A number of recent medical procedures such as histotripsy rely on inertially-dominated oscillating gas cavities (i.e. bubbles) inside soft tissue. As a first approximation, soft tissue can be modeled by linear or nonlinear elasticity models and the equations describing bubble dynamics in such media have been derived in previous works. However, these models assume that the bubble remains perfectly spherical at all times for all initial conditions, which is in contradiction with any practical setting or experiments. Ignoring non-spherical behavior could for instance lead to inaccurate predictions for the extent of tissue damage generated during these procedures. The use of such models in practice thus requires one to predict departures from spherical behavior. In this article, departures from sphericity are expressed by non-spherical perturbations. Two sets of equations describing the dynamics of all non-spherical modes are derived for a bubble surrounded by a medium described using linear elasticity and Neo-Hookean hyperelasticity. For both elasticity models and for given initial conditions, bubble shape stability is shown to be controlled by five dimensionless parameters: the Weber number We, the Cauchy number Ca, the dimensionless vapor pressure inside the bubble, the dimensionless initial non-condensible gas pressure inside the bubble and the dimensionless far-field pressure. A growth criterion indicating whether the amplitude of a given non-spherical mode increases exponentially with time is also derived for both models. Bubble shape stability is then compared for both elasticity models during a Rayleigh collapse. Overall, it is found that shape stability is promoted when the shear modulus of the surrounding medium is increased and when the initial step increase in the external pressure is reduced. It is also established that the bubble shape during a Rayleigh collapse is stable over a much wider range of parameters for a surrounding medium described using Neo-Hookean hyperelasticity as opposed to linear elasticity with a similar shear modulus. This could lead to the overprediction of the occurrence of bubble shape instabilities if the surrounding medium is described using linear elasticity, which is particularly problematic during violent bubble collapse.

许多最近的医疗程序（例如组织曲张）依赖于软组织内部的惯性主导的振荡气腔（即气泡）。作为第一近似，可以通过线性或非线性弹性模型对软组织进行建模，并且在先前的工作中已经得出了描述此类介质中气泡动力学的方程式。但是，这些模型假定气泡在所有初始条件下始终保持完美的球形，这与任何实际设置或实验相矛盾。忽略非球形行为，例如可能导致在这些过程中产生的组织损伤程度的预测不准确。因此，在实践中使用此类模型需要人们预测与球形行为的偏离。在本文中，通过非球面扰动来表示偏离球面。对于用线性弹性和新霍克超弹性描述的介质围绕的气泡，导出了描述所有非球形模式动力学的两组方程式。对于弹性模型和给定的初始条件，气泡形状的稳定性均受五个无因次参数控制：韦伯数我们柯西数Ca，气泡内部的无量纲蒸汽压，气泡内部的无量纲初始不可凝气体压力和无量纲的远场压力。对于两个模型，还导出了一个增长准则，该准则指示给定非球形模式的幅度是否随时间呈指数增长。然后在瑞利坍缩过程中比较两个弹性模型的气泡形状稳定性。总的来说，发现当周围介质的剪切模量增加并且外部压力的初始步骤减小时，形状稳定性得到提高。还确定了，对于使用新霍克超弹性描述的周围介质，与具有类似剪切模量的线性弹性相反，在瑞利塌陷期间的气泡形状在参数的更大范围内都是稳定的。