Optimum acoustic frequency for focused ultrasound surgery

A model is described that enables calculation of ultrasound lesioning rate (inverse of time to achieve a threshold lesion in the absence of thermal redistribution) as a function of acoustic frequency, tissue penetration depth, d, attenuation coefficient at specific frequency, mu, and power of dependence of attenuation on frequency, n. Two acoustic power conditions are considered: unlimited power, and power limited by the material properties of the transducer and the constraint that its dimensions be scaled to tissue penetration depth. Optimum frequencies for these two conditions are found to be, respectively, [(2 + n)/n mu d]1/n and [(3 - n)/n mu d]1/n. The tissue path attenuation, for both conditions, is independent of frequency, with a value of approximately 10 dB. Values of predicted lesioning rates under optimum frequency conditions are presented, and the likely constraints imposed by cavitation and propagation nonlinearity are considered.