A model for the dynamics of ultrasound contrast agents in vivo

The Rayleigh-Plesset (RP) equation for a clean gas bubble in an incompressible and infinite liquid has previously been applied to approximately simulate the behavior of ultrasound contrast agents (UCA) in vivo, and extended RP equations have been proposed to account for the effects of the UCA shell or surrounding soft tissue. These models produce results that are consistent with experimental measurements for low acoustic pressure scenarios. For applications of UCAs in therapeutic medicine, the transmitted acoustic pulse can have a peak negative pressure (PNP) up to a few megapascals, resulting in discrepancies between measurements and predictions using these extended RP equations. Here, a model was developed to describe the dynamics of UCAs in vivo while taking account of the effects of liquid compressibility, the shell and the surrounding tissue. Liquid compressibility is approximated to first order and the shell is treated either as a Voigt viscoelastic solid or a Newtonian viscous liquid. Finite deformation of the shell and tissue is derived. Dynamics of UCAs with a shell of lipid, polymer, albumin and liquid are investigated for typical therapeutic ultrasound pulses. The effects of liquid compressibility and shell and tissue parameters are analyzed.