Mathematical modeling of microbubble cavitation at 70 kHz and the importance of the subharmonic in drug delivery from micelles

In order to gain insight into the experimental observation of ultrasound-induced release of drugs from micelles, we modeled the dynamic oscillations of a 10-μm-diameter bubble insonated at 70 kHz. The Parlitz modification of the Keller–Miksis model was employed to generate bubble dynamics over a wide range of mechanical index values. The resulting Poincaré maps and bifurcation diagram show that bubble oscillations bifurcate at a MI value of 0.32, then return apparently to a single mode before displaying a sudden onset of chaotic behavior at 0.35. The experimental release of drug from micelles occurs at a MI value of 0.37 and correlates with the intensity of the subharmonic in (μW/cm²) of the acoustic spectrum. The dynamic model shows the return to single mode at a MI value of 0.43, and bifurcation leading to chaos at values above 0.5. The correlation between the chaotic behavior predicted by the model and drug release hints at insonation conditions that could facilitate drug delivery.