Levine H A, Sleeman B D, Nilsen-Hamilton M
Department of Mathematics, Iowa State University, Ames, IA 50011, USA.
J Math Biol. 2001 Mar;42(3):195-238. doi: 10.1007/s002850000037.
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.
人们普遍认为，新血管形成可分为三个主要阶段（可能会相互重叠）：（1）现有血管内的变化；（2）新通道的形成；（3）新血管的成熟。在本文中，我们基于强化随机游走理论，提出了一种新的血管生成方法，并结合米氏（Michaelis-Menten）型机制，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分隔开。推导出了一个常微分方程和偏微分方程的耦合系统，在存在血管生成剂的情况下，该系统预测内皮细胞的聚集和血管层的塌陷，从而打通进入细胞外基质的通道。我们将此称为血管芽生的起始。子宫内乳头的形成表明了我们模型正确性的一些生物学证据。该模型预测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，这进一步证明了模型的正确性。
