Mathematical modeling of the onset of capillary formation initiating angiogenesis
Mathematical modeling of the onset of capillary formation initiating angiogenesis
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DOI：
10.1007/s002850000037
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发表时间：
2001-03-01
影响因子：
1.9
通讯作者：
Nilsen-Hamilton, M
中科院分区：
文献类型：
--
作者：
Levine, HA;Sleeman, BD;Nilsen-Hamilton, M
新生血管的形成可以分为三个主要阶段(可能是重叠的)：(1)现有血管内的变化，(2)新通道的形成，(3)新血管的成熟。本文基于增强的随机行走理论，结合Michaelis-Menten型机制，提出了一种新的血管生成途径，该机制将内皮细胞受体视为将血管生成因子转化为蛋白水解酶的催化剂，以便对第一阶段进行建模。在这个模型中，单层内皮细胞被血管壁与细胞外组织基质隔开。导出了一个常微分方程组和偏微分方程组，在血管生成剂的存在下，它预测了内皮细胞的聚集和血管板层的崩溃，打开了一条进入细胞外基质的通道。我们把这称为维管萌发的开始。子宫内乳头的形成表明了我们模型的正确性的一些生物学证据。该模型的预测进一步证明了该模型的正确性，即内皮细胞将在毛细血管生成开始时排列在新生毛细血管内。
It is well accepted that neo-vascular formation can be divided into three main stages (which may be overlapping): (1) changes within the existing vessel, (2) formation of a new channel, (3) maturation of the new vessel.In this paper we present a new approach to angiogenesis, based on the theory of reinforced random walks, coupled with a Michaelis-Menten type mechanism which views the endothelial cell receptors as the catalyst for transforming angiogenic factor into proteolytic enzyme in order to model the first stage. In this model, a single layer of endothelial cells is separated by a vascular wall from an extracellular tissue matrix. A coupled system of ordinary and partial differential equations is derived which, in the presence of an angiogenic agent, predicts the: aggregation of the endothelial cells and the collapse of the vascular lamina, opening a passage into the extracellular matrix. We refer to this as the onset of vascular sprouting. Some biological evidence for the correctness of our model is indicated by the formation of teats in utero. Further evidence for the correctness of the model is given by its prediction that endothelial cells will line the nascent capillary at the onset of capillary angiogenesis.