Narrowband Transmit Beam Pattern in medical ultrasound: a stochastic approach to delays optimization

Transmit Beam Pattern (TBP) optimization is an important task in medical ultrasound especially in some advanced applications like continuous wave Doppler or shear wave generation in acoustic radiation force impulse elastography. Standard TBP is based on transmission focused at a fixed focal depth: this results in 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, in this work we present a novel optimization approach for TBP by focusing the analysis on the narrow band approximation of the TBP 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. The narrow band case leads naturally to reformulate the problem in the frequency domain, with a significant computational saving with respect to time domain. The optimized narrowband beam patterns have been compared with a large set of standard ones, showing an overall improvement of desired features, thus demonstrating the effectiveness of the proposed approach. Moreover, in order to allow a quantitative evaluation of the improvement, a novel set of metrics is introduced.