The effect of particle density on ultrasound-mediated transport of nanoparticles

A significant barrier to successful drug delivery is the limited penetration of nanoscale therapeutics beyond the vasculature. Building on recent in vivo findings in the context of cancer drug delivery, the current study investigates whether modification of nanoparticle drug-carriers to increase their density can be used to enhance their penetration into viscoelastic materials under ultrasound exposure. A computational model is first presented to predict the transport of identically sized nanoparticles of different densities in an ultrasonic field in the presence of an oscillating microbubble, by a combination of primary and secondary acoustic radiation forces, acoustic streaming and microstreaming. Experiments are then described in which near monodisperse (polydispersity index  <0.2) nanoparticles of approximate mean diameter 200 nm and densities ranging from 1.01 g cm−3 to 5.58 g cm−3 were fabricated and delivered to a tissue-mimicking material in the presence or absence of a microbubble ultrasound contrast agent, at ultrasound frequencies of 0.5 MHz and 1.6 MHz and a peak negative pressure of 1 MPa. Both the theoretical and experimental results confirm that denser particles exhibit significantly greater ultrasound-mediated transport than their lower density counterparts, indicating that density is a key consideration in the design of nanoscale therapeutics.

Keywords: ultrasound, cavitation, microstreaming, nanoparticles, density, drug delivery (Some figures may appear in colour only in the online journal)

Introduction
Cancerous tissue is highly heterogeneous in terms of perfusion and the pressure and composition of the extracellular matrix, posing a number of significant barriers to drug delivery. Consequently, current methods of systemic drug delivery often do not enable therapeutics to penetrate sufficiently deep into tumour tissue for effective treatment (Minchinton et al 2006). This is particularly problematic for relatively large therapeutics such as nanoparticles. Strategies for enhancing the transport of nanoscale drug carriers have included modifying their size, shape and surface chemistry -primarily surface charge and biological targeting (Blanco et al 2015). Tailoring the size and shape of nanoparticles can increase their ability to pass through pores in the 'leaky' vasculature that is characteristic of cancerous blood vessels and to be retained in the surrounding tumour tissue-an effect known as enhanced permeability and retention (EPR) (Maeda 2010, Prabhakar et al 2013. Exploiting the EPR effect in this way is classified as passive targeting. In contrast, using surface charge or ligands to enable particles to bind to specific receptors on cancer or endothelial cells is classed as active targeting (Kamaly et al 2012).
It has been shown that neither passive (Popović et al 2010) nor active targeting alone can provide significant enhancements in nanoparticle delivery (Wilhelm et al 2016). In combination with physical stimuli, however, much greater penetration depths can be achieved. These stimuli include magnetic fields (Lübbe et al 2001), electromagnetic radiation (Dougherty et al 1992) and ultrasound. Of these, ultrasound has been shown to achieve the greatest penetration depths and has the advantage of being cost-effective and already clinically approved as an imaging and therapeutic modality (Mo et al 2012). The combination of a nanoparticle with microbubbles driven in a sustained inertial cavitation regime has shown promise as a means of enhancing transport, enabling the delivery of nanoparticulate therapeutics to some 200 µm from the nearest blood vessel (Carlisle et al 2013). Although size and shape modifications have been heavily explored, relatively little attention has been given to the influence of particle density on the delivery and penetration distance of nanoscale drug carriers when exposed to ultrasound.
It has been shown previously that coating an adenovirus of mean size 140 nm with gold nanoparticles can enhance its ultrasound-mediated transport in a mouse model in the presence of a microbubble ultrasound contrast agent (Mo et al 2015). It was hypothesised that this enhancement was due to the polymer-gold coating providing both reduced immunogenicity, and hence increased circulation time, and an increase in density that facilitates transport by cavitational microstreaming. The current study aims to test this hypothesis and to determine how the ultrasound-mediated transport of a nanoscale object is affected by its density. Additionally, the influence of ultrasound exposure conditions and the incidence of cavitation will also be examined.

