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Research Papers

# Simulation of Drug-Loaded Nanoparticles Transport Through Drug Delivery MicrochannelsOPEN ACCESS

[+] Author and Article Information
Yongting Ma

Department of Mechanical
and Nuclear Engineering,
Virginia Commonwealth University,
Richmond, VA 23284

Ramana M. Pidaparti

College of Engineering,
University of Georgia,
Athens, GA 30602
e-mail: rmparti@uga.edu

1Corresponding author.

Manuscript received October 22, 2013; final manuscript received September 30, 2014; published online November 11, 2014. Assoc. Editor: Malisa Sarntinoranont.

J. Nanotechnol. Eng. Med 5(3), 031002 (Aug 01, 2014) (7 pages) Paper No: NANO-13-1078; doi: 10.1115/1.4028732 History: Received October 22, 2013; Revised September 30, 2014; Online November 11, 2014

## Abstract

Ocular drug delivery is a complex and challenging process and understanding the transport characteristics of drug-loaded particles is very important for designing safe and effective ocular drug delivery devices. In this paper, we investigated the effect of the microchannel configuration of the microdevice, the size of drug-loaded nanoparticles (NPs), and the pressure gradient of fluid flow in determining the maximum number of NPs within a certain outlet region and transportation time of drug particles. We employed a hybrid computational approach that combines the lattice Boltzmann model for fluids with the Brownian dynamics model for NPs transport. This hybrid approach allows to capture the interactions among the fluids, NPs, and barriers of microchannels. Our results showed that increasing the pressure gradient of fluid flow in a specific type of microchannel configuration (tournament configuration) effectively decreased the maximum number of NPs within a certain outlet region as well as transportation time of the drug loaded NPs. These results have important implications for the design of ocular drug delivery devices. These findings may be particularly helpful in developing design and transport optimization guidelines related to creating novel microchannel configurations for ocular drug delivery devices.

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## Introduction

Designing an ocular drug delivery system is among the most formidable tasks for pharmacologists and drug delivery scientists. Ocular diseases such as age-related macular degeneration, glaucoma, diabetic retinopathy, and retinitis pigmentosa [1] need lifelong treatment through orally administered medications, intraocular injections or biodegradable implants. However, frequently administered medications and intravitreal injections can lead to intraocular infections, intraocular hemorrhage, and retinal detachment. In order to overcome such adverse effects, many controlled delivery systems, such as biodegradable and nonbiodegradable implants and NPs, have been developed. Drug delivery to the eye can be classified into systems that address the anterior and posterior segments. There are many challenges in delivering drugs to the retina since the tight junctions of the blood retinal barrier (BRB) restrict the entry of drugs into the retina [2]. The BRB is composed of two types of cells, i.e., retinal capillary endothelial cells and retinal pigment epithelium cells (RPE). The tight junctions of the RPE efficiently restrict intercellular permeation, and restrict further entry of drugs from the choroid into the retina. Although it is ideal to deliver the drug to the retina through systemic administration, it is still a challenge because the BRB strictly regulates drug permeation from blood to the retina [3]. Thrimawithana et al. [4] also discussed the challenges and opportunities of drug delivery to the posterior segment of the eye.

In addition, the design of ocular drug delivery devices is very difficult due to the area and size limitations in the eye. To address the spatial constraints posted by ocular drug delivery, various microelectromechanical system (MEMS) devices, such as microreservoirs and micropumps, have been designed [1,2]. Microreservoirs provide the maximum control of drug delivery but cannot be refilled. Peristaltic micropumps offer targeted drug delivery through active pumping but need considerable space to achieve the required flow rate. Lo et al. [5] developed a prototype polymer MEMS delivery device, which is refillable and requires only a single surgical intervention, is compact and fits within the limited volume, but needs patient's intervention in dispersion of the drug. Staples et al. [6] designed another nano/microchannel-based drug delivery device which provides unique performance based on diffusion and kinetics. Saati et al. [7] developed a novel mini controlled and programmable ocular drug pump which can control the flow rate by changing the applied current. Amrite et al. [8] evaluated how the size of NPs affects the ocular disposition and distribution of particles in Sprague Dawley rats. Recently, Lee et al. [9] developed a novel implantable ocular drug delivery device which is composed of micro/nanochannels embedded between top and bottom covers with a drug reservoir with different microchannel configurations. However, this device cannot vary the flow rate of the fluid flow and the size of drug-loaded particles, which is critically important for the transport of ocular drug delivery. Also, keeping and maintaining an effective drug concentration at the site of action for an appropriate period of time is critical to obtain the desired pharmacological responses of the eye.

