Material properties, dissolution and time evolution of PEGylated lipid-shelled microbubbles: effects of the PEG hydrophilic chain configurations

Abstract

Poly(ethylene glycol) (PEG) is often added to the lipid coating of a contrast microbubble to prevent coalescence and improve circulation. At high surface density, PEG chains are known to undergo a transition from a mushroom configuration to an extended brush configuration. We investigate the effects of PEG chain configuration on attenuation and dissolution of microbubbles by varying the molar ratio of the PEGylated lipid in the shell with three (0%, 2%, and 5%) in the mushroom configuration, and two (10% and 20%) in the brush configuration. We measure attenuation through the bubble suspensions and use it to obtain the characteristic rheological properties of their shells according to two interfacial rheological models. The interfacial elasticity was found to be significantly lower in the brush regime (~0.6 N/m) than in the mushroom regime (~1.3N/m), but of similar values within each regime. The dissolution behavior of microbubbles under acoustic excitation inside an air-saturated medium was studied by measuring the time-dependent attenuation. Total attenuation recorded a transient increase because of growth due to air influx, and an eventual decrease due to dissolution. Microbubbles’ shell composition with varying PEG concentrations had significant effects on the dissolution dynamics.

Introduction

Microbubbles coated by a shell of surface-active substances such as lipids and proteins are well-known contrast agents for ultrasound imaging. Due to the compressive gas core, they oscillate in response to an acoustic wave and generate fundamental as well as various harmonic responses (Azmin, et al. 2012, de Jong, et al. 2002, Helfield 2019, Katiyar and Sarkar 2011, Paul, et al. 2014). They could also act as potential drug carriers with drugs loaded in the core or on the shell, which can be released at the desired region in a controlled way by using external acoustic excitation (Kooiman, et al. 2014, Marik, et al. 2007, Mulvana, et al. 2017). Such applications warrant stable microbubbles with a long circulation lifetime inside the body. Poly (ethylene glycol) (PEG) is commonly incorporated in the microbubble shells to improve circulation by protecting them against macromolecule absorption and coalescence by creating a steric barrier of hydrophilic chains of the grafted PEG (Chen and Borden 2010). In addition, PEG chains can allow the linkage of drugs to the shell (Mulvana, et al. 2017). Here, we investigate the effects of PEG concentrations on the behaviors of microbubbles, specifically how they change the shell properties which in turn affect bubble dissolution and their acoustic responses.

PEG is a long-chain molecule, which when absorbed at an interface can take two different configurations, brush and mushroom, depending on the PEG molecular weight and its surface concentration (de Gennes 1987). If the surface concentration is high enough so that the distance between chains (D) is smaller than the Flory radius of the grafted PEG chain (R_F), the chains extend and form a brush configuration (D < R_F). For lower PEG concentrations, the distance between chains is higher than the Flory radius, therefore PEG chains form a mushroom-like configuration (D > R_F) (de Gennes 1987, Kenworthy, et al. 1995). These alterations in PEG chains configuration and the shell chemistry, as we will show, have profound effects on the encapsulation properties, in turn determining the microbubbles’ behavior under acoustic excitation.

The stability of microbubble in a multi-gas medium is dependent on the shell properties. Permeability of the encapsulation to the gas core and the dissolved gas in the surrounding liquid can change the lifespan of microbubbles from seconds to hours (Kwan and Borden 2010, Sarkar, et al. 2009). On the other hand, shell properties also critically determine the acoustic response of a microbubble. Therefore, an optimized balance between the acoustic response and stability of microbubbles is highly desirable for maximizing their performance and clinical usability. This needs a proper understanding of the relation between shell chemistry and its stability and mechanical properties.

Shell composition can alter its material properties and in turn the acoustic response and stability of microbubbles (de Jong, et al. 2002, Sboros 2008, van der Meer, et al. 2007). Several models have been proposed to model the response of a microbubble to an acoustic pressure wave. Taking into consideration that the protective coatings of surface-active molecules are only a few-molecule thick, our group has proposed an interfacial rheological model to account for its effects (Chatterjee and Sarkar 2003), which subsequently became a standard approach. Over the years, we and others have developed several different interfacial rheological models in terms of interfacial material properties such as interfacial elasticity, interfacial viscosity, and surface tension and applied them to experimental observations to estimate the properties of the microbubble coating (Chatterjee and Sarkar 2003, Doinikov and Bouakaz 2011, Kumar and Sarkar 2016, Marmottant, et al. 2005, Paul, et al. 2010, Paul, et al. 2013, Sarkar, et al. 2005). In addition, direct measurement methods, such as Langmuir trough (Lozano and Longo 2009), atomic force microscopy (AFM) (Sboros, et al. 2006), and photoacoustic technique (Lum, et al. 2016) have been utilized.

