Model for an encapsulated microbubble using transient network theory*

Encapsulated microbubbles (EMBs) are widely used to enhance contrast in ultrasound sonography and are finding increasing use in biomedical therapies such as drug/gene delivery and tissue ablation. EMBs consist of a gas core surrounded by a shell made of protein, polymer, or lipid. We present a novel model for an EMB based on a statistically-based continuum theory for the encapsulating material using transient networks. The use of transient network theory provides a general framework that allows a variety of viscoelastic shell materials to be simulated, including a purely elastic solid or a viscous fluid. The model permits local stress in the shell to be calculated, and can be readily extended to modeling nonspherical EMB deformations. The model accurately reproduces the experimentally-measured radial response of an ultrasonically-driven, spherical, lipid-coated microbubble, and provides a better fit than that given by common spherical EMB models by Marmottant et al., Chatterjee and Sarkar, and Hoff. Extensions of the model to nonspherical EMB oscillations are discussed.