element method

KW - Multiple linear regression analysis

KW - Probabilistic analysis

KW - Wound contraction

UR - http://www.scopus.com/inward/record.url?scp=84994475188&partnerID=8YFLogxK

U2 - 10.1007/s00285-016-1075-4

DO - 10.1007/s00285-016-1075-4

M3 - Article

C2 - 27826736

AN - SCOPUS:84994475188

SP - 1

EP - 31

JO - Journal of Mathematical Biology

JF - Journal of Mathematical Biology

SN - 0303-6812

ER -