In this work, we present and analyze a mathematical model for tumor growth incorporating ECM erosion, interstitial flow, and the effect of vascular flow and nutrient transport. The model is of phase-field or diffused-interface type in which multiple phases of cell species and other constituents are separated by smooth evolving interfaces. The model involves a mesoscale version of Darcy’s law to capture the flow mechanism in the tissue matrix. Modeling flow and transport processes in the vasculature supplying the healthy and cancerous tissue, one-dimensional (1D) equations are considered. Since the models governing the transport and flow processes are defined together with cell species models on a three-dimensional (3D) domain, we obtain a 3D–1D coupled model.

在这项工作中，我们提出并分析了包含ECM侵蚀，间质流以及血管流和营养运输的影响在内的肿瘤生长的数学模型。该模型为相场或扩散界面类型，其中细胞物种和其他成分的多个相通过平滑演化的界面分开。该模型涉及达西定律的中尺度版本，以捕获组织基质中的流动机制。为提供健康和癌性组织的脉管系统中的流动和运输过程建模，需要考虑一维（1D）方程。由于控制运输和流动过程的模型是与三维（3D）域中的细胞物种模型一起定义的，因此我们获得了3D-1D耦合模型。