Ultrasound contrast agents inside a microvessel, when driven by ultrasound, oscillate and induce mechanical stresses on the vessel wall. These mechanical stresses can produce beneficial therapeutic effects but also induce vessel rupture if the stresses are too high. Therefore, it is important to use sufficiently low pressure amplitudes to avoid rupturing the vessels while still inducing the desired therapeutic effects. In this work, we developed a comprehensive three dimensional model of a confined microbubble inside a vessel while considering the bubble shell properties, blood viscosity, vessel wall curvature and the mechanical properties of the vessel wall. Two bubble models with the assumption of a spherical symmetric bubble and a simple asymmetrical bubble were simulated. This work was validated with previous experimental results and enabled us to evaluate the microbubbles’ behaviour and the resulting mechanical stresses induced on the vessel walls. In this study the fluid shear and circumferential stresses were evaluated as indicators of the mechanical stresses. The effects of acoustical parameters, vessel viscoelasticity and rigidity, vessel/bubble size and off-center bubbles on bubble behaviour and stresses on the vessel were investigated. The fluid shear and circumferential stresses acting on the vessel varied with time and location. As the frequency changed, the microbubble oscillated with the highest amplitude at its resonance frequency which was different from the resonance frequency of an unbound bubble. The bubble resonance frequency increased as the rigidity of a flexible vessel increased. The fluid shear and circumferential stresses peaked at frequencies above the bubble’s resonance frequency. The more rigid the vessels were, the more damped the bubble oscillations. The synergistic effect of acoustic frequency and vessel elasticity had also been investigated, since the circumferential stress showed either an increasing trend or a decreasing one versus the vessel rigidity at difference acoustic frequencies. When the acoustic pressure was increased from 52 kPa to 680 kPa, the maximum bubble radius increase by 2.5 folds and the maximum shear and circumferential stress increased by 15.7 and 18.3 folds respectively. The shear stress was largest when the acoustic frequency was higher (3.25 MHz) and the ratio of the vessel radius to the bubble radius was lower. The circumferential stress was largest when the bubble wall was closer to the vessel wall. An oscillating off-center bubble forms a mushroom shape with the most damping on the points closest to the vessel wall.
Oscillating microbubbles within microvessels could induce stresses that lead to bioeffects or vascular damage. Previous work has attributed vascular damage to the vessel expansion or bubble jet. However, ultra-high speed images of recent studies suggest that it could happen due to the vascular invagination. Numerical simulations of confined bubbles could provide insight into understanding the mechanism behind bubble-vessel interactions. In this study, a finite element model of a coupled bubble/fluid/vessel system was developed and validated with experimental data. Also, for a more realistic study viscoelastic properties of microvessels were assessed and incorporated into this comprehensive numerical model. The wall shear stress (WSS) and circumferential stress (CS), metrics of vascular damage, were calculated from these simulations. Resultant amplitudes of oscillation were within 15% of those measured in experiments (four cases). Among the experimental cases, it was numerically found that maximum WSS values were between 1.1-18.3 kPa during bubble expansion and 1.5-74 kPa during bubble collapse. CS was between 0.43-2.2 MPa during expansion and 0.44-6 MPa while invaginated. This finding confirmed that vascular damage could occur during vascular invaginations. Predicted thresholds in which these stresses are higher during vessel invagination were calculated from simulations.
Focused ultrasound with microbubbles is an emerging technique for blood brain barrier (BBB) opening. Here, a comprehensive theoretical model of a bubble-fluid-vessel system has been developed which accounts for the bubble’s non-spherical 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.
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