三维相场与一维血管网络耦合的多物种肿瘤生长模型分析
Analysis of a new multispecies tumor growth model coupling 3D phase-fields with a 1D vascular network
摘要：
在这项工作中，我们提出并分析了一个数学模型的肿瘤生长纳入ECM侵蚀，间质流，血管流动和营养物质运输的影响。该模型是相场或扩散界面类型，其中细胞物种和其他成分的多个相被平滑的演化界面分离。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。在供应健康和癌组织的脉管系统中建模流动和运输过程，考虑一维（1D）方程。由于管理的运输和流动过程的模型定义在一起的三维（3D）域上的细胞物种模型，我们得到一个3D-1D耦合模型。我们给出了关于弱解存在性的一些数学结果。此外，模拟结果说明肿瘤的演变和ECM侵蚀的影响。
英文摘要：
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. We show some mathematical results on the existence of weak solutions. Furthermore, simulation results are presented illustrating the evolution of tumors and the effects of ECM erosion.
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