Focused ultrasound transducer spatial peak intensity estimation: a comparison of methods

Characterisation of the spatial peak intensity at the focus of high intensity focused ultrasound transducers is difficult because of the risk of damage to hydrophone sensors at the high focal pressures generated. Hill et al (1994 Ultrasound Med. Biol. 20 259-69) provided a simple equation for estimating spatial-peak intensity for solid spherical bowl transducers using measured acoustic power and focal beamwidth. This paper demonstrates theoretically and experimentally that this expression is only strictly valid for spherical bowl transducers without a central (imaging) aperture. A hole in the centre of the transducer results in over-estimation of the peak intensity. Improved strategies for determining focal peak intensity from a measurement of total acoustic power are proposed. Four methods are compared: (i) a solid spherical bowl approximation (after Hill et al 1994 Ultrasound Med. Biol. 20 259-69), (ii) a numerical method derived from theory, (iii) a method using measured sidelobe to focal peak pressure ratio, and (iv) a method for measuring the focal power fraction (FPF) experimentally. Spatial-peak intensities were estimated for 8 transducers at three drive powers levels: low (approximately 1 W), moderate (~10 W) and high (20-70 W). The calculated intensities were compared with those derived from focal peak pressure measurements made using a calibrated hydrophone. The FPF measurement method was found to provide focal peak intensity estimates that agreed most closely (within 15%) with the hydrophone measurements, followed by the pressure ratio method (within 20%). The numerical method was found to consistently over-estimate focal peak intensity (+40% on average), however, for transducers with a central hole it was more accurate than using the solid bowl assumption (+70% over-estimation). In conclusion, the ability to make use of an automated beam plotting system, and a hydrophone with good spatial resolution, greatly facilitates characterisation of the FPF, and consequently gives improved confidence in estimating spatial peak intensity from measurement of acoustic power.