In this paper, we investigated fluid flow through different microchannel configurations of a microdevice since part of our objective is to determine how the microchannel configuration of the device affects the transport properties of fluid flow with NPs. We used a hybrid computational approach [10], which integrates the lattice Boltzmann method (LBM) for fluid [11] with a Brownian dynamics model for NPs [10], to simulate the pressure driven fluid flow through different microchannel configurations of the microdevice. Several simulations on a two-dimensional grid of three microchannel configurations: straight channel, meshed channel, and tournament channel were considered based on a previous study by Lee et al. [9]. The results of transport time of drug-loaded particles and the maximum number of NPs within a certain outlet region at a given point in time obtained from the computational simulations are presented and discussed below.

## Methodology

###### Drug-Loaded NPs and Device Concept.

NPs have been effectively used in drug delivery applications since they can easily cross tissue barriers and provide active doses [12,13]. Recent studies on intraocular kinetics of biodegradable NPs have shown that NPs can be used to deliver drugs to the retina and the particle sizes (2000, 200, and 50 nm) of polymeric nanospheres can affect intravitreal kinetics [14]. The investigations suggest that biodegradable NPs carrying incorporated drugs may serve as new therapies for vitreoretinal disorders due to efficient targeting and sustained drug retention [14]. NPs with basic fibroblast growth factor (bFGF) can increase the efficacy of bFGF in preventing photoreceptor degeneration [15]. Rh-6 G encapsulated within NPs could diffuse and stain the retina and RPE cells [16]. Here, we examined an ocular drug-loaded NP delivery device which could deliver bFGF or Rh-6G-loaded PLA(polylactide)-NPs to the retina. An ocular drug-loaded NP delivery device incorporating nano/microchannels is shown in Fig. 1 [9]. The drug-loaded NPs are introduced in the top of the reservoir at one end of the device. A minipump with an electrolysis mechanism [7] that can precisely pump the dosage volume is installed at the bottom of the reservoir. Electrolysis is a low power process in which the pressure in the reservoir is generated by electrochemically induced phase change of water to hydrogen and oxygen gas. The magnitude of pressure is controlled by the generated gas volume and the fluid flow rate through adjusting the current of the implanted batteries [7] with a check valve located at the middle of the reservoir. Microchannels are coated with hydrophilic coating so that the drug-loaded NPs from the reservoir deliver through the channels at a specified rate into the eye. In order for the drug-loaded NPs to be delivered freely through the channels and reach the outlet for delivery, hydrogels at the top of the reservoir are used to passively induce the drug-loaded NP delivery into the microchannels [9]. The device would be surgically implanted in the vitreous body, flushed with the sclera of the eyes and sutured with fine 10-0 nylon in place [9].

###### Model.

In our study, we modeled the behavior of fluid flow that contains mobile drug-loaded NPs, and that move through a microchannel with different configurations due to the pressure gradient of the fluid flow. The fluid velocity, u(x), is evolved using the LBM, which is an efficient solver for the Navier–Stokes equation. Periodic boundary conditions are applied at the top and bottom of the channel as well as left and right sides. No-slip boundary conditions are applied to the fluid at the solid barriers of the microchannels. Particles that are nanoscopic in size can be modeled as point (tracer) particles and as described further below, we introduced a Gaussian noise term to simulate the Brownian motion of these traces. Excluded volume forces are applied between the NPs and solid barriers of the microchannels in order to avoid overlapping between them. The LBM has proven to be a computationally efficient solver for the Navier–Stokes equation and is particularly useful for simulating the flow through the complex geometry. The dynamics of the fluid with NPs is described by the Navier–Stokes equationsDisplay Formula

