Statistical properties of elastograms

Accurate and precise displacement estimates are the key to obtaining high-quality elastograms. In elastographic imaging, echo-signals acquired before and after tissue compression are cross-correlated and the location of the cross-correlation maximum is used for determining the local tissue displacement and deformation. A stochastic strain model under static compression is discussed, and an inverse coordinate transformation relating the post-compression coordinate to the pre-compressed coordinate is introduced. Analytic formulas for the cross-correlation are provided and used to analyse stochastic strain-induced effects. Displacement causes decorrelation of the pre- and post-compression signals and consequently results in a nonstationary cross-correlation function. Adjusting experimental and signal processing variables, such as stretching the post-compression echo-signal and/or shaping the ultrasonic pulse are shown to significantly increase the accuracy of the displacement estimates.