High-frequency linear rheology of hydrogels probed by ultrasound-driven microbubble dynamics

Abstract

Ultrasound-driven microbubble dynamics are central to biomedical applications, from diagnostic imaging to drug delivery and therapy. In therapeutic applications, the bubbles are typically embedded in tissue, and their dynamics are strongly affected by the viscoelastic properties of the soft solid medium. While the behaviour of bubbles in Newtonian fluids is well characterised, a fundamental understanding of the effect on ultrasound-driven bubble dynamics of a soft viscoelastic medium is still being developed. We characterised the resonant behaviour in ultrasound of isolated microbubbles embedded in agarose gels, commonly used as tissue-mimicking phantoms. Gels with different viscoelastic properties were obtained by tuning agarose concentration, and were characterised by standard rheological tests. Isolated bubbles (100-200 µm) were excited by ultrasound (10-50 kHz) at small pressure amplitudes (< 1 kPa), to ensure that the deformation of the material and the bubble dynamics remained in the linear regime. The radial dynamics of the bubbles were recorded by high-speed video microscopy. Resonance curves were measured experimentally and fitted to a model combining the Rayleigh-Plesset equation governing bubble dynamics, with the Kelvin-Voigt model for the viscoelastic medium. The resonance frequency of the bubbles was found to increase with increasing shear modulus of the medium, with implications for optimisation of imaging and therapeutic ultrasound protocols. In addition, the viscoelastic properties inferred from ultrasound-driven bubble dynamics differ significantly from those measured at low frequency with the rheometer. Hence, rheological characterisation of biomaterials for medical ultrasound applications requires particular attention to the strain rate applied.

Oscillations of small bubbles and medium yielding in elastoviscoplastic fluids

“…We considered the case of a bubble with equilibrium radius al. [48], driven at ∆p = 100 Pa in the Carbopol gel ( Figure 1(b)) and at ∆p = 1 Pa in the Kaolin suspension (Figure 1(a)). Such a small acoustic pressure is required to ensure that the dynamics remains in the linear regime.…”

“…In viscoelastic media, the interplay between the bubble shape and the rheological response of the fluid in bubble rise experiments are now well understood [25][26][27][28][29] whereas the abundant literature on acoustically-driven bubble oscillation revealed delayed collapse [30][31][32][33] and chaotic bubble oscillations [34][35][36][37]. Focus has progressively shifted from the initial context of damage to military ships towards damage in soft tissues for biomedical applications [38][39][40][41][42][43][44][45][46] and high-frequency rheology of soft materials [47][48][49], as recently reviewed by Dollet et al [50].…”

Bulk rheometry at high frequencies: a review of experimental approaches

“…-Characterise local stress contributions (Schroyen et al 2019) or determine interaction strengths in colloidal suspensions (Bergenholtz et al 1998b;Fritz et al 2002b); -Investigate local dynamics in emulsions (Liu et al 1996;Romoscanu et al 2003a); -Obtain detailed insights in the dynamics of glasses (Hecksher et al 2017), hydrogels (Jamburidze et al 2017), and wormlike micellar solutions ; -Identify fast relaxation processes in polymers and the effects of monomer friction (Kirschenmann 2003;Szántó et al 2017) or bond characteristics in associative polymer systems (Goldansaz et al 2016;Zhang et al 2018).…”

Acoustic bubble dynamics in a yield-stress fluid

“…Eqn (2) is a standard second-order linear differential equation that we can reformulate in the frequency domain. We then obtain the second-order transfer function for the bubble oscillation amplitude z in the spirit of earlier works on bubble spectroscopy: 16,25,26…”

“…by the direct role played by bubble collapse in therapeutic laser or ultrasound tissue ablation. 14,15 Bubble radius time profiles are now even used either in the linear regime 16 or the strongly non-linear, cavitation regime 17 to extract local rheological properties of soft solids.…”