A Newtonian rheological model for the interface of microbubble contrast agents

Abstract

A quantitative model of the dynamics of an encapsulated microbubble contrast agent will be a valuable tool in contrast ultrasound (US). Such a model must have predictive ability for widely varying frequencies and pressure amplitudes. We have developed a new model for contrast agents, and successfully investigated its applicability for a wide range of operating parameters. The encapsulation is modeled as a complex interface of an infinitesimal thickness. A Newtonian rheology with surface viscosities and interfacial tension is assumed for the interface, and a modified Rayleigh-Plesset equation is derived. The rheological parameters (surface tension and surface dilatational viscosity) for a number of contrast agents (Albunex, Optison and Quantison) are determined by matching the linearized model dynamics with experimentally obtained attenuation data. The model behavior for Optison (surface tension 0.9 N/m and surface dilatational viscosity 0.08 msP) was investigated in detail. Specifically, we have carried out a detailed interrogation of the model, fitted in the linear regime, for its nonlinear prediction. In contrast to existing models, the new model is found to capture the characteristic subharmonic emission of Optison observed by. A detailed parametric study of the bubble behavior was executed using the ratio of scattering to attenuation (STAR). It shows that the encapsulation drastically reduces the influence of resonance frequency on scattering cross-section, suggesting possible means of improvement in imaging at off-resonant frequencies. The predictive capability of the present model indicates that it can be used for characterizing different agents and designing new ones.