A Facile Method to Probe the Vascular Permeability of Nanoparticles in Nanomedicine Applications

The effectiveness of nanoparticles (NP) in nanomedicine depends on their ability to extravasate from vasculature towards the target tissue. This is determined by their permeability across the endothelial barrier. Unfortunately, a quantitative study of the diffusion permeability coefficients (Pd) of NPs is difficult with in vivo models. Here, we utilize a relevant model of vascular-tissue interface with tunable endothelial permeability in vitro based on microfluidics. Human umbilical vein endothelial cells (HUVECs) grown in microfluidic devices were treated with Angiopoietin 1 and cyclic adenosine monophosphate (cAMP) to vary the Pd of the HUVECs monolayer towards fluorescent polystyrene NPs (pNPs) of different sizes, which was determined from image analysis of their fluorescence intensity when diffusing across the monolayer. Using 70 kDa dextran as a probe, untreated HUVECs yielded a Pd that approximated tumor vasculature while HUVECs treated with 25 μg/mL cAMP had Pd that approximated healthy vasculature in vivo. As the size of pNPs increased, its Pd decreased in tumor vasculature, but remained largely unchanged in healthy vasculature, demonstrating a trend similar to tumor selectivity for smaller NPs. This microfluidic model of vascular-tissue interface can be used in any laboratory to perform quantitative assessment of the tumor selectivity of nanomedicine-based systems.

The effectiveness of nanoparticles (NP) in nanomedicine depends on their ability to extravasate from vasculature towards the target tissue. This is determined by their permeability across the endothelial barrier. Unfortunately, a quantitative study of the diffusion permeability coefficients (P d ) of NPs is difficult with in vivo models. Here, we utilize a relevant model of vascular-tissue interface with tunable endothelial permeability in vitro based on microfluidics. Human umbilical vein endothelial cells (HUVECs) grown in microfluidic devices were treated with Angiopoietin 1 and cyclic adenosine monophosphate (cAMP) to vary the P d of the HUVECs monolayer towards fluorescent polystyrene NPs (pNPs) of different sizes, which was determined from image analysis of their fluorescence intensity when diffusing across the monolayer. Using 70 kDa dextran as a probe, untreated HUVECs yielded a P d that approximated tumor vasculature while HUVECs treated with 25 μg/mL cAMP had P d that approximated healthy vasculature in vivo. As the size of pNPs increased, its P d decreased in tumor vasculature, but remained largely unchanged in healthy vasculature, demonstrating a trend similar to tumor selectivity for smaller NPs. This microfluidic model of vascular-tissue interface can be used in any laboratory to perform quantitative assessment of the tumor selectivity of nanomedicine-based systems.
Nanoparticles (NPs) are widely studied as drug delivery vehicles to maximize drug efficacy through effective targeting of diseased tissue [1][2][3][4] . The most common delivery route of NPs is through the blood stream. Before NPs can reach the target tissue, they need to escape vascular flow through the fluid dynamic process of margination towards the vascular walls, adhere to the vascular endothelium, and extravasate across the endothelial cell (EC) barrier into the target tissue. This is true for both active 5,6 and passive targeting of NPs 7 .
Therefore, the effectiveness of NP-based drug delivery systems depends on their ability to extravasate into the target tissue. This is determined by the permeability of the endothelial barrier to the NPs which is in turn dependent on different physical attributes of the NPs. Unlike the abundance of studies that characterize cell adhesion and uptake of NPs with different shape, size and surface functionalities [8][9][10][11] , much less is known about how these attributes affect NPs extravasation. A systematic quantitative study of the permeability coefficients of the endothelium to NPs exiting the vasculature would enable a better understanding of how different physical characteristics affect their extravasation, and eventually guide their rational design towards an effective payload delivery.
Although permeability assays utilizing animal models are the most physiologically relevant, permeability measurements with in vivo or ex vivo systems often involve tedious and delicate creation of an experimental viewing window of the vasculature within the animal model 12,13 . This is before intravenous introduction of a Scientific RepoRts | 7: 707 | DOI: 10.1038/s41598-017-00750-3 Human umbilical vein endothelial cell culture. Human umbilical vein endothelial cells (HUVECs) (Lonza, Basel, Switzerland) were chosen as the model endothelial barrier in this study. The HUVECs were expanded and passaged 5 times (P + 5) before being introduced into the devices. All HUVECs were cultured in EGM-2 (Lonza, Basel, Switzerland) and trypsinized (Lonza, Basel, Switzerland) when ~70-80% confluent before being seeded into the microfluidic devices. Cells were cultured in incubators at 37 °C and 5% CO 2 . All HUVECs were purchased commercially and all methods and experimental protocols involving HUVECs in this work were conducted with protocols in accordance with relevant guidelines and regulations stipulated and approved by the Singapore MIT alliance for Research and Technology's review board.
