Theoretical analysis of tissue axial stretching model in elastography

The performance of axial displacement estimation in ultrasound elastography can be degraded by tissue lateral displacements, mainly because of the move-in and move-out of tissue scatterers. In our previous work, a tissue axial stretching model was proposed to separate the decorrelation effect induced by lateral displacements from other decorrelation sources. In this paper, the tissue axial stretching model is analyzed theoretically. The theoretical result in a closed form indicates that the peak value of the cross-correlation function between the pre- and post-compression echoes is determined mainly by the beam width, the beam position and the lateral strain. Computer simulations are carried out to verify the theoretical conclusion. The theoretical analysis and simulation results can help to understand more clearly the decorrelation effect of tissue lateral displacements and the 2-D spatial comprehensive cross-correlation method presented previously to reduce the decorrelation effect.