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

Ultrasound imaging is extensively employed in clinical settings due to its non-ionizing nature and real-time capabilities. The beamformer represents a crucial component of an ultrasound machine, playing a significant role in shaping the ultimate quality of the reconstructed image. Therefore, Transmit Beam Pattern (TBP) optimization is an important task in medical ultrasound, but 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 its narrowband approximation, particularly suited for Acoustic Radiation Force Impulse (ARFI) elastography, and considering transmit delays as free variables instead of linked to a specific focal depth. 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. In order to quantitatively evaluate the results, we define three quality metrics based on main lobe width, side lobe level, and central line power. Results obtained by our synthetic software simulation show that the main lobe width is considerably more intense and uniform over the whole depth range with respect to classical focalized Beam Patterns, and our optimized delay profile results in a combination of standard delay profiles at different focal depths. The application of the proposed method to ARFI elastography shows improvements in the concentration of the ultrasound energy along a desired axis.