论文标题
分析新的多物种肿瘤生长模型与1D血管网络耦合3D相位
Analysis of a new multispecies tumor growth model coupling 3D phase-fields with a 1D vascular network
论文作者
论文摘要
在这项工作中，我们介绍并分析了一种数学模型，用于融合ECM侵蚀，间质流以及血管流量和营养转运的作用的数学模型。该模型是相位或扩散接口类型的模型，其中细胞物种和其他成分的多个阶段通过平滑演化的界面分离。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理。考虑到供应健康和癌性组织的脉管系统中的建模流量和运输过程，考虑了一维（1D）方程。由于管理传输和流动过程的模型与三维（3D）域上的细胞物种模型一起定义，因此我们获得了3D-1D耦合模型。我们对弱解决方案的存在显示了一些数学结果。此外，给出了模拟结果，说明了肿瘤的演变和ECM侵蚀的影响。
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.