Gel filling and seeding of HUVECs into the microfluidic devices. PDMS microfluidic devices were sterilized with UV irradiation for 25 min prior to cell seeding. Fibrin solution was then prepared by mixing 5 mg/ mL fibrinogen from bovine plasma (Sigma Aldrich, Missouri, USA) in 1x phosphate buffer saline (PBS) with 1.24 units/mL of thrombin in 1x PBS (Sigma Aldrich, Missouri, USA) in a 1:1 ratio. The middle gel region of the microfluidic devices was filled with 7 µL of the fibrin solution via the gel loading port (Fig. 1A) and allowed to polymerize at 37 °C for 30 min to form a gel. Based on images of fluorescently tagged fibrin gel, we obtained an approximate pore sizes ranging from ≈6 to 9 µm which were much larger than the largest 200 nm pNPs used in this study (data not shown), thus suggesting that the pore size of the fibrin gel would not limit the diffusion of pNPs in the central gel region and thereby affecting the calculated P d .
After gelation, the side media channels were incubated with 50 µg/mL fibronectin from human plasma (Sigma Aldrich, Missouri, USA) dissolved in EGM-2 for 1 h at 37 °C and 5% CO 2 to provide a conducive surface for HUVEC attachment. This is followed by the addition of 30 µL of cell suspension to the cell loading port (Fig. 1A). The seeding concentration varied with different treatments. Untreated and Ang-1 treated devices were seeded with 10 × 10 6 cells/mL whereas pCPT-cAMP treated devices were seeded at a lower concentration of 5 × 10 6 cells/mL because they proliferated much faster than in the untreated case. We also observed that with these cells seeding concentrations, a confluent monolayer would form within the microfluidic device four days after seeding.
After cell seeding, the devices were incubated at 37 °C, 5% CO 2 for 4 h to allow for cell attachment before replacing the culture medium within the cell-seeded channel with 120 µL of fresh medium. Cell culture medium was subsequently changed every 24 h. The cells were cultured to confluence in order to form a complete monolayer at the gel interface by day 4. The devices were then kept for an additional day to allow them to stabilize before experiments were conducted on days 5 and 6. All devices were checked for a complete HUVEC monolayer under phase contrast microscopy before the permeability measurements (Fig. 1B).
Ang-1 and cAMP treatment to tune vascular permeability. For Ang-1 (R&D Systems, Minnesota, USA) treatment, seeded HUVECs were cultured in the device with EGM-2 until confluence and treated for 24 h with Ang-1 in EGM-2 at four concentrations: 100, 300, 500 and 5000 ng/mL before the permeability experiments. For pCPT-cAMP (Sigma-Aldrich, Missouri, USA) treatment, HUVECs were treated starting 4 h after the cell seeding at five concentrations: 0.5, 25, 50, 200, and 250 μg/mL, and then cultured with EGM-2 containing pCPT-cAMP until confluence. Permeability assay. The method for quantifying diffusional permeability in our PDMS microfluidic devices was modified based on first principles from a previously established protocol taking into account the differences in channel geometry between the rectangular lumen of the microfluidic device used in this study and circular lumen used in the previous study 31 . Prior to the experiments, the cell culture medium was aspirated from all media ports within the device. The device was then placed on the stage of an Olympus IX81 inverted microscope (Olympus, Tokyo, Japan). Fluorescence images were acquired to determine the background intensity. 15 μL of fluorescent dextran (both 10 kDa and 70 kDa as described earlier) or pNPs was then added through the media port and allowed to completely fill the HUVEC channels before starting the time lapse image acquisition at intervals of 30 s to observe the diffusion of fluorescent material across the endothelial barrier into the gel region (Fig. 1C). The total acquisition time was 30 min for dextran and 45 min for pNPs due to their slower diffusion.
