Shear stress induced by a gas bubble pulsating in an ultrasonic field near a wall

Some of the effects that therapeutic ultrasound has in medicine and biology may be associated with steady oscillations of gas bubbles in liquid, very close to tissue surface. The bubble oscillations induce on the surface steady shear stress attributed to microstreaming. A mathematical simulation of the problem for both free and capsulated bubbles, known as contrast agents, is presented here. The simulation is based on a solution of Laplace´s equation for potential flow and existing models for microstreaming. The solution for potential flow was obtained numerically using a boundary integral method. The solution provides the evolution of the bubble shape, the distribution of the velocity potential on the surface, and the shear stress along the surface. The simulation shows that significant shear stresses develop on the surface when the bubble bounces near the tissue surface. In this case, pressure amplitude of 20 kPa generates maximal steady shear stress of several kilo Pascal. Substantial shear stress on the tissue surface takes place inside a circular zone with a radius about half of the bubble radius. The predicted shear stress is greater than stress that causes hemolysis in blood and several orders of magnitude greater than the physiological stress induced on the vessel wall by the flowing blood.