Despite the availability of multiple ultrasound approaches to left ventricular (LV) flow characterization in two dimensions, this technique remains in its childhood and further developments seem warranted. This article describes a new methodology for tracking the 2-D LV flow field based on ultrasound data. Hereto, a standard speckle tracking algorithm was modified by using a dynamic kernel embedding Navier-Stokes-based regularization in an iterative manner. The performance of the proposed approach was first quantified in synthetic ultrasound data based on a computational fluid dynamics model of LV flow. Next, an experimental flow phantom setup mimicking the normal human heart was used for experimental validation by employing simultaneous optical particle image velocimetry as a standard reference technique. Finally, the applicability of the approach was tested in a clinical setting. On the basis of the simulated data, pointwise evaluation of the estimated velocity vectors correlated well (mean r = 0.84) with the computational fluid dynamics measurement. During the filling period of the left ventricle, the properties of the main vortex obtained from the proposed method were also measured, and their correlations with the reference measurement were also calculated (radius, r = 0.96; circulation, r = 0.85; weighted center, r = 0.81). In vitro results at 60 bpm during one cardiac cycle confirmed that the algorithm properly measures typical characteristics of the vortex (radius, r = 0.60; circulation, r = 0.81; weighted center, r = 0.92). Preliminary qualitative results on clinical data revealed physiologic flow fields.

Ultrasonography is a convenient and widely used technique to look into the longitudinal muscle motion as it is radiation-free and real-time. The motion of localized parts of the muscle, disclosed by ultrasonography, spatially reflects contraction activities of the corresponding muscles. However, little attention was paid to the estimation of longitudinal muscle motion, especially towards estimation of dense deformation field at different depths under the skin. Yet fewer studies on the visualization of such muscle motion or further clinical applications were reported in the literature. A primal-dual algorithm was used to estimate the motion of gastrocnemius muscle (GM) in longitudinal direction in this study. To provide insights into the rules of longitudinal muscle motion, we proposed a novel framework including motion estimation, visualization and quantitative analysis to interpret synchronous activities of collaborating muscles with spatial details. The proposed methods were evaluated on ultrasound image sequences, captured at a rate of 25 frames per second from eight healthy subjects. In order to estimate and visualize the GM motion in longitudinal direction, each subject was asked to perform isometric plantar flexion twice. Preliminary results show that the proposed visualization methods provide both spatial and temporal details and they are helpful to study muscle contractions. One of the proposed quantitative measures was also tested on a patient with unilateral limb dysfunction caused by cerebral infarction. The measure revealed distinct patterns between the normal and the dysfunctional lower limb. The proposed framework and its associated quantitative measures could potentially be used to complement electromyography (EMG) and torque signals in functional assessment of skeletal muscles.

Inverse problems are very frequent in computer vision and machine learning applications. Since noteworthy hints can be obtained from motion data, it is important to seek more robust models. The advantages of using a more general regularization matrix such as Λ=diag{λ1,…,λ K } to robustify motion estimation instead of a single parameter λ (Λ=λ I ) are investigated and formally stated in this paper, for the optical flow problem. Intuitively, this regularization scheme makes sense, but it is not common to encounter high-quality explanations from the engineering point of view. The study is further confirmed by experimental results and compared to the nonregularized Wiener filter approach.