Modeling nonlinear scattering of phospholipid-coated microbubbles in elastic media

Microbubble contrast agents are well-known in the biomedical field for their ability to enhance the contrast in ultrasound imaging and to facilitate targeted drug delivery within the body. Upon injection into the vasculature, these bubbles are strongly influenced by the viscoelastic properties of surrounding soft tissues. Here, we simulate the scattered pressure from a single phospholipid-coated microbubble placed in a uniform viscoelastic medium. We use a modified Rayleigh-Plesset equation that incorporates the viscoelastic response of the phospholipid shell and a Kelvin-Voigt model to represent tissue viscoelasticity. Our simulations aim to investigate the relationship between the viscoelasticity of the medium and that of the bubble shell, and its influence on bubble dynamics as a function of driving pressure, bubble radius, and medium elastic modulus. Results show that the frequency of maximum scatter response increases with the elastic modulus of the medium. While the radial excursion of a 2.0μm radius bubble can decrease by as much as 45% in a medium with an elastic modulus of 200 kPa as compared to that in water, the scattered pressure can increase by 50%. In contrast, the change in harmonic scattering is negligible: simulations predict a increase of only 5% for a 2.0μm bubble when increasing the medium elasticity from 0 to 200 kPa at a driving pressure of 120 kPa. Furthermore, subharmonics generated by driving the bubble at its resonance frequency (TR) are comparable to the subharmonics generated at twice the resonance frequency at lower driving pressures. For elevated pressures the TR/T2R subharmonic ratio increases with increasing elastic modulus. This is in sharp contrast with the resonance behavior of a microbubble in water. These results bear consequences for strategies that exploit the fundamental, harmonic, and subharmonic response of microbubble contrast agents.