Modeling of acoustically enhanced bubble growth in supersaturated biological media

Abstract

Recent measurements and predictions of dissolved nitrogen concentration in tissues of dolphins and whales following repeated dives have indicated that the gas concentration may reach 300% of saturation [Houser et al., ‘‘Can diving-induced tissue nitrogen supersaturation increase the chance of acoustically driven bubble growth in marine mammals?,’’ J. Theor. Biol. 213, 183–195 (2001)]. This has generated renewed interest in whether underwater sound may increase the likelihood of decompression sickness in these cetaceans. One potential mechanism is bubble growth due to rectified diffusion. Eller and Flynn [‘‘Rectified diffusion during nonlinear pulsations of cavitation bubbles,’’ J. Acoust. Soc. Am. 37, 493–503 (1965)] modeled rectified diffusion by solving a Rayleigh-Plesset equation for the acoustically driven bubble dynamics, coupled to a quasianalytical diffusion model that accounts for increase of the equilibrium bubble radius. Crum and Mao [‘‘Acoustically enhanced bubble growth at low frequencies and its implications for human diver and marine mammal,’’ J. Acoust. Soc. Am. 99, 2898–2907 (1996)] used similar models to consider dissolved gas saturations up to 223% and demonstrated significantly enhanced bubble growth at sound-pressure levels above 210 dB (re: 1 μPa). We are revisiting this problem by extending these models and considering wider ranges of parameters. A principal difference is that the gas diffusion is modeled by solving the full partial differential equation numerically. Not only does this approach circumvent analytical approximations, it permits taking into account variations in gas concentration associated with dive-profile-dependent hydrostatic pressure variations. [Work supported by ONR.]