Amplitude and phase relation of harmonics in nonlinear focused ultrasound

High intensity focused ultrasound has gained rapid clinical acceptance as a noninvasive treatment for solid tumors. As implied by the name, the intensity of sound at the focus is generally large. In a nonlinear ultrasound field, where the acoustic spectrum contains a considerable spread of harmonics, the pressure waveform is asymmetrically distorted, with a discrepancy between the peak compressional pressure and the peak rarefactional pressure, which are required in FDA and IEC regulations. Therefore, the amplitude and phase of the harmonics matter. In order to better understand nonlinear focused ultrasound, the amplitude and phase relation of the harmonics are investigated through both numerical simulations and measurements. The first three harmonics are extracted from the distorted wave by a zero-phase band-pass filter. It is demonstrated that, as the source pressure increases, the focusing gain for the fundamental component tends to decrease while the focusing gains for the second and third harmonics rise. The relative phases show very little change. There is a substantive agreement between the simulated and measured results for the focusing gain of the harmonics. The relative phase of the harmonics needs to be further verified after the calibration of the phase response of the hydrophone is well-developed.