3D FEA model for quantifying bound/free microbubble: Displacement, stress, and resonance frequencies

Molecularly targeted ultrasound contrast agents provide for the potential to form an image responsive to early expression of molecular pathology in vivo and ex vivo. While 1D models are routinely employed to estimate the dynamics of the microbubbles for imaging and therapeutic applications, these models are incapable of capturing asymmetric microbubble behavior or space-variant mechanical properties of microbubble´s shell. Additionally, information arising from asymmetric boundary conditions may provide insight into multiple microbubble interaction, and microbubble cavitation limits. In this work, we apply a previously reported 3D FEA model to quantify the difference between free/adherent microbubbles behavior and propose a shell stress/strain bounds hypothesis for estimating the free/adherent microbubble cavitation threshold. From 3D FEA simulations and high-speed camera experiments, it is concluded that linear and non-linear temporal variation in shell stress/strain (as a function of insonation pressure) is an indicator of stable and unstable microbubble oscillation regime. Furthermore, it is also inferred that adherent microbubbles have higher thresholds for unstable cavitation than free microbubbles. Additionally, adherent microbubbles are predicted to possess higher natural resonance frequencies than free microbubbles of similar sizes.