Krasovitski Boris, Kimmel Eitan
Technion, Biomedical Engineering, Haifa, Israel.
IEEE Trans Ultrason Ferroelectr Freq Control. 2004 Aug;51(8):973-9. doi: 10.1109/tuffc.2004.1324401.
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.
治疗性超声在医学和生物学中的一些效应可能与液体中非常靠近组织表面的气泡的稳态振荡有关。气泡振荡在表面诱导出归因于微流的稳态剪应力。本文给出了对自由气泡和封装气泡（即造影剂）问题的数学模拟。该模拟基于势流的拉普拉斯方程的解以及现有的微流模型。势流的解通过边界积分法数值获得。该解给出了气泡形状的演变、表面速度势的分布以及沿表面的剪应力。模拟表明，当气泡在组织表面附近反弹时，表面会产生显著的剪应力。在这种情况下，20 kPa的压力振幅会产生几kPa的最大稳态剪应力。组织表面的大量剪应力发生在半径约为气泡半径一半的圆形区域内。预测的剪应力大于导致血液溶血的应力，并且比流动血液在血管壁上诱导的生理应力大几个数量级。
