Introduction

Clinical ultrasound probably meets all essential requirements to be the ideal medical imaging modality: an excellent safety record, good imaging resolution and penetration depth, and a real-time, or even faster, acquisition speed. However, its specificity remains limited. Microbubble ultrasound contrast agents can alleviate this shortcoming. Clinical use of microbubbles has been made possible by their core physical property, namely resonance. Upon exposure to the oscillatory pressure variations of an ultrasound wave, compressibility of the gas core combined with inertia of the surrounding liquid leads to a mass-spring-like resonance behavior whose Minnaert eigenfrequency obeys an inverse relation with the bubble radius1. The unique acoustic properties of microbubbles that present a typical radius of 1−3 μm have also been used for two decades to boost perfusion imaging in the clinic, making them unrivaled blood pool agents2.

In vivo, microbubbles have to circulate in the blood stream until reaching the target area. Extensive efforts have therefore been put into enhancing the stability of microbubbles by coating them with polymers, proteins, or lipids. Among these coatings, phospholipid shells have been the most widely used owing to their high biocompatibility, flexibility, and enhanced non-linear acoustic properties3. Furthermore, a lipid coating can be easily functionalized, e.g. by including stealth capability by adding polyethylene glycol (PEG), which prevents interactions with the immune system and prolongs the circulation time4. Moreover, targeting ligands can be attached to the periphery of the shell to specifically recognize and adhere to diseased cells and tissues5, 6, thereby bringing a molecular imaging dimension to the clinical use of microbubbles. The same ligands can also be used to load the microbubbles with various nanoconstructs, turning them into efficient microcarriers. The number of formulations for drug-loaded microbubbles has vastly expanded. These include a broad range of interfacial structures, from simple drugs loaded onto the bubble shell7, 8 to more complex nanoconstructs that can entrap genes or chemotherapeutics9, 10.

Driven near its resonance frequency, a bubble displays maximal radial response and generates secondary effects, such as harmonics and subharmonics11, 12, streaming, acoustic radiation forces, shape instabilities13, and non-spherical oscillations14, 15. These effects are of prime importance in applications such as cleaning, (bacterial) biofilms removal16, mechanical destruction of thrombus17 or tumors18, 19 or inducing vessel wall permeation, e.g for blood brain barrier opening20. The combination of the mechanical action of targeted microbubbles adherent to a surface with the release of a drug payload is of great interest for therapeutic applications as medicine is becoming increasingly focused towards personalized21 and localized therapy22, 23.

Although there is convincing experimental evidence for controlled release of the payload, the physical mechanisms behind it remain unclear. Some attempts were made to explain these phenomena: Borden et al.24 proposed that the surface area reduction leads to the expulsion of excessive shell material, which is, however, difficult to assess owing to the nanoseconds timescales and nanometer length scales governing the problem. O’Brien et al.25 attempted to explain the shedding in relation to bubble stability by looking at molecular viscosity, while Kwan et al.26 concluded that the release could originate from a cyclic nucleation and aggregation of lipid folding events. This, however, is difficult to combine with the observation that shedding can occur within just a few ultrasound cycles27.

Here, we take a major step forward, both in the experimental observation of the microbubble shedding and in its physical description within the relevant pressure regime28. Time-resolved observation of the release was performed in an unconventional side view, which allowed the visualization of the release in the relevant plane of sight. The setup combines two high-speed cameras in order to simultaneously record the bubble oscillations at a tens of nanoseconds timescale, together with high-speed fluorescence imaging of the release and transport of the bubble payload at a tens of microseconds timescale. To this end, a fluorescent dye (DiI) was incorporated into the bubble shell to serve as a model drug to unravel the release and transport mechanisms of the payload at a range of acoustic parameters. We also study the controlled release theoretically, where we show good agreement with the experimental observations. These observations shed light on the physical mechanisms involved in drug delivery with microbubbles, and demonstrate the importance of the physical environment for the efficacy of the controlled release.

