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. 2012 Dec 11;2(12):1140–1159. doi: 10.7150/thno.4305

Figure 2.

Figure 2

Predicted Cavitation Destruction Profiles: We use eqn (8) to predict the magnitude of microbubble oscillations as a function of time for a specified value of the area expansion modulus, KA (as well as other material properties) and for a specified ultrasound pressure (KA = 50 mN/m, σ = 51 mN/m, and κs = 7 x 10 -6 sP) . The result is a “radius-time” plot, in which the ratio of radius to resting radius (R/Ro) is plotted versus insonification time. Four radius-time plots are shown for four different ultrasound peak negative pressures (0.05, 0.2, 0.5, and 1.0 MPa), each exhibiting a different maximal value of R/Ro (~1.1, 1.4, 2.3, and 4.1, respectively). Such information can be used to predict cavitation destruction profiles if one specifies a critical value, (R/Ro)*, at which cavitation occurs; that is, cavitation is predicted to occur only when the maximal value of (R/Ro) in the radius time plot exceeds (R/Ro)*. For example, if (R/Ro)* is 2, then cavitation is not predicted to occur at 50 kPa or 200 kPa but is predicted to occur at 500 kPa and 1 MPa. If (R/Ro)* is 3 or 4 (or strictly speaking, anywhere in the range 2.5 - 4.1 as (R/Ro)* need not be a whole number), then cavitation is predicted to occur at 1 MPa but not at the lower pressures. If (R/Ro)* is greater than 4.1, then cavitation is not predicted to occur at any of the four pressures shown; cavitation would require a pressure greater than 1 MPa. Generating radius-time plots for a large number of pressures leads to the predicted cavitation destruction profiles shown in the rightmost panel. Predictions are shown for (R/Ro)* values in the range 2 - 8. Given that the ultrasound frequency is fixed (here, 2.25 MHz), a single (R/Ro)* value will translate to different microbubble wall velocities for different resting radii (Ro). It is therefore unlikely that inertial cavitation can be predicted using a single value of (R/Ro)*; alternatively, one could potentially use microbubble wall velocity, rather than (R/Ro)*, as a criterion for predicting inertial cavitation (see Fig. 3).