Performance evaluation of different implementations of the Lagrangian speckle model estimator for non-invasive...

Non-invasive vascular ultrasound elastography (NIVE) was recently introduced to characterize mechanical properties of carotid arteries for stroke prevention. Using the Lagrangian speckle model estimator (LSME), the four components of the 2D deformation matrix (delta), which are the axial strain (delta(yy)) and shear (delta(yx)) and the lateral strain (delta(xx)) and shear (delta(xy)), can be computed. This paper overviews four different implementations of the LSME and addresses their reliability. These implementations include two unconstrained (L&M and L&M+) and one constrained (ITER(c)) iterative algorithms, and one optical flow-based (OF-based) algorithm. The theoretical frameworks were supported by biomechanical simulations of a pathology-free vessel wall and by one single layer vessel-mimicking phantom study. Regarding simulations, the four LSME implementations provided similar biases on axial motion parameters, except the L&M that outperformed other methods with a minimum strain bias of -3%. LSME axial motion estimates showed good consistence with theory, namely the OF-based algorithm that in a specific instance estimated delta(yy) with no relative error on the standard deviation. With regards to lateral motion parameters, ITER(c) exhibited a minimum strain bias of -8.5% when ultrasound beam and motion mostly run parallel, whereas L&M performs strain and shear estimates with less than 23% bias independently of orientations. The in vitro vessel phantom data showed LSME delta(yy) and delta(yx) maps that were qualitatively equivalent to theory, and noisy delta(xx) and delta(xy) elastograms. In summary, the authors propose to promote the OF-based LSME as an optimal choice for further applications of NIVE, because of its reliability to compute both axial strain and shear motion parameters and because it outperformed the other implementations by a factor of 30 or more in terms of processing time.