Department of Physics, The University of Warwick, Coventry, UK.
Ultrasound Med Biol. 2010 Mar;36(3):410-8. doi: 10.1016/j.ultrasmedbio.2009.11.010. Epub 2010 Feb 4.
Modeling provides an attractive approach for the design of phased array ultrasound transducers for hyperthermia. However, measurements on physical transducers reveal differences from the idealized field profiles predicted by simulation. In this paper we report a method of analyzing the origins of these differences. The measured performance of a 15-element sparse phased array is described and compared with simulated fields calculated using the point source method. It highlighted two notable differences: First, that the focal region was located closer to the surface of the physical transducer than in the simulated fields; and second, that numerous intensity maxima were present between the surface of the transducer and the focal zone in the experimental data, but not in the simulated fields. We identified six factors that could potentially affect the field but were not taken into account by the default simulations, and we performed a sensitivity analysis on these: (i) Variation in the amplitude of the output from each element, (ii) the presence of square-wave harmonics in the drive signals, (iii) nonpistonlike vibration of elements, (iv) quantization of the applied phases, (v) errors in the spatial positioning of each element; and (vi) interelement cross-coupling. Both the independent impact of each factor and the interactions between multiple factors were analyzed by using a full-factorial experimental design composed of 64 (2(6)) simulations. The results indicated that nonpistonlike motion of elements is likely to be the primary cause of differences between the measured and modelled fields. Determination of the precise vibrational modes of elements in an array is complex and would require full finite element analysis. However, the simple vibrational mode considered within the present work, corresponding to the addition of a surface Rayleigh wave originating at the element center and propagating radially, produced simulation results that were in good agreement with the measured data.
建模为用于热疗的相控阵超声换能器的设计提供了一种有吸引力的方法。然而，对物理换能器的测量显示出与模拟预测的理想化场分布的差异。在本文中，我们报告了一种分析这些差异起源的方法。描述并比较了 15 个稀疏相控阵的测量性能与使用点源法计算的模拟场。结果突出了两个显著的差异：首先，焦点区域更靠近物理换能器的表面，而不是在模拟场中；其次，在实验数据中，在换能器表面和焦区之间存在许多强度极大值，但在模拟场中没有。我们确定了六个可能影响场的因素，但默认模拟未考虑这些因素，并对这些因素进行了敏感性分析：（i）每个元件输出幅度的变化，（ii）驱动信号中存在方波谐波，（iii）元件的非活塞式振动，（iv）施加相位的量化，（v）每个元件的空间定位误差；以及（vi）元件间的交叉耦合。通过使用由 64 个（2^6）模拟组成的完全因子实验设计，分析了每个因素的独立影响和多个因素之间的相互作用。结果表明，元件的非活塞式运动可能是测量和建模场之间差异的主要原因。确定阵列中元件的确切振动模式很复杂，需要进行全有限元分析。然而，本工作中考虑的简单振动模式，对应于在元件中心添加起源并径向传播的表面瑞利波，产生的模拟结果与测量数据非常吻合。