The stiffness of the lipid encapsulation of microbubbles was reported to show different trends with increasing PEG concentration in the shell in previous studies. Dicker et al.(2013) showed that the elasticity of the shell decreases when the DSPE-PEG (molecular weight: 2000 to 5000) concentration in the microbubble DSPC shell changed from 1% to 7.5% molar ratio. However, Segers et al.(2018) reported insignificant changes in the shell elasticity for DPPC shelled microbubble with 5%, 7.5%, and 10% DPPE-PEG5000. Abou-Saleh et al.(2014) used AFM to measure the stiffness of microbubbles with DPPC shell mixed with DSPE-B-PEG2000 in molar fractions ranging from 0% to 35% and reported that the stiffness increases with PEG percentage. These contradicting results warrant further investigation of the effects of PEG concentration on the microbubble dynamics to provide a better understanding in designing microbubbles with appropriate qualities for specific imaging and drug delivery applications.

Here, we synthesized perfluorocarbon microbubbles with varying PEG concentrations in their lipid shells. We acoustically characterized them using attenuation to examine the change in their shell properties, specifically the interfacial elasticity, relating them to the conformation of PEG molecules absorbed at the gas-liquid interface. We also investigated the time evolution of the dissolution of microbubbles dispersed inside the air-saturated water, relating the observed behaviors to the change in shell permeability with increasing PEG concentrations.

Materials and method

Preparation and characterization of lipid-coated microbubbles

The synthesis of lipid-shelled microbubbles with perfluorobutane (PFB) gas cores has been described by our group previously (Aliabouzar, et al. 2016, Osborn, et al. 2019). Briefly, 1,2-dipalmitoyl-sn-glycero-3-phosphatidylcholine (DPPC), and 1,2-dipalmitoyl-sn-glycero-3-phosphatidylethanolamine-polyethyleneglycol-2000 (DPPE-PEG-2000) (Avanti Polar Lipids, Alabaster, AL, USA) were used to create microbubbles with different shell compositions by varying the ratio of DPPE-PEG-2000 to DPPC (Table 1) along with a PFB (FlouroMed L.P., Round Rock, TX, USA) core. First, the desired amount of lipid powders was dissolved in propylene glycol at 50°C (above the transition temperature of DPPC) and stirred for 60 minutes to ensure proper mixing of lipids. Note that different lipid handlings were found to affect the microstructure in the lipid shell. First dissolving the lipids in propylene glycol as adopted here (called an indirect method), in contrast to direct dispersion in the aqueous medium leads to less structural heterogeneity and more liquid-condensed (LC) area in the coating (Langeveld, et al. 2020). After achieving a clear solution, a mixture of phosphate buffer saline (PBS) and glycerol was added. The final mixture containing 10 mg of lipids in 10 mL aqueous mixture of PBS, glycerol, and propylene glycol in 80:5:15 volume ratio, was stirred for an additional 60 minutes at 50°C. The mixture was allowed to cool down at room temperature and stored at 4C° for further use.

Table 1.

Shell formulations of microbubbles

Name	Shell composition (Molar ratio)		Distance between PEG chains (nm)	Configuration
	DPPE-PEG2000 (mol %)	DPPC (mol %)
0%PEG	0	100	-	-
2%PEG	2	98	5	Mushroom
5%PEG	5	95	3.2	Mushroom–Brush border
10%PEG	10	90	2.4	Brush
20%PEG	20	80	1.5	Dense brush

Microbubbles were made by a mechanical agitation method. First, 1.5 mL of the lipid solution was placed in 2mL glass vials (Med Lab Supply, FL, USA). After sealing and clamping the vial with a rubber head and metal cap (Med Lab Supply, FL, USA), the air inside the vial was removed and replaced with PFB. A vial mixer (VIALMIX, Lantheus, Billerica, MA, USA) was used to shake the vial in high frequency for 45 seconds to produce the microbubble suspensions. The resultant microbubbles were allowed to rest at 4^oC for 15 minutes before experiments.

Inverted optical microscopy (Amscope, California, USA) was used to measure the size distribution and total concentration of the microbubbles following a method described in the literature (Sennoga, et al. 2015, Sennoga, et al. 2010, Sennoga, et al. 2012). A 10 μL aliquot of 50x diluted microbubble solution in PBS was inserted in a hemocytometer (VWR, New Jersey, USA). A CCD camera (Amscope, California, USA) connected to an objective lens of 40x magnification with an optical resolution of 580 nm (for the wavelength of 700 nm) was used to capture optical images with a pixel size of 60 nm. ImageJ software (https://imagej.nih.gov/ij/) was used for the counting and size distribution determination of microbubbles. Using the printed grid on the hemocytometer, one can calibrate the pixel to distance ratio and calculate the scanned area. Therefore, knowing the depth of the counting chamber (100 μm in this experiment), the volume of the scanned region was obtained. The total concentration is reported as the average number of microbubbles in the respective scanned region volume. For each measurement, at least 9 images from different regions of the counting chamber were processed and more than 1300 microbubbles were counted. This procedure was replicated at least three times, using a new batch of microbubbles each time.