(1)$∂∂t(ρu)+∇·(ρuu)=-∇·P+η∇2u+GDrag$

for a fluid with local velocity $u(r,t)$ and viscosity $η$ and body force $GDrag(r)=-∑iδ(r-ri)FDrag,i$, arising from viscous drag. Here, $FDrag,i=-ζ[r·i-u(ri,t)]$ is the reaction to the drag acting on the ith NP, where $ζ=6πηRp$ is the drag coefficient, with $Rp$ being the particle radius.

The dynamic behavior of the NPs is governed by the following stochastic differential equation:Display Formula

(2)$dri(t)=u(ri,t)dt+2DpdW(t)+dtζFie(t)$

The first term is the advection term in the presence of the local velocity field $u(r,t)$ (given by Eq. (1) and obtained using the LBM). The second term in Eq. (2) describes the Brownian dynamics of the NPs, where Dp is the particles' diffusion coefficient and $W(t)$ is a Gaussian random variable with variance $2Δt$ in a two-dimensional system. The last term in Eq. (2) is excluded volume force between the particle $i$ and the rest of the particles defined as $Fie(t)=-∑j=1,j≠iN∂ψm(|ri-rj|)/∂ri$. Here, we model excluded volume interaction between the pair of particles separated by the distance $r$ by the repulsive part of the Morse potential [17]Display Formula

(3)$ψm(r)=ɛ(1-exp[-λ(r-re)])2 for r

where $ɛ$ and $λ$ characterize the respective strength and the range of the interaction potential, and $re$ is the distance between the NPs where the force is equal to zero. The positions of the NPs are updated by integration of Eq. (2) via second-order Runge–Kutta method where we take the time step dt 20 times smaller than the time step in the LBM. This original code [17] was developed at the University of Pittsburgh and implemented in this study. We performed several tests [17] to ensure that spurious effects were negligible due to the presence of the particles.

###### Model Simulations, Dimensionless Simulation Parameters, and Experimental Values.

Figure 2 shows the isometric and close-up views (simulation area) in our simulation of various microchannel configurations: straight, meshed and tournament configurations [9]. The geometry of microchannels is specified by the length $H$ and width $W$. The length of channel inflow is $L1$, the length of channel outflow is $L2$, and the length of the microchannel is $H-L1-L2$. Initially, the total number NPs (N) are distributed randomly inside a box of size $L1×W$ that is located at the inlet of the microchannel. As the NPs move through the microchannel, some of the particles arrive at a box of size $L2×W$ that is located at the outlet of the microchannel. Here, we set $H=180$, $L1=50$, $L2=40$, $W=220$, and $N=1100$. In order to reduce the cost of simulation, we only modeled two-dimensional sections of the microchannels, which are shown in Figs. 2(d)2(f) (close-up view of microchannels). Our simulation boxes are $H×W1$ ($180×20$), $H×W2$ ($180×40$), and $H×W3$ ($180×55$) LB units in size for straight microchannel, meshed microchannel, and tournament microchannel, respectively, which are equivalent to 1/11 of straight microchannel, 2/11 of meshed microchannel and 1/4 of tournament microchannel. The initial numbers of NPs at the upper reservoir are 100, 200, and 275 for straight microchannel, meshed microchannel, and tournament microchannel, respectively, which are equivalent to 1/11 of straight microchannel, 2/11 of meshed microchannel, and 1/4 of tournament microchannel. The LB nodes lying on the left and right boundaries satisfy periodic boundary conditions (as specified below). The dark color in the central portion represents solid barriers of microchannels, which is composed of stationary NPs. The interaction of mobile NPs and solid barrier NPs of microchannels is through excluded volume interaction. We imposed no-slip boundary condition for solid barriers of the microchannels. We also applied periodic boundary conditions in the Y direction.

