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.

翻译：目的。发射波束图（TBP）优化是医学超声中的一项重要任务。现有最优TBP方法存在众所周知的缺点，如波束宽度随深度非均匀、显著旁瓣以及聚焦深度后能量快速衰减。为克服这些局限性，我们提出了一种新的TBP优化方法，重点分析TBP的窄带近似，尤其适用于连续波多普勒（CWD）和声辐射力脉冲（ARFI）弹性成像，并将发射时延视为自由变量而非与特定聚焦深度关联。方法。将问题表述为非线性最小二乘问题，以最小化对应一组时延的TBP与目标TBP（建模为沿波束轴方向拉伸的二维矩形）之间的差异。窄带情形自然引导至频域重构问题，相比时域显著减少计算量。主要结果。合成软件仿真结果表明，与现有最优优化相比，主瓣宽度在整个深度范围内更显著且均匀。波束强度增益相比标准聚焦波束模式提高17%至54%，波束宽度均匀性增益为标准水平的3.5至9倍，旁瓣变异度降低为标准水平的1.1至2.8倍。优化的时延剖面由不同聚焦深度的标准时延剖面组合而成。意义。所提方法增强了沿目标轴的超声能量集中度，从而提高了ARFI弹性成像和CWD模态的测量精度。