Avner Friedman, PhD, MS
Professor, Department of Mathematics, Mathematical Biosciences Institute
Phone number: (614) 292-5296, MBI Office: (614) 292-3648
The project theme will be centered at developing mathematical models for the progression and healing of wounds, which, along with experimental verification, can lead to prediction of wound development and treatment. Two projects are under this theme: (1) chronic wounds; (2) propagation of burn wounds.
Chronic wounds represent a major public health problem affecting 6.5 million people in the United States. The healing of these wounds is a complex phenomenon that involves interactions among a large array of soluble chemical mediators, cell types, and the extracellular matrix (ECM). We developed mathematical models in parallel to the preclinical experiments performed in the lab of Dr. Chandan K. Sen. The models showed tight agreement with experimental measurements of wound size and macrophage number at different time points, and could be used to test new hypotheses of treatments (Fig. 1).
Immediately after skin burn injury, the volume of the wound burn expands due to lipid peroxidation chain reactions. Such expansion threatens lives and is therefore highly clinically significant. We developed a three-dimensional mathematical model to quantify the propagation of tissue damage within 12 hours post burn. The model showed that vitamin E tocotrienol could significantly slow down the lipid peroxide propagation post burn.
Ching-Shan Chou (Assistant professor, Department of Mathematics, Mathematical Biosciences Institute)
Chiu-Yen Kao (Associate professor, Department of Mathematics, Mathematical Biosciences Institute)
Chuan Xue (Assistant professor, Department of Mathematics, Mathematical Biosciences Institute)
R. C. Schugart, A. Friedman, R. Zhao, and C. K. Sen, Wound angiogenesis as a function of tissue oxygen tension: a mathematical model, PNAS 105: 2628 - 33, 2008.
C. Xue, A. Friedman, and C. K. Sen, A mathematical model of ischemic cutaneous wounds, PNAS, Vol. 106, No. 39, pp. 16782-16787, 2009.
A. Friedman, B. Hu, and C. Xue, Analysis of a mathematical model of ischemic cutaneous wounds, SIAM J. Math. Anal. Vol 42, Issue 5, pp. 2013-2040, 2010.
A. Friedman and C. Xue, A mathematical model of chronic wounds, Mathematical Biosciences and Engineering, 8(2): 253-61, 2011.
A. Friedman, B. Hu, and C. Xue, A three-dimensional model of chronic wound healing: analysis and computation, DCDS-B, to appear, 2012.
C. Xue, C.-S., Chou, C.-Y. Kao, C. K. Sen, and A. Friedman (2012), Propagation of cutaneous thermal injury: A mathematical model. Wound Repair and Regeneration, 20: 114–122. doi: 10.1111/j.1524-475X.2011.00759.x