On ultrasound-induced microbubble oscillation in a capillary blood vessel and its implications for the blood–brain barrier

Abstract

The complex interaction between an ultrasound-driven microbubble and an enclosing capillary microvessel is investigated by means of a coupled, multidomain numerical model using the finite volume formulation. This system is of interest in the study of transient blood-brain barrier disruption (BBBD) for drug delivery applications. The compliant vessel structure is incorporated explicitly as a distinct domain described by a dedicated physical model. Red blood cells (RBCs) are taken into account as elastic solids in the blood plasma. We report the temporal and spatial development of transmural pressure (P tm ) and wall shear stress (WSS) at the luminal endothelial interface, both of which are candidates for the yet unknown mediator of BBBD. The explicit introduction of RBCs shapes the P tm and WSS distributions and their derivatives markedly. While the peak values of these mechanical wall parameters are not affected considerably by the presence of RBCs, a pronounced increase in their spatial gradients is observed compared to a configuration with blood plasma alone. The novelty of our work lies in the explicit treatment of the vessel wall, and in the modelling of blood as a composite fluid, which we show to be relevant for the mechanical processes at the endothelium.

The breakup of intravascular microbubbles and its impact on the endothelium

“…The magnitude of P tm and τ wss observed prior to MB shell breakup agrees with values previously derived with different models (Hosseinkhah and Hynynen 2012;Wiedemair et al 2012). Post-rupture wall parameter levels are in the same range as reported by (Hosseinkhah et al 2015) using a different numerical approach and a model equivalent in complexity to Setup I.…”

“…The transient problem is treated in a time-marching manner with uniform time step size and an implicit, second-order accurate time integration scheme (Ferziger and Peric 1995). Wiedemair et al (2012) provides details on the employed coupling algorithm and a thorough description of the solid and fluid modelling, including the formulations of constitutive equations as well as references to model derivation.…”

“…Validation studies for both methods have been performed and are provided in Wiedemair et al (2012) and Wiedemair et al (2014), respectively. A validation of the novel generalized IFT algorithm for scalable viscoelastic shell properties is provided in the "Appendix" section, where we established close correspondence of numerically determined results with analytical predictions from Eq.…”

“…The oscillation of MBs in flexible, plain tubes (Ye and Bull 2006) was studied, and lumped parameter solid models allowed investigation of the interaction of MBs with compliant microvessels (MVs) of variable size (Qin and Ferrara 2006). The mechanical stresses at the endothelial interface were assessed using coupled solid and fluid models (Hosseinkhah et al 2013;Wiedemair et al 2012). The breakup of MBs near rigid walls (Hsiao and Chahine 2013) and inside MVs (Hosseinkhah et al 2015) was also studied numerically.…”

Microbubbles and Blood–Brain Barrier Opening: A Numerical Study on Acoustic Emissions and Wall Stress Predictions

“…However, this experiment was performed in static conditions without bubbles. The stresses calculated from other numerical simulations [32] are in the same order of magnitude as those reported in the current study. Furthermore, our bubble model was validated previously with experimental data, in which vessel wall movements were measures and resultant vascular wall stresses were calculated [16].…”