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Multiphasic Mixture Modeling and Simulation of Coronary Circulation

冠状动脉循环的多相混合建模和模拟

基本信息

批准号：
18360054
负责人：
CHEN Xian
金额：
$ 6.21万
依托单位：
Kyushu University
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (B)
财政年份：
2006
资助国家：
日本
起止时间：
2006 至 2007
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-18360054/
关键词：
Coronary Circulation Mixture Theory Finite Element Method Biomechanics Bio-material Modeling 生体材料モデル

项目摘要

In this research, based on the multiphasic mixture theory, a hierarchical coronary theoretical model is proposed for the coronary system, in which the vessels have tree structure gradually bifurcating from artery and vein to capillary bed, by treating the myocardial matrix as solid phase and blood in each hierarchy of the vessel tree as specific fluid phase. Furthermore, the incompressible condition of the solid and fluid phases was imposed by applying Lagrange multiplier method. The residual weighted method was introduced for finite element formulation and followed by the descritization. The tangential stiffness matrix was derived for iterative computation of the nonlinear problems. Since the fluid variables have large degrees of freedom at a node due to the hierarchy structure, for the computational efficiency, the finite element equations were reformulated by adopting pressure as nodal variable instead of the relative velocity of fluid phase. The formulation was implemented into a home-made program and built in a multi-scale and multi-physics heart simulator. The numerical examples show that the characteristic predominate wave form of arteries (or veins) blood flow in diastolic (or systolic) can be represented by applying the proposed model and thus suggest the usability in the clinical application. It is expected that the effect of the myocardial contraction on the intramyocardial pressure and furthermore on the blood perfusion in coronary system can be elucidated by applying the proposed approach and to make contribution to etiology elucidation of the ischemic heart disease and diagnostic treatment.

本研究以多相混合物理论为基础，将心肌基质视为固相，将血管树各层次中的血液视为特定的液相，建立了冠状动脉系统的层次化理论模型，该模型中血管具有从动脉和静脉到毛细血管床逐渐分叉的树状结构。应用拉格朗日乘子法对固、液两相施加不可压缩条件。采用加权余量法建立有限元方程，并进行描述。推导了用于非线性问题迭代计算的切线刚度矩阵。由于流体变量在节点处具有较大的自由度，为了提高计算效率，采用压力代替流体相的相对速度作为节点变量，对有限元方程进行了重构。该公式被实施到自制的程序中，并建立在多尺度和多物理心脏模拟器中。数值算例表明，该模型能够反映动脉（或静脉）舒张期（或收缩期）血流的特征主导波形，具有一定的临床应用价值。应用该方法可望阐明心肌收缩对心肌内压的影响，进而对冠状动脉系统血流灌注的影响，为缺血性心脏病的病因学研究和诊断治疗做出贡献。