Correcting for Diffraction and Quantifying Volumetric Scatterer Concentration Using First-order Speckle Statistics

Speckle statistics are fundamentally related to the resolution of an ultrasound image. Existing models for speckle statistics do not account for changes in resolution with imaging depth, a reality of clinical pulse-echo ultrasound, thereby posing challenges to interpretation. The purpose of this work is to evaluate and address this shortfall in first-order speckle statistics analysis.

Simulated ultrasonic speckle from a low scatterer density medium was created with known acquisition parameters, and speckle statistics of the Nakagami and homodyned K distributions were estimated with and without compensating for the expected change in the resolution cell size, defined by the ultrasound pulse volume, over the field of view. Compensation methods using resolution estimates from the predicted acoustic field, image autocorrelation, or spectral analysis were compared. The absolute number of scatterers per cubic millimeter was also calculated from corrected speckle statistics estimates. The results were validated with experiments in a low scatterer density phantom using a clinical scanner, and in in vivo rhesus macaque cervix and human Achilles tendon images.

It was shown in both simulations and phantoms that, when no compensation was applied, the expansion of the resolution cell size caused a saturation of Nakagami m and homodyned K parameter estimates at depths beyond the focal distance, even when scatterer concentration was constant throughout the depth of the phantoms. This confounding factor was reduced by compensating for the changing resolution cell size, resulting in a decrease in the normalized root mean squared errors between estimates at focus and estimates at all depths (7.8 ± 0.3% to 5.1 ± 0.3% in m, 68 ± 2% to 9.1 ± 0.3% in α, and 40 ± 1% to 6.8 ± 0.3% in k in simulated acquisitions; 21.5 ± 0.4% to 15.4 ± 0.4% in m, 291 ± 15% to 76 ± 12% in α, and 39 ± 1% to 21 ± 1% in k in phantom acquisitions). Images from in vivo analysis before and after compensation resulted in an increase in median contrast-to-noise ratio between the cervix and background and the Achilles tendon and background.

Compensation for changes in ultrasonic resolution with depth prevents saturation in speckle statistics estimates, thus providing more relevant information about tissue properties. The methods described in this work reduce the system dependence of speckle statistics analysis, thus addressing a barrier to the clinical application and adoption of speckle statistics.