Nonlinear Derating of High-Intensity Therapeutic Ultrasound Beams Using Gaussian Modal Sums

High intensity focused ultrasound (HIFU) is a noninvasive medical procedure during which a large amount of energy is deposited in a short duration which causes sudden localized rise in tissue temperature, and ultimately, cell necrosis. In assessing the influence of HIFU on biological tissue, semi-empirical mathematical models can be useful for predicting thermal effects. These models require values of the pressure amplitude in the tissue of interest, which can be difficult to obtain experimentally. One common method for estimating the pressure amplitude in tissue is to operate the HIFU transducer in water, measure the pressure amplitude, then multiply by a scaling factor that accounts for the difference in attenuation between water and tissue. This procedure can be accurate when the ultrasound amplitude is low, and the pressure trace in tissue is proportional to that in water. Because of this proportionality, the procedure for reducing the amplitude from water to tissue is called linear derating. At higher intensities, however, harmonics of the fundamental frequency are generated due to nonlinear propagation effects. Higher harmonics are attenuated differently in water and tissue (Hamilton and Blackstock [1]), and the pressure waves in water and tissue are no longer proportional to one another. Techniques for nonlinearly transforming pressure amplitudes measured in water to values appropriate for tissue are therefore desirable when bioeffects of higher intensity procedures are being studied. These techniques are labeled “nonlinear derating”.