We set the fluid density to $ρ=1$ and dynamic viscosity of the fluid to $η=1/6$ [17,18]. The NPs are assumed to be neutrally buoyant. Their radius and diffusion coefficients are $Rp=0.1$ and $Dp=3.18×10-6$, respectively. The Morse potential used for modeling the excluded volume interactions between NPs (see Eq. (3)) has an inverse length scale of $λ=1.0$, adhesion strength of $ɛ=1.0$, and a cutoff distance of $re=1.2$ [18]. We assume the characteristic length scale, $L0=10-7m$, and time scale, $T0=1.0×10-9 s$. Recall that in the simulations, we set the length and width of channel to $H=180$ and $W=220$ LB units, from the above estimates, we can specify these values in physical units as $H=18 μm$ and $W=22 μm$. Thus, the device can be placed under the eyelid. Given $Rp=0.1$ LB units, the size of a NP in physical units can be specified as 100 nm. Similarly, given $Dp=3.18×10-6$ LB units, we obtain the diffusivity of a NP in physical units to be $3.18×10-11 m2/s$, which is close to the diffusion coefficient of PLA NPs $8.03×10-12 m2/s$ [19]. The size and diffusion coefficient of NPs used in our model are realistic and comparable to values used in previous ocular drug delivery studies.

## Results and Discussion

###### Microchannel Configurations.

Figures 3(a)3(c) show the snapshots of pressure driven fluid flow containing NPs moving through a straight microchannel at different time steps. At the beginning of the simulation (Fig. 3(a)), we introduced N = 100 (1/11 of straight microchannel) particles into the upper fluid chamber. The motion of the fluid advects the NPs through a straight microchannel. The NPs are separated by the solid barriers of the microchannel through the excluded volume force (Fig. 3(b)). Due to the convection of the fluid, the number of NPs reaches the maximum number within a certain outlet region (Fig. 3(c)).

Figures 4(a)4(c) represent the snapshots of NPs in a pressure driven fluid in a meshed microchannel at different time steps. At the onset of the simulation (Fig. 4(a)), we entered N = 200 (2/11 of meshed microchannel) particles into the upper fluid chamber. Due to the convection of the fluid, the NPs are driven down the outlet of the microchannel. In addition, the NPs spread in the whole domain due to the diffusion of NPs (Fig. 4(b)). Finally, the NPs arrive at the maximum number within a certain outlet region (Fig. 4(c)).

Below, we show pressure driven fluid flow with NPs down the tournament microchannel. Figs. 5(a)5(c) show the snapshots of the morphology within a tournament microchannel at different time steps. Here, we initially place N = 275 (1/4 of tournament microchannel) particles at the upper fluid chamber. These images show that the NPs advect through a tournament microchannel and spread out through the microchannel for a long period of time (Fig. 5(b)). Due to the convection of the fluid, the number of NPs reaches the maximum number within a certain outlet region (Fig. 5(c)).

We can obtain additional insights into the dynamic behavior of the system by examining Fig. 6, which shows the number of NPs within a certain outlet region as a function of time as measured from the simulations. In order to study the effect of the configuration of microchannels, we used the same initial number of NPs ($N=1100$) at the reservoirs for three different configurations of the same width ($W=220$ LB unit) in the microchannels. The initial density of NPs in the top box ($22 μm×5 μm$) is $1013 N/m2$. In addition, each NP is loaded with drug, which is sufficient for drug delivery to the retina. For all cases, the number of NPs within a certain outlet region is initially zero, then the numbers increase and approach a constant value. One important thing is that most drugs should stay inside the NPs in this time period. In order to evaluate the potential release rate of NPs, the NPs were prepared with nanoprecipitation from dimethyl sulfoxide (DMSO), which is so-called Rh-6G-loaded PLA NPs [16]. A concentration of Rh values ranging from 7% to 9% of total Rh released is usually obtained from the NPs for up to and after 36 days [16], and similar results were obtained in our simulation time period.

As can been seen from Fig. 6, the transport rates (slopes of lines) of NPs are approximately the same for meshed and straight microchannels. The transport rate of the tournament microchannel is smaller than those of the meshed and straight microchannels, which is better for ocular drug delivery. Another important point, the maximum number of NPs within a certain outlet region for the straight microchannel is larger than those of the meshed and tournament microchannels. More important, the duration of the constant delivery rate for the tournament microchannel is longer than the other two cases. Thus, we chose tournament microchannel as an optimum configuration for ocular drug delivery.

