Gauging the likelihood of stable cavitation from ultrasound contrast agents

Abstract

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 I(CAV) = P(r)/f (where P(r) 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.

Figure 1

(a) Representative calculated radius–time curve using the Gilmore equation. The driving frequency is 1 MHz, R₀=3.0 µm, and the peak rarefactional pressure is 0.26 MPa. The host fluid is blood at atmospheric pressure. (b) FFT of the bubble’s radiated pressure waveform, normalized to the amplitude of the fundamental component. The subharmonic component at 500 kHz is ~20 dB lower than the fundamental, and thus the subharmonic threshold has been reached.

Figure 2

The threshold for subharmonic emissions, P_SH, as a function of initial bubble size, R₀, normalized to the resonant size, R_RES, at 1, 3, and 5 MHz. The host fluid is water (a) and blood at atmospheric pressure (b). The legend is shown in the top panel only.

Figure 3

Calculated thresholds reported in peak rarefaction pressure (P_r) for inertial cavitation and subharmonic emissions from resonant and optimal size bubbles. The host fluids are water (a) and blood (b) at atmospheric pressure.

Figure 4

UCA rupture threshold, PRUPT, as a function of UCA size and frequency for steady state acoustic excitation (a) and single cycle acoustic excitations (b). Contour lines are shown for the peak rarefaction pressure at 0.02, 0.05, 0.1, and 0.15 MPa. The host fluid is blood at atmospheric pressure, and the shell properties of the UCA correspond to Definity.

Figure 5

UCA rupture threshold, PRUPT, near the linear resonant size at 1 MHz, 3 MHz and 5 MHz in water (a) and blood (b) at atmospheric pressure. The shell properties of the UCA correspond to Definity. All plots are for steady state acoustic excitations, except for the solid line, which corresponds to single cycle acoustic excitation at 1 MHz.

Figure 6

The threshold for subharmonic emissions (bubble sizes above the dashed and dotted line) and inertial cavitation (bubble sizes below the dashed and dotted line) as a function of bubble size and frequency. The solid lines demark the point at which the cavitation index (I_CAV) is 0.45 and 0.09 (I_CAV = 0.09 indicates the optimal bubble size for subharmonic emissions). The striped region indicates subharmonic emissions are due to inertial cavitation. The region labeled ‘No subharmonic emissions, No inertial cavitation,’ indicate neither subharmonic emissions nor inertial cavitation are likely for peak rarefactional pressures less than 1 MPa.

Figure 7

The peak rarefactional pressures (P_r) required as a function of frequency for the MI to be 0.4 and 1.9. The lines labeled I_CAV = 0.09 and I_CAV = 0.45 demarcate the parameter space over which subharmonic emissions from stable cavitation are likely. The shaded region indicates overlay between the MI and cavitation index. The line demarking ‘UCA Rupture’ indicates the P_r required for the cavitation index to be 0.02 as a function of frequency. Bioeffects from sonoporation ( (Greenleaf et al 1998), (Juffermans et al 2009), (Rahim et al 2006), (Miller and Dou 2004)), thrombolysis ( (Datta et al 2008), (Prokop et al 2007), (Porter et al 2001), (Petit et al 2012)), drug delivery ( (Hitchcock et al 2010), (McDannold et al 2008)), and petechial hemorrhage ( (Miller et al 2008)) are also shown.