Freund Jonathan B
Mechanical Science and Engineering and Aerospace Engineering, University of Illinois at Urbana-Champaign, 1206 West Green Street MC-244, Urbana, Illinois 61801, USA.
J Acoust Soc Am. 2008 May;123(5):2867-74. doi: 10.1121/1.2902171.
Estimates are made of the effect of tissue confinement on the response of small bubbles subjected to lithotriptor shock pressures. To do this the Rayleigh-Plesset equation, which governs the dynamics of spherical bubbles, is generalized to treat a bubble in a liquid region (blood), which is in turn encased within an elastic membrane (like a vessel's basement membrane), beyond which a Voigt viscoelastic material models the exterior tissue. Material properties are estimated from a range of measurements available for kidneys and similar soft tissues. Special attention is given to the constitutive modeling of the basement membranes because of their expected importance due to their proximity to the bubble and their toughness. It is found that the highest expected values for the elasticity of the membrane and surrounding tissue are insufficient to suppress bubble growth. The reduced confinement of a cylindrical vessel should not alter this conclusion. Tissue viscosities taken from ultrasound measurements suppress bubble growth somewhat, though not to a degree expected to resist injury. However, the higher reported viscosities measured by other means, which are arguably more relevant to the deformations caused by growing bubbles, do indeed significantly suppress bubble expansion.
研究人员对组织限制对承受碎石机冲击压力的小气泡响应的影响进行了估算。为此，对控制球形气泡动力学的瑞利 - 普莱斯方程进行了推广，以处理处于液体区域（血液）中的气泡，该液体区域又被包裹在弹性膜（如血管基底膜）内，弹性膜之外则用沃伊特粘弹性材料来模拟外部组织。材料特性是根据一系列可用于肾脏及类似软组织的测量数据估算得出的。由于基底膜靠近气泡且具有韧性，预计其很重要，因此对基底膜的本构模型给予了特别关注。研究发现，膜和周围组织弹性的最高预期值不足以抑制气泡生长。圆柱形血管限制的降低不应改变这一结论。从超声测量中获取的组织粘度对气泡生长有一定程度的抑制作用，尽管抑制程度未达到预期的抗损伤程度。然而，通过其他方法测得的较高粘度值，可论证其与气泡生长引起的变形更相关，确实能显著抑制气泡膨胀。
