Optimization of correlation kernel size for accurate estimation of myocardial contraction and relaxation

For noninvasive and quantitative measurements of global two-dimensional (2D) heart wall motion, speckle tracking methods have been developed and applied. In these conventional methods, the frame rate is limited to about 200 Hz, corresponding to the sampling period of 5 ms. However, myocardial function during short periods, as obtained by these conventional speckle tracking methods, remains unclear owing to low temporal and spatial resolutions of these methods. Moreover, an important parameter, the optimal kernel size, has not been thoroughly investigated. In our previous study, the optimal kernel size was determined in a phantom experiment under a high signal-to-noise ratio (SNR), and the determined optimal kernel size was applied to the in vivo measurement of 2D displacements of the heart wall by block matching using normalized crosscorrelation between RF echoes at a high frame rate of 860Hz, corresponding to a temporal resolution of 1.1 ms. However, estimations under low SNRs and the effects of the difference in echo characteristics, i.e., specular reflection and speckle-like echoes, have not been considered, and the evaluation of accuracy in the estimation of the strain rate is still insufficient. In this study, the optimal kernel sizes were determined in a phantom experiment under several SNRs and, then, the myocardial strain rate was estimated such that the myocardial function can be measured at a high frame rate. In a basic experiment, the optimal kernel sizes at depths of 20, 40, 60, and 80mm yielded similar results: in particular, SNR was more than 15 dB. Moreover, it was found that the kernel size at the boundary must be set larger than that at the inside. The optimal sizes of the correlation kernel were seven times and four times the size of the point spread function around the boundary and inside the silicone rubber, respectively. To compare the optimal kernel sizes, which was determined in a phantom experiment, with other sizes, the radial strain rates estimated using different kernel sizes were examined using the normalized mean-squared error of the estimated strain rate from the actual one obtained by the 1D phase-sensitive method. Compared with conventional kernel sizes, this result shows the possibility of the proposed correlation kernel to enable more accurate measurement of the strain rate. In in vivo measurement, the regional instantaneous velocities and strain rates in the radial direction of the heart wall were analyzed in detail at an extremely high temporal resolution (frame rate of 860 Hz). In this study, transition in contraction and relaxation was able to be detected by 2D tracking. These results indicate the potential of this method in the high-accuracy estimation of the strain rates and detailed analyses of the physiological function of the myocardium.