Formulas for Maximum Appropriate Hydrophone Sensitive Element Size and Hydrophone Spatial Averaging Correction Factors for Therapeutic Ultrasound System Characterization

Therapeutic ultrasound devices can generate beams that are tightly focused or very nonlinear or both. When these beams are detected with hydrophones, pressure measurements are reduced due to spatial averaging of the incident pressure field across the phase sensitive hydrophone active element. Numerical simulations were conducted for 9 spherically focused transducers, with center frequencies ranging from 1 to 10 MHz and F numbers (ratio of focal length to diameter) ranging from 1.4 to 3.2. The simulated transducers were subjected to 6 levels of transmit voltage, resulting in a 6 levels of beam nonlinearity ranging from low to high harmonic content. The beams were detected with 8 different simulated hydrophones, one at a time, at the focal point. Simulation code was tested with experiments performed using 7 spherically focused transducers, with frequencies ranging from 2 to 10 MHz and F numbers ranging from 1 to 3. Five hydrophones were used, one at a time, to measure beam pressures at the focal point. Formulas were derived to mitigate measurement errors due to spatial averaging. These formulas are briefly summarized in Appendix A of [1]. Formulas for maximum acceptable active element diameter as functions of required measurement accuracy were also obtained [1]. While the commonly used IEC formula for maximum acceptable active element diameter [2] is based on linear beams from planar sources, the new formulas apply to both linear and nonlinear beams from focused sources. Therefore, the new formulas are more suitable for therapeutic ultrasound.