Results

Microbubble dynamics theory and modeling

The dynamics of free bubbles is described by the Rayleigh−Plesset equation and has been investigated for a century. It can theoretically account for large oscillation amplitudes and water compressibility29, non-adiabatic compression30 and complex viscoelastic behavior of the bubble shell31, 32. In practice, however, microbubbles are never in free space and further modifications were made to the primary models to account for the presence of a substrate. The so-called method of images is such an example in potential flow theory that considers the substrate as an acoustic reflector and offers an easy way to account for its effect on the bubble dynamics33. More extended spherical models were developed34, 35 and tested36, 37 to investigate the effect of the distance between the bubble and the substrate. However, the present physical problem requires going beyond the spherical models by considering the non-spherical dynamics of microbubble oscillations and the subsequent release and transport of the bubble payload.

Successfully explaining the physical aspects involved in shedding from microbubbles implies an understanding and description of the microbubble oscillations without the constraint of spherical symmetry. In this section we therefore build a potential flow model based on a simple idealization of the flow kinematics for the microbubble dynamics near a substrate, where the bubble is allowed a non-spherical axisymmetric motion (see Fig. 1).

Fig. 1
figure 1

Schematic description of the model. a Description of a bubble targeted to a substrate including the geometrical parameters. b The bubble undergoes volumetric oscillations and oscillatory translations under ultrasound exposure, thereby generating streaming

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First, we evaluate the expected displacement of the substrate as a result of the arrival of ultrasound, which can be estimated from a no-slip boundary condition and from liquid compressibility. For the studied range of pressures (150−400 kPa) at a driving frequency of 1 MHz, the amplitude of motion of a water fluid particle induced by the ultrasound wave is not more than 50 nm38. Such a displacement is negligible as compared to the observed bubble oscillation amplitude that typically reaches a few micrometers. Consequently, the displacement of a substrate with larger acoustic impedance is therefore also negligible. In addition, an oscillating bubble will preferentially displace water rather than inducing a local deformation of the substrate owing to the substrate’s elasticity (E = 3 GPa for polystyrene). Thus, the substrate can then be identified as a rigid plane where we neglect its deformation along the contact area with the bubble. The center of this contact area is then taken as the origin to build our axisymmetric model. We now describe the radius R not only as a function of time but also of the elevation angle ϑ, Fig. 1a. Note that in the following the geometry used for the mathematical derivation remains spherical, since that condition is required to make use of the Rayleigh−Plesset dynamics. We consider in first approximation the velocity potential as radial in this coordinate system. The error associated with this assumption is discussed in Supplementary Note 1. This now allows us to rewrite the Rayleigh−Plesset equation in spherical coordinates (r, ϑ):

$$\rho _\ell \left( {\ddot R\left( {\vartheta ,t} \right)R(\vartheta ,t) + \frac{3}{2}\dot R(\vartheta ,t)^2} \right) = P_{\mathrm{i}}(t) - P_{\mathrm{e}}(t),$$
(1)

with \(\rho _\ell\) the liquid density, and R(ϑ, t) the time-dependent and angle-dependent radius with the overdots representing its time derivatives. Pi is the internal gas pressure:

$$P_{\mathrm{i}}(t) = - \frac{{4\mu _\ell \dot R(\vartheta ,t)}}{{R(\vartheta ,t)}} - \frac{{4\kappa _{R_0}\dot R(\vartheta ,t)}}{{R(\vartheta ,t)^2}} - {\mathrm{\Delta }}P(\vartheta ,t) + P_0\left( {\frac{{V(t)}}{{V_0}}} \right)^\gamma ,$$
(2)

and Pe is the external gas pressure:

$$P_{\mathrm {e}}(t) = P_{\mathrm{0}} + P_{\mathrm{A}}(t).$$
(3)

Here, \(\mu _\ell\) is the liquid dynamic viscosity, P0 is the ambient pressure, PA is the applied ultrasound pressure, V is the bubble volume with V0 the initial bubble volume, γ is the polytropic exponent of the gas, and \(\kappa _{R_0}\) is the shell viscosity. ΔP is the local pressure drop across the interface and the Young−Laplace equation is used to generalize the pressure drop due to surface tension:

$${\mathrm{\Delta }}P(\vartheta ,t) = \sigma _{\mathrm{w}}\left( {\frac{1}{{R_{\mathrm{c}}(t)}} + \frac{1}{{r_{{\mathrm{loc}}}(\vartheta ,t)}}} \right),$$
(4)

where σw is the surface tension of water, rloc is the time-dependent local curvature on the bubble surface in the observation plane and Rc is the time-dependent radius of curvature in the orthogonal direction. The radius of curvature Rc can be estimated from the bubble volume \(V = (4 \pi R_{\mathrm{c}}^3)/{3}\). The exact derivation of the curvature of the bubble and a discussion on this estimation can be found in Supplementary Note 2.

