Simultaneous Estimation of the Nonlinearity Parameter and the Attenuation Coefficient

Tissue characterization by the nonlinearity parameter (B/A) can add additional quantitative ultrasound information regarding the tissue structure. Recently, a method to estimate B/A from the depletion of the fundamental band data and the use of a reference phantom for calibration was presented. However, one requirement of the depletion method is to use an accurate estimate of the attenuation coefficient of the assessed medium (which is limited by the accuracy of the pulse-echo attenuation estimation method). In this work, an alternative approach to simultaneously estimate B/A and the attenuation coefficient is explored in the framework of the depletion method to leverage the a priori knowledge of the sample attenuation. First, these two parameters B/A and attenuation coefficient are related as dependent and independent variables, by more than one equation. Then, a brute-force search of the optimal attenuation coefficient that minimized the variance of the B/A across the equations gives the B/A optimal as the average of the available equations within a data block. Tests were performed using the k-Wave toolbox with uniform media and acquisition with geometry of that a linear array. and a narrowband ultrasonic pulse. The uniform sample media tested had B/A=9 and attenuation coefficient 2.5 dB/cm at 5 MHz and the reference phantom had B/A=6 and the same attenuation coefficient. Data blocks with 10% overlap and sizes in wavelengths ranging from 5 wavelengths up to 50 wavelengths were used to construct B/A maps. Moreover, the simultaneous estimation of B/A and attenuation coefficient was compared to the depletion method with biased attenuation coefficient using +/-20% of bias. The B/A maps when using overestimated or underestimated value of the attenuation produced bias of 1.2. In contrast, the bias of the simultaneous estimation was only 0.2 when using 50 wavelengths data blocks. The variance in the presented method was strongly dependent on the blocks' size used for estimating the B/A. In summary, the results suggest preliminary feasibility of jointly estimation of the B/A and attenuation coefficient with low relative bias.