An analysis of the origin of differences between measured and simulated fields produced by a 15-element ultrasound...

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.