A coupled immersed boundary-lattice Boltzmann approach for simulating the acoustic response of nonspherical encapsulated microbubbles

Encapsulated microbubbles (EMBs) are utilized intravenously in biomedicine to enhance ultrasound imaging and drug delivery, and are activated by ultrasound. EMBs consist of a gas core encased in a thin, viscoelastic shell and are suspended in a viscous liquid, making the simulation of their acoustic response a challenging multiphase flow problem. When exposed to ultrasound, EMBs can exhibit both volumetric (spherical) and shape (nonspherical) oscillations. In this work, we employ a multicomponent multiphase lattice Boltzmann method (LBM) to simulate the fluid dynamics inside and outside the bubble, and couple it with the immersed boundary (IB) method to model the interaction between the encapsulation and the surrounding fluids. This combined IB-LBM framework tracks Lagrangian markers positioned on the bubble interface to capture the surface deformation and permits the modeling of nonspherical behavior, which arises due to the oscillation of EMBs near the endothelial surface of blood vessels and is important for enhancing both diagnostic and therapeutic effects. The mechanical influence of the encapsulating shell on the fluid domains is represented using a viscoelastic constitutive model integrated into the solver. We validate the IB-LBM simulations of the EMB behavior under both step and sinusoidal far-field pressures by comparing them with a modified Rayleigh-Plesset equation and other relevant data in the literature. The effects of shell elasticity, viscosity, and interior gas on the acoustic response of the bubbles are investigated.