Microbubbles and blood-brain barrier opening: a numerical study on acoustic emissions and wall stress predictions

Focused ultrasound with microbubbles is an emerging technique for blood-brain barrier opening. Here, a comprehensive theoretical model of a bubble-fluid-vessel system has been developed which accounts for the bubble's nonspherical oscillations inside a microvessel, and its resulting acoustic emissions. Numerical simulations of unbound and confined encapsulated bubbles were performed to evaluate the effect of the vessel wall on acoustic emissions and vessel wall stresses. Using a Marmottant shell model, the normalized second harmonic to fundamental emissions first decreased as a function of pressure (>50 kPa) until reaching a minima ("transition point") at which point they increased. The transition point of unbound compared to confined bubble populations occurred at different pressures and was associated with an accompanying increase in shear and circumferential wall stresses. As the wall stresses depend on the bubble to vessel wall distance, the stresses were evaluated for bubbles with their wall at a constant distance to a flat wall. As a result, the wall stresses were bubble size and frequency dependent and the peak stress values induced by bubbles larger than resonance remained constant versus frequency at a constant mechanical index.