Page 35 - Volume 8, Issue 4 - Winter 2012

proportional to the shock amplitude As cubed: Hshock = bf0A3s / 4 2 32
(6c0r0). In addition, when shocks form at the focus of an acoustic beam, rather than in a plane wave, nonlinear effects combined with a different diffraction phase shift between harmonics lead to the asymmetry of the waveform and about 1.5 times higher shock amplitude than it would
be expected for a plane wave.
shocks are present. Moreover, rapid tissue heating by shocks can initiate boiling in milliseconds that, surpris- ingly, results in histotripsy rather than thermal ablation.
Millisecond boiling
Shock fronts are superfocused to a localized volume within the focal region of the HIFU beam leading to very precise heating at the focus. Simulations of acoustic fields from var- ious HIFU transducers based on the Khokhlov-Zabolotskaya-Kuznetsov (KZK) nonlinear propagation model combined with the heat transfer equa- tion have shown that if shock fronts of about 40 – 80 MPa develop at the focus, boiling temperatures are reached in
14
milliseconds (Fig. 10). Once shocks
form, spatial distributions of ultra-
sound-induced heating (frame c)
becomes much more localized than
acoustic intensity (frame a). Even
though heating by shocks is concen-
trated in a very small volume of about
0.1 mm radius, heat diffusion from vol-
ume of this size occurs in about 20
14
ms. If boiling starts within several
milliseconds, heat diffusion is almost negligible. Time-to-boil therefore can be easily predicted from the shock wave amplitude and thermal parame-
15
Contrary to cavi- tation inception, which is a stochastic phenomenon and may occur in a much larger volume within the focus (frame b), shock heating and boiling are high-
ters of the medium.
33
Figure 9 compares heat dep- osition at the focus in tissue due to absorption of a har- monic wave Hlin (red curves) and shock waves Hshock (blue curves) against their intensity. Curves are calculated for a 2 MHz transducer, absorption in tissue a0 = 0.5 dB/cm/MHz, sound speed c0 = 1500 m/s, density r0 = 1000 kg/m3, and nonlinear parameter b = 4. Corresponding waveforms are presented in inset frames. The ratio of heating rates shows that at focal intensities > 10 kW/cm2 heating efficiency from shock waveform is more than 20 times higher than that from the harmonic waves. This indicates that using shock waves is beneficial to accelerate thermal effects in HIFU and that intensity by itself cannot be used as a metric of the field to quantify heating if strong nonlinear effects and
ly predictable and occur locally at the focal center, where shock amplitude is the largest. Tissue is heated to high tem- peratures in a very small volume of 0.2 mm width, then, a boiling bubble starts to grow (frame d) to a much larger vol- ume creating a mm-sized vapor cavity. The incident shocks interact with the tissue–bubble interface, causing mechanical fragmentation of tissue in a much larger volume than that heated to create the initial bubble.
Boiling histotripsy lesions
Mechanically emulsified lesions without visible thermal damage can be produced under the conditions that the pulse length is not significantly greater than the time-to-boil and the pulse rate is low enough to provide tissue cooling
13,15
The results of such a boiling-histotripsy protocol are very repeatable in terms of the location, shape, size, and the content of the lesions (Fig. 11). As an example, a sequence of four single lesions was produced in ex-vivo bovine liver using a typical pulsing protocol: 2-MHz HIFU frequency, 70 MPa shock amplitude at the focus, 10 ms pulse
between pulses.
Fig. 10. Modeling of the acoustic field from a 2 MHz HIFU transducer of 4.4 cm diameter and focal length in a tissue-mimicking gel phantom (a-c) and corresponding visualization of initiation of boiling at the focus after 9 ms of exposure (d). Irradiation was from the bottom, 2 D distributions of intensity (a), peak negative pressure (b), heat deposition rate (c) were simulated in the axial plane of the transducer using the KZK equation. Focal intensity was 12 kW/cm2, pressure waveforms with 70 MPa shocks formed at the focus. Cavitation was also observed in a larger volume around the focus following the peak negative pressure pattern, but did not affect heat- ing at the focus. Modeling predicted heating by shocks to boiling temperature in 7 ms and initiation of boiling was detected in measurements in 9 ms. (10d adapted from part of a figure in reference 14)
Disintegration of Tissue Using HIFU 31