We note that the presence of noise in the image acquisition and analysis process may introduce inaccuracies to the P d obtained. Price and Tien et al. 31 suggest that at low permeability, the change in fluorescence intensity with time in the middle gel region is low, and therefore susceptible to artefacts arising from low signal-to-noise ratio, leading to potentially inaccurate P d values. Here, we maximize the signal-to-noise ratio by using an electron multiplying CCD camera (Andor iXon + EMCCD camera, Andor, Belfast, Northern Ireland) with a sensitivity capable of measuring single photons to reduce the possibility of artefacts for low permeability barriers.
Image analysis to determine diffusional permeability. The time lapse images were analyzed by dividing the field of view into different regions of interest (ROI) (as delineated by different colors in Fig. 2A and B, with the green oval delineating a single data point from a single device). At time t = 0 s, the dextran or pNPs-containing solution filled the lumen of the HUVEC side channels before diffusing into the middle gel region (Fig. 2B). The average intensity values were extracted from each ROI using MATLAB and then used to calculate the P d as described below. Data points arising from obvious focal leaks within the HUVEC monolayer were omitted. Focal leaks were defined based on the method previously described 31 . Background fluorescent intensity was subtracted from all fluorescent intensity values used in the calculation.
In calculating the diffusional permeability, we assumed negligible convective contribution to transport since care was taken to ensure that no pressure difference existed between the two fluid-filled channels. The transport of solute across the endothelial monolayer was therefore attributed solely to static diffusion. The P d , when the lumen was completely filled with solute, was then defined as 31, 33 : where C denotes the local solute concentration in number of NPs per unit volume, and dV, an infinitesimal volume within the gel region. Considering C being directly proportional to its fluorescence intensity, I, and substituting Equation (2) into (1):  Since larger nanoparticles or diffusing materials would experience slower diffusion within the gel region, it is imperative that the control volume within the gel region (demarcated by the red ROI within the gel in Fig. 2) includes the interface between the HUVEC monolayer and the gel (blue ROI in Fig. 2), so that any changes in fluorescence intensity due to the slow diffusion and accumulation of larger materials within the gel region would still be accounted for in quantifying its P d .
Immunostaining and confocal imaging. HUVECs were fixed with 4% paraformaldehyde (PFA) (Sigma Aldrich, USA), permeabilized with 0.1% Triton X (Sigma Aldrich, Missouri, USA) and blocked with 3% bovine serum albumin (BSA) (Sigma Aldrich, Missouri, USA) reconstituted in 1x PBS for 3 h at room temperature. The microfluidic devices were then incubated with either rabbit anti-VE-Cadherin (Enzo life sciences, New York, USA) or mouse anti-ZO-1 (Life Technologies, Massachusetts, USA) primary antibodies overnight at 4 °C, followed by Alexa Fluor 488 chicken anti-rabbit (Life Technologies, Massachusetts, USA) or goat anti-mouse (Life Technologies, Massachusetts, USA) secondary antibodies for VE-Cadherin and ZO-1 staining, respectively. Hoescht (Life Technologies, Massachusetts, USA) and Rhodamine Phalloidin (Life Technologies, Massachusetts, USA) were used to stain the nuclei and F-actin cytoskeleton of HUVECs, respectively. The microfluidic devices were then imaged under an Olympus IX83 confocal microscope (Olympus, Tokyo, Japan) for a cross sectional z-stack of the HUVEC channel.

Results and Discussion
Diffusional permeability coefficients of dextran across HUVEC monolayers. Untreated HUVEC monolayers were first characterized for their diffusional permeability coefficients, P d to both 10 kDa and 70 kDa dextrans. The measurements showed size-selectivity as observed in vascular networks in vivo [38][39][40] , with a mean P d of the smaller-sized molecules (10 kDa dextran, P d = 3.50 × 10 −5 cm/s) being significantly higher (p ≤ 0.0001) than the mean P d of the larger-sized molecules (70 kDa dextran, P d = 2.47 × 10 −5 cm/s) (Fig. 3A, with no Ang-1 or pCPT-cAMP). These values of P d obtained with 10 and 70 kDa dextran were comparable to the values reported with 40 kDa dextran on untreated HUVEC monolayers in conventional transwell assays 41 . These observations  suggest that the HUVEC monolayers form slightly tighter para-cellular junctions in our microfluidic devices compared to conventional two component transwell permeability assays, thus resulting in the slightly lower P d values even for smaller sized 10 kDa dextran.
