Analysis of a Mathematical Model of Ischemic Cutaneous Wounds
Analysis of a Mathematical Model of Ischemic Cutaneous Wounds
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DOI：
10.1137/090772630
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发表时间：
2009-09
期刊：
影响因子：
--
通讯作者：
A. Friedman;Bei Hu;Chuan Xue
中科院分区：
文献类型：
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作者：
A. Friedman;Bei Hu;Chuan Xue
慢性伤口是影响美国650万人的一个主要公共卫生问题。缺血是伤口愈合中的一个严重的复杂因素。在这篇文章中，我们分析了最近发展起来的缺血型真皮损伤的数学模型。该模型由部分愈合区域中的偏微分方程组耦合而成，伤口边界为自由边界。假设细胞外基质(ECM)是粘弹性的，自由边界随着ECM在开放伤口边界处的运动速度而移动。模型方程包括氧浓度、细胞因子和几种类型细胞的密度。缺血程度由一个出现在边界条件中的参数来表示，$0\leq\Gamma<；1$；$\Gamma$接近1对应于极端缺血，$\Gamma=0$对应于正常非缺血条件。我们证明了自由边界问题的整体存在唯一性，并研究了自由边界对$\r的依赖性。
Chronic wounds represent a major public health problem affecting 6.5 million people in the United States. Ischemia represents a serious complicating factor in wound healing. In this paper we analyze a recently developed mathematical model of ischemic dermal wounds. The model consists of a coupled system of PDEs in the partially healed region, with the wound boundary as a free boundary. The extracellular matrix (ECM) is assumed to be viscoelastic, and the free boundary moves with the velocity of the ECM at the boundary of the open wound. The model equations involve the concentrations of oxygen, cytokines, and the densities of several types of cells. The ischemic level is represented by a parameter which appears in the boundary conditions, $0\leq\gamma<1$; $\gamma$ near 1 corresponds to extreme ischemia and $\gamma=0$ corresponds to normal nonischemic conditions. We establish global existence and uniqueness of the free boundary problem and study the dependence of the free boundary on $\gamma$.