In echocardiography, blood-flow measurement is important, and several methods of measuring the velocity vector of blood flow have been proposed including echographic speckle tracking. Echographic speckle tracking is typically based on blockmatching algorithms; however, they incur high calculation cost; thus, are time-consuming. To enable real-time blood-flow vector measurement, we applied the Kanade-Lucas-Tomasi (KLT) algorithm to echographic speckle tracking, but the measurement accuracy was low in preliminary trial. This is mainly because echographic speckles deform as speckles move due to the acoustic pressure field of a transmitting beam. The objective of this study was to minimize the estimation error of KLT-based speckle tracking by analyzing error propagation. We analyzed error propagation from the acoustic pressure field to the velocity error by simplifying speckle deformation and formulated the major error factors. From this analysis, we propose a policy of determining the measurement conditions, which are region-of-interest (ROI) size, waveform, and number of ROI divisions, for minimizing estimation error. We verified the proposed policy through numerical simulations. As a result of the analysis and simulations, the gradient of the pressure field, number of ROI divisions, and moving distance of a speckle accounted for most of the estimation error. In addition, optimizing these conditions restricted the mean estimation error to less than 10%. These results indicate that the accuracy of KLT-based speckle tracking can reach a practical level by designing measurement conditions based on the proposed policy.
Arteriosclerosis, increasing future risks of cardiovascular events even in its early stages, occurs in the vessel walls where stimulation stress, known as wall shear stress (WSS), is constantly lower than 0.4 Pa (referred to as low-WSS vessels). For early arteriosclerosis detection, we previously proposed a WSS-measurement method and detected low-WSS vessels by comparing the threshold value with the WSS calculated at a given moment when the mean flow-velocity maximized, presuming that the WSS maximized simultaneously at all measurement points. However, in reality, the moments were different between the upstream and downstream of blood flows because of the pulse wave propagation, and this difference resulted in false identification of low-WSS vessels. The objective of this study is to precisely identify low-WSS vessels by detecting the maximum-WSS during heartbeat cycles for each measurement point. We propose a method for identifying low-WSS vessels by calculating the WSS distributions in every frame and comparing the maximum-WSS with the threshold value for each measurement point. To evaluate the method, we compared it with the conventional one while identifying low-WSS vessels in a carotid-artery phantom. The precision of the classifications was assessed by the agreement rate between the echographic method and the ground truth, which was classified by the maximum-WSS measured by particle image velocimetry (PIV). The results revealed that the classification by our method agreed with that by the PIV in 84% of cases, and that by the conventional method agreed in 64%. In conclusion, our method increases the precision of low-WSS vessel identification.