Effects of Acoustic Nonlinearities on the Estimation of Attenuation from Ultrasonic Backscatter

The attenuation coefficient (AC) has demonstrated the ability to classify tissue state. Linear acoustic propagation is assumed when estimating the AC using spectral-based methods from the ultrasonic backscatter. However, the effects of acoustic nonlinearities can distort the backscattered power spectra versus depth. The distortion of the power spectra could result in a bias in the estimation of the AC. The goal of the study was to quantify the effects of nonlinear distortion on the estimation of AC from ultrasonic backscatter using spectral methods. We computed the AC from backscattered signals using the spectral log difference method and a reference phantom to account for diffraction effects. Computational simulations and experiments in phantoms were performed. In the experiments, three tissue-mimicking phantoms, named A, B and C having estimated AC values of 0.60, 0.90, and 0.20 dB/cm/MHz, respectively, and B/A ≈ 6.6 for each phantom were scanned using a single-element focused transducer (f/2) having a 0.5" diameter and 5-MHz center frequency. The phantoms were scanned using six excitation levels from a high-power (HP) pulsing apparatus (RAM-5000, Ritec, USA). The AC was estimated from phantom A using either phantom B (high attenuation) or phantom C (low attenuation) as the reference. The AC was estimated at each excitation level over the analysis bandwidth (− 6-dB criterion) to determine the effects of acoustic nonlinearity on estimation of AC. The presence of nonlinear distortion can be quantified through the Gol’dberg number, which is inversely proportional to the product of the nonlinearity coefficient and attenuation. We hypothesized that because the B/A values were approximately the same for each phantom, the effects of nonlinear distortion would be more pronounced when using phantom C, which had much lower attenuation. Specifically, increased excess attenuation due to transfer of energy from the fundamental to the harmonics would be observed more in phantom C. The AC estimate increased from 0.57 to 0.67 dB/cm/MHz as the excitation levels increased from level one to six when using phantom B as a reference. In contrast, when using phantom C as reference, the estimated AC slope of phantom A decreased from 0.57 to 0.43 dB/cm/MHz as the excitation levels increased from level one to six. Therefore, use of a reference with different attenuation resulted in increased bias of AC estimates due to nonlinear distortion being this deviation larger when using low attenuating media.