In this work, we present a coupled 3D–1D model of solid tumor growth within a dynamically changing vascular network to facilitate realistic simulations of angiogenesis. Additionally, the model includes erosion of the extracellular matrix, interstitial flow, and coupled flow in blood vessels and tissue. We employ continuum mixture theory with stochastic Cahn–Hilliard type phase-field models of tumor growth. The interstitial flow is governed by a mesoscale version of Darcy’s law. The flow in the blood vessels is controlled by Poiseuille flow, and Starling’s law is applied to model the mass transfer in and out of blood vessels. The evolution of the network of blood vessels is orchestrated by the concentration of the tumor angiogenesis factors (TAFs); blood vessels grow towards the increasing TAFs concentrations. This process is not deterministic, allowing random growth of blood vessels and, therefore, due to the coupling of nutrients in tissue and vessels, makes the growth of tumors stochastic. We demonstrate the performance of the model by applying it to a variety of scenarios. Numerical experiments illustrate the flexibility of the model and its ability to generate satellite tumors. Simulations of the effects of angiogenesis on tumor growth are presented as well as sample-independent features of cancer.

在这项工作中，我们提出了一个动态变化的血管网络内实体肿瘤生长的耦合 3D-1D 模型，以促进血管生成的真实模拟。此外，该模型还包括细胞外基质的侵蚀、间质流动以及血管和组织中的耦合流动。我们采用连续混合理论和随机 Cahn-Hilliard 型肿瘤生长相场模型。间隙流动受达西定律的中尺度版本控制。血管中的流动是由控制的Poiseuille 流和 Starling 定律适用于模拟进出血管的质量传递。血管网络的演变是由肿瘤血管生成因子 (TAF) 的浓度精心策划的；血管朝着增加的 TAF 浓度生长。这个过程不是确定性的，允许血管随机生长，因此，由于组织和血管中营养物质的耦合，使肿瘤随机生长。我们通过将模型应用于各种场景来展示模型的性能。数值实验说明了该模型的灵活性及其生成卫星肿瘤的能力。呈现了血管生成对肿瘤生长影响的模拟以及癌症的样本独立特征。