Gotteiner N L, Han G, Chandran K B, Vonesh M J, Bresticker M, Greene R, Oba J, Kane B J, Joob A, McPherson D D
Department of Medicine and Surgery, Northwestern University Medical School, Chicago, IL, USA.
Am J Card Imaging. 1995 Jul;9(3):185-94.
In vitro data have shown that the myocardium exhibits nonlinear passive stress-strain relationship and a non-linear pressure-volume relationship. A finite element (FE) analysis and optimization algorithm was used on three-dimensional reconstructed left ventricular (LV) geometry using echocardiographic images, along with hemodynamic measurements, in seven closed-chest dogs to show a nonlinear stress-strain relationship in vivo. Our analysis included the computation of Poisson's ratio from the measured volumetric strain of the myocardium and a simulated pericardial pressure load ("equivalent pericardial pressure") applied to the epicardial surface of the reconstructed LV. LV geometry was reconstructed in three or four incremental time steps in diastasis and the myocardium was assumed to be homogeneous, isotropic, and linearly elastic during these short intervals in this initial study. Simultaneous LV chamber pressure and equivalent pericardial pressure were incorporated into the algorithm to predict actual LV expansion. Computations were performed iteratively at each interval to compute the optimized elastic modulus. By performing the FE analysis and optimization at each interval (a step-wise linear analysis approach), a linear relationship between the myocardial elastic modulus and LV chamber pressure was derived (r = .87 to .98). Such a linear relationship is equivalent to an exponential myocardial stress-strain relationship in vivo. Detailed measurement of nonhomogeneous regional deformation are becoming possible with the advent of sophisticated imaging techniques. The methodology described in this study, with appropriate modifications in the FE analysis and optimization algorithms, can be applied to assess the complex three-dimensional pressure-deformation characteristics in vivo.
体外数据表明，心肌呈现非线性被动应力-应变关系和非线性压力-容积关系。在七只开胸犬中，利用超声心动图图像对三维重建的左心室（LV）几何结构进行有限元（FE）分析和优化算法，并结合血流动力学测量，以显示体内的非线性应力-应变关系。我们的分析包括根据测量的心肌容积应变计算泊松比，以及将模拟的心包压力负荷（“等效心包压力”）施加于重建左心室的心外膜表面。在舒张期以三个或四个增量时间步长重建左心室几何结构，并且在这项初步研究的这些短时间间隔内，假定心肌是均匀、各向同性且线弹性的。将左心室腔压力和等效心包压力同时纳入算法以预测左心室的实际扩张。在每个时间间隔迭代进行计算以计算优化的弹性模量。通过在每个时间间隔进行有限元分析和优化（逐步线性分析方法），得出心肌弹性模量与左心室腔压力之间的线性关系（r = 0.87至0.98）。这种线性关系等同于体内指数形式的心肌应力-应变关系。随着先进成像技术的出现，对非均匀区域变形进行详细测量已成为可能。本研究中描述的方法，在有限元分析和优化算法中进行适当修改后，可应用于评估体内复杂的三维压力-变形特征。
