Nonlinearity parameter estimation based on quantifying excess ultrasonic attenuation

The attenuation coefficient has potential in tissue characterization. Previously, it was observed that the accuracy of estimates of the attenuation coefficient slope (ACS) obtained using the spectral-log-difference technique (SLD) degraded due to nonlinear distortion. Based on these observations regarding estimates of the ACS, (i.e., the difference between ACS estimated at high and low pressures, which is called excess ACS in this work), a heuristic approach was devised for determining the nonlinearity parameter, B/A, of a medium. A total of 16 numerical phantoms using the k-Wave simulation package were constructed having spatially random distributions of acoustic density in a 3D grid to generate backscattered signals. To estimate ACS values from the phantoms, we used the SLD technique. The uniform numerical phantoms varied in their properties with B/A values of 6, 8, 10 or 12 and ACS values of 0.3, 0.7, 1.1 or 1.5 dB/cm/MHz. A focused source (f/2) with 1” focal length transmitted a 3.5-MHz centered Gaussian pulse at two different source pressures: 100 kPa (quasi-linear) and 1.3 MPa (nonlinear). Using one of the 16 phantoms as a sample (`sam') and another one as a reference (`ref'), we obtained 240 separate ACS estimates using the SLD for both the low and high pressures. The excess attenuation estimated was related to values of the Gol'dberg number, Γ, which is a parameter that predicts the degree of nonlinear distortion in plane waves. The excess ACS versus log
₁₀
(Γ
_sam
/Γ
_ref
) had a correlation coefficient of 0.96. The results indicate that a larger mismatch of Gol'dberg numbers between sample and reference resulted in larger excess ACS estimate. Therefore, whenever a large excess attenuation was observed, the Γ mismatch was also large. Using each of the 14 residual phantoms as a second reference (`ref2') with assumed known B/A and ACS leads to (ExcessAttsam)/(ExcessAtt
<sub>ref2</sub>
) ≈ log
<sub>10</sub>
(Γ
<sub>sam</sub>
/Γ
<sub>rer</sub>
)/log
<sub>10</sub>
(Γ
<sub>ref2</sub>
/Γ
<sub>ref</sub>
) from which up to 3360 B/Asam could be estimated. Errors for estimated B/A were small (≤10%) and high (2≥50%) for 31% and 22% of 1536 cases when the phantoms (`sam', `ref', and `ref2') had different preset ACS values. When the ACS was identical among the phantoms, the errors for the estimated B/A were relatively small (≤10%) and high (≥50%) for 46% and 6% of 96 cases, which can be explained by having better correlation.