Three-dimensional numerical analysis of wall stress induced by asymmetric oscillation of microbubble trains inside micro-vessels

Understanding the stress patterns produced by microbubbles (MB) in blood vessels is important in enhancing the efficacy and safety of ultrasound-assisted therapy, diagnosis, and drug delivery. In this study, the wall stress produced by the non-spherical oscillation of MBs within the lumen of micro-vessels was numerically analyzed using a three-dimensional finite element method. We systematically simulated configurations containing an odd number of bubbles from three to nine, equally spaced along the long axis of the vessel, insonated at an acoustic pressure of 200 kPa. We observed that 3 MBs were sufficient to simulate the stress state of an infinite number of bubbles. As the bubble spacing increased, the interaction between them weakened to the point that they could be considered to act independently. In the relationship between stress and acoustic frequency, there were differences between the single and 3 MB cases. The stress induced by 3 MBs was greater than the single bubble case. When the bubbles were near the wall, the shear stress peak was largely independent of vessel radius, but the circumferential stress peak increased with the radius. This study offers further insight into our understanding of the magnitude and distribution of stresses produced by multiple ultrasonically excited MBs inside capillaries.