Dynamics of errors in 3D motion estimation and implications for strain-tensor imaging in acoustic elastography

Abstract

For the purpose of quantifying the noise in acoustic elastography, a displacement covariance matrix is derived analytically for the cross-correlation based 3D motion estimator. Static deformation induced in tissue from an external mechanical source is represented by a second-order strain tensor. A generalized 3D model is introduced for the ultrasonic echo signals. The components of the covariance matrix are related to the variances of the displacement errors and the errors made in estimating the elements of the strain tensor. The results are combined to investigate the dependences of these errors on the experimental and signal-processing parameters as well as to determine the effects of one strain component on the estimation of the other. The expressions are evaluated for special cases of axial strain estimation in the presence of axial, axial-shear and lateral-shear type deformations in 2D. The signals are shown to decorrelate with any of these deformations, with strengths depending on the reorganization and interaction of tissue scatterers with the ultrasonic point spread function following the deformation. Conditions that favour the improvements in motion estimation performance are discussed, and advantages gained by signal companding and pulse compression are illustrated.

Correlation analysis of the beam angle dependence for elastography

“…[26][27][28][29][30] The correlation coefficient with motion compensation due to the axial deformation of elastic tissue was derived by Meunier and Bertrand 26 using a two-dimensional (2D) Gaussian model. Cross-correlation functions for tissue like media that exhibit deterministic and stochastic strain profiles were derived by Bilgen and Insana.…”

Recent Results in Nonlinear Strain and Modulus Imaging

“…The acoustic pressure field has amplitude and phase modulation in the direction of the acoustic beam but varies only in amplitude in the perpendicular (azimuthal and elevational) directions. The lack of phase information, along with the more coarse spatial sampling in the perpendicular directions, greatly reduces the accuracy and increases the variance of displacement estimates perpendicular to the acoustic beam [17]. Therefore, most methods for inducing motion in quasi-static elastography attempt to create uniaxial deformation parallel to the beam line.…”

A model-based time-reversal of left ventricular motion improves cardiac motion analysis using tagged MRI data

“…In the presence of large motions, signal decorrelation between two image frames becomes a prominent factor in determining the errors. That is, a severe decorrelation between two windowed signals subsequently contributes to a motion estimation outcome with poor performance [ 13 - 15 ].…”