Backscatter Coefficient Estimation Bias under Acoustic Nonlinearities

The backscatter coefficient (BSC) describes the scattering properties of a medium and can be used to characterize tissue. To calculate the BSC a calibration spectrum is required, which can be acquired using either a reference phantom method (RPM) or the planar reflector method (PRM). Although ultrasonic propagation is quasilinear at low acoustic pressures, for high acoustic pressures, acoustic nonlinear distortion becomes prevalent. Because water is low loss, use of the PRM method may introduce significant nonlinearities to the BSC estimation. In this study, we assessed the effects of the acoustic nonlinearities on BSC estimation when using the RPM and the PRM. Phantoms were scanned by exciting a single-element focused transducer (f/2) using one excitation level from low-power (LP) equipment (5800 PR, Panametrics Olympus, USA) and six excitation levels (EL1 to EL6) from high-power (HP) equipment (RAM-5000, Ritec, USA). This resulted in scanning the phantoms with increasingly higher pressures, but still within FDA limits for diagnostic ultrasound. The two phantoms, labelled phantoms A and B, had glass beads with diameters in the range 75-90 and 9-43 μm, respectively. The BSCs estimated with the LP system were used as a baseline. The normalized root-mean-squared error (RMSE) was calculated from BSCs estimated using the HP system with respect to the baseline. The BSC was parameterized to estimate the effective scatterer diameters (ESD) for each phantom using Faran's scattering theory. The BSC estimates resulted in smaller variations versus excitation levels for the RPM compared to the PRM. In the PRM, the RMSE was 0.62 ± 0.42 and 0.98 ± 0.77 for phantoms A and B, respectively; whereas, in the RPM, the RMSE was 0.21 ± 0.06 and 0.25 ± 0.12 for phantoms A and B, respectively. The ESD for the phantom A using the PRM decreased from 75 μm for EL1 to 39 μm for EL6; and using the RPM the ESD was 74.7 ± 2.3 μm across all settings. The ESD for the phantom B using the PRM decreased from 47 μm for EL1 to 0.5 μm for EL6; and using the RPM the ESD was 39.2 ± 5.6 μm across all settings. The RPM method was more robust against nonlinear distortion compared to the PRM because the PRM was used in water, where low loss resulted in large nonlinear distortion of the reference pulse.