In vivo assessment of nonlinear myocardial deformation using finite element analysis and three-dimensional echocardiographic reconstruction.

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.