For numerical evaluation each bubble can be discretized and divided into angular segments of length R = R(ϑ, t) and width dϑ that link the surface of the bubble to the origin at an elevation angle ϑ (see Fig. 1b). In general, each segment of the microbubble is considered to obey Eq. (1) and all segments together are coupled through the gas volume V, that in turn determines the internal gas pressure Eq. (2), and through rloc, that is calculated using a finite difference method from the two closest neighbors. In many cases, the use of functionalized bubbles includes targeting to specific cell receptors. As a consequence, bubbles adhere to the functionalized supports upon contact and this adherence translates into the pinning of the triple line separating liquid, gas, and the substrate. The proposed way of modeling the non-spherical bubble dynamics gives a convenient and straightforward way of handling this pinning by setting the velocity of the first segment to zero. The resulting set of differential equations (one equation per segment) is then solved using the ODE113 solver in Matlab.

Describing the microbubble in this segmented picture has implications that we discuss in more detail now. First, the bubble volume being a summation of all segment volumes can be expressed as the sum of the volume fraction belonging to the segment with index i and the remaining volume Vr:

$$V = \frac{{2\pi d\vartheta }}{3}\mathop {\sum}\limits_{j = 1}^n {\kern 1pt} R_j^3cos\left( {\vartheta _j} \right) = \frac{{2\pi d\vartheta }}{3}R_i^3cos(\vartheta _i) + V_{\mathrm{r}},$$
(5)

with dϑ the angle discretization step chosen for the model. When introducing Eq. (5) into Eq. (2), it becomes clear from Eq. (1) that (i) each segment will be a second-order oscillator whose eigenfrequency and phase behavior depends entirely on its initial length, identical to the Minnaert eigenfrequency of a spherical bubble. And (ii), that there is now an additional driving term Vr in Eq. (1) that is governed by the dynamics of all the other segments and that interferes (physically) with the original acoustic driving term. As a direct consequence of (i), the phase of the oscillations will increase for increasing initial segment length and therefore with increasing ϑ (see Supplementary Note 3). The segments with the smallest angles expand first, leading to an oblate shape during microbubble growth. The segments with the smallest angles also retract first, leading to a prolate shape upon collapse. This phase difference along the surface of the microbubble will prove crucial for both the release of the shell material and its subsequent transport.

The numerical model treats coupled oscillating segments and therefore allows for the existence of surface waves at the bubble interface. These surface waves are known to attenuate over a typical time that scales with the wavelength as λ2 \(\left( {\tau = \lambda ^2\rho {\mathrm{/}}4\pi ^2\mu _\ell } \right)\)33. To account for this, we implement a damping correction for each segment in the numerical model with a damping term of the form \(\kappa \dot R\):

$$\frac{\kappa }{{\left( {2R_{\mathrm{0}}{\mathrm{d}}\vartheta } \right)^2}}\left( {\dot R\left( {\vartheta ,t} \right) - \frac{{\dot R\left( {\vartheta - d\vartheta ,t} \right) + \dot R\left( {\vartheta + d\vartheta ,t} \right)}}{2}} \right),$$
(6)

with κ = 2.3×10−5 m2 s−1 the only empirical parameter of the model.

Non-spherical bubble oscillations

Figure 2a shows a typical radius−time curve Rc(t) of a 3.9 μm radius targeted microbubble driven by a 100-cycle ultrasound pulse at a pressure of 166 kPa. The recording was taken at a frame rate near 7.5 million frames per second, and are shown here together with the simulated response at this pressure and for this particular bubble size. Figure 2b shows the corresponding simulated and measured contours R(ϑ, t). Figure 2c, d also shows simulated and experimental contours of microbubbles exposed to pressures of 249 and 331 kPa, respectively. Supplementary Movie 4 shows the simulated bubble dynamics for a 3.1-μm bubble exposed to 84, 166, and 210 kPa and Supplementary Movie 5 shows the simulated bubble dynamics for a 2.4, 3.1, and 4-μm bubble exposed to 210 kPa. From these contours, one can appreciate how the bubbles take an oblate shape while growing and a prolate shape while collapsing, as predicted. Such observations were made earlier14, 15 and the physical explanation is now provided here.

