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.
Highlights
Burns are a significant global problem; they constitute the second highest incidence of trauma related deaths worldwide and every year nearly half a million citizens of the US require medical treatment as a result of acute thermal injury (Gibran et al 2013; Goel and Shrivastava 2010)
After having used a regression analysis, a probabilistic analysis was used in order to investigate in more detail the effect of variability in the values for the collagen molecule secretion rate and the myofibroblast apoptosis rate, on both the cell density of the myofibroblasts and the concentration of the collagen molecules at day 42, and the relative surface area of the healing burn at day 42 compared to its surface area at day 0
The adjusted squared multiple correlation of 0.936 indicates that more than 93% of the variability in the relative surface area of the healing burn at day 42 compared to the size of the burn at day 0 is predicted by variability in the values for the factors of the factorial design
Summary
Burns are a significant global problem; they constitute the second highest incidence of trauma related deaths worldwide and every year nearly half a million citizens of the US require medical treatment as a result of acute thermal injury (Gibran et al 2013; Goel and Shrivastava 2010). In this study we develop a mathematical model for the simulation of the contraction of burns in order to gain new insights into which elements of the wound healing response might have a substantial influence on the contraction of such wounds For this end we first show good agreement with respect to the variability in the evolution of the surface area of burns over time between the outcomes of computer simulations obtained in this study and measurements obtained in a previously conducted experimental study. A probabilistic analysis is used in this study in order to investigate in more detail the effect of variability in the values for the myofibroblast apoptosis rate and the collagen molecule secretion rate on the healing of burns More details about this probabilistic analysis are presented in Sect.
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