Mechanisms of microbubble–vessel interactions and induced stresses: A numerical study

Abstract

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.

A two-criterion model for microvascular bioeffects induced in vivo by contrast microbubbles exposed to medical ultrasound

“…First, the range in values for air bubbles is 0.76 -2.34 µm. This range encompasses the bubble radii studied by Hosseinkhah and Hynynen (2012) and Hosseinkhah et al (2013), providing support for their results as well as suggesting that it may prove profitable to extend their approach to include the rate of strain in the search for an understanding of the mechanism for capillary rupture. It is interesting to note that rate of strain is an important parameter in the failure of viscoplastic materials, e.g., Silly Putty ® .…”

“…While the changes in the radii of curvature (radial and axial) are rather small during bubble expansion, they can be much larger during the collapse phase. The small radius of curvature that obtains during the invagination of the vessel wall, shown in some detail in the photomicrographs and movies acquired by Chen et al (2011), tends to maximize the stress and strain within the wall Hosseinkhah et al 2013), potentially leading directly to its failure. The role of liquid jetting is less clear.…”

“…process would first create moderate outward stress, followed by strong inward stress and invagination possibly comparable to that observed by Hosseinkhah et al (2013). The threshold acoustic pressure p t , is taken as the lowest value required to satisfy both criteria for any bubble radius in the range investigated.…”

“…Once this is accomplished, the capillary wall is sufficiently flexible that it will "follow" the radial motion of the bubble and thus allow little or no fluid to reinsert itself between the bubble and capillary wall. This assumption is based on the results of Hosseinkhah and Hynynen (2012) and Hosseinkhah et al (2013) who modeled the responses of bubbles in capillaries of various sizes. In general, they found that the shear stress was greater when the ratio of the bubble radius to the vessel radius was larger, and the circumferential stress was largest when the bubble wall was closest to the vessel wall.…”

“…This bioeffect is readily observable, of clear biological significance and serves as the threshold of concern for patient risk. While the modeling of specific mechanisms of capillary injury, such as capillary stretching (Qin and Ferrara, 2006;Miao et al 2008), vessel invagination (Hosseinkhah et al 2013), jet impingement (Chen et al 2011), and fluid stress (Hosseinkhah et al 2015), and possibly others, is an ultimate goal, such modeling likely would require extensive detailed theoretical analysis by three-dimensional finite-amplitude methods for any full accounting of the complex microbubble-capillary problem. Here, we pursue the general approach of the MI which was based primarily on theoretical microbubble behavior in an effort to obtain general insights into the problem.…”