Abstract
A model for the contrast agent Sonazoid is presented. The model is based on a modified Rayleigh–Plesset equation, with the shell added as an incompressible viscoelastic solid. Different models for the shell’s nonlinear stress–strain relationship are discussed. Shell elasticity and viscosity were estimated from experiments, and the model was used to simulate bubble radius and scattered sound. Pulse-inversion imaging was simulated. The amplitude was increased from 20 to 500 kPa, giving scattered pulses that changed from inverted to time-shifted versions of each other. This effect was best seen in the cross correlation of the responses. The nonlinear response was strongest for frequencies below bubble resonance. Compared to unshelled bubbles, Sonazoid required higher drive amplitudes to respond nonlinearly. The Sonazoid bubbles responded similarly to unshelled bubbles of smaller diameter. A subharmonic response was found in a limited frequency band and only for diameters above 3 μm. An amplitude threshold was found around 500 kPa, depending on diameter and frequency. This threshold is higher than for unshelled bubbles. A chaotic oscillation pattern was found for some diameter–frequency combinations, in agreement with published results. For some situations where the cw results predicted a subharmonic mode, this mode was not obtained from finite-length pulses.
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