###### Size of NPs.

The size of NPs is very important for ocular tissue distribution. Sakurai et al. [14] studied the kinetics of fluorescein NPs with different sizes following intravitreal injection in rabbits. Here, we show how the size of NPs affects the maximum number of NPs within a certain outlet region and the transportation time of drug particles. In Sec. 3.1, we showed that only the tournament configuration could provide constant delivery rate for a longer time as compared to straight and mesh configurations, and that it works well for ocular drug delivery. Thus, we chose tournament configuration as an optimum configuration to investigate how the size of NPs affects the maximum number of NPs within a certain outlet region and transportation time of drug particles. In the studies below, we set the pressure gradient of fluid flow $P=-5.5×10-6$ and the initial number of NPs $N=275$ for 0.03, 0.1, and 0.48 (related to 30 nm, 100 nm, and 480 nm) different radiuses of NPs with $Dp=1.06×10-5$, $Dp=3.18×10-6$, and $Dp=6.63×10-7$ diffusion coefficients, respectively. We also fixed the rest of the properties of fluid and NPs. The plot in Fig. 7 shows the maximum number of NPs within a certain outlet region and transportation time of drug particles as a function of the size of NPs. The error bars represent simulation data averaged over three independent runs with different random initial NP positions. As can be seen in Fig. 7(a), the maximum number of NPs within a certain outlet region is indeed smaller than that for larger sized NPs. For the lowest value of $Rp$, drag force is smallest, and the maximum number of NPs within a certain outlet region is larger. For higher values of $Rp$, the drag force is larger, and the maximum number of NPs within a certain outlet region is smaller. Figure 7(b) shows the transportation time of drug particles in the tournament configuration for different sizes of NPs. Interestingly, varying the size of NPs, $Rp$, does not affect the transportation time of drug particles. This is because the transportation time of drug particles mostly depends on the convection of the fluid flow, and the drag force does not make a significant impact.

To investigate the effect of the pressure gradient of fluid flow, we performed several simulations at different pressure gradients of fluid flow, setting the initial number of NPs $N=275$ with the size of NPs $Rp=0.1$ (100 nm) and keeping all other parameters constant. Here, we still chose tournament configuration of microchannel as our reference configuration. The plot in Fig. 8 shows the maximum number of NPs within a certain outlet region and transportation time of drug particles as a function of pressure gradient of fluid flow. The error bars also represent simulation data with three different random initial NP positions. The effect of pressure gradient of the fluid flow on the maximum number of NPs within a certain outlet region is shown in Fig. 8(a). It is noteworthy that the maximum number of NPs within a certain outlet region decreases with increasing pressure gradient of fluid flow. At a low value of pressure gradient of the fluid flow, the velocity of fluid is small, and the convection contribution of the NPs is small, and the residence time of NP at this region is larger, thus the maximum number of NPs within a certain outlet region is larger. At a higher value of pressure gradient of fluid flow, the convection contribution of the NPs is larger, and the residence time of NP at this region is smaller, thus the maximum number of NPs within a certain outlet region is smaller. Figure 8(b) shows the transportation time of drug particles for different pressure gradients of fluid flow. As can be anticipated, transportation time of drug particles decreases with increasing pressure gradient of fluid flow. Notably, at a lower pressure gradient of fluid flow, the velocity of fluid is smaller, and NPs take a longer time to reach the outlet of microchannel. At a higher pressure gradient of the fluid flow, the velocity of fluid is larger, and NPs take a shorter time to arrive at the outlet of the microchannel.

