Maxwell rheological model for lipid-shelled ultrasound microbubble contrast agents

The present paper proposes a model that describes the encapsulation of microbubble contrast agents by the linear Maxwell constitutive equation. The model also incorporates the translational motion of contrast agent microbubbles and takes into account radiation losses due to the compressibility of the surrounding liquid. To establish physical features of the proposed model, comparative analysis is performed between this model and two existing models, one of which treats the encapsulation as a viscoelastic solid following the Kelvin-Voigt constitutive equation and the other assumes that the encapsulating layer behaves as a viscous Newtonian fluid. Resonance frequencies, damping coefficients, and scattering cross sections for the three shell models are compared in the regime of linear oscillation. Translational displacements predicted by the three shell models are examined by numerically calculating the general, nonlinearized equations of motion for weakly nonlinear excitation. Analogous results for free bubbles are also presented as a basis to which calculations made for encapsulated bubbles can be related. It is shown that the Maxwell shell model possesses specific physical features that are unavailable in the two other models.