Methodology
A simple computational model was first developed to compare the magnitude of the different forces acting on a 200 nm diameter nanoparticle suspended in water and subjected to an ultrasound field, under different exposure conditions, in the presence or absence of a 3 µm diameter microbubble. This model was then used to predict the distance that the particle would travel beyond a planar water/agarose boundary into agarose gel. Agarose was used here both in the computational and experimental models as a tissue-mimicking material, having similar density, acoustic properties and pore size to those of human tissue (Maaloum et al 1998). A particle size of 200 nm was chosen as being representative of larger nanoparticulate therapeutics, such as viruses or liposomes, whilst still being small enough to extravasate through leaky tumour vasculature (Hobbs et al 1998).
A schematic of the system is shown in figure 1. In the absence of the microbubble, the particle will experience an acoustic radiation force (F AR1 ) due to the propagating ultrasound field and a second force due to acoustic streaming (F D1 ). The latter was calculated using Stoke's equation for drag (equation (1)). This was deemed to be justified since the regimes considered relate to a nanoscale object and low streaming velocities, on the order of cm s −1 , producing Reynolds numbers on the order of 1 10 3 × − . In the presence of the microbubble, the particle will experience two additional forces: a secondary acoustic radiation force (F AR2 ) and a force due to microstreaming (F D2 ). The response of a 3 µm diameter microbubble in free-field conditions was modelled using the Keller-Miksis equation (equation (2)) (Keller et al 1980), and the predicted radial oscillations for driving frequencies of 0.5 MHz and 1.6 MHz and a peak negative pressure of 1 MPa are shown in figure 2. To account for the sulphur hexafluoride encapsulated inside SonoVue ® (Bracco Imaging, France) contrast agent microbubbles used in the experiments, a specific heat ratio (γ) of 1.098 was used to describe the internal gas (Schneider et al 1995). The effect of the microbubble coating was neglected in order to simplify the model. Initial simulations (appendix) indicated that the influence of the coating on microbubble dynamics, for the ultrasound exposure parameters used in the study, was negligible. The scattered pressure field was calculated from the corresponding potential flow (equation (3)) (Ilinskii 1992), which was in turn used to determine the magnitude of the secondary radiation force. The microstreaming model published by Doinikov (2010) was implemented to assess the velocity field around the microbubble (equation (32), Doinikov 2010). The radial component of microstreaming taken in the positive 'r' direction (i.e. towards the water/agar boundary) was used to determine the corresponding force on the particle that would lead to penetration into the agar, again assuming Stoke's drag. Figure 1. Schematic of the model-system used to estimate the primary acoustic radiation force (F AR1 ), acoustic streaming force (F D1 ), secondary radiation force (F AR2 ) and microstreaming force (F D2 ) on a 200 nm solid particle in aqueous suspension, and predict the resultant penetration distance (z p ).
The relative magnitudes of the four forces acting on the particle are shown in table 1. These values illustrate that within therapeutically relevant acoustic regimes, such as 0.5 MHz and 1.6 MHz in which the bubble is excited at or below resonance, the greatest of the four forces is provided by the microstreaming. Since depth of penetration was the primary quantity of interest, only the z-axis component of these forces was considered. The nanoparticle was assumed to be located initially at a distance of twice the viscous penetration depth from the bubble outer surface (equation (4)) (Doinikov 2010) and to be travelling at the velocity of the fluid by the time it had reached the aqueous/agarose boundary (equation (5)). The effective particle mass accounts for the mass of the particle and the added mass due to the inertia of the displaced fluid (equation (6)). Penetration depth into the agarose gel was predicted using a non-Newtonian fluid model (equation (7)) (de Bruyn et al 2004), in which agarose viscosity and yield strength are free parameters that may be determined from experimental observations. Since published parameters vary considerably however, for the purposes of this study, the predicted penetration depths were normalised to the peak penetration depth found across any of the ultrasound exposure conditions, with the maximum normalised value being 1000.
where u 1 and u 2 are determined from the microstreaming model (Doinikov 2010