Fig. 2
figure 2

Non-spherical microbubble oscillations. a Simulated and experimental radius−time curve Rc(t) (as calculated from the time-dependent volume) of a 3.9 μm radius microbubble exposed to a 166 kPa ultrasound burst at a frequency of 1 MHz. b Snapshots of the simulated and experimental contours of the bubbles depicted in (a) at the times indicated by the circles. c, d. Snapshots of simulated and experimental contours of bubbles with similar radii exposed to pressures of 249 and 331 kPa, respectively. See Supplementary Movies 1 and 2 for the ultra-high-speed recordings of the non-spherical bubble oscillations and Supplementary Movie 3 for the details of the bubble dynamics simulation

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Lipid oversaturation

An important implication of considering the phase as a function of the elevation angle is that the collapse of the bubble is now regarded as non-spherical. This becomes obvious when taking a closer look at the oscillation dynamics near the substrate, where the contact line is pinned. Until now, ultrasound-mediated release mechanisms of lipids or nanoparticles from microbubbles have been described in the context of spherical oscillations alone24,25,26 and the most commonly considered mechanism to explain detachment of the shell material from the surface of a microbubble involves oversaturation of the lipid layer due to the surface area reduction upon compression, as it is the most intuitive. As mentioned before, in practice, both in vitro and in vivo microbubbles are never in free space. In the free field, the total collapse of a spherical bubble is prevented by a rapid increase of pressure and temperature in the gas core. In the presence of highly non-spherical oscillations, however, the earlier collapse of the bubble segment at small elevation angles is not prevented by such a pressure increase, owing to the phase lag of the bubble segments at a larger elevation angle. Thus, given a sufficiently high acoustic driving pressure, one can expect that nothing prevents this particular segment of the bubble from fully collapsing. This cusp formation process is demonstrated in Fig. 3, showing a simulated lipid shell collapse for such a pinned microbubble for increasing pressures. From Fig. 3a it also becomes clear that the aspherical collapse leads to an oversaturation of phospholipids at a localized position between the cusp and the substrate. Plotted in an angle-resolved view, Fig. 3b shows the change in surface area of each segment in the collapse phase for increasing acoustic pressure. The corresponding increase in the local phospholipid concentration exceeds a factor of ten at pressures in excess of 166 kPa. Figure 3c also shows that the cusp formation becomes less pronounced for larger bubble sizes, away from resonance, as will be detailed in the following section.

Fig. 3
figure 3

Lipid oversaturation. a Shape of the cusp in the collapse phase for increasing pressures showing how the bubble (R0 = 2.4 μm) deforms and the phospholipids oversaturate. b Reduction in the surface area for the phospholipids in the compression phase for the same bubble size and for the same pressures as in (a) as a function of the elevation angle. c gives the simulated shape of the bubble in the compression phase for a targeted bubble with different initial radii driven at a pressure of 210 kPa. See Supplementary Movie 6 for an animation of the cusp formation and the corresponding surface area decrease

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Although it is well-known that the presence of a substrate can change bubble resonance behavior34, 39, little investigations were performed on its effect on the sphericity of the oscillations in this pressure range and in this plane of observation. Unlike our preliminary study27 where we studied microbubbles floating up against a substrate by buoyancy, here targeted microbubbles were used, resulting in the pinning of the area in contact with the Opticell™ membrane. It was found experimentally, see Supplementary Note 4, that the radius of the pinned contact line was on average half the bubble radius with no significant dependency on the bubble size or other quantifiable parameter. rcontact = R0/2 was therefore used for the simulation. It should be kept in mind that there is a fair amount of variability and the contact radius can vary from 25% up to 70% of the bubble radius for the extreme cases. On the other hand, the size of the contact area has limited impact on the simulation output, see Supplementary Note 5. Even removing the pinning altogether (while the bubble kept contact with the substrate) in the simulation leads to the very same conclusions. With decreasing contact area the shape of the bubble at small ϑ angle turns from a cusp into a tip for which all the following arguments also apply. We note that this tip-like shape was observed before15 for the bubbles presenting the smallest contact areas. Also, the pinning behavior of the targeted bubble did not change the previously observed release behavior27, as confirmed by our preliminary experimental verifications and by the simulations.

