Costa K D, Hunter P J, Wayne J S, Waldman L K, Guccione J M, McCulloch A D
Department of Bioengineering, University of California San Diego, La Jolla, CA, USA.
J Biomech Eng. 1996 Nov;118(4):464-72. doi: 10.1115/1.2796032.
A three-dimensional finite element method for nonlinear finite elasticity is presented using prolate spheroidal coordinates. For a thick-walled ellipsoidal model of passive anisotropic left ventricle, a high-order (cubic Hermite) mesh with 3 elements gave accurate continuous stresses and strains, with a 69 percent savings in degrees of freedom (dof) versus a 70-element standard low-order model. A custom mixed-order model offered 55 percent savings in dof and 39 percent savings in solution time compared with the low-order model. A nonsymmetric 3D model of the passive canine LV was solved using 16 high-order elements. Continuous nonhomogeneous stresses and strains were obtained within 1 hour on a laboratory workstation, with an estimated solution time of less than 4 hours to model end-systole. This method represents the first practical opportunity to solve large-scale anatomically detailed models for cardiac stress analysis.
提出了一种使用长椭球坐标的非线性有限弹性三维有限元方法。对于被动各向异性左心室的厚壁椭球模型，一个具有3个单元的高阶（三次Hermite）网格给出了精确的连续应力和应变，与一个70单元的标准低阶模型相比，自由度（dof）节省了69%。与低阶模型相比，一个定制的混合阶模型在自由度上节省了55%，在求解时间上节省了39%。使用16个高阶单元求解了被动犬左心室的非对称三维模型。在实验室工作站上1小时内获得了连续的非均匀应力和应变，估计模拟心动末期的求解时间不到4小时。该方法为解决用于心脏应力分析的大规模解剖详细模型提供了第一个实际机会。