Results
The penetration depth is predicted for particles of three different densities, with cores of polystyrene (PS), silica (SiO 2 ) and gold (Au) and a polymer coating, giving final particle densities of 1.01 g cm −3 , 1.41 g cm −3 and 5.58 g cm −3 respectively, under four acoustic regimes (figure 3). The first two acoustic regimes correspond to the case in which no cavitation nuclei are present. Therefore the particle is driven only by the primary acoustic radiation force (F AR1 ) and the force due to acoustic streaming (F D1 ). In this non-cavitational regime the model predicts greater penetration depths at 1.6 MHz compared to 0.5 MHz. This is as expected because at higher frequencies the ultrasound energy is more likely to be attenuated by the surrounding fluid, transferring more momentum from the propagating wave to the fluid, in turn inducing greater acoustic streaming velocities. Even at the higher frequency, however, the predicted penetration depth is relatively small compared to that observed with a microbubble present.
When an oscillating microbubble is introduced, much greater penetration depths are predicted for all three types of particle. For example, the greatest predicted penetration depth achieved by the gold nanoparticle without cavitation is 0.2% of the greatest predicted penetration depth achieved by the gold nanoparticle with cavitation. In this cavitation regime the particles experience the additional secondary acoustic radiation force (F AR2 ) and the force generated by microstreaming (F D2 ). With cavitation nuclei at 0.5 MHz, the predicted penetration depths are greater for all three particles than in the 1.6 MHz regime. As shown in figure 2(a), at 0.5 MHz the 3 µm bubble experiences a longer negative pressure phase than at 1.6 MHz (figure 2(b)), and is therefore able to achieve greater expansion ratios which are associated with greater microstreaming velocities (table 1).

Methodology
Ultrasound-mediated transport of contrasting-density nanoparticles was investigated experimentally using the apparatus shown in figure 4, building on similar experimental setups used in previous studies (Bhatnagar et al 2014). A high-intensity focussed ultrasound (HIFU) transducer (H-107F-18; Sonic Concepts, USA) with fundamental frequency 0.5 MHz and third harmonic 1.6 MHz was used, allowing two contrasting acoustic regimes to be studied with the same experimental setup. Ultrasound was delivered at a pulse repetition frequency of 10 Hz and 2% duty cycle, with pulse repetition period of 100 ms over a total exposure time of 10 s. Transmission of ultrasound from the HIFU transducer to the aqueous sample of nanoparticles was achieved using a Perspex coupling cone containing degassed deionised (DI) water. Average cavitation signals were captured using a passive cavitation detection (PCD) transducer (V319; Panametrics, Olympus NDT UK Ltd, England) coaxially aligned with the HIFU transducer. High-pass filtering at 5 MHz was implemented to remove the driving signal from the PCD signal. The 'donor' chamber, a Perspex cylinder with diameter 12 mm and internal volume of 1.7 ml, was placed beneath the coupling cone and filled with each population of density-contrasting nanoparticles in aqueous suspension and SonoVue ® (SV) microbubbles. Nanoparticles were transported from the donor chamber into the receiver chamber, which was filled with a volume of 1% concentration (wt%) agarose gel.
The agarose sample was removed from the receiver chamber and prepared for microscopy, as illustrated in figure 6. Confocal microscopy was used to capture a volumetric scan of the sample. These data were then processed by applying a thresholding function to detect the location of each particle. By locating each particle and measuring the distance from the agarose boundary, a value for penetration depth was obtained. Statistical significance was assessed using analysis of variance (ANOVA), comparing the variation between groups with the variation within groups, and was felt to be a more robust measure than a simple t test. A p-value < 0.05 was used to disprove the null hypothesis (table 2). Figure 7 shows the results from three sets of experiments. In the absence of ultrasound exposure, the average penetration by diffusion alone was limited to less than 30 µm. In the presence of acoustic excitation, the penetration depth exceeded 80 µm in all cases. It can be seen that in each of the acoustic regimes the penetration depth was greatest for the densest particle.

Results
A significant difference can also be seen between the cavitation and non-cavitation regimes; the presence of SV microbubbles significantly enhanced the penetration depths of all particles. An ultrasound frequency of 0.5 MHz was found to be most favourable for particle transport when compared to exposure at 1.6 MHz, in agreement with the theoretical predictions. Figure 8 shows the frequency composition of averaged PCD data during ultrasound exposure at 1.6 MHz and 0.5 MHz. More harmonic peaks were seen during insonation at 1.6 MHz, whereas greater broadband frequency content was seen during insonation at 0.5 MHz.