Microstreaming and transport

It was proposed before that microstreaming surrounding the microbubble during ultrasound exposure is an important transport mechanism following the release events27. The axisymmetric velocity field resulting from simplified non-spherical bubble oscillations was calculated before by Marmottant and Hilgenfeldt40 by assuming the bubble motion to be a superposition of a volumetric oscillation and an oscillatory translation perpendicular to the substrate and with a crucial phase difference Δφ between the two. The resulting flow field, u(r, z), see Fig. 1, is given by a combination of three Stokes singularities: a stokeslet (stk), a dipole (dip), and a hexadecapole (hexdp)41.

The streamlines calculated for a 2.5 μm radius bubble exposed to a burst of 100 cycles at 1 MHz are shown in Fig. 4 and explain the trajectory followed by the released material: the phospholipids detach due to the local oversaturation near the substrate (see subsection Lipid oversaturation) and are dragged along the microbubble surface with the local flow field. Once at the top of the bubble, the material is transported along the centerline (z-axis in our nomenclature) and away from the bubble as illustrated in Fig. 4a. The experimental evidence of this unintuitive behavior is captured in a side view recording using high-speed fluorescence imaging at a frame rate of 50,000 frames per second. Figure 4b shows a typical example of fluorescent material transported during several tens of microseconds. In about one third of the cases, a secondary pinched-off bubble, itself carrying some fluorescent material, was traveling along the central streamline together with the shed material without, however, having a measurable effect on the transport. The velocities observed were typically of the order of 0.1 m s−1. The velocity of the fluorescently labeled molecules drops to zero as soon as ultrasound stops. This is a consequence of the highly viscous behavior of the surrounding water at these ultrashort length scales.

Fig. 4
figure 4

Release and bubble streaming mechanism. a Schematics of the shedding process of the released material (red) with the calculated streamlines (solid black lines). b Experimental recording of the release of the fluorescent material from a targeted oscillating microbubble driven at a pressure of 331 kPa showing a clear transport over a distance several times larger than the bubble size. The fluorescence high-speed recording was taken in a side-view at 50,000 frames per second. Scale bar indicates a length of 10 μm. See Supplementary Movie 7 for a compilation of four high-speed fluorescence recordings showing the release and subsequent transport for different bubble sizes and different driving pressures

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To describe the centerline transport along the z-axis (r = 0) the general flow field description u(r, z) can be simplified to give:

$$u(z) = \epsilon _{\mathrm{z}}\epsilon _{\mathrm{R}}sin\left( {{\mathrm{\Delta }}\varphi } \right)R_{\mathrm{0}}\omega ({\tt{stk}} + {\tt{dip}} + {\tt{hexdp}}),$$
(7)

where

$${\tt{stk}} = \frac{2}{{\bar z - \bar d}} - \frac{1}{{\bar z + \bar d}} - \frac{{(\bar z - \bar d)^2}}{{(\bar z + \bar d)^3}} - \frac{{8\bar d\bar z}}{{(\bar z + \bar d)^3}},$$
(8)
$${\tt{dip}} = - \left( {\frac{1}{{(\bar z - \bar d)^3}} - \frac{7}{{(\bar z + \bar d)^3}} + \frac{{6\bar d}}{{(\bar z + \bar d)^4}}} \right),$$
(9)
$${\tt{hexdp}} = - \frac{1}{2}\left( {\frac{1}{{(\bar z - \bar d)^6}} - \frac{1}{{(\bar z + \bar d)^6}}} \right),$$
(10)

with z as described in Fig. 1, d the initial distance of the center of the bubble to the substrate, thus slightly smaller than the bubble radius due to the pinning, and where the overbars are used to indicate that the space variable is non-dimensionalized with the initial bubble radius R0. \(\epsilon _{\mathrm{z}}\) and \(\epsilon _{\mathrm{R}}\) are the relative volumetric oscillation amplitudes and the relative oscillatory translation amplitudes, respectively, as defined in ref. 40. The prefactor in Eq. (7) gives the typical velocity of the streaming and is proportional to the sine of the phase difference Δφ between volumetric oscillations and oscillatory translations. Thus, in this description, streaming can indeed only arise from non-spherical oscillations.