Determination of PEG chain configuration

To determine the configuration of PEG chains, the distance between chains and the Flory radius of the grafted PEG were calculated as follows (Abou-Saleh, et al. 2014, Kenworthy, et al. 1995):

$$R_F=a{N}^{3/5},D=\sqrt{A_{lipid}/m},$$ (1)

where R_F is the Flory radius, a is the monomer size (=0.35nm for PEG2000) and N is the number of monomer units per chain which is 45 for PEG2000. D is the distance between chains, A_lipid is area per lipid molecule(=0.5nm²) (Abou-Saleh, et al. 2014), and m is the molar fraction of the PEG in the shell. The Flory radius (R_F ) calculated for DPPC and DPPE-PEG2000 system is roughly 3.4 nm. The distance between chains (D) and corresponding configuration are listed in Table 1. PEG chains form a mushroom-like configuration when the distance between them is greater than the Flory radius (D>R_F). As the distance between the chains becomes smaller than the Flory radius (D< R_F) the PEG chains are forced to stretch and form a brush configuration. The different concentration and their configurations are listed in Table 1. We refer to 10% and 20% as in a “brush regime” and the others in a “mushroom regime”. Note that the above analysis assumes a uniform distribution of PEG chains over the surface of a microbubble, which is only approximately true on average because of phase separations in the lipid shell and the microstructural inhomogeneity, observed in experiments (Langeveld, et al. 2021, Langeveld, et al. 2020). Such structural inhomogeneity depends on lipid handling, chemical composition, and cooling rate (Borden, et al. 2006). However, note that an experimental determination of Langmuir isotherm offered a reasonable match with the theoretical transition threshold using the above analysis in a similar binary (DPPC-DSPE-PEG2000) (and even in a ternary) system with phase separation (Langeveld, et al. 2020). It gives us confidence in the method of determining the phase behaviors of our system. However, we should note that due to phase separation and resulting nonuniform PEG distributions, areas of brush conformation is possible for PEG percentages lower than the nominal brush-mushroom transition value.

Attenuation measurement

Frequency-dependent attenuation of the microbubble solution was measured using the custom setup illustrated in Fig.1. A desired aliquot of microbubbles was dispersed in deionized (DI) water to ensure limited damping and a signal above the noise level. The final number of bubbles per mL employed in the sample chamber were 74000 (0%PEG), 58000 (2%PEG), 64000 (5%PEG), 142000 (10%PEG), and 96000 (20%PEG). To ensure a homogenous distribution of microbubbles, measurements were done 30 seconds after the injection of microbubbles into the chamber and a magnetic bar was gently stirring the suspension inside a polycarbonate rectangular chamber throughout the experiments. All experiments were performed at room temperature.

Fig. 1.

Experimental setup to measure ultrasound attenuation in a dispersion of microbubbles in DI water.

Unfocused single element transducers (Olympus NDT Corporation, Waltham, MA) with central frequencies of 2.25 MHz (−6dB: 1.6–3.28 MHz) and 5MHz (−6dB: 3.2–6.4 MHz) were driven by a pulser-receiver (5800PR, Panametrics-NDT, Waltham, MA) in pulse-echo mode to send and receive pulses with a 100Hz repetition frequency (PRF). The driving pulse was a negative impulse resulting in a short acoustic pulse of about 1 μSec temporal duration. An external attenuator was used to keep the peak excitation pressure sufficiently small, 17.4 kPa and 18.2 kPa for the 2.25 MHz and 5 MHz transducers respectively, to guarantee linear dynamics. Previous studies have demonstrated attenuation to be independent of the acoustic pressure and the central frequency of the transducer for this pressure range (Chatterjee, et al. 2005, Raymond, et al. 2014, Shekhar, et al. 2018). Here also we have studied the effects of different peak acoustic pressures to obtain little variation in the range of 9–40 kPa (shown in Figs. 3C and D) A bandpass filter was applied from 100 kHz to 35 MHz. An oscilloscope (Tektronix, MDO3024, Beaverton, OR) then gated the received signal with a delay time of 73 μs, which is the time for the acoustic wave to travel the width of the sample chamber forward and back and digitized at a sampling rate of 1.5 GHz. 50 signals were acquired in averaging mode (64 sequences) and then recorded by an in-house MATLAB (Mathworks, Natick, MA) code for further processing. Measurement with each formulation was repeated with a fresh sample of suspension at least three times.

Fig. 3.

(A) Example voltage-time signals and (B) Power spectrum of received signals before (control) and after injection microbubbles (MB) into the sample chamber. Attenuation curves measured using 2.25 MHz (C) and 5 MHz (D) transducers at varying acoustic amplitude.