While these P d values obtained in vitro agree with those previously reported in other microfluidic in vitro systems 42, 43 , they were significantly higher than the P d values in healthy vasculature in vivo. In the microvessels of mammalian skeletal muscles, 10 kDa and 70 kDa dextran were reported to have a P d in the range of ~10 −6 cm/s and 10 −7 cm/s, respectively 38,44 . The thickness of the HUVEC monolayer could influence the P d values measured. Physiologically, endothelial cells vary in thickness depending on the vessel type and location, with cell thickness ranging from ≈0.1 µm for capillaries and veins, to 1 µm for aortas 45 . Based on the thickness of the fluorescent cross section of the monolayer in our confocal images (Fig. 3C), we determined our HUVEC cell thickness to be ≈2 µm, comparable to values expected of human endothelial cells.
However, the human vasculature consists of multiple supporting stromal cells such as fibroblasts, vascular smooth muscle cells and pericytes working in concert with the parenchymal epithelial cells to regulate vascular permeability. The significantly lower permeability in vivo could be attributed to tighter cell-cell junctions and/or the presence of these multiple supporting cells that were not present in the in vitro assays, which consisted of a mono-culture of ECs. These various supporting cells work in concert with ECs to maintain and regulate vascular integrity and permeability through a variety of mechanisms [46][47][48] .
In contrast, the P d values of dextran we obtained are closer to tumor vascular permeability, which is known to be leakier compared to healthy vessels 49,50 . Previous studies showed that the P d of 10 kDa and 70 kDa dextran across murine tumor vasculature ranged between 1 and 3 × 10 −6 cm/s, with 10 kDa expectedly having a higher P d than 70 kDa in these tumor models 13,42 .
Here, we tuned the vascular diffusional permeability coefficient to attain values closer to physiologically healthy levels by treating the ECs in the microfluidic device with both Ang-1 and pCPT-cAMP. This allows us to maintain an easy-to-handle system and to obtain relevant physiological response from the in vitro model despite phenotypical differences. Furthermore, the tuning of permeability by cytokines introduced an additional level of control of the system that allows systematic permeability studies over a range of vasculature permeabilities, lending versatility to the microfluidic model.
Ang-1 is a cytokine known to reduce vascular permeability through several mechanisms 15-17, 51, 52 . First, Ang-1 binds antagonistically with Ang-2 to tyrosine kinase receptor (Tie-2) to promote vascular maturation and stabilization 53,54 . It also modulates the increase in vascular permeability due to other growth factors such as VEGF, thrombin, histamine, and bradykinin 55 through inhibiting the c-Src pathway that leads to the phosphorylation and eventual internalization of VE-Cadherin 17, 55 . Ang-1 also reduces vascular permeability by reducing the basal phosphorylation of PECAM-1 56 . In addition to maintaining the integrity of junctional proteins, Ang-1 signaling reduces intracellular Ca 2+ concentration, which at high levels, is known to increase vascular permeability [57][58][59] .
In addition to the reduced permeability after Ang-1 treatment, an enhancement in size-selectivity was also observed, as the larger 70 kDa dextrans registered a significantly lower P d value compared to their 10 kDa counterparts across all concentrations of Ang-1 (p < 0.05). The decrease in permeability with Ang-1 treatment appeared more pronounced for larger molecules, even though the P d values of the endothelial monolayer for both sizes of dextran were still above physiological levels.
Tuning vascular permeability with pCPT-cAMP. Similar to Ang-1, cAMP also reduces vascular paracellular permeability by promoting the expression of adherens and tight junction proteins such as ZO-1, VE-cadherin, claudin-5, and junction adhesion molecules (JAMs) 19,39,[60][61][62] . Here, treatment with pCPT-cAMP resulted in a concentration dependent decrease in P d across the ECs for both 10 kDa and 70 kDa dextran (Fig. 3B). While the P d for 10 kDa dextran exhibited a 2.87-fold decrease to 1.22 × 10 −5 cm/s with treatment of 25 µg/mL of pCPT-cAMP, the same treatment caused the P d of 70 kDa dextran to decrease 5.05-fold to 4.88 × 10 −6 cm/s. As with Ang-1, we observed size selective permeability for all concentrations of pCPT-cAMP (70 kDa dextran having significantly lower P d values compared to 10 kDa dextran, p < 0.05) and a more pronounced decrease in permeability for the larger molecular weight dextran with pCPT-cAMP treatment. Such size selectivity was in line with what is expected in vivo 38 .
