Moulton M J, Creswell L L, Actis R L, Myers K W, Vannier M W, Szabó B A, Pasque M K
Department of Surgery, Washington University, St. Louis, Missouri, USA.
J Biomech. 1995 Aug;28(8):935-48. doi: 10.1016/0021-9290(94)00144-s.
Passive myocardial material properties have been measured previously by subjecting test samples of myocardium to in vitro load-deformation analysis or, in the intact heart, by pressure-volume relationships. A new method for determining passive material properties, described in this paper, couples a p-version finite element model of the heart, a nonlinear optimization algorithm and a dense set of transmural measured strains that could be obtained in the intact heart by magnetic resonance imaging (MRI) radiofrequency tissue tagging. Unknown material parameters for a nonlinear, nonhomogeneous material law are determined by solving an inverse boundary value problem. An objective function relating the least-squares difference of model-predicted and measured strains is minimized with respect to the unknown material parameters using a novel optimization algorithm that utilizes forward finite element solutions to calculate derivatives of model-predicted strains with respect to the material parameters. Test cases incorporating several salient features of the inverse material identification problem for the heart are formulated to test the performance of the inverse algorithm in typical experimental conditions. Known true material parameters can be determined to within a small tolerance and random noise is shown not to affect the stability of the inverse solution appreciably. On the basis of these validation experiments, we conclude that the inverse material identification problem for the heart can be extended to solve for unknown material parameters that describe in vivo myocardial material behavior.
以往被动心肌材料特性的测量，是通过对心肌测试样本进行体外负荷-变形分析，或者在完整心脏中通过压力-容积关系来实现的。本文描述了一种测定被动材料特性的新方法，该方法将心脏的p型有限元模型、非线性优化算法与一组密集的透壁测量应变相结合，这些应变可通过磁共振成像（MRI）射频组织标记在完整心脏中获得。通过求解一个逆边值问题，来确定非线性、非均匀材料定律的未知材料参数。使用一种新颖的优化算法，相对于未知材料参数，使与模型预测应变和测量应变的最小二乘差相关的目标函数最小化，该算法利用正向有限元解来计算模型预测应变相对于材料参数的导数。构建了包含心脏逆材料识别问题几个显著特征的测试案例，以测试逆算法在典型实验条件下的性能。已知的真实材料参数可以在很小的公差范围内确定，并且随机噪声对逆解的稳定性影响不大。基于这些验证实验，我们得出结论，心脏逆材料识别问题可以扩展到求解描述体内心肌材料行为的未知材料参数。
