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

For the purpose of quantifying the noise in acoustic elastography, a displa cement covariance matrix is derived analytically for the cross-correlation based 3D motion estimator. Static deformation induced in tissue from an ext ernal mechanical source is represented by a second-order strain tensor. A g eneralized 3D model is introduced for the ultrasonic echo signals. The comp onents of the covariance matrix are related to the variances of the displac ement errors and the errors made in estimating the elements of the strain t ensor. The results are combined to investigate the dependences of these err ors on the experimental and signal-processing parameters as well as to dete rmine the effects of one strain component on the estimation of the other. T he expressions are evaluated for special cases of axial strain estimation i n the presence of axial, axial-shear and lateral-shear type deformations in 2D. The signals are shown to decorrelate with any of these deformations, w ith strengths depending on the reorganization and interaction of tissue sca tterers 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 compres sion are illustrated.