The amplitude of the volumetric oscillations and the oscillatory translations, as well as their phases, and their phase difference, follow directly from the simulation. Figure 5a displays the volumetric oscillation and oscillatory translation amplitudes as a function of the bubble radius at a driving pressure of 100 kPa and a frequency of 1 MHz. It is evident that it displays strong resonance behavior. Similarly, the corresponding phase of the simulated volumetric oscillations and oscillatory translations, Fig. 5b, displays the characteristics of a resonant system. In addition, Fig. 5b plots the calculated phase difference for different pressures. Note that the bubble size corresponding to the maximum phase difference is found to increase with increasing pressure.

Fig. 5
figure 5

Non-spherical oscillation amplitude and phase. a The volumetric oscillation amplitudes \(\epsilon _{\mathrm {R}}\) (solid black line) and oscillatory translation amplitude \(\epsilon _{\mathrm{z}}\) (dashed black line) as a function of the bubble radius at a driving pressure of 84 kPa and a frequency of 1 MHz. b Phase φ (left y-axis) of the volumetric oscillations (solid black line) and oscillatory translations (dashed black line) for the same conditions as in (a). The colored lines denote the resulting phase difference Δφ (right y-axis) between volumetric oscillations and oscillatory translations for different driving pressures

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Bubble streaming-induced transport

The transport distance s(t) of a fluid element along the centerline (z-axis) is calculated by integrating the Lagrangian velocity of the particle, Eq. (7), from time zero to t:

$$s(t) = {\int}_0^t {\kern 1pt} u(z(t)){\mathrm {d}}t.$$
(11)

The transport distance is measured directly from the high-speed fluorescence recordings.

Figure 6a plots the experimental transport distance vs. time. The integration in Eq. (11) is carried out over the duration of the ultrasound burst, in this case 100 μs. The calculated transport distance is valid for bubbles in a stationary oscillation regime and in a stationary streaming flow field, i.e. in the absence of transient effects, and with the bubble kept at a fixed location. Sometimes, and even more so at elevated pressures, the bubbles break-up, jet, pinch-off daughter bubbles or move rapidly along the substrate while disturbing the streaming field. For the targeted microbubbles that do fulfill the conditions of the model, the measured transport distance is plotted in Fig. 6c–e together with the predicted transport distance (see Supplementary Note 6 for details), where we find overall very good agreement. Note that the experimental results show some variability in the observed transport distance, owing to the large variations in the non-linear bubble response and subsequent second-order effects, which includes bubble streaming. Finally, coming back to the time evolution of the bubble streaming-induced transport, Fig. 6b shows the calculated transport distances at resonance, showing that most efficient transport is achieved within the first 200 μs and that the effect of longer pulse duration, and notably increased pressure, is only marginal, since a doubling of the pressure only leads to a 25% increase of the transport distance.

Fig. 6
figure 6

Transport of the microbubble payload. a Experimental (red triangles) and computed (solid black line) transport distance vs. time plot of the fluorescent material shed by a 2.0 μm radius microbubble driven at a pressure of 84 kPa. b Calculated transport distance at resonance vs. time for acoustic pressures of 166, 249, and 331 kPa and 1 MHz excitation frequency. c–e Simulated (solid lines) and measured (circles) transport distance for microbubbles exposed to a 100-cycle, 1 MHz ultrasound burst of 166, 249, and 331 kPa. The gray areas denote the standard deviation of the scaled model for all pressures computed; see Supplementary Note 6

