论文标题
1D-0D-3D耦合模型,用于模拟乳房组织中的血流和运输过程
A 1D-0D-3D coupled model for simulating blood flow and transport processes in breast tissue
论文作者
论文摘要
在这项工作中,我们提出了混合尺寸模型,以模拟乳房组织中的血流和运输过程,并提供其供应其血管树。这些过程被认为是从主动脉入口到乳房的毛细血管和组织的开始。该系统中存在生物物理特性和流动条件的较大变化,因此需要将不同的流量模型用于不同的几何形状和流动状态。该系统中存在生物物理特性和流动条件的较大变化,因此需要将不同的流量模型用于不同的几何形状和流动状态。我们总共考虑了四种不同的模型类型。首先,认为1D非线性双曲线PDE的系统被认为可以模拟具有高弹性血管壁的较大动脉中的血流。其次,我们为1D线性化双曲线PDE分配,以用更硬的容器壁对较小的动脉进行建模。第三个模型类型由ODE系统(0D模型)组成。它用于对小动脉和周围循环进行建模。最后,均质化的3D多孔介质模型被认为是在乳房体积内模拟毛细血管和组织中的流动和运输。水槽项用于说明静脉和淋巴系统的影响。结合了四种模型类型,我们获得了两个不同的1D-0D-3D耦合模型,用于模拟血流和传输过程:第一个1D-0D-3D模型涵盖了从主动脉到乳房的整个路径,而第二个模型是通过限制到乳房脉管和组织的限制,可以显着降低计算成本。进行了几项数值实验,这些实验证明了与人类乳房和血管系统中血流的现有数据相比,进行了逼真的流动模拟。
In this work, we present mixed dimensional models for simulating blood flow and transport processes in breast tissue and the vascular tree supplying it. These processes are considered, to start from the aortic inlet to the capillaries and tissue of the breast. Large variations in biophysical properties and flow conditions exist in this system necessitating the use of different flow models for different geometries and flow regimes. Large variations in biophysical properties and flow conditions exist in this system necessitating the use of different flow models for different geometries and flow regimes. In total, we consider four different model types. First, a system of 1D nonlinear hyperbolic PDEs is considered to simulate blood flow in larger arteries with highly elastic vessel walls. Second, we assign 1D linearized hyperbolic PDEs to model the smaller arteries with stiffer vessel walls. The third model type consists of ODE systems (0D models). It is used to model the arterioles and peripheral circulation. Finally, homogenized 3D porous media models are considered to simulate flow and transport in capillaries and tissue within the breast volume. Sink terms are used to account for the influence of the venous and lymphatic systems. Combining the four model types, we obtain two different 1D-0D-3D coupled models for simulating blood flow and transport processes: The first 1D-0D-3D model covers the whole path from the aorta to the breast, while the second model is a sub-model obtained by restriction to breast vasculature and tissue making possible a significant reduction in computational cost. Several numerical experiments are conducted that demonstrate realistic flow simulations compared to existing data on blood flow in human breast and vascular system.