Prediction of rectified diffusion during nonlinear bubble pulsations at biomedical frequencies.

A computer study of rectified diffusion was made over the biomedical frequency range (1-10 MHz). Solutions of the Gilmore-Akulichev [E. Cramer, in Cavitation and Inhomogeneities in Underwater Acoustics, edited by W. Lauterborn (Springer, New York, 1980), pp. 54-63] formulation for bubble dynamics were combined with the Eller-Flynn [A. Eller and H.G. Flynn, J. Acoust. Soc. Am. 37, 493-503 (1965)] approach to rectified diffusion in order to calculate thresholds and growth rates. It is found that: (1) for frequencies above 1 MHz, the widely held view that small bubbles grow by rectified diffusion to "resonance size" and then collapse violently is true only for narrow ranges of bubbles; (2) growth rates in the low megahertz range can be quite high for medically relevant pressures, approximately 20 micron/s at 1 MHz, 1 bar; (3) thresholds derived analytically are accurate for low frequencies over a wide range of bubble radii but, for high frequencies, only near the fundamental resonance radius; and (4) thresholds are quite sensitive to dissolved gas concentration at low frequencies.