Depletion of backscattered fundamental band signal for nonlinearity parameter imaging

The estimation of the nonlinearity parameter (B/A) has potential to be used in the diagnosis of conditions such as liver steatosis. Recently, a pulse-echo method to estimate B/A using: a dual-energy approach, one reference phantom, and the approximation of the 2nd harmonic in terms of envelopes of fundamental band of RF data was presented. However, the performance of this method degrades when the reference phantom and sample medium have different attenuation coefficient slope (ACS). In the present work, the method is modified to overcome this limitation, estimating B/A by quantifying a term we named the depletion of the fundamental band. In a dual-energy model, using two source pressure levels P0 and vP0 (i.e., P0 scaled by a known factor v), the depletion term (vP1-P2) can be obtained, where P1 and P2 are the envelopes of fundamental band of RF data at the used pressure levels. From the nonlinear acoustic theory in fluid-like media, we found that (vP1-P2) is proportional to the square of (1+B/2A) and could be used to estimate the B/A. We tested the depletion model in numerical phantoms simulated using the k-Wave toolbox. A nonuniform B/A sample with ACS= 0.5 dB/cm/MHz had an 18-mm diameter inclusion (B/A=11) embedded in an otherwise homogeneous background (B/A=6), whereas three different phantoms with constant B/A=6 but ACS of 0.5, 0.6 or 0.4 dB/cm/MHz were tested. RF data were generated using the geometry of the L9-4/38 transducer and exciting all elements simultaneously with a 50% -6-dB bandwidth, 5 MHz Gaussian pulse with pressures of 80 kPa (low energy) and 400 kPa (high energy). The estimated cumulative B/A were converted to local B/A estimates by solving an inverse problem with the Total Variation regularization approach in order to report the mean percentage error (MPE) vs ground truth B/A. The results had higher accuracy using the new model (MPEs of 7.9%, 10.3%, and 9.6%), unlike the previous model (MPEs of 7.9%, 25.9%, and 25.4%). Despite having a mismatch of attenuation of sample and reference of 20%, the new model provides a more robust imaging of the B/A.