A multiphase model describing vascular tumour growth
A multiphase model describing vascular tumour growth
复制标题
DOI：
10.1016/s0092-8240(03)00027-2
复制
发表时间：
2003-07-01
影响因子：
3.5
通讯作者：
Lewis, CE
中科院分区：
文献类型：
--
作者：
Breward, CJW;Byrne, HM;Lewis, CE
在本文中，我们提出了一个新的模型框架，研究血管肿瘤的生长，其中血管密度被明确考虑。我们的连续体模型包括肿瘤细胞，细胞外物质和血管的体积分数的质量和动量守恒方程。我们包括我们认为占主导地位的物理机制，即肿瘤细胞的出生和死亡，通过血液和淋巴引流管供应和清除细胞外液，血管生成和血管闭塞。我们假设肿瘤细胞的移动是为了减轻由于其增殖而引起的机械应力的增加。我们展示了如何减少模型的体积分数的肿瘤细胞和血管和相平均速度的混合物的耦合偏微分方程的系统。我们认为可能的参数制度所产生的模型。在这些情况下，我们数值求解方程，并讨论由此产生的行为。该模型能够再现在某些情况下在体内发现的肿瘤结构。我们的框架可以很容易地修改，以纳入其他阶段的影响，或包括药物的影响。(C)2003年，数学生物学。由爱思唯尔科技有限公司出版。保留所有权利。
In this paper we present a new model framework for studying vascular tumour growth, in which the blood vessel density is explicitly considered. Our continuum model comprises conservation of mass and momentum equations for the volume fractions of tumour cells, extracellular material and blood vessels. We include the physical mechanisms that we believe to be dominant, namely birth and death of tumour cells, supply and removal of extracellular fluid via the blood and lymph drainage vessels, angiogenesis and blood vessel occlusion. We suppose that the tumour cells move in order to relieve the increase in mechanical stress caused by their proliferation. We show how to reduce the model to a system of coupled partial differential equations for the volume fraction of tumour cells and blood vessels and the phase averaged velocity of the mixture. We consider possible parameter regimes of the resulting model. We solve the equations numerically in these cases, and discuss the resulting behaviour. The model is able to reproduce tumour structure that is found in vivo in certain cases. Our framework can be easily modified to incorporate the effect of other phases, or to include the effect of drugs. (C) 2003 Society for Mathematical Biology. Published by Elsevier Science Ltd. All rights reserved.