# Iterative 2D Tissue Motion Tracking in Ultrafast Ultrasound Imaging
## 4 Discussion  
Frame-to-frame tracking of lateral tissue motion of the arterial wall using ultrafast ultrasound imaging is difficult as the movement per frame (<15 \(\upmu\)m) is very small compared to the line distance (100-200 \(\upmu\)m). The relative motion estimation error increases with decreasing movement per frame and the resulting movement curves become noisy and unreliable. To overcome this problem, we propose an iterative tracking scheme, with a Lagrangian viewpoint, based on temporarily down-sampling the frame-rate, anteroposterior tracking, and unbiased block-matching using two kernels per position estimate. The proposed motion estimation scheme performed well in the phantom study when estimating both velocity and displacement. The results showed increased tracking accuracy using longer initial length of iterations (\(k\geq 64\)). The tracking performance was better using the 100 \(\upmu\)m pitch transducer than the 200 \(\upmu\)m pitch transducer. The limited in vivo study showed that the proposed 2D tissue motion estimation tracking scheme can be used in vivo and is one step towards pulse-wave velocity estimations of the longitudinal movement of the arterial wall. As the relative motion estimation error increases with decreasing movement per frame [26], we hypothesized that it would be easier to accurately estimate a large motion than a small motion. To achieve a larger motion per frame, we used temporary down-sampling of the frame-rate. The temporary down-sampling of the frame rate also made it possible to perform anteroposterior tracking--tracking both forward and backward in the cine loop--and use two kernels per position estimate in the next iteration. The benefit of anteroposterior tracking is that bias of the motion estimate is reduced, and if the forward and the backward movements are equal, the bias is cancelled. We have previously shown that the use of an extra kernel per position reduces the mean tracking estimation errors [28]. The tracking scheme also uses much fewer estimations from the start of the tracking before reaching the investigated frame compared to frame-to-frame tracking. The combined effect of these factors is clearly shown in Figures 3, 6 and 7 as the accumulated motion estimation errors decrease with a larger initial length of iteration (\(k\)). In this study, both the velocity and the displacement were evaluated. The rationale is that these parameters investigate different features of a tracking method: the velocity evaluation gives an indication of the instantaneous uncertainty, whereas the displacement gives an indication of the accumulated uncertainty. In this study, the standard deviations of the velocity estimates are seemingly large. However, it should be noted that a velocity error of 1.3 mm/s corresponds to a displacement error of 1 \(\upmu\)m/frame (frame rate = 1302 Hz) and this is one reason why frame-to-frame tracking is likely to fail. In the evaluation, the velocity was estimated between two consecutive frames and only one estimate per kernel was used. Despite this, our proposed iterative tracking scheme based on temporarily down-sampling of the frame-rate and anteroposterior tracking enables the displacement to be accurately tracked (Figure 3, Tables 3 and 4). Averaging of two independent sources is a common method to obtain a more robust measurement. Time-averaging over multiple frames can be performed but acts as a low-pass filter in the time domain and can hide vital information. The averaging in our method is fundamentally different in that it averages the positions of the kernels and not its movement. We achieve a more robust estimate of the position of the kernel in each frame without affecting the time resolution using an extra kernel per position estimate [28]. The signal-to-noise ratio, speckle decorrelation, out-of-plane movement, and biasing are important factors for the size of the estimation uncertainty.