Viscoelastic material properties at high strain rates are needed to model many biological and medical systems. Bubble cavitation can induce such strain rates, and the resulting bubble dynamics are sensitive to the material properties. Thus, in principle, these properties can be inferred via measurements of the bubble dynamics. Estrada et al. (2018) demonstrated such bubble-dynamic high-strain-rate rheometry by using least-squares shooting to minimize the difference between simulated and experimental bubble radius histories. We generalize their technique to account for additional uncertainties in the model, initial conditions, and material properties needed to uniquely simulate the bubble dynamics. Ensemble-based data assimilation minimizes the computational expense associated with the bubble cavitation model , providing a more efficient and scalable numerical framework for bubble-collapse rheometry. We test an ensemble Kalman filter (EnKF), an iterative ensemble Kalman smoother (IEnKS), and a hybrid ensemble-based 4D-Var method (En4D-Var) on synthetic data, assessing their estimations of the viscosity and shear modulus of a Kelvin–Voigt material. Results show that En4D-Var and IEnKS provide better moduli estimates than EnKF. Applying these methods to the experimental data of Estrada et al. (2018) yields similar material property estimates to those they obtained, but provides additional information about uncertainties. In particular, the En4D-Var yields lower viscosity estimates for some experiments, and the dynamic estimators reveal a potential mechanism that is unaccounted for in the model, whereby the apparent viscosity is reduced in some cases due to inelastic behavior, possibly in the form of material damage occurring at bubble collapse.

许多生物和医学系统都需要高应变率下的粘弹性材料特性。气泡空化可以引起这样的应变率，并且由此产生的气泡动力学对材料特性很敏感。因此，原则上，这些特性可以通过气泡动力学的测量来推断。埃斯特拉达等人。（2018 年）通过使用最小二乘射击来最小化模拟和实验气泡半径历史之间的差异，证明了这种气泡动态高应变率流变测量。我们推广他们的技术以解释模型中的额外不确定性、初始条件和唯一模拟气泡动力学所需的材料特性。基于集合的数据同化最小化与气泡空化模型相关的计算费用，为气泡破裂流变测量提供更有效和可扩展的数值框架。我们在合成数据上测试集成卡尔曼滤波器 (EnKF)、迭代集成卡尔曼平滑器 (IEnKS) 和基于混合集成的 4D-Var 方法 (En4D-Var)，评估他们对开尔文粘度和剪切模量的估计– 福格特材料。结果表明，En4D-Var 和 IEnKS 提供比 EnKF 更好的模量估计。将这些方法应用于 Estrada 等人的实验数据。(2018) 产生了与他们获得的相似的材料属性估计，但提供了有关不确定性的额外信息。特别是，En4D-Var 对某些实验产生较低的粘度估计，动态估计揭示了模型中未解释的潜在机制，