人类左心室3D重构及相关流固耦问题的数值方法研究

项目名称： 人类左心室3D重构及相关流固耦问题的数值方法研究

项目编号： No.11471261

项目类型： 面上项目

立项/批准年度： 2015

项目学科： 数理科学和化学

项目作者： 蔡力

作者单位： 西北工业大学

项目金额： 60万元

中文摘要： 人类左心室在血液循环中起着关键的作用。本项目主要研究左心室3D重构方法及血液-左心室流固耦合相关问题的数值求解方法，以建立左心室重构-计算-分析-应用研究平台为目标，主要研究内容包括：针对心脏图像数据，建立有效的分割及泡泡动力学网格重构方法；改进组合杂交元方法和全局最优化方法来有效逆向求解左心室非线性复合材料参数；增加弹性力和电势-体力源项来建立改进的IB/FE流固耦合模型；提出相关高效数值方法来求解上述耦合模型，完成左心室周期性舒张和收缩过程的计算，解释医学临床现象。从中可能发掘出如下主要创新点：建立高效的变分水平集分割模型；提出针对3D复杂区域的泡泡动力学网格节点的并行生成与疏密控制方法；改进N-S方程组，建立模拟血液-左心室耦合系统的IB/FE模型；建立求解IB/FE流固模型的高分辨率数值方法。本项目的研究将促进计算数学与图像处理、计算心脏力学等领域在相关问题上的交叉研究。

中文关键词： 流固耦合；偏微分方程数值解；图像分割；网格生成

英文摘要： The human left ventricle (LV) plays a key role in blood circulation. In this project, researches on 3D reconstruction of the human left ventricle and numerical solutions for corresponding fluid-structure interaction problems are given. The object of the project is to construct the frame which includes reconstruction-computation-analysis-application. The following researches will be studied in detail: based on images of heart, some efficient segmentation methods and reconstruction methods via bubble dynamic meshes are proposed; the combined hybrid element method and global optimization method are modified to calculate the nonlinear composite material parameters of the left ventricle; the elastic force and electrical potential terms are added in N-S equations to get the corresponding immersed boundary/finite element (IB/FE) fluid-structure interaction model; some high resolution methods are presented to solve the IB/FE model, and corresponding numerical results are analyzed to explain some medical phenomenon. The main innovations lie in: efficient variational level set segmentation models will be proposed; the parallel generation and density control method of bubble nodes in 3D complex domain will be studied; based on the modified N-S equations, the IB/FE model for blood-LV coupling system can be established; some high-resolution numerical methods for this kind of IB/FE model should be presented. The corresponding researches will promote the crossover studys between different fields, such as computational mathematics, image processing and computational cardiac mechanics, on some relevant issues.

英文关键词： fluid-structure interaction;numerical solution for PDE;image segmentation;mesh generation