Existing continuum multiphase tumor growth models typically do not include microvasculature, or if present, this is modeled as a non-deformable network of vessels. Vasculature behavior and blood flow are usually non-coupled with the underlying tumor phenomenology from the mechanical viewpoint; hence, phenomena like vessel compression/occlusion modifying microcirculation and oxygen supply cannot be taken into account. Here, the tumor tissue is modeled as a reactive bi-compartment porous medium: the extracellular matrix constitutes the solid scaffold; blood flows in the vascular porosity, whereas the extravascular porous compartment is saturated by two cell phases and interstitial fluid (mixture of water and nutrient species). The pressure difference between blood and the extravascular overall pressure is sustained by vessel walls and drives shrinkage or dilatation of the vascular porosity. Model closure is achieved thanks to a consistent non-conventional definition of the Biot’s effective stress tensor. Angiogenesis is modeled by introducing a vascularization state variable and accounting for tumor angiogenic factors and endothelial cells. Closure relationships and mass exchange terms related to vessel formation are detailed in a numerical example reproducing the principal features of angiogenesis. This example is preceded by a first pedagogical numerical study on one-dimensional bio-consolidation. Results demonstrate that the bi-compartment poromechanical model is fully coupled (the external loads impact fluid flow in both porous compartments) and that it can serve as a basis for further applications like modeling of drug delivery and tissue ulceration.

现有的连续多相肿瘤生长模型通常不包括微脉管系统，或者如果存在，则将其建模为不可变形的血管网络。从机械的角度来看，血管的行为和血流通常与潜在的肿瘤现象学无关。因此，不能考虑诸如血管压缩/阻塞改变微循环和供氧的现象。在这里，肿瘤组织被建模为反应性的双室多孔介质：细胞外基质构成了固体支架；血液在血管孔隙中流动，而血管外多孔室则被两个细胞相和间质液（水和营养物质的混合物）所饱和。血液与血管外总压力之间的压力差由血管壁维持，并驱动血管孔隙收缩或扩张。由于对Biot有效应力张量的一致非常规定义，因此实现了模型闭合。通过引入血管化状态变量并考虑肿瘤血管生成因子和内皮细胞来模拟血管生成。在再现血管生成的主要特征的数值示例中详细描述了与血管形成有关的闭合关系和质量交换术语。在此示例之前，首先进行了关于一维生物固结的教学数值研究。