## Conclusions

In this study, computational simulations were carried out to investigate the transport characteristics of drug particles for ocular drug delivery in a microdevice. Three different microchannel configurations were used and the transport characteristics of drug particles were analyzed. Our results showed that the tournament microchannel can provide a reasonable and longer duration of constant delivery rate, which satisfies the transport characteristics of drug particles for ocular drug delivery. In addition, we showed that the observed changes in the maximum number of NPs within a certain outlet region can be enhanced by increasing the size of drug NPs. We also found that the maximum number of NPs within a certain outlet region and transportation time of drug particles can be effectively decreased by increasing pressure gradient of fluid flow. These findings have important implications for the design and development of microchannel configurations for ocular drug delivery devices.

## Acknowledgements

The authors thank the U.S. National Science Foundation for supporting this research through Grant No. NSF-ECCS-1430374. Y. Ma gratefully thanks A. C. Balazs and colleagues for the original code, which was developed at the University of Pittsburgh as a Post-Doctorial Associate.

## References

Geroski, D. H., and Edelhauser, H. F., 2000, “Drug Delivery for Posterior Segment Eye Disease,” Invest. Ophthalmol. Vis. Sci., 41(5), pp. 961–964. [PubMed]
Gaudana, R., Jwala, J., Boddu, S. H. S., and Mitra, A. K., 2009, “Recent Perspectives in Ocular Drug Delivery,” Pharm. Res., 26(5), pp. 1197–1216. [PubMed]
Gaudana, R., Krishna, H., Parenky, A., and Mitra, A., 2010, “Ocular Drug Delivery,” AAPS J., 12(3), pp. 348–360. [PubMed]
Thrimawithana, T. R., Young, S., Bunt, C. R., Green, C., and Alany, R. G., 2011, “Drug Delivery to the Posterior Segment of the Eye,” Drug Discov. Today, 16(5–6), pp. 270–277. [PubMed]
Lo, R., Li, P. Y., Saati, S., Agrawal, R. N., Humayun, M. S., and Meng, E., 2009, “A Passive MEMS Drug Delivery Pump for Treatment of Ocular Diseases,” Biomed. Microdevices, 11(5), pp. 959–970. [PubMed]
Staples, M., Daniel, K., Cima, M. J., and Langer, R., 2006, “Application of Micro- and Nano-Electromechanical Devices to Drug Delivery,” Pharm. Res., 23(5), pp. 847–863. [PubMed]
Saati, S., Lo, R., Li, P. Y., Meng, E., Varma, R., and Humayun, M. S., 2010, “Mini Drug Pump for Ophthalmic Use,” Curr. Eye Res., 35(3), pp. 192–201. [PubMed]
Amrite, A. C., Edelhauser, H. F., Singh, S. R., and Kompella, U. B., 2008, “Effect of Circulation on the Disposition and Ocular Tissue Distribution of 20 nm Nanoparticles After Periocular Administration,” Mol. Vis., 14, pp. 150–160. [PubMed]
Lee, J. H., Pidaparti, R. M., Atkinson, G. M., and Moorthy, R. S., 2012, “Design of an Implantable Device for Ocular Drug Delivery,” J. Drug Delivery, 2012, p. 527516.
Verberg, R., Yeomans, J. M., and Balazs, A. C., 2005, “Modeling the Flow of Fluid/Particle Mixtures in Microchannels: Encapsulating Nanoparticles Within Monodisperse Droplets,” J. Chem. Phys., 123(22), p. 224706. [PubMed]
Succi, S., 2001, The Lattice Boltzmann Equation for Fluid Dynamics and Beyond, Oxford University, Oxford, UK.
Allen, T. M., and Cullis, P. R., 2004, “Drug Delivery System: Entering the Mainstream,” Science, 303(5665), pp. 1818–1822. [PubMed]
Brigger, I., Dubernet, C., and Couvreur, P., 2002, “Nanoparticles in Cancer Therapy and Diagnosis,” Adv. Drug Delivery Rev., 54(5), pp. 631–651.
Sakurai, E., Ozeki, H., Kunou, N., and Ogura, Y., 2001, “Effect of Particle Size of Polymeric Nanospheres on Intravitreal Kinetics,” Ophthalmic Res., 33(1), pp. 31–36. [PubMed]
Sakai, T., Kuno, N., Takamatsu, F., Kimura, E., Kohno, H., Okano, K., and Kitahara, K., 2007, “Prolonged Protective Effect of Basic Fibroblast Growth Factor-Impregnated Nanoparticles in Royal College of Surgeons Rats,” Invest. Ophthalmol. Vis. Sci., 48(7), pp. 3381–3387. [PubMed]
Bourges, J., Gautier, S. E., Delie, F., Bejjani, R. A., Jeanny, J., Gurny, R., BenEzra, D., and Behar-Coben, F. F., 2003, “Ocular Drug Delivery Targeting the Retina and Retinal Pigment Epithelium Using Polylactide Nanoparticles,” Invest. Ophthalmol. Vis. Sci., 44(8), pp. 3562–3569. [PubMed]
Alexeev, A., Verberg, R., and Balazs, A. C., 2005, “Modeling the Motion of Microcapsules on Compliant Polymeric Surfaces,” Macromolecules, 38(24), pp. 10244–10260.
Ma, Y. T., Bhattacharya, A., Kuksenok, O., Perchak, D., and Balaza, A. C., 2012, “Modeling the Transport of Nanoparticle-Filled Binary Fluids Through Micropores,” Langmuir, 28(31), pp. 11410–11421. [PubMed]
Gorrasi, G., Tammaro, L., Vittoria, V., Paul, M., Alexandre, M., and Dubois, P., 2004, “Transport Properties of Water Vapor in Polylactide/Montmorillonite Nanocomposites,” J. Macromol. Sci., 43(3), pp. 565–575.
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## References

