Effect of fibre orientation and bulk modulus on the electromechanical modelling of human ventricles
Effect of fibre orientation and bulk modulus on the electromechanical modelling of human ventricles
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DOI：
10.3934/mine.2020028
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发表时间：
2020-01-01
影响因子：
1
通讯作者：
Quarteroni, Alfio
中科院分区：
文献类型：
--
作者：
Azzolin, Luca;Dede, Luca;Quarteroni, Alfio
这项工作涉及心脏的数学和数值建模。其目的是加强对生理和病理条件下心脏功能的理解。沿着这条路，挑战来自手头数学问题的多尺度和多物理性质。在本文中，我们提出了一个机电模型，在双心室的几何形状，结合单域方程，Bueno-Orovio最小离子模型，和Holzapfel-Ogden应变能量函数的被动心肌组织建模与主动应变的方法相结合的模型transmartally异质增厚的心肌。由于电信号的分布依赖于心室的纤维方向，我们使用基于Laplace-Dirichlet规则的算法来确定整个双心室中的心肌纤维和片的配置。在本文中，我们研究了不同的纤维方向和不可压缩性约束和惩罚的材料的可压缩性（体积模量）的压力-体积关系模拟一个完整的心脏跳动的影响。机电耦合的问题是通过一个完全隔离的计划。数值离散是基于有限元法的空间离散和向后微分公式的时间离散。应用隐式格式所产生的非线性代数方程组用牛顿法求解。在患者特定的双心室几何形状中进行数值模拟，以突出电生理学和力学的最相关结果，并将其与生理数据和测量结果进行比较。我们展示了各种纤维配置和体积模量如何修改相关的临床数量，如每搏输出量，射血分数和心室收缩力。
This work concerns the mathematical and numerical modeling of the heart. The aim is to enhance the understanding of the cardiac function in both physiological and pathological conditions. Along this road, a challenge arises from the multi-scale and multi-physics nature of the mathematical problem at hand. In this paper, we propose an electromechanical model that, in bi-ventricle geometries, combines the monodomain equation, the Bueno-Orovio minimal ionic model, and the Holzapfel-Ogden strain energy function for the passive myocardial tissue modelling together with the active strain approach combined with a model for the transmurally heterogeneous thickening of the myocardium. Since the distribution of the electric signal is dependent on the fibres orientation of the ventricles, we use a Laplace-Dirichlet Rule-Based algorithm to determine the myocardial fibres and sheets configuration in the whole bi-ventricle. In this paper, we study the influence of different fibre directions and incompressibility constraint and penalization on the compressibility of the material (bulk modulus) on the pressure-volume relation simulating a full heart beat. The coupled electromechanical problem is addressed by means of a fully segregated scheme. The numerical discretization is based on the Finite Element Method for the spatial discretization and on Backward Differentiation Formulas for the time discretization. The arising non-linear algebraic system coming from application of the implicit scheme is solved through the Newton method. Numerical simulations are carried out in a patient-specific bi-ventricle geometry to highlight the most relevant results of both electrophysiology and mechanics and to compare them with physiological data and measurements. We show how various fibre configurations and bulk modulus modify relevant clinical quantities such as stroke volume, ejection fraction and ventricle contractility.