Attenuation analysis assumes a sufficiently small excitation to ensure a linear propagation of sound with no nonlinear transfer across different frequencies. Therefore, each frequency ω component has its independent attenuation α(ω) (Chatterjee, et al. 2005). To compute it the signals were taken before and after injection of microbubbles in DI water. The response in the frequency domain was calculated by taking fast Fourier transform (FFT) of the recorded voltagetime signals. The frequency-dependent attenuation coefficient (dB/cm) was calculated as:

$$\alpha (\omega )=10\log \left(V_{\text{control}}^2(\omega )/V_{\text{bubble}}^2(\omega )\right)/d$$ (2)

where V_control and V_bubble are the response without and with microbubbles in the frequency domain respectively. The amplitudes are squared to account for the relationships between ultrasound intensity, pressure amplitude, and voltage amplitude.

Modeling attenuation and interfacial parameter estimation

We use a strain-softening interfacial rheological model, the exponential elasticity model (EEM) developed in our lab (Paul, et al. 2010) for the encapsulation. We introduce it to the incompressible Rayleigh-Plesset type of equation of bubble dynamics:

$$\begin{gathered} \rho \left(R\ddot{R}+\frac{3}{2}{\dot{R}}^2\right)=P_{G0}{\left(\frac{R_0}{R}\right)}^{3k}\left(1-3k\frac{\dot{R}}{c}\right)-4\mu \frac{\dot{R}}{R}-\frac{4{\kappa }^s\dot{R}}{R^2}-\frac{2\gamma (R)}{R}-P_0+P_A\sin \omega t \\ \gamma (R)={\gamma }_0+E^s\beta ,E^s=E_0^s{e}^{-{\alpha }^s\beta },\beta ={\left(R/R_E\right)}^2-1 \end{gathered}$$ (3)

Here, ρ is the density, μ, the viscosity, and c, the speed of sound in the liquid. R(t) is the instantaneous radius of the oscillating bubble, R₀ is the initial radius of the bubble, and R_E is the radius of the bubble in its unstressed state. P_G0 is the initial gas pressure of the core of the bubble, k, the polytrophic constant, P₀, the ambient pressure, and P_A, the amplitude of the sinusoidal ultrasound excitation with an angular frequency ω. The coating is characterized under the EEM model by the surface tension γ₀, the interfacial viscosity K^s, and the interfacial dilatational elasticity E^s, the latter defined by reference elasticity $E_0^s$ and the strain-softening parameterα^s. Under sufficiently low excitation, the oscillation is small enough to warrant a linearization of the Rayleigh-Plesset equation (3) to obtain a simple harmonic oscillator with a resonance frequency ω₀ :

$${\omega }_0^2=\frac{1}{\rho R_0^2}\left[3k{P}_{\text{0}}+\frac{2E_0^s}{R_0}\left(\frac{\eta }{{\alpha }^s}\right)\left(1+2{\alpha }^s-\eta \right)\right],\eta =\sqrt{1+\frac{4{\gamma }_0{\alpha }^s}{E_0^s}}.$$ (4)

Different models of the coating give rise to different expressions for effective surface tension γ(R)and the surface dilatational viscosity k^s(R) (Katiyar and Sarkar 2011, Paul, et al. 2013). Marmottant model (MM) (Marmottant, et al. 2005) defines the surface tension term in (3) as $\gamma (R)=\gamma \left(R_0\right)+\chi \left[{\left(R/R_0\right)}^2-1\right]$ in a range of radius (R_buckle, R_rupture). The surface tension becomes zero below R_buckle and assumes the value of the pure air-water interface above R_rupture. Note that the model is identical in the above range to the constant elasticity model proposed by us (Sarkar, et al. 2005) with χ being identical to a constant dilatational elasticity $E_0^s$. Assuming that the oscillation remains entirely in the linear regime, one obtains a resonance frequency for MM:

$${\omega }_0^2=\frac{1}{\rho R_0^2}\left[3k{P}_0+(3k-1)\frac{2\gamma \left(R_0\right)}{R_0}+\frac{4\chi }{R_0}\right].$$ (6)

For both models the damping term δ is same

$$\delta =\frac{1}{\rho {\omega }_0{R}_0^2}\left(4\mu +4\frac{{\kappa }^s}{R_0}+\frac{3k{P}_0{R}_0}{c}\right).$$ (7)

Accordingly, one obtains the attenuation α(ω) in terms of the individual extinction cross-section ${\sigma }_e$ of a microbubble of initial radius R₀ by integrating over the bubble size distribution:

$$\begin{array}{c}\alpha (\omega )=10\log e{\int }_{R_{\min }}^{R_{\max }}{\sigma }_e(R;\omega )n(R)dR,\\ {\sigma }_e=4\pi R_0^2\frac{c\delta }{{\omega }_0{R}_0}\frac{{\text{Ω}}^2}{\left[{\left(1-{\text{Ω}}^2\right)}^2+{\text{Ω}}^2{\delta }^2\right]},\text{Ω}=\frac{{\omega }_0}{\omega }\end{array}$$ (8)

where n(R)dR is the number of the bubbles with a radius between (R, R+dR) in the range of (R_min, R_max) per unit volume. The experimental attenuation curve obtained from Eq. (2) was compared with the theoretical value from Eq. (8) to formulate an error function. The error function was minimized using a MATLAB program to obtain the interfacial rheological parameters. The values were changed until the summed squared error between the measured and the calculated attenuation curve doubles to obtain the confidence intervals listed in Table 2 and Fig. 6 (Hoff, et al. 2000).