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Discussion

The presence of a shell has two effects on bubble dynamics: an increased damping due to shell viscosity and an increased stiffness due to shell elasticity. Several models were proposed to account for bubble shells42, 43. The present model includes a shell viscosity (see Eq. (2)), which mainly increases the required pressure to reach the same oscillation amplitude and has otherwise negligible impact on the response. Rigorously considering the shell elasticity for non-spherical oscillation is complex as the response of a lipid monolayer to bending and the phospholipids dynamics on the bubble surface at MHz rates and on the microscale is unknown. Here, the coating is almost entirely shed within the first few microseconds, and therefore shell elasticity is neglected to compute the streaming. Adding shell elasticity to our computation, according to the Marmottant model31, induces a shift in the resonant radius but resulted in comparable surface reduction plots at resonance (Fig. 3a) and led to the same physical description of the shedding process. A contribution of shell elasticity was therefore not included.

The release of material from the bubble coating is often accompanied by the pinch-off of smaller submicron-sized bubbles. A direct implication is the immediate size reduction of the mother microbubble. This pinch-off process was also reported in earlier work44, 45. In the present experiments, these events were very difficult to control and highly irreproducible. It appears that the secondary bubbles carry some fluorescent shell material with them, while moving away from the bubble. Pinch-off occurred in about one third of the cases, with no obvious dependency on bubble size or oscillation amplitude.

For larger bubbles (≥4 μm) and higher pressures (≥350 kPa), jet formation was often observed. Such jets were reported before46: following asymmetrical collapse, the jet penetrates the bubble core and impinges onto the substrate. The role of jetting on cell poration is often discussed, but its resulting effects on the microbubble shell or on the delivery of a payload has received little attention. During collapse, the fluorescent coating appears to be following the jet, leading to its deposition onto the supporting substrate. Although jetting is not our present focus, this effect could certainly be of further interest for drug delivery with microbubbles.

The present study was performed on a model drug inserted between the phospholipids that coat the microbubble. A previous study27 has demonstrated that microbubbles loaded with liposomes or polymeric nanoparticles quantitatively display identical behavior when compared in terms of microbubble oscillation amplitude. Changing the type of payload is therefore not expected to change the conclusions presented here. The ability of the targeted microbubbles to deliver various payloads over a distance several times larger than their own size presents great potential for targeted drug delivery and theranostic applications.

The behavior of phospholipid molecules on the microbubble surface is highly complex and the subject of much attention from researchers in the field of interfacial chemistry. Quasi-static Langmuir trough measurements state that the shell should collapse when reducing the bubble size by only a few percent26, 47. It is however known not to hold for ultrasound-driven microbubbles, in particular due to the fast dynamical aspects48. On short timescales, the residence time of molecules at the interface will be related to the desorption potential barrier and to the viscosity associated with molecular motion49. Also, the compression of the phospholipids in a localized area of the surface can be expected to result in molecular transport along the shell, motion that is also subjected to molecular friction. Motion of individual molecules and the associated molecular processes remain to be explored. Interesting insights here may be provided, e.g. by molecular dynamic simulations.

Finally, this work highlights the importance of the substrate that supports the microbubble. Note that in the proposed model, the substrate is considered rigid in a fluid dynamical sense, which is justified by the very short length scales involved, as well as what is observed in experiment. The results presented here improve our understanding of the delivery of a drug from targeted microbubbles and thereby our control over microbubble shedding. The present configuration of payload release along the symmetry axis of the adherent bubble can be highly efficient in small vessels and capillaries. However, this configuration may be suboptimal for sonoporation or sonothrombolysis, where the transport should preferentially be directed toward the target cells. In order to optimize drug delivery, next steps should extend the present work towards more compliant substrates, as found in vivo, and define more advanced strategies to control the transport direction.

Methods

Numerical methods

The set of second-order differential equations of Eq. (1) was solved numerically using the ODE113 solver in MATLAB (v. R2016b, The MathWorks, Natick, MA). The pressure inside the bubble, Eq. (2), was calculated from the summation of the individual segment volumes. The number of segments was varied between 20, sufficient for convergence of the model, and 100 for an optically pleasant rendering; see e.g. Supplementary Movies 4 and 5. The physical constants used for the simulation are as follows: density of water \(\rho _\ell\) = 1000 kg m−3, liquid viscosity \(\mu _\ell\) = 1 mPa s, surface tension of water σw = 72 mN m−1, and polytropic exponent of the C4F10 gas γ = 1.05. The damping contributions, including the more extended formalism for the thermal damping, were modeled along the work of Prosperetti50. The empirical damping term κ = 2.3×10−5 m2 s−1 was fixed for all simulations. The acoustic driving pressure was increased from 42 to 331 kPa in nine steps with a frequency of 1 MHz.

