Thermodynamic state of the interface during acoustic cavitation in lipid suspensions

The thermodynamic state of lipid interfaces was observed during shock wave induced cavitation in water with submicrosecond resolution, using the emission spectra of hydration-sensitive fluorescent probes colocalized at the interface. The experiments show that the cavitation threshold is lowest near a phase transition of the lipid interface. The cavitation collapse time and the maximum state change during cavitation are found to be a function of both the driving pressure and the initial state of the lipid interface. The experiments show dehydration and crystallization of lipids during the expansion phase of cavitation, suggesting that the heat of vaporization is absorbed from within the interface, which is adiabatically uncoupled from the free water. The study underlines the critical role of the thermodynamic state of the interface in cavitation dynamics, which has mechanistic implications for ultrasound-mediated drug delivery, acoustic nerve stimulation, ultrasound contrast agents, and the nucleation of ice during cavitation.

Figure 1

Experimental setup. (a) The shock wave source is coupled to a temperature controlled water tank. The optical system consists of a LED light source (380 nm) which is focused by an objective in the water, coincident with the shock source, and fluorescent signals are detected by two photomultiplier tubes recording simultaneously at two different wavelengths (438 and 470 nm). An unfocused monitoring transducer is used to detect acoustic emissions from the vicinity of the focal region. During experiments multilamellar lipid vesicles (MLVs), embedded with the dye Laurdan, are present everywhere in the tank. (b) Measured focal pressure waveforms for shock waves at four different energy settings.

Figure 2

(a) Optical intensity $\frac{\mathrm{\Delta }I}{\mathrm{I}}$ at 470 nm, acoustic emissions, and rate of deformation $\dot{\gamma }$ measured during a single cavitation event in DOPC suspension at 20 °C in response to a shock impulse of energy level 20. The shock wave arrives at 50 µs resulting in an acoustic emission, a drop in optical intensity, and a peak of rate of deformation. The cavitation bubble/cluster grows to a maximum extent at 170 µs and then collapses at around 350 µs producing a strong acoustic emission and a knee in the optical intensity. (b) The distribution of cavitation time for 200 such shock waves as determined from the acoustic and optical signals.

Figure 3

Dependence of cavitation time as a function of shock wave energy level for four different initial lipid states. The initial state ranges from the condensed state, $T^{*}=\text{–}0.067$ (top) to the fluid state, $T^{*}=0.15$ (bottom). A cavitation time of zero indicates the absence of cavitation. For the gel initial state $T^{*}=0.15$, cavitation starts at EL 10 and the cavitation time increases with EL to a maximum of 200 µs. At $T^{*}=\text{–}0.045$ significant cavitation occurs for EL 8 and cavitation time increases with EL but again does not exceed 200 µs. At $T^{*}=0.046$, the threshold is lowered and cavitation occurs at all energy levels settings with a maximum cavitation time of 250 µs. For $T^{*}=0.15$ cavitation starts at EL 12 and the cavitation time exceeds 250 µs at the highest setting. Dots indicate the outliers that are more than 1.5 times the upper/lower quartile.

Figure 4

Cavitation rate of aqueous suspension of liposomes measured as a function of the energy level, the thermodynamic state, and the repetition rate. Cavitation rate defined as number of cavitation events per 100 shocks has been plotted at two different shock repetition rates 1 Hz (solid curves) and 3 Hz (dashed curves). The markers show data and the curves show fitted sigmoids. Three different liposome suspensions were tested. The mean hydrodynamic radius and polydispersity index were as follows: DOPC (160 nm, 0.2), DMPC (140 nm, 0.17), and DPPC (452 nm, 0.44). All samples were tested at a temperature of 24 °C and $p\mathrm{H}7$.

Figure 5

Optical intensity $\frac{\mathrm{\Delta }I}{\mathrm{I}}$ and ratiometric parameter $\frac{\mathrm{\Delta }RP}{R{P}_0}$ are plotted as a function of time for four initial conditions. Lipids and temperature give the initial condition, which is also reported by $R{P}_0$, These are (a) DPPC, $T=20{}^{\circ }\mathrm{C}$, EL 15; (b) DMPC, $T=10{}^{\circ }\mathrm{C}$, EL 15; (c) DMPC, $T=37{}^{\circ }\mathrm{C}$, EL 10; (d) DOPC, $T=20{}^{\circ }\mathrm{C}$, EL 12. The optical intensity change is greatest when $T^{*}$ is closest to zero indicating that the cavitation bubbles/cluster attains the greatest volume when the lipid is close to a transition. $\frac{\mathrm{\Delta }RP}{R{P}_0}$ is greater for lipids in the fluid state than in the gel state, indicating a greater state change.

Figure 6

$\mathrm{\Delta }RP/R{P}_0$ and $\dot{\gamma }$ averaged over 500 shocks at energy levels (a) 12 and (b) 15 for DMPC suspension at 23 °C. At the higher energy level the growth rate $\dot{\gamma }$ (solid line) was larger, indicating the cavitation was driven harder, but the $\mathrm{\Delta }RP/R{P}_0$ (dashed line) plateaued to the same value, suggesting the lipid obtained the same condensed state.

Figure 7

The rate of mechanical deformation $\left(\dot{\gamma }\right)$ and $\mathrm{\Delta }RP/R{P}_0$ for a DMPC solution at 37 °C (a) waveforms averaged with $t_r>270\mu \mathrm{s}$ gives high peak $\dot{\gamma }$, and $\frac{\mathrm{\Delta }RP}{R{P}_0}>0$ indicates the lipid condenses during cavitation; (b) waveforms averaged with $t_r<270\mu \mathrm{s}$ give low peak $\dot{\gamma }$ while $\frac{\mathrm{\Delta }RP}{R{P}_0}<0$ indicates the lipid fluidizing during cavitation. The distribution of $t_r$ is given in Fig. S2 in the SM [23].

Figure 8

Illustration of the proposed evolution of the interface during cavitation in a lipid environment. The interface is represented by the dense blue strip, the lighter shade the surrounding water, and white is the vapor cavity. (a) Due to reversible heat exchanges between lipids and interface water $\left(\delta Q\right)$, microscopic vapor cavities are formed at the interface of a liposome. (b) The initial cavity grows recruiting more lipid vesicles at the cavity interface. Water will be lost from the lipid as vapor to the cavity, which requires heat of vaporization, which is compensated by the irreversible heat flow $\left(\mathrm{\Delta }Q\right)$ within the interface from lipids to water vapor (white arrows), whereas no heat flow from bulk to the interface (black arrow) due to dynamic decoupling of the interface (see text), resulting in condensation of the interface.

Figure 9

(a) Generalized quadratic entropy potential for two experimental observables $S\left(x_1,x_2\right)$ [60]. The bases $x_1,x_2$ are not necessarily orthogonal; however, corresponding $e_1,e_2$ can be found that are orthogonal along the principle curvatures of the quadratic potential. The projections indicate how the susceptibility of a particular observable is related to principle curvatures of the potential. The probability distribution is obtained from the entropy potential $w\sim e^S$, which gives fluctuations as the width of the distribution. Notice that for an arbitrary orientation of $e_1,e_2$ fluctuations as projected on $x_1,x_2$ will generally be coupled. (b) Projection of the potential on principal axis ${\widehat{e}}_1$ shows the effect of change in state in terms of change in the curvature of the potential (thermodynamic susceptibility). Near phase transition, the decreased curvature implies higher probability such that $\sqrt{|{\left(\delta V\right)}^2|}>\delta V_{\mathrm{act}}$ and hence lowered threshold.