In addition to the differences in diffusion coefficients, the differences in P d observed were also a result of different molecular weight dextrans experiencing different degrees of exclusion due to molecular size when passing through the endothelial barrier 12, 63 . Michel and Curry et al. observed that the ratio of a molecule's P d over its diffusivity, D i.e. P d /D followed a non-linear decline against the molecular radius 38,64 . This suggests that the decrease in permeability may not be due solely to the decrease in diffusivity following the increase in the particle's size, although the scatter in our data prevents us from drawing any definite conclusions on the role of exclusion. Therefore, additional effects such as increased viscous drag and an exclusion mechanism at the inter-endothelial junctions for larger sized particles moving across the endothelial barrier may also play a role in mediating the observed size-selective permeability 38 .
With increasing pCPT-cAMP concentrations that reduce paracellular permeability, the increase in viscous drag and exclusion experienced by larger sized 70 kDa dextran could, as a result, be more significant than the one for the smaller sized 10 kDa dextran. This may explain the more pronounced decrease in permeability for larger molecular weight dextran as pCPT-cAMP treatment concentrations increase.
Scientific RepoRts | 7: 707 | DOI:10.1038/s41598-017-00750-3 Taken together these results show that untreated cells and 25 μg/mL pCPT-cAMP treated cells both resulted in P d values an order higher than that reported in vivo for cancer and normal healthy vasculature, respectively. While this microfluidic model did not achieve the exact permeability values in vivo, it did provide approximate in vivo values that showed the right trend in permeability moving from a healthy to tumor vasculature. We can subsequently address the differences with an appropriate constant correction. Nonetheless, we would consider 25 µg/mL pCPT-cAMP treated devices and untreated devices to approximate normal and tumor vascular permeabilities respectively.
Confocal imaging of the endothelial monolayer in the microfluidic devices stained for adherens junction protein VE-cadherin and tight junction linker protein ZO-1 have demonstrated inter-endothelial adherens and gap junctions formation for both untreated and 25 μg/mL pCPT-cAMP-treated microfluidic devices (Fig. 3C). Interestingly, treatment of HUVECs with 25 μg/mL pCPT-cAMP resulted in a more localized expression of VE-cadherin compared to the untreated counterpart as indicated by the less "fuzzy", "thinner" and more defined staining, even at the gel-lumen interface (Fig. 3C). Treatment by pCPT-cAMP also led to cells growing in a more ordered manner as compared to the untreated counterparts. These are characteristics of a decreased vascular permeability due to reduced angiogenic potential following treatment with pCPT-cAMP 65 . On the other hand, there was no observable difference in the ZO-1 staining between 25 μg/mL pCPT-cAMP treated and untreated cells.
Characterization of polystyrene nanoparticles. The pNPs used in this study aggregated easily in cell culture medium. To maintain their colloidal stability, we reconstituted them in FBS to pre-form a protein corona coating around them. The average hydrodynamic diameter, D H of all the pNPs increased by ~32 nm with the formation of a protein corona (Fig. 4). We observed a similar increase in the D H previously upon formation of a protein corona 66,67 . The formation of protein corona on all NPs in contact with biological media e.g. cell culture media and blood, and the consequent increase in D H is inevitable. As such, we characterized the size change of the pNPs upon protein corona formation (Fig. 4) and reported subsequent P d measurements of the pNPs according to their measured D H .
Since the increase in hydrodynamic diameter was consistent across all sizes of pNPs, this would not affect any size-dependent trend in their permeability caused by the increase in size due to the protein corona. Furthermore, while it is true that the protein corona may evolve with time due to protein exchanges between those on the pNP's surface and the free proteins in the medium 68 , such an exchange is unlikely in our study as the pre-formed protein corona was formed from FBS following an overnight incubation before being flowed in EGM medium also containing FBS as the serum component so as to minimize this exchange. This ensured that the protein corona stayed relatively constant over the vascular flow.
Permeability measurements for nanoparticles. We probed 20, 40, 100, and 200 nm pNPs for their P d across untreated and 25 µg/mL pCPT-cAMP treated endothelial monolayers in microfluidic devices (Fig. 5A). Here, endothelial permeability was determined by two main routes: transcellularly through the cell via transcytosis, and paracellularly via the inter-endothelial junctions 52 . The P d values of pNPs across untreated leaky endothelial monolayers decreased with increased particle size, following a non-linear curve (Fig. 5A), similar to that observed in vivo for the microvessels of skeletal muscle 38,64 .
Furthermore, the P d values of pNPs showed statistically significant difference