Growth and Collapse of an Isolated Bubble Driven by a Single Negative Histotripsy Cycle in Agarose Gel: Stress, Strain, and Strain Rate Fields

Abstract

Histotripsy relies on cavitation to mechanically homogenize soft tissue. There is strong evidence that the high stresses, strains, and strain rates developed as bubbles grow and collapse contribute to this tissue homogenization. While such stresses and strains have been examined computationally in model systems with assumed constitutive models (e.g., finite-deformation Neo-Hookean model) and viscoelastic properties determined under quasi-static conditions, recent studies proposed that the Quadratic Law Kelvin-Voigt (QLKV) constitutive model, which additionally accounts for strain stiffening, more accurately represents the viscoelastic response of soft materials subjected to cavitation; this model has also been used to infer viscoelastic properties at high rates. In this work, we use the QLKV model and these properties to calculate the time-dependent stress, strain, and strain rate fields produced during the growth and collapse of individual bubbles subjected to a histotripsy-relevant pressure waveform in agarose gels of 0.3~\% and 1.0~\% concentration and corresponding to actual (past) experiments. We find that, as the gel concentration is increased, strain stiffening manifests in larger elastic stresses and compressive stresses extending into the collapse phase, particularly for the 1.0~\% concentration gel. As a result, the duration of the collapse phase also increases. In comparison with the conventional Neo-Hookean model, the compressive stress has a larger magnitude, extends farther into the surrounding medium, and shows an increased departure from growth/collapse symmetry close to the bubble; all of these effects are magnified in the stiffer gel.