Table 2.

Material properties of the shells with different molar ratios of DPPE-PEG2000 mixed with base lipid DPPC.

PEG molar ratio (%)	Shell Elasticity (N/m)		Shell Viscosity (×e-08 N.s/m)		α (EEM)	γ0 (N/m) (EEM)
	E0s (EEM)	χ (MM)	κs (EEM)	κs (MM)
0	1.19 [1.14–1.24]	1.21 [1.16–1.27]	1.21 [1.07–1.38]	1.21 [1.07–1.38]	1.7 (0–4.3]	0.011 [0–0.035]
2	1.25 [1.22–1.28]	1.28 [1.25–1.31]	2.88 [2.79–2.96]	2.88 [2.8–2.96]	1.7 [0.5–2.9]	0.012 [0–0.024]
5	1.39 [1.27–1.52]	1.42 [1.3–1.55]	2.34 [2.0–2.7]	2.35 [1.99–2.71]	2.0 [0.6–3.4]	0.013 [0–0.07]
10	0.54 [0.48–0.59]	0.54 [0.49–0.60]	4.01 [3.68–4.37]	4.01 [3.68–4.37]	1.8 (0–7.3]	0.005 [0–0.057]
20	0.67 [0.61–0.73]	0.68 [0.62–0.74]	3.51 [3.09–3.93]	3.51 [3.07–3.94]	1.4 (0–6.1]	0.007 [0–0.052]

Fig. 6.

Interfacial elasticity for microbubbles with different PEG molar fractions in their shells. Limits corresponding to a doubling of the summed error are shown as a confidence interval

Microbubble stability

We investigated the stability of microbubbles in suspension by monitoring the change in the attenuation curve over a time interval. The frequency-dependent attenuation was measured every two minutes for 60 minutes with the acoustic excitation turned on during the time at 100Hz PRF and the suspension stirred continuously. Here, we use a 5MHz transducer which has a sufficiently broad range to capture the bubble behaviors evolving over the entire time interval. For each sampling time, we compute the total attenuation A(t) summing over all frequencies shown in Eq. (2) as:

$$A(t)=10{\log }_{10}\left(\frac{\sum _{\omega }{V}_{control}^2(\omega )}{\sum _{\omega }{V}_{Bubble}^2(\omega )}\right)/d.$$ (5)

Results and discussion

Characterization of microbubbles

Optical microscopy was used to measure the size distribution of the microbubbles. Fig. 2A–E shows the microbubble size distributions for each shell composition. Due to optical resolution limitations (Sennoga, et al. 2010, Sennoga, et al. 2012), only microbubbles bigger than 0.6 μm were counted. A bin width of 0.1 μm was used to plot the histograms. There are slight variations in the size distributions from different PEG concentrations. However, the mean diameter of microbubbles for different samples was ~2.2–2.6 μm as can be seen in Fig. 2 with about 80–86% of the total bubbles in any sample having a radius between 1 μm and 4 μm. The polydispersity of the size distributions was characterized by computing Span = (D₉₀-D₁₀)/D₅₀ (noted in Fig.2), where D_n is the diameter with n% of the total microbubbles below this size, leading to values very similar to what was previously obtained in similar preparation methods (Langeveld, et al. 2021, Langeveld, et al. 2020). Previously Dicker et al. (2013) reported no significant change in the size distribution of DSPC based microbubbles with varying molar ratios and molecular weights of DSPE-PEG emulsifiers.

Fig. 2.

Size distribution of microbubbles with (A) 0% PEG, (B) 2% PEG, (C) 5% PEG, (D) 10% PEG, and (E) 20 % PEG with. Corresponding number weighted mean size and span value of the distribution are on top right corner of each. A photo of 20% microbubbles under a microscope is shown as an example. (F) Total concentration (microbubbles/mL) as a function of the PEG percentage in microbubble shell. Concentration reaches to a maximum at 2% PEG. Further addition of PEG is accompanied by a decrease in the total microbubble concentration.

Fig. 2F shows microbubble yield as a function of PEG concentration. The addition of PEG as an emulsifier to the lipid shell resulted in a 10-fold increase in the total concentration in comparison to 0%PEG. Microbubbles with 2% PEG in the shell showed the highest number concentration (6.04 × 10⁹ microbubbles /mL). The steric hindrance caused by PEG chains helps to increase the yield in microbubble production by inhibiting the coalescence (Chen and Borden 2010). Further addition of PEG resulted in about 50% reduction in the total concertation, a trend also observed by Abou-Saleh et al.(2014). They found that the microbubble yield reached a maximum at shell composition of 5% DSPE-PEG2000 and 95% DPPC, and further addition of emulsifiers caused a gradual decrease in the total concentration. The decrease in the concentration was attributed to a disruption in base lipid structure due to increased repulsive forces between PEG chains.

