The nonstationary strain filter in elastography: Part II. Lateral and elevational decorrelation

The nonstationary evolution of the strain filter due to lateral and elevational motion of the tissue scatterers across the ultrasound beam is analyzed for the 1-D cross-correlation-based strain estimator. The effective correlation coefficient that includes the contributions due to lateral and elevational signal decorrelation is used to derate the upper bound of the signal-to-noise ratio in the elastogram (SNR_e) predicted by the ideal strain filter. In the case of an elastically homogeneous target, if the transducer is on the axis of symmetry of such target in the elevational direction, the motion of the scatterers out the imaging plane is minimized. In addition, the ultrasound beam along the elevational direction is broader, allowing scatterers to stay longer within the beam during tissue compression. Under these conditions, lateral signal decorrelation becomes the primary contributor to the nonstationary behavior of the strain filter. Both the elastographic SNR_e and the dynamic range are reduced, with an increase in lateral decorrelation. Finite element simulations and phantom experiments are presented in this paper to corroborate the theoretical strain filter. The nonstationary behavior of the strain filter is reduced by confining the tissue in the lateral direction (minimizing motion of tissue scatterers), thereby improving the quality of the elastogram.