A stochastic approach to delays optimization for narrowband transmit beam pattern in medical ultrasound

Objective. Transmit Beam Pattern (TBP) optimization is an important task in medical ultrasound. State-of-the-art TBP optimization has well-known drawbacks like non-uniform beam width over depth, presence of significant side lobes and quick energy drop out after the focal depth. To overcome these limitations, we developed a novel optimization approach for TBP by focusing the analysis on the narrow band approximation of the TBP, particularly suited for Continuous Wave Doppler (CWD) and Acoustic Radiation Force Impulse (ARFI) elastography, and considering transmit delays as free variables instead of linked to a specific focal depth. Approach. We formulate the problem as a non linear Least Squares problem to minimize the difference between the TBP corresponding to a set of delays and the desired one, modeled as a 2D rectangular shape elongated in the direction of the beam axis. The narrow band case leads naturally to reformulate the problem in the frequency domain, with a significant computational saving with respect to time domain. Main Results. Results obtained by our synthetic software simulation show the main lobe width is considerably more intense and uniform over all the depth range with respect to the state-of-the-art optimization. The intensity gain of the beam ranges from $17\%$ to $54\%$ with respect than the standard focused beam patterns, the uniformity gain of the beam width ranges from $3.5$ to $9$ times the standard level and the side lobe variability reduction ranges from $1.1$ to $2.8$ times the standard level. Our optimized delay profile results in a combination of standard delay profiles at different focal depths. Significance. The proposed method improves the concentration of the ultrasound energy along a desired axis resulting in increased measurement accuracy in ARFI elastography and CWD modalities.