Evaluation of nonlinearity parameter estimation in convex array transducers using the depletion method

Nonalcoholic fatty liver disease (NAFLD) is characterized by the excessive accumulation of triglycerides in hepatocytes, typically diagnosed through non-invasive imaging techniques such as ultrasound. Among emerging quantitative diagnostic approaches is the nonlinearity parameter (B/A), which correlates with liver fat content. The depletion method, a dual-energy pulse-echo technique, estimates the B/A using a reference phantom and radio frequency data from the fundamental band. The present work explores the use of the depletion method to estimate the B/A using convex arrays, commonly used in clinical ultrasound due to their wider imaging field. The modeled convex arrays were configured to mimic the C5-2v convex probe, whereas the linear arrays were configured with the same characteristics except for the curvature. Simulations representing increasing levels of B/A (7, 9, and 11) were conducted using the k-Wave MATLAB toolbox to assess the accuracy of this method given the differences in the wave diffraction pattern of convex and linear arrays. The pulse frequency was set to 3.5 MHz (22.7% bandwidth at -6 dB) with peak pressure at 100 kPa for the low energy acquisitions, whereas the high energy pressure levels were 200, 600, or 1000 kPa, corresponding to a scaling factor of 2, 6, or 10. Despite its different divergence, the results demonstrated that the convex arrays provided reliable estimates of B/A within the region of interest (ROI), which considered an axial depth between 2 and 9.5 cm. The mean absolute percentage error (MAPE) was approximately 3% lower in convex arrays compared to linear arrays in the obtained B/A maps because of the underestimation of B/A at deeper regions of the latter. These findings suggest that convex arrays, with their wider and deeper imaging capabilities, are well-suited for B/A estimation using the depletion method.