Improving the stability of cardiac mechanical simulations.
Improving the stability of cardiac mechanical simulations.
复制标题
DOI：
10.1109/tbme.2014.2373399
复制
发表时间：
2015-03
期刊：
影响因子：
--
通讯作者：
Smith NP
中科院分区：
文献类型：
--
作者：
Land S;Niederer SA;Lamata P;Smith NP
在心脏建模领域，通常使用有限元方法模拟心脏的力学作用。这些模拟正变得越来越具有挑战性，因为计算领域是根据患者的解剖结构定制的，其中通过驱动心脏泵周期模拟的生物物理细胞模型产生了大的异质张力梯度。大变形力学模拟中非线性解的收敛性取决于许多因素。当极端应力或不规则变形建模时，常用的数值方法往往无法找到解决方案，这可能会妨碍对有趣的参数变化的调查或在具有高鲁棒性标准的临床环境中使用模型。本文概述了一种新的数值方法，该方法易于实现，并显著提高了这些模拟的稳定性。该方法涉及在大变形力学的标准不可压缩公式中加入可压缩性惩罚。我们将该方法的性能与不可压缩固体力学方程的直接离散化以及基于变形梯度的等时/偏差分裂的公式进行了比较。这种惩罚的增加减少了解偏离不可压缩约束的趋势，并显著提高了牛顿求解器寻找解的能力。此外，我们的方法在网格细化下保持预期的收敛顺序，对压力-体积关系具有几乎相同的解，并稳定求解器，以便在个性化患者几何形状上模拟舒张和收缩功能。
In the field of cardiac modelling, the mechanical action of the heart is often simulated using finite element methods. These simulations are becoming increasingly challenging as the computational domain is customized to a patient’s anatomy, within which large heterogeneous tension gradients are generated via biophysical cell models which drive simulations of the cardiac pump cycle. The convergence of nonlinear solvers in simulations of large deformation mechanics depends on many factors. When extreme stress or irregular deformations are modelled, commonly used numerical methods can often fail to find a solution, which can prevent investigation of interesting parameter variations or use of models in a clinical context with high standards for robustness. This article outlines a novel numerical method that is straightforward to implement and which significantly improves the stability of these simulations. The method involves adding a compressibility penalty to the standard incompressible formulation of large deformation mechanics. We compare the method’s performance when used with both a direct discretization of the equations for incompressible solid mechanics, as well as the formulation based on an isochoric/deviatoric split of the deformation gradient. The addition of this penalty decreases the tendency for solutions to deviate from the incompressibility constraint, and significantly improves the ability of the Newton solver to find a solution. Additionally our method maintains the expected order of convergence under mesh refinement, has nearly identical solutions for the pressure-volume relations, and stabilizes the solver to allow challenging simulations of both diastolic and systolic function on personalized patient geometries.