Analytical and numerical calculations of optimum design frequency for focused ultrasound therapy and acoustic radiation force

Focused ultrasound therapy relies on acoustic power absorption by tissue. The stronger the absorption the higher the temperature increase is. However, strong acoustic absorption also means faster attenuation and limited penetration depth. Hence, there is a trade-off between heat generation efficacy and penetration depth. In this paper, we formulated the acoustic power absorption as a function of frequency and attenuation coefficient, and defined two figures of merit to measure the power absorption: spatial peak of the acoustic power absorption density, and the acoustic power absorbed within the focal area. Then, we derived "rule of thumb" expressions for the optimum frequencies that maximized these figures of merit given the target depth and homogeneous tissue type. We also formulated a method to calculate the optimum frequency for inhomogeneous tissue given the tissue composition for situations where the tissue structure can be assumed to be made of parallel layers of homogeneous tissue. We checked the validity of the rules using linear acoustic field simulations. For a one-dimensional array of 4cm acoustic aperture, and for a two-dimensional array of 4×4cm(2) acoustic aperture, we found that the power absorbed within the focal area is maximized at 0.86MHz, and 0.79MHz, respectively, when the target depth is 4cm in muscle tissue. The rules on the other hand predicted the optimum frequencies for acoustic power absorption as 0.9MHz and 0.86MHz, respectively for the 1D and 2D array case, which are within 6% and 9% of the field simulation results. Because radiation force generated by an acoustic wave in a lossy propagation medium is approximately proportional to the acoustic power absorption, these rules can be used to maximize acoustic radiation force generated in tissue as well.