Acoustic droplet vaporization is initiated by superharmonic focusing

Abstract

Acoustically sensitive emulsion droplets composed of a liquid perfluorocarbon have the potential to be a highly efficient system for local drug delivery, embolotherapy, or for tumor imaging. The physical mechanisms underlying the acoustic activation of these phase-change emulsions into a bubbly dispersion, termed acoustic droplet vaporization, have not been well understood. The droplets have a very high activation threshold; its frequency dependence does not comply with homogeneous nucleation theory and localized nucleation spots have been observed. Here we show that acoustic droplet vaporization is initiated by a combination of two phenomena: highly nonlinear distortion of the acoustic wave before it hits the droplet and focusing of the distorted wave by the droplet itself. At high excitation pressures, nonlinear distortion causes significant superharmonics with wavelengths of the order of the droplet size. These superharmonics strongly contribute to the focusing effect; therefore, the proposed mechanism also explains the observed pressure thresholding effect. Our interpretation is validated with experimental data captured with an ultrahigh-speed camera on the positions of the nucleation spots, where we find excellent agreement with the theoretical prediction. Moreover, the presented mechanism explains the hitherto counterintuitive dependence of the nucleation threshold on the ultrasound frequency. The physical insight allows for the optimization of acoustic droplet vaporization for therapeutic applications, in particular with respect to the acoustic pressures required for activation, thereby minimizing the negative bioeffects associated with the use of high-intensity ultrasound.

Fig. 1.

Schematic of the diffraction of an acoustic plane wave within a spherical droplet. Incoming plane wave propagating from left to right, scattered wave outside the droplet and refracted wave inside the droplet.

Fig. 2.

Snapshot of the superharmonic focusing effect within a spherical droplet. The black line represents the acoustic pressure waveform on the axis of symmetry (θ = 0) as a function of the z coordinate in the absence of a droplet. The red solid line is the focused pressure in the presence of the droplet. The snapshot is taken right at the moment of minimum focused pressure. The horizontal axis displays one full wavelength in the medium outside the droplet. The gray shaded region depicts the position of the droplet, R = 10 μm. The focusing spot lies around and the pressure is amplified 5.8 times compared with the incident acoustic pressure .

Fig. 3.

Dependence of the pressure amplification factor at the focusing spot for three microdroplet radii (A) as a function of the incident acoustic peak negative pressure at a driving frequency of 3.5 MHz and (B) as a function of the driving frequency f for a peak negative pressure of −4.5 MPa.

Fig. 4.

(A) The dependence of the pressure amplification factor at the focusing spot as a function of the droplet radius R for three incident acoustic peak negative pressures . (B) The position of the nucleation site as a function of the droplet size. The position is taken along the axis of ultrasound propagation on the axis of symmetry of the system. The solid lines represent the calculated positions of maximal peak negative pressure for a frequency of 3.5 MHz (red) and 5.0 MHz (blue), respectively. The circles represent measured nucleation spots for a range of droplet sizes for the two frequencies.

Fig. 5.

(A) A set of consecutive images showing acoustic droplet vaporization of a 7.4-μm-radius PFP droplet taken at a frame rate of 12.6 million frames per second. The droplet is triggered by an eight-cycle, 5-MHz frequency ultrasound pulse. The nucleation is initiated between frames 3 and 4. Frames 4 and 5 show the subsequent vapor bubble growth (24). (B) Nucleation maps for the two frequencies and for a range of droplet sizes. The histogram shows the focused positions z/R for a frequency of 3.5 MHz for the 10- to 14-μm droplet sizes and for a frequency of 5.0 MHz for the 6- to 10-μm droplet sizes. US, ultrasound.