Attenuation measurements

Fig. 3A and Fig. 3B show example voltage-time signals and the corresponding power spectra before and after injection of microbubbles (10% PEG percentage for the 2.25 MHz transducer and 2% PEG concentration one for the 5 MHz one) into the sample chamber. With the microbubble concentrations used, they are typically separated from each other by more than 200 microbubble radii. Figs. 3C and 3D plots attenuation for the same cases with varying peak acoustic pressure amplitude. They demonstrate that attenuation is insensitive, as it should be, to a slight variation of the peak pressure amplitude range (Chatterjee, et al. 2005, Raymond, et al. 2014, Shekhar, et al. 2018). As noted, all experiments were performed with 17.4 kPa and 18.2 kPa for the 2.25 MHz and 5 MHz transducers respectively.

The frequency-dependent attenuation coefficient measured for different PEG concentrations is shown in Fig. 4A and Fig. 4B. Typically the maximum attenuation occurs at an excitation frequency close to the microbubble resonance frequency. Here, a polydisperse bubble population resulted from the mechanical agitation method, and the broad peak represents a weighted average of the resonance frequencies of different sized bubbles (Kumar and Sarkar 2015) and therefore is representative of the resonance frequency corresponding to that particular microbubble formulation. Microbubbles with higher PEG percentages (Fig. 4A), which fall into the brush regime (Table 1), resonate at lower frequencies—between 1.5 to 2 MHz—while microbubbles with lower PEG percentages (Fig. 4B), corresponding to the mushroom regime, resonate at relatively higher frequencies—between 4 to 6 MHz. Eq. (4) indicates that the initial size and surface elasticity play critical roles in determining the resonance frequency. As the size distribution of the microbubbles does not vary significantly for different PEG concentrations (section 3.1), the difference in resonance frequency for different shell compositions is caused mainly by the difference in shell elasticity.

Fig. 4.

Frequency-dependent attenuation for (A) 10% and 20 % PEG measured at 2.25 center frequency and (B) 0%, 2%, and 5%PEG samples measured at 5 MHz center frequency. While microbubbles in brush regime resonate at frequencies between 1–2 MHz, microbubbles in the mushroom regime resonate at higher frequencies. (4–6 MHz).

Material property estimation

Analyzing the measured attenuation using the bubble dynamics model we estimate the material properties of the shell. Fig.5 displays the EEM model fitted to the experimental attenuation data. The estimated values for the material properties of all samples are summarized in Table 2. Previously, the EEM model was used to estimate the material properties of commercial phospholipid shelled microbubbles such as Definity (Kumar and Sarkar 2015), Sonazoid (Paul, et al. 2014), and Targestar P (Kumar and Sarkar 2016) with comparable values for the properties. The interfacial elasticity value changes drastically among microbubbles with different shell materials (Paul, et al. 2013). Here, the interfacial elasticity of the shell for 0%, 2%, and 5% PEG, all in the mushroom regime, is significantly higher than that of 10% and 20% PEG in the brush regime. However, within one of the two conformational regimes, the change in the PEG molar faction does not affect the stiffness of the shell. For comparison, we have also provided the characteristic parameter values according to the MM model in the same Table 2. Following Marmottant et al (2005), we assumed γ(R₀) =0. Note that the similarity of the values between $E_0^s$ and X as well as identical values of k^s between MM and EEM underscore the similarity between the MM and EEM models.

Fig. 5.

Exponential Elasticity Model (EEM) applied to experimental attenuation data to estimate the shell material properties. (A) 10%PEG and 20%PEG. (B) 0%PEG, 2%PEG, and 5%PEG.

As can be seen from Eq. (4), the shell elasticity of coated microbubbles increases the resonance frequency (van der Meer, et al. 2007). The estimated values for interfacial elasticity (Table 2 and Fig. 6) correlate well with the peak in the attenuation (Fig. 4 A–B). Microbubbles with higher PEG concentrations (10% and 20% PEG) in the brush region showed resonance peaks at lower frequencies due to the lower estimated shell elasticity. Conversely, the other three (0%, 2%, and 5% PEG) in mushroom region with peaks at higher frequencies result in higher elasticities.