Comparison of predictions and results
When comparing the computational and experimental results it can be seen that the model predicts almost negligible penetration distances in the non-cavitation regime. However in practice, cavitation activity was detected even without artificially introduced cavitation nuclei. The peak power of cavitation emissions measured using the passive cavitation detection (PCD) transducer was found to be 0.0002 mV 2 Ω −1 at baseline, and raised to 0.0016 mV 2 Ω −1 and 0.0120 mV 2 Ω −1 when the sample was exposed to 1.6 MHz and 0.5 MHz respectively. As expected, peak cavitational power was significantly greater when SV microbubbles were introduced, reaching 0.2404 mV 2 Ω −1 and 0.7361 mV 2 Ω −1 at 1.6 MHz and 0.5 MHz, Figure 6. Schematic representation of (a) gel sample and (b) preparation for confocal microscopy by slicing the central plane and applying to a microscope slide. Confocal microscopy was used to obtain (c) a volumetric scan of the sample and particle detection to locate and map the distribution of nanoparticles.  respectively. Figure 8 shows the cavitation behaviour recorded during exposure using SV at 1.6 MHz and 0.5 MHz, with clear harmonic peaks present at 1.6 MHz and a broadband frequency response at 0.5 MHz. Greater qualitative agreement for penetration depths is seen when computational predictions and experimental observations are compared in the cavitation regime, supporting the hypothesis that increasing particle density increases penetration depth. Furthermore, SV microbubbles excited at 0.5 MHz were both predicted and observed to induce greater particle transport than at 1.6 MHz.
It should be emphasised, however, that the computational model implemented in the current study is a substantial simplification of the true experimental conditions experienced by the suspended nanoparticle. Firstly, the simulation is only concerned with a single-bubble-single-particle interaction, negating bubble-bubble or particle-particle interactions. In reality a population of microbubbles was observed, with a size distribution spanning a range of radii and resonant frequencies. Furthermore the nanoparticle is assumed to be rigid and sufficiently small that the scattered pressure field is negligible; therefore the incident pressure field is assumed to be unchanged by the presence of the particle.
The value of using a simple numerical model to predict ultrasound-mediated transport of nanoparticles has been shown in the context of elucidating the impact of nanoparticle density on penetration depth. In future work, however, it may be advantageous to add complexity to such a simulation, allowing the confines of a viscoelastic vasculature to be accounted for (Sassaroli et al 2005), rather than a free-field bubble, as well as bubble-bubble interactions (Parlitz et al 1999, Lauterborn et al 2010. The tissue mimicking phantom, 1% concentration (wt%) agarose gel, was chosen because of its similar acoustic properties to tissue. The gel also has a porous structure, and at this concentration the pore size has been measured as ~200 nm (Narayanan et al 2006) which is in the range of pore sizes, 50-400 nm (Yuan et al 1995), observed between endothelial cells in cancerous vasculature. However, the homogeneity of this model must be acknowledged, and thus an agarose gel is inherently limited in representing the complex and chaotic structure of the cancerous tumour. Nevertheless, many studies have shown good agreement between in vitro experiments carried out in cell-embedded agarose phantoms and in vivo studies (Mo et al 2015). To enable translation into an in vivo context, further investigations using a more realistic vessel model to study the influence of particle density on ultrasound-mediated transport are recommended. Potential methods include using a dissected section of vessel or a tissueengineered vascular graft (Mitchell et al 2003).
As discussed in the introduction, the results support the hypothesis that increased density played a significant role in enhancing the penetration depth of the modified adenovirus studied by Mo (2015). However, the potential applications of the current findings go beyond the field of virotherapy, arguably to all five major categories of tumour-targeted therapeuticliposomal drug carriers, polymer-based carriers, micelles, solid nanoparticles (lipid-based, viral and 'multistage') and antibodies-by incorporating an inert, biocompatible dense metal, such as gold.

Conclusions
The overall conclusion of this study is that the penetration depth achieved by a nanoparticle under ultrasound exposure is significantly influenced by particle density. It has been shown that a denser particle will be transported further when exposed to ultrasound and cavitating microbubbles than its less dense counterpart. It has also been shown that exposing SonoVue ® microbubbles to ultrasound at a frequency of 0.5 MHz induces greater nanoparticle transport than exposing at 1.6 MHz, due to the higher microstreaming velocities. Since limited penetration depth of nanoscale therapeutics is a current limitation in oncolytic drug delivery, these findings are important in designing density-modified drug carriers that can penetrate deep into cancerous tumours.

Appendix. Dynamics of a coated and free microbubble
The amplitude of oscillation is predicted for a free bubble (as predicted by the Keller-Miksis equation) and for a coated bubble (as predicted by the Marmottant model). Figure A1 shows a comparison of oscillation amplitudes for a 3 µm bubble driven at 0.5 MHz or 1.6 MHz, at 1 MPa. The shell of the coated bubble is defined using experimentally derived parameters for a SonoVue ® microbubble (Marmottant 2005) shown above. It can be seen that at these acoustic exposures this type of coating has very little influence on the amplitudes of oscillation.