[Paper Review] Parsimonious inertial cavitation rheometry via bubble collapse time

Zhiren Zhu, Remillard, Sawyer+6 more|arXiv (Cornell University)|Feb 8, 2023

Ultrasound and Cavitation PhenomenaMaterials Science3 citations

TL;DR

This paper introduces a reduced-order inverse modeling framework for inertial microcavitation rheometry (RO-IMR) that efficiently characterizes high-strain-rate viscoelastic properties of soft materials using bubble collapse time scaling. By leveraging size-dependent collapse time ratios relative to an inviscid fluid, the method directly estimates elastic and viscous moduli with minimal numerical simulations, enabling rapid, physics-informed calibration of complex viscoelastic models in polyacrylamide and simulated tissues.

ABSTRACT

The rapid and accurate characterization of soft, viscoelastic materials at high strain rates is of interest in biological and engineering applications. Examples include assessing the extent of tissue ablation during histotripsy procedures and developing injury criteria for the mitigation of blast injuries. The inertial microcavitation rheometry technique (IMR, Estrada et al., 2018) allows for the characterization of local viscoelastic properties at strain rates up to 1E8 per second. However, IMR now typically relies on bright-field videography of a sufficiently translucent sample at >1 million frames per second and a simulation-dependent fit optimization process that can require hours of post-processing. Here, we present an improved IMR-style technique, called parsimonious inertial microcavitation rheometry (pIMR), that parsimoniously characterizes surrounding viscoelastic materials. The pIMR approach uses experimental advancements to estimate the time to first collapse of the laser-induced cavity within approximately 20 ns and a theoretical energy balance analysis that yields an approximate collapse time based on the material viscoelasticity parameters. The pIMR method closely matches the accuracy of the original IMR procedure while decreasing the computational cost from hours to seconds while potentially reducing reliance on ultra-high-speed videography. This technique can enable nearly real-time characterization of soft, viscoelastic hydrogels and biological materials with a numerical criterion assessing the correct choice of model. We illustrate the efficacy of the technique on batches of tens of experiments for both soft hydrogels and fluids.

Motivation & Objective

• To address the high computational cost and difficulty in calibrating viscoelastic models for soft biological materials under inertial cavitation.
• To develop a parsimonious inverse method that bypasses brute-force parameter iteration in inertial microcavitation rheometry (IMR).
• To enable efficient, localized characterization of rate-dependent mechanical properties in soft solids such as polyacrylamide and biological tissues.
• To improve experimental accuracy by focusing on collapse time as a key physical observable, reducing sensitivity to model overfitting.
• To extend the applicability of IMR to real-time, high-rate mechanical characterization in biomedical and bioengineering contexts.

Proposed method

• The method uses a reduced-order model based on the scaling of bubble collapse times across two different initial radii in the same material.
• It derives a closed-form relation (Equation 45) linking the ratio of collapse times to the material's elastic and viscous moduli, assuming a Kelvin-Voigt-type constitutive model.
• The approach assumes spherical symmetry and uses a Rayleigh-Plesset-type equation with a viscoelastic stress term derived from the material's relaxation behavior.
• It bypasses full numerical solution of the full fluid-structure interaction problem by focusing on collapse time scaling, drastically reducing computational cost.
• The method is validated by comparing predicted collapse dynamics against numerical simulations and experimental data from polyacrylamide specimens.
• It employs high-speed shadowgraphy and multi-strobing to measure collapse times with sub-microsecond precision, minimizing measurement error amplification.

Experimental results

Research questions

• RQ1 Can collapse time scaling across two bubble sizes be used to directly infer viscoelastic moduli without iterative parameter fitting?
• RQ2 How does the reduced-order model perform in reproducing numerically simulated inertial cavitation dynamics for soft materials?
• RQ3 What is the sensitivity of the method to experimental uncertainty in collapse time measurements?
• RQ4 Can the framework accurately characterize complex, rate-dependent viscoelastic behavior in polyacrylamide and soft tissues?
• RQ5 How can the experimental design be optimized to maximize the range of measurable viscoelastic properties using collapse time ratios?

Key findings

• The RO-IMR method successfully reproduces target numerical simulations of inertial cavitation dynamics with high fidelity using only a small number of simulations.
• The method enables accurate inverse characterization of both standard nonlinear solid and fractional Kelvin-Voigt models in polyacrylamide specimens.
• The approach reduces the need for brute-force parameter calibration, significantly lowering computational cost while maintaining predictive accuracy.
• Measurement uncertainty in collapse time is a critical limitation; sub-microsecond precision is required to avoid amplification of errors in the collapse time ratio.
• The method is most effective when the collapse time ratio spans a wide range—particularly when one experiment is significantly faster (elastic) and another significantly slower (viscous) than the inviscid case.
• Pairs of experiments with similar maximum bubble radii (R_max^B / R_max^A < 1.3) and close collapse times to the inviscid case led to solution failure due to error amplification in the ratio term.