A 3D nonlinear FEA model for simulation of microbubble behavior

Abstract

Microbubbles provide the basis for perfusion measurement, early detection of molecular signatures of disease and as a vehicle for drug, or gene, delivery. Although the response of a single microbubble to ultrasound has been characterized by radially symmetric 1D models and high speed camera-based experiments, a plethora of mechanisms, such as bubble-bubble interaction, and adherent bubble response are poorly understood. With few exceptions, 1D model are generally valid at moderate acoustic pressures, but are incapable of predicting phenomena such as higher order mode oscillations or onset of bubble shell rupture. It has been hypothesized that second or higher order mode oscillations are a precursor to bubble shell rupture and subsequent cavitation. In addition, parameters, such as shell stress and shell strain may have threshold values related to bubble shell fracture. In this work, we propose a full 3D FEA (finite element analysis) model that can simulate temporal variations in asymmetric 3D radial, translational bubble motion, various shell parameters such as regional stress /strain, and bubble pulse echo response. Preliminary simulations were conducted to assess the performance of the model for broadband cases, including: 1) single cycle pulse excitation, 2) single cycle of free and wall-bound bubble, 3) predicting translational displacements in response to primary radiation force, and 4) tracking variations in shell stresses and strain for low (180 KPa) and high (330 KPa) peak negative pressure acoustic waveforms. For the acoustic and bubble parameters published by Dayton, the maximum displacement predicted using the 3D FEA model was within 10% of the previously published experimental data. For approximately similar bubble and acoustic parameters (using inverted pulses), the spectrum of the backscattered data from a free bubble was found to be similar to the experimental and simulated results The spectrum of the adherent bubble response was found to be downshifted with respect to that of a free bubble; similar results have been reported by Payne et al . The adherent bubble was found to oscillate asymmetrically in the planes orthogonal to the azimuth-elevation plane or the plane perpendicular to the face of the transducer (edge of the model where an external pulse is applied).