Bubble preparation

Biotinylated microbubbles6 were prepared by sonication. The coating was composed of DSPC (59.4 mol%; Sigma-Aldrich, Zwijndrecht, The Netherlands), polyoxyethylene-40 stearate (35.7 mol%; Sigma-Aldrich), DSPE-PEG(2000) (4.1% mol; Avanti Polar Lipids, Alabaster, AL, USA) and DSPE-PEG(2000)-biotin (0.8 mol%; Avanti Polar Lipids). For fluorescence labeling, DiI (Molecular Probes, Eugene, OR, USA) was dissolved in ethanol and added to the solution before sonication.

Sample preparation

The topside of an OptiCell (Thermo Fisher Scientific, Waltham, MA, USA) was coated by adding 1 mL of 1 μg mL−1 solution of NeutrAvidin (Life Technologies Europe, Bleiswijk, The Netherlands) in phosphate-buffered saline (PBS) (Life Technologies Europe) 24 h prior to the experiment. The surface was then rinsed with PBS to remove all unbound proteins and incubated for 1 h with 1% bovine serum albumin (Sigma-Aldrich) to prevent unspecific binding. Afterwards, the surface was cut into rectangular pieces of 5 mm × 20 mm. Biotinylated microbubbles were injected into the tank and allowed to adhere to the surface by flotation for 5 min.

Experimental methods

The substrate was immersed in a water bath (T ≈ 22 °C), filled with demineralized water, under a 45° angle with respect to the vertical, and could be moved with a 3D micropositioning stage. A focused, single-element ultrasound transducer (C302, Panametrics, Waltham, MA, USA) with a center frequency of 1 MHz was fixed on one side of the water tank and used for insonation. A detailed schematic of the setup is given in Supplementary Note 7. For each recording, a single microbubble was exposed to a single ultrasound burst. The acoustic pressures were measured with a calibrated needle hydrophone (0.2 mm, Precision Acoustics, Dorchester, UK). Optical recordings were performed using a microscope equipped with a 20x water-immersion objective (LUMPFL, Olympus, Zoeterwoude, The Netherlands) that was fixed at a 45° angle relative to the vertical (with the optical axis parallel to the substrate). A continuous-wave diode laser (5 W, λ = 532 nm; Cohlibri, Lightline, Osnabrück, Germany) was focused onto the sample through the same objective, using a dichroic mirror. The laser light was gated using an acousto-optic modulator (AOTF.nC-VIS, AA Optoelectronic, Orsay, France) to generate a 500 μs laser pulse. Simultaneously, a KL 2500 LED light source (Schott, Mainz, Germany) was used to superimpose bright-field and fluorescence. High-speed recordings were acquired with a high-speed camera (SA-X, Photron, West Wycombe, UK), operating at 5000 to 50,000 fps. Ultra-high-speed imaging was performed with the Brandaris 128 camera51 at frame rates ranging from 5 to 10 million fps. Using a beam splitter, 80% of the light was directed into the Brandaris camera, while the remaining 20% was directed towards the Photron camera. A test was performed for 12 targeted microbubbles recorded in a top-view configuration. Identical shedding was observed as compared to our previous study27, demonstrating that the targeting did not significantly alter the process.

Analysis

The recordings were contrast-enhanced, and analyzed using a thresholding method in MATLAB to extract the bubble contours R(ϑ, t). The bubble volume was obtained by assuming axial symmetry. Due to the more complex aspect of the released fluorescent material, the transport distance was extracted by manually selecting the center of the fluorescence patch in each frame of the recordings.

Data availability

The authors declare that all the data acquired during this study, as well as the Matlab codes used for simulating microbubbles responses and analyses will remain stored within the servers of the University of Twente and will be made available on request by the authors.