Encapsulated contrast microbubble radial oscillation associated with postexcitation pressure peaks
Typical passive cavitation detection signals presenting postexcitation events for Optison, Definity, and Sonovue microbubbles (incident ).
Illustration of group selection criteria and average spectra. The signals shown were acquired with the passive cavitation detector from Definity insonified at an incident PRPA of (5 cycles, 2.8 MHz). (a) PCD signals presenting a postexcitation signal after the principle response. (b) PCD signal showing only the principle response; no postexcitation signal. (c) Average power spectral density for signals with postexcitation response and signals without postexcitation response .
Simulated radius-time and radiated pressure for a Definity microbubble at resonance radius with a break-up radius . Incident pulse at 2.8 MHz with 5 cycles. (a) Incident PRPA of 100 kPa. Radial expansion does not exceed the break-up radius . Radiated pressure does not exhibit a postexcitation signal. (b) Incident PRPA of 400 kPa. Radial expansion exceeds the break-up radius. Radiated pressure does not exhibit a postexcitation signal. (c) Incident PRPA of 2 MPa. Radial expansion exceeds the break-up radius . Postexcitation signals are observed.
Postexcitation responses predicted with the model relative to maximum radial expansion and break-up radius . Radius-time and pressure-time responses were simulated for each microbubble type as a function of the initial microbubble radius for a 2.8 MHz, 5-cycle incident pulse with PRPA of 2 MPa. The value of on each radius-time curve divided by the initial radius is plotted as a function of for each microbubble type. Cases for which the associated pressure-time response exhibited a postexcitation signal are plotted as filled symbols, and cases with no postexcitation signal are plotted as open symbols. For display, every other data point is plotted (steps of 40 nm). Simulated responses for large microbubbles presenting just above the shell break-up threshold, but below a value of two do not present postexcitation signals.
Simulated spectral responses for a Definity microbubble at resonance radius with a break-up radius . Incident pulse at 2.8 MHz with 5 cycles. All spectra are presented with spectral amplitude relative to the peak value of the spectrum calculated for the response to the incident 2 MPa PRPA pulse. Incident PRPA: (a) 100 kPa, (b) 400 kPa, and (c) 2 MPa. (d) The average broadband noise (9.3–17.6 MHz) as a function of peak rarefactional pressure in the incident pulse. Error bars represent the standard deviation in the bandwidth. Stars indicate at which PRPA levels postexcitation emissions were identified on the simulated pressure-time curves.
Comparison of average spectra from signals with and without postexcitation response for simulated (dashed lines) and experimental (solid lines) results for (a) Definity, (b) Sonovue, and (c) Optison (incident peak rarefactional pressure amplitude of 2.0 MPa). All experimentally estimated spectra are presented on the same scale relative (re: 0 dB) to the peak value for Definity with postexcitation signals. The scaling factor that provided best alignment between simulated and experimental curves for Definity with postexcitation signals was calculated. This uniform off-set was applied to all simulated spectra. Highest broadband noise levels are observed for Definity and lowest levels for Optison. For each microbubble type, the average spectrum is higher for the case with postexcitation response than for the case without postexcitation response. Overall, the amplitudes of the simulated spectra vary consistently with the amplitudes of the experimentally assessed spectra (similar differences between microbubble types and between cases with and without postexcitation signals).
Average difference between the mean power spectrum from signals with postexcitation response and the mean power spectrum from signals without postexcitation response are summarized for spectra from experimental data and for spectra calculated from simulated pressure-time responses. Spectral differences are calculated within a bandwidth from 9.3 to 17.6 MHz.
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