Geroski, D. H., and Edelhauser, H. F., 2000, “Drug Delivery for Posterior Segment Eye Disease,” Invest. Ophthalmol. Vis. Sci., 41(5), pp. 961–964. [PubMed]
Gaudana, R., Jwala, J., Boddu, S. H. S., and Mitra, A. K., 2009, “Recent Perspectives in Ocular Drug Delivery,” Pharm. Res., 26(5), pp. 1197–1216. [PubMed]
Gaudana, R., Krishna, H., Parenky, A., and Mitra, A., 2010, “Ocular Drug Delivery,” AAPS J., 12(3), pp. 348–360. [PubMed]
Thrimawithana, T. R., Young, S., Bunt, C. R., Green, C., and Alany, R. G., 2011, “Drug Delivery to the Posterior Segment of the Eye,” Drug Discov. Today, 16(5–6), pp. 270–277. [PubMed]
Lo, R., Li, P. Y., Saati, S., Agrawal, R. N., Humayun, M. S., and Meng, E., 2009, “A Passive MEMS Drug Delivery Pump for Treatment of Ocular Diseases,” Biomed. Microdevices, 11(5), pp. 959–970. [PubMed]
Staples, M., Daniel, K., Cima, M. J., and Langer, R., 2006, “Application of Micro- and Nano-Electromechanical Devices to Drug Delivery,” Pharm. Res., 23(5), pp. 847–863. [PubMed]
Saati, S., Lo, R., Li, P. Y., Meng, E., Varma, R., and Humayun, M. S., 2010, “Mini Drug Pump for Ophthalmic Use,” Curr. Eye Res., 35(3), pp. 192–201. [PubMed]
Amrite, A. C., Edelhauser, H. F., Singh, S. R., and Kompella, U. B., 2008, “Effect of Circulation on the Disposition and Ocular Tissue Distribution of 20 nm Nanoparticles After Periocular Administration,” Mol. Vis., 14, pp. 150–160. [PubMed]
Lee, J. H., Pidaparti, R. M., Atkinson, G. M., and Moorthy, R. S., 2012, “Design of an Implantable Device for Ocular Drug Delivery,” J. Drug Delivery, 2012, p. 527516.
Verberg, R., Yeomans, J. M., and Balazs, A. C., 2005, “Modeling the Flow of Fluid/Particle Mixtures in Microchannels: Encapsulating Nanoparticles Within Monodisperse Droplets,” J. Chem. Phys., 123(22), p. 224706. [PubMed]
Succi, S., 2001, The Lattice Boltzmann Equation for Fluid Dynamics and Beyond, Oxford University, Oxford, UK.
Allen, T. M., and Cullis, P. R., 2004, “Drug Delivery System: Entering the Mainstream,” Science, 303(5665), pp. 1818–1822. [PubMed]
Brigger, I., Dubernet, C., and Couvreur, P., 2002, “Nanoparticles in Cancer Therapy and Diagnosis,” Adv. Drug Delivery Rev., 54(5), pp. 631–651.
Sakurai, E., Ozeki, H., Kunou, N., and Ogura, Y., 2001, “Effect of Particle Size of Polymeric Nanospheres on Intravitreal Kinetics,” Ophthalmic Res., 33(1), pp. 31–36. [PubMed]
Sakai, T., Kuno, N., Takamatsu, F., Kimura, E., Kohno, H., Okano, K., and Kitahara, K., 2007, “Prolonged Protective Effect of Basic Fibroblast Growth Factor-Impregnated Nanoparticles in Royal College of Surgeons Rats,” Invest. Ophthalmol. Vis. Sci., 48(7), pp. 3381–3387. [PubMed]
Bourges, J., Gautier, S. E., Delie, F., Bejjani, R. A., Jeanny, J., Gurny, R., BenEzra, D., and Behar-Coben, F. F., 2003, “Ocular Drug Delivery Targeting the Retina and Retinal Pigment Epithelium Using Polylactide Nanoparticles,” Invest. Ophthalmol. Vis. Sci., 44(8), pp. 3562–3569. [PubMed]
Alexeev, A., Verberg, R., and Balazs, A. C., 2005, “Modeling the Motion of Microcapsules on Compliant Polymeric Surfaces,” Macromolecules, 38(24), pp. 10244–10260.
Ma, Y. T., Bhattacharya, A., Kuksenok, O., Perchak, D., and Balaza, A. C., 2012, “Modeling the Transport of Nanoparticle-Filled Binary Fluids Through Micropores,” Langmuir, 28(31), pp. 11410–11421. [PubMed]
Gorrasi, G., Tammaro, L., Vittoria, V., Paul, M., Alexandre, M., and Dubois, P., 2004, “Transport Properties of Water Vapor in Polylactide/Montmorillonite Nanocomposites,” J. Macromol. Sci., 43(3), pp. 565–575.

