Scatterer size estimation using a generalized ultrasound attenuation-compensation function to correct for focusing

The frequency statistics of the backscattered waveform observed between tissue boundaries can be matched to a model to estimate the characteristic size of the scatterer in the tissue region of interest. In the past, the models have all assumed plane wave propagation requiring the use of unfocused or weakly focused sources in the experiment. In our work, we challenged this assumption by re-deriving the scattering equations assuming that the focused field can be accurately modeled as a 3D Gaussian distribution in addition to the traditional assumptions that the scatterers are a sufficient distance from the source and that the field is approximately constant across the scatterer. We showed that correcting for focusing when estimating the scatterer size only requires a generalized attenuation-compensation function that includes the impact of focusing along the beam axis. We then generated computer simulations to aid in the understanding of the impact of diffraction along the beam axis and compared the performance of our attenuation-compensation function to the performance of previously proposed attenuation-compensation functions for various levels of focusing (f/1, f/2, f/4), attenuation (0.05 to 1 dB/cm/MHz), and rectangular window length used to gate the time domain signal (1 to 13 mm). The generalized attenuation-compensation function yielded results accurate between 2% and 7.2% while the traditional attenuation-compensation functions that neglected focusing had errors greater than 50% for moderate attenuation and window lengths.