The Dynamics and Acoustic Emission of Bubbles Driven by a Sound Field

“…The general approach used here for determining the response of a bubble suspended in an unbounded, infinite liquid exposed to an acoustic field has been described in detail previously (Cramer 1980; Church 1989). The Gilmore-Akulichev formulation for bubble dynamics is:

(1 - \frac{\overset{R}{true}}{C}) R \overset{R}{true} + \frac{3}{2} (1 - \frac{\dot{R}}{3 C}) {\dot{R}}^{2} = (1 + \frac{\dot{R}}{C}) H + (1 - \frac{\dot{R}}{C}) \frac{\dot{R}}{C} R \frac{d H}{d R},

where R , is the bubble radius, C is the calculated speed of sound in the liquid, H is the enthalpy of the liquid, and t is time; the single and double overdots indicate first and second derivatives with respect to time.…”

Section: Methodsmentioning

confidence: 99%

A Theoretical Study of Inertial Cavitation from Acoustic Radiation Force Impulse Imaging and Implications for the Mechanical Index1

Church

Labuda

Nightingale

2015

Ultrasound in Medicine & Biology

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The mechanical index (MI) attempts to quantify the likelihood that exposure to diagnostic ultrasound will produce an adverse biological effect by a nonthermal mechanism. The current formulation of the MI implicitly assumes that the acoustic field is generated using the short pulse durations appropriate to B-mode imaging. However, acoustic radiation force impulse (ARFI) imaging employs high-intensity pulses up to several hundred acoustic periods long. The effect of increased pulse durations on the thresholds for inertial cavitation was studied computationally in water, urine, blood, cardiac and skeletal muscle, brain, kidney, liver and skin. The results show that while the effect of pulse duration on cavitation thresholds in the three liquids can be considerable, reducing them by, e.g., 6% – 24% at 1 MHz, the effect in tissue is minor. More importantly, the frequency dependence of the MI appears to be unnecessarily conservative, i.e., that the magnitude of the exponent on frequency could be increased to 0.75. Comparison of these theoretical results with experimental measurements suggests that some tissues do not contain the pre-existing, optimally sized bubbles assumed for the MI. This means that in these tissues the MI is not necessarily a strong predictor of the probability for an adverse biological effect.

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“…Note, however, damping due to acoustic radiation and viscosity dominates over thermal damping for bubbles larger than resonant size (Leighton 1994), and that the optimal size bubble for subharmonic emissions are well-known to be larger than resonant size (Eller and Flynn 1969, Prosperetti 1974). The details of the Gilmore equation are discussed in further detail by Gilmore (1952), Cramer (1980), and Church (1989). Briefly, the Gilmore equation has the form

true(1 - \frac{Ṙ}{C} true) R Ṙ + \frac{3}{2} true(1 - \frac{Ṙ}{3 C} true) Ṙ^{2} = true(1 + \frac{Ṙ}{C} true) H + \frac{R}{C} true(1 - \frac{Ṙ}{C} true) \frac{normald H}{normald R},

where R is the time dependent bubble radius, the diacritical dot denotes the derivative with respect to time, C is the sound speed in the fluid at the bubble wall, and H is the liquid enthalpy.…”

Section: Methodsmentioning

confidence: 99%

Gauging the likelihood of stable cavitation from ultrasound contrast agents

Bader¹,

Holland²

2012

Phys. Med. Biol.

114

121

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The mechanical index (MI) was formulated to gauge the likelihood of adverse bioeffects from inertial cavitation. However, the MI formulation did not consider bubble activity from stable cavitation. This type of bubble activity can be readily nucleated from ultrasound contrast agents (UCAs) and has the potential to promote beneficial bioeffects. Here, the presence of stable cavitation is determined numerically by tracking the onset of subharmonic oscillations within a population of bubbles for frequencies up to 7 MHz and peak rarefactional pressures up to 3 MPa. In addition, the acoustic pressure rupture threshold of an UCA population was determined using the Marmottant model. The threshold for subharmonic emissions of optimally sized bubbles was found to be lower than the inertial cavitation threshold for all frequencies studied. The rupture thresholds of optimally sized UCAs were found to be lower than the threshold for subharmonic emissions for either single cycle or steady state acoustic excitations. Because the thresholds of both subharmonic emissions and UCA rupture are linearly dependent on frequency, an index of the form ICAV = Pr/f (where Pr is the peak rarefactional pressure in MPa and f is the frequency in MHz) was derived to gauge the likelihood of subharmonic emissions due to stable cavitation activity nucleated from UCAs.

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The Dynamics and Acoustic Emission of Bubbles Driven by a Sound Field

Cited by 24 publications

References 3 publications

Mapping the cavitation intensity in an ultrasonic bath using the acoustic emission

Mapping the cavitation intensity in an ultrasonic bath using the acoustic emission

A Theoretical Study of Inertial Cavitation from Acoustic Radiation Force Impulse Imaging and Implications for the Mechanical Index1

Gauging the likelihood of stable cavitation from ultrasound contrast agents

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