## Figures

Fig. 1

Device design concept for ocular drug delivery, adopted from Ref. [9]

Fig. 2

Isometric microchannel configurations ((a)–(c)) and computational setups ((d)–(f)) used to examine the ocular drug delivery driven by pressure gradient of fluid flow. The geometry of the two-dimensional channel is specified by the length L and width W. Periodic boundary conditions are applied at the left and right sides as well as at the top and bottom sides. Dark and light are used to represent barriers of microchannel and fluid.

Fig. 3

Snapshots of pressure driven fluid flow through straight microchannel with 100 NPs at: (a) t = 0.0, (b) t = 3.2 × 105, and (c) t = 6.6 × 105

Fig. 4

Snapshots of pressure driven fluid flow through meshed microchannel with 200 NPs at: (a) t = 0.0, (b) t = 2.7 × 105, and (c) t = 4.98 × 105

Fig. 5

Snapshots of pressure driven fluid flow through tournament microchannel with 275 NPs at: (a) t = 0.0, (b) t = 5.4 × 105, and (c) t = 1.46 × 106

Fig. 6

Number of NPs within a certain outlet region as a function of time for pressure driven fluid flow with different microchannel configurations. Snapshots represent the maximum number of NPs at the outlet of microchannels.

Fig. 7

(a) Maximum number of NPs within a certain outlet region as a function of size of NPs. (b) Transportation time of drug particles at the outlet of tournament microchannel as a function of size of NPs. Each bar is the average of three independent runs; the error bars are the standard deviations.

Fig. 8

(a) Maximum number of NPs within a certain outlet region as a function of pressure gradient of fluid flow. (b) Transportation time of drug particles at the outlet of tournament microchannel as a function of pressure gradient of fluid flow. Each bar is the average of three independent runs; the error bars are the standard deviations.

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