Pressure dependence of the attenuation and sound speed in a bubbly medium: Theory and experiment

Abstract

Results of the measurements of sound speed and attenuation in a bubbly medium are reported. Monodisperse bubble solutions are sonicated with broadband ultrasound pulses with pressure amplitudes ranging between 12.5-100 kPa. Fundamental relationships between the frequency dependent attenuation, sound speed and pressure are established. A new model for the estimation of sound speed and attenuation is derived that incorporates the effect of nonlinear bubble oscillations on the wave propagation in the bubbly media. Model predictions are in good agreement with experimental results. PACS numbers: 43.25.Yw, 43.35.Bf, 43.35.Ei Acoustically excited microbubbles (MBs) are present in a wide range of phenomena; they have applications in sonochemistry [1]; oceanography and underwater acoustics [2, 3]; material science [4], sonoluminescence [5] and in medicine [6][7][8][9][10][11][12]. Due to their broad and exciting biomedical applications, it has been stated that˝The future of medicine is bubbles˝ [12]. MBs are used in ultrasound molecular imaging [6,7] and recently have been used for the non-invasive imaging of the brain microvasculature [7]. MBs are being investigated for site-specific enhanced drug delivery [8][9][10][11] and for the non-invasive treatment of brain pathologies (by transiently opening the impermeable blood-brain barrier (BBB) to deliver macromolecules [9]; with the first in human clinical BBB opening reported in 2016 [8]). However several factors limit our understanding of MB dynamics which consequently hinder our ability to optimally employ MBs in these applications. The MB dynamics are nonlinear and chaotic [13][14][15]; furthermore, the typical lipid shell coatings add to the complexity of the MBs dynamics due to the nonlinear behavior of the shell (e.g., buckling and rupture [16]). Importantly, the presence of MBs changes the sound speed and attenuation of the medium [17][18][19][20][21]. These changes are highly nonlinear and depend on the MB nonlinear oscillations which in turn depend on the ultrasound pressure and frequency, MB size and shell characteristics [17][18][19][20]. The increased attenuation due to the presence of MBs in the beam path may limit the pressure at the target location. This phenomenon is called pre-focal shielding (shadowing) [21,22]. Additionally, changes in the sound speed can change the position and dimensions of the focal region; thus, reducing the accuracy of focal placement (e.g., for targeted drug delivery). In imaging applications, MBs can limit imaging in depth due to the shadowing caused by prefocal MBs [21,22]. In sonochemistry, changes in the attenuation and sound speed impact the pressure distribution inside the reactors and reduces the procedure efficacy [23]. An accurate estimation of the pressure dependent atten-uation and sound speed in bubbly media remains one of the unsolved problems in acoustics [24]. Most current models are based on linear approximations which are only valid for small amplitude MB oscillations [17]. Linear approximations, however, are no...

Nonlinear power loss in the oscillations of coated and uncoated bubbles: Role of thermal, radiation and encapsulating shell damping at various excitation pressures

“…Because of the changes in the acoustic properties of the medium (e.g. increased pressure dependent attenuation [34,37,43,45]), knowledge of just the nonlinear bubble behavior is not enough to control and optimize applications. One must have sufficient knowledge on the relationship between the nonlinear bubble oscillations and changes in the acoustic properties of the medium.…”

“…Increased attenuation of bubbles can also create shielding of the post-focal tissue and bubbles in contrast enhanced diagnostic ultrasound and deteriorate the ultrasound images [65,66]. In bubble characterization applications like oceanography studies [4,5] or characterization of ultrasound contrast agents [38][39][40][41][42][43] pressure dependent changes in the attenuation are of significant importance and should be understood in detail.…”

“…Bubbles attenuate ultrasound through viscous damping due to liquid (Ld) and coating (Cd) viscous effects, radiation damping (Rd) and thermal damping (Td) [33][34][35][36][37][38][39]. The changes in attenuation of bubbly media has significance in studies related to oceanography [4,5] and acoustic characterization of coated bubbles used as ultrasound contrast agents (UCAs) [38][39][40][41][42][43]. Furthermore, knowledge of the nonlinear attenuation in the medium will help in optimization of applications related to sonochemistry [35][36][37] and medical ultrasound [11-13, 44, 45] by enhancing and controlling the acoustic energy at the target.…”

Toward Precisely Controllable Acoustic Response of Shell-Stabilized Nanobubbles: High Yield and Narrow Dispersity

“…Nevertheless, the estimated values for the NB shell parameters here are consistent with the reported values for MBs with similar shell compositions 82 − 84 (using linear estimations) and parameters that were extracted using optical measurements of radius–time curves 59 and pressure-dependent attenuation measurements. 85 , 86 …”

Critical corrections to formulations of nonlinear energy dissipation of ultrasonically excited bubbles and a unifying parameter to asses and enhance bubble activity in applications

“…Additionally, the role of Td is simplified using models that are derived based on linear approximations [4,5,6,7,8,9]. A more complete estimation of the wave attenuation in bubbly media requires a realistic estimation of the power dissipated by the nonlinear oscillations of the bubbles that includes all forms of damping [1,2,3,10,11]. Louisnard [1], starting with mass and momentum conservation equations for a bubbly liquid and using Rayleigh-Plesset equation [12] have derived the nonlinear energy terms for Td and Ld.…”