Assessing the limits of ultrasonic focusing through tissue from scattering measurements

The spatial inhomogeneity of sound speed in tissue sets a fundamental limit on the ability to focus on ultrasonic beam in that tissue. The authors show how this speed inhomogeneity can be quantified from measurements of the differential angular scattering cross section. They give an expression for the statistical variations in acoustic path length as an integral of the correlation function-or, equivalently, the power spectrum-of density and compressibility fluctuations. Measurements of average differential scattering cross section yield values for the fluctuations in a model random medium and calf liver. Since the measured power spectra extend over only a finite wave-number window, they are fit to analytic functions to extend them over the whole region for which the integral must be evaluated. Results from the analysis of the model medium validate this approach, and those from calf liver provide insights into the limits of ultrasonic imaging resolution in living tissue