Analysis of motion tracking in echocardiographic image sequences: Influence of system geometry and point-spread function

Abstract

This paper focuses on motion tracking in echocardiographic ultrasound images. The difficulty of this task is related to the fact that echographic image formation induces decorrelation between the underlying motion of tissue and the observed speckle motion. Since Meunier’s seminal work, this phenomenon has been investigated in many simulation studies as part of speckle tracking or optical flow-based motion estimation techniques. Most of these studies modeled image formation using a linear convolution approach, where the system point-spread function (PSF) was spatially invariant and the probe geometry was linear. While these assumptions are valid over a small spatial area, they constitute an oversimplification when a complete image is considered. Indeed, echocardiographic acquisition geometry relies on sectorial probes and the system PSF is not perfectly invariant, even if dynamic focusing is performed. This study investigated the influence of sectorial geometry and spatially varying PSF on speckle tracking. This was done by simulating a typical 64 elements, cardiac probe operating at 3.5 MHz frequency, using the simulation software Field II. This simulation first allowed quantification of the decorrelation induced by the system between two images when simple motion such as translation or incompressible deformation was applied. We then quantified the influence of decorrelation on speckle tracking accuracy using a conventional block matching (BM) algorithm and a bilinear deformable block matching (BDBM) algorithm. In echocardiography, motion estimation is usually performed on reconstructed images where the initial sectorial (i.e., polar) data are interpolated on a cartesian grid. We therefore studied the influence of sectorial acquisition geometry, by performing block matching on cartesian and polar data. Simulation results show that decorrelation is spatially variant and depends on the position of the region where motion takes place relative to the probe. Previous studies did not consider translation in their experiments, since their simulation model (spatially invariant PSF and linear probe) yields by definition no decorrelation. On the opposite, our realistic simulation settings (i.e., sectorial probe and realistic beamforming) show that translation yields decorrelation, particularly when translation is large (above 6 mm) and when the moving regions is located close to the probe (distance to probe less than 50 mm). The tracking accuracy study shows that tracking errors are larger for the usual cartesian data, whatever the estimation algorithm, indicating that speckle tracking is more reliable when based on the unconverted polar data: for axial translations in the range 0–10 mm, the maximum error associated to conventional block matching (BM) is 4.2 mm when using cartesian data and 1.8 mm for polar data. The corresponding errors are 1.8 mm (cartesian data) and 0.4 mm (polar data) for an applied deformation in the range 0–10%. We also show that accuracy is improved by using the bilinear deformable block matching (BDBM) algorithm. For translation, the maximum error associated to the bilinear deformable block matching is indeed 3.6 mm (cartesian data) and 1.2 mm (polar data). Regarding deformation, the error is 0.7 mm (cartesian data) and 0.3 mm (polar data). These figures also indicates that the larger improvement brought by the bilinear deformable block matching over standard block matching logically takes place when deformation on cartesian data is considered (the error drops from 1.8 to 0.7 mm is this case). We give a preliminary evaluation of this framework on a cardiac sequence acquired with a Toshiba Powervision 6000 imaging system using a probe operating at 3.25 MHz. As ground truth reference motion is not available in this case, motion estimation performance was evaluated by comparing a reference image (i.e., the first image of the sequence) and the subsequent images after motion compensation has been applied. The comparison was quantified by computing the normalized correlation between the reference and the motion-compensated images. The obtained results are consistent with the simulation data: correlation is smaller for cartesian data, whatever the estimation algorithm. The correlation associated to the conventional block matching (BM) is in the range 0.45–0.02 when using cartesian data and in the range 0.65–0.2 for polar data. The corresponding correlation ranges for the bilinear deformable block matching are 0.98–0.2 and 0.98–0.55. In the same way these figures indicate that the bilinear deformable block matching yield a larger improvement when cartesian data are considered (correlation range increases from 0.45–0.02 to 0.98–0.2 in this case).