The observations here are consistent with Dicker et.al (2013) who found that for DSPC-DSPE-PEG microbubbles, shells with 1% DSPE-PEG-2000 (mushroom regime) showed higher surface dilatational modulus, E^s of 2.4 N/m, than shells with 7.5% DSPE-PEG-2000 (brush regime, E^s = 1.4 N/m). They also observed the same trend for PEG with higher molecular weights. On other hand, Segers et al (Segers, et al. 2018) reported that the molar ratio of the DPPE-PEG5000 did not affect the stiffness when mixed with DPPC in 5%, 7.5%, and 10% molar ratios. However, for DPPE-PEG5000, the number of monomers per chain is 2.5 times higher than DPPE-PEG2000 resulting in PEG concentrations above ~2% molar ratio forming brush chains (Kenworthy, et al. 1995). Therefore, all their configurations were in the brush regime, and the absence of variation in elasticity by them is consistent with our finding. This explanation resolves the apparent difference in trends observed by the two groups for the change in shell elasticity with PEG molar ratio applying an acoustic means of characterization, like here. Abou-saleh et al. (2014) used AFM to mechanically characterize the stiffness of the microbubbles with shells made of DPPC as the base lipid mixed with different percentages of DSPE-B-PEG2000. They observed a slight increase in the effective stiffness with increasing PEG concentrations for molar ratios below 10%, and a steep linear increase with higher PEG concentrations. The static compressive stress used in an AFM measurement applied to a single bubble is in sharp contrast to the MHz-frequency acoustic probe and disallows direct comparison.

The decrease in the interfacial dilatational elasticity E^s in the brush region seen here as well as by Dicker et al (2013) can be explained to be caused by the same repulsive force between the PEG chains which leads to the brush conformation to avoid their mutual overlap. In lipid bilayers with polymer-grafted lipids, Hristova et al (1994) showed using a simplified scaling analysis, that such a polymer-polymer repulsive force gives rise to a negative contribution “K_polymer” increasing in strength linearly with polymer concentration, i.e., it reduces the area expansion elasticity.

The dilatational viscosity k^s has a higher value in the brush region compared to in the mushroom region (Table 2). It could be explained by thinking of pegylated lipids as heterogeneity in a two-dimensional lipid layer continuum. Increasing the concentration of heterogeneities increases the dilatational viscosity similar to the case of increase in shear viscosity with particle concentration in bulk suspension rheology (Brady and Bossis 1988), where for a dilute suspension, Einstein’s expression of the effective shear viscosity shows a linear increase with concentration (Einstein 1906).

Stability of microbubbles

We measured attenuation over a period to investigate the stability of the microbubbles in air-saturated DI water (Chatterjee, et al. 2005). In Fig. 7 (A–E), we plot attenuation for each of the compositions, every six minutes over 60 minutes showing how the frequency-dependent curves evolve. Except for the highest PEG concentration of 20%, all the curves show similar behavior— they are initially broad, over time evolving into ones with a narrow peak, the peak value moving to lower frequencies. Eventually the peak value as well as the overall attenuation decreases, but initially the curves indicate a growth, which is clear in the total attenuation (integrated over the frequency domain) plotted in Fig. 7F. The total attenuations in that figure have been normalized by their initial values. The figure shows that as PEG content increases, the initial increase occurs over longer times, and its magnitude decreases until there is no increase for 20% PEG microbubbles.

Fig.7.

Frequency-dependent attenuation curves measured at 5 MHz with six minutes intervals for 60 minutes. (A) 0%PEG, (B) 2%PEG, (C) 5%PEG, (D) 10%PEG, (E) 20%PEG. (F) Normalized total attenuation of microbubbles solution as a function of time.

The initial growth in the total attenuation and the subsequent reduction seen here are related to the growth of microbubbles due to relatively higher air influx into initially perfluorocarbonfilled microbubbles because of air’s higher diffusivity and lower solubility of perfluorocarbon in water. The decay in later times is due to eventual outward gas diffusion and dissolution. An increase in attenuation initially with time has been noted before by Shi et al. (2000) for Optison and Chatterjee et al. (2005) for Definity (both perfluorocarbon based agents), but not for airfilled Albunex agent, which expectedly only showed a decay (Hoff 1996, Wu and Tong 1998). In a time-dependent attenuation study over 10 minutes (in contrast to the present 60 minutes) period, Chatterjee et al. (2005) observed three different amplitude dependent behaviors: for low amplitudes, total attenuation grew (compare with Fig. 7F); for less than 1.2 MPa amplitudes, it grew and decayed slowly; but at higher amplitudes, it decayed exponentially indicating catastrophic shell disruption. A gas diffusion model for this process was proposed by our group (Katiyar, et al. 2009, Sarkar, et al. 2009) which showed the initial growth due to the faster influx of air dissolved in the surrounding water with its relatively higher diffusivity compared to the less soluble out-flowing perfluorocarbon. Lower gas permeability delays growth and eventual dissolution, the process taking from fractions of a second to hours for different permeability (Sarkar, et al. 2009). Smaller microbubbles grow and dissolve faster than larger microbubbles, while larger ones display bigger initial growth (Katiyar, et al. 2009).

Scrutiny of Figs. 7 A–D reveals that the high frequency contribution to the attenuation corresponding to smaller bubbles increases very early on (till about 12 min), which also coincides with a slight decrease in total attenuation in Fig. 7 F. Such an initial shift of the attenuation peak towards high frequency seen also for Sonovue (Li, et al. 2018) is due to the bigger microbubbles experiencing quick shrinkage at this time increasing the contribution due to smaller bubbles. Borden et al (Borden, et al. 2005) have observed that while bigger microbubbles under insonation shrink to a stable size, smaller ones, already at a stable size, don’t change much. Also shrinking of microbubbles compresses the lipid shell increasing its elasticity, leading to the resonance moving to a higher frequency. Segers et al. (2016) observed a similar shift in attenuation peak to the higher frequency, i.e., increase in the resonance frequency, with time under repeated low amplitude insonations on monodisperse microbubbles with Definity like lipid composition (DPPC:DPPA:DPPE-PEG5000 in 80:10:10 molar ratio). They related it to an increase of shell elasticity and discussed lipid-shedding as a possible mechanism. Lipid-shedding was also implicated in reducing the size of a Definity microbubbles oscillating near resonance under repeated insonations of 100kPa and 1.6 MHz (Thomas, et al. 2012). However, note that the acoustic excitation (~18 kPa) employed here is below the trigger pressure for lipid shedding (85 kPa as reported in the literature (Luan, et al. 2014)).

All curves in Fig. 7 A–D after 12 minutes show a shift of peak towards lower frequency and an overall self-similar reduction. This shift to a lower frequency, i.e., larger microbubbles, stems from the initial growth of microbubbles due to enhanced air-influx noted above as well as slower dissolution of bigger microbubbles. Such a shift of resonance peak towards lower frequency was seen by Shi et al. in the first 10 minutes after injection, and then a reversal back to the original frequency and a reduction in the attenuation. Growth of microbubbles followed by contraction to a single size was also seen in monodisperse microbubbles synthesized in a microfluidic setup (Segers, et al. 2016), where the growth was thought to be due to Ostwald ripening of larger microbubbles at the expense of smaller microbubbles, and the eventual shrinkage due to outward diffusion reaching a stable shape accompanied by a lowering of surface tension in the contracting lipid shell. However, system confinement and therefore proximity of bubbles facilitated interbubble gas transport in that system, which is not the case here with bubbles separated by more than 200 radii.

All the curves showed an eventual overall decrease of attenuation with time due to dissolution, the rate of decrease lowering with increasing PEG percentage (Fig. 7 A–E, F) indicating a decreased permeability with increasing PEG. It also contributes to the longer transient growth period for higher PEG microbubbles (Fig. 7 F). The highest concentration with 20% PEG in Fig. 7E shows a steady decrease without growth.

Coalescence can give rise to higher volumes, stronger attenuation, bigger bubbles with lower resonance frequencies, and therefore larger contributions at the low frequencies, which seems to appear in all curves eventually except for the 20% PEG case. Microbubbles in the mushroom regime, with lower PEG concentrations and shorter chains, might be more vulnerable to coalescence due to lower steric hindrance compared to those in the brush region. However, due to the large inter-bubble separation for the concentrations considered, coalescence may be rare.

Conclusion

In this study, lipid shelled microbubbles synthesized with DPPC and with a varying DPPE-PEG2000 molar fraction as an emulsifier were studied. It is well known that increasing PEG concentration leads to a transition from their being in a mushroom configuration at the absorbed interface to a brush configuration. Five different shell concentrations with roughly three in mushroom and two in brush configurations have been investigated using acoustic attenuation experiments. We observed that microbubbles with their shells in brush and mushroom regimes show distinct behaviors. A nonlinear strain-softening interfacial rheological model (EEM), was used to characterize the five different microbubble formulations determining the rheological properties of the shell monolayer. The interfacial elasticity of microbubbles with their shells in the mushroom regime is significantly higher than those in the brush regime. Microbubbles with varying concentrations but in the same configuration regime did not show significant variations in their shell properties. We also studied time-dependent attenuation to investigate the stability and evolution of microbubbles in air-saturated water under acoustic excitation. It indicated that the microbubbles with the highest PEG concentration of 20%, and thereby in a dense brush conformation, have behaviors different from the other microbubbles. The lower PEG microbubbles showed nonmonotonic behavior in total attenuation: first a very small decrease accompanying a shift of the attenuation peak towards lower frequency, then a transient increase in total attenuation and shift of peak to higher frequency due to higher air influx into perfluorocarbon microbubble, and an eventual overall decrease. The 20% PEG microbubbles showed a steady decrease in total attenuation. With increasing PEG content, the dynamics is slowed with longer transient growth and slower decay. The evolution is seen to be a result of different permeability critically affected by the PEG conformation, which in turn changes dynamics of the size change. Overall, the shell composition, specifically the PEG concentration and their resulting conformations play a significant role in the acoustic behaviors of microbubbles.