Appropriate Window Function and Window Length in Multifrequency Velocity Estimator for Rapid Motion and Locality of Layered Myocardium

The heart wall has a multilayered structure and moves rapidly during ejection and rapid filling periods. Local strain rate (SR) measurements of each myocardial layer can contribute to accurate and sensitive evaluations of myocardial function. However, ultrasound-based velocity estimators using a single-frequency phase difference cannot realize these measurements owing to insufficient maximum detectable velocity, which is limited by a quadrature frequency. We previously proposed a velocity estimator using multifrequency phase differences to improve the maximum detectable velocity. However, the improvement is affected by a spatial discrete Fourier transform (DFT) window length that represents the locality of the velocity estimation. In this article, we theoretically describe that shortening the window increases the interference between different frequency components and decreases the maximum detectable velocity. The tradeoff between the maximum detectable velocity and the window length was confirmed through simulations and a water-tank experiment. Under the tradeoff, the Hanning window, which was used in previous studies, is not always appropriate for the local measurement of the velocity, which sometimes exceeds 100 mm $/\text{s}$ depending on the subject, direction of the ultrasound beam to the heart wall, and cardiac periods. In the in vivo measurement with the short window, the Tukey window with a large flat part that has a high-frequency resolution and ameliorates the discontinuity at both edges of the windowed signal was appropriate to measure the maximum velocity. This study offers the potential for local measurements of each myocardial layer using the multifrequency velocity estimator with the appropriate window function and window length.