A numerical investigation of the resonance of gas-filled microbubbles: resonance dependence on acoustic pressure amplitude

The general Keller-Herring equation for free gas bubbles is augmented by specific terms to describe the elasticity, viscosity and thickness of the encapsulating shell in ultrasound contrast agent microbubbles. A numerical investigation that analyses the acoustic backscatter from bubbles is employed to identify resonance frequencies that can be compared, for increasing driving pressure amplitude, with linear approximations obtained via analytical considerations. Calculations for bubbles of the size employed in diagnostic ultrasound, between 2 and 6 mum diameter, that are immersed in water and blood and exposed to monochromatic insonation, causing the bubbles to undergo stable cavitation, reveal that the resonance frequency diverges from the linear approximation as the pressure amplitude is increased. The shift in resonance, to lower frequency values, is found to be more pronounced for larger bubbles with the calculated value differing by up to 40% from the linear approximation. The results of this simulation might be potentially useful in preparation of formulations of ultrasound contrast agents with the specifically desired features, such as for instance resonance frequency.