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

Abstract

For the purpose of quantifying the noise in acoustic elastography, adisplacement covariance matrix is derived analytically for thecross-correlation based 3D motion estimator. Static deformation induced intissue from an external mechanical source is represented by a second-orderstrain tensor. A generalized 3D model is introduced for the ultrasonic echosignals. The components of the covariance matrix are related to the variancesof the displacement errors and the errors made in estimating the elements ofthe strain tensor. The results are combined to investigate the dependences ofthese errors on the experimental and signal-processing parameters as well asto determine the effects of one strain component on the estimation of theother. The expressions are evaluated for special cases of axial strainestimation in the presence of axial, axial-shear and lateral-shear typedeformations in 2D. The signals are shown to decorrelate with any of thesedeformations, with strengths depending on the reorganization and interactionof tissue scatterers with the ultrasonic point spread function following thedeformation. Conditions that favour the improvements in motion estimationperformance are discussed, and advantages gained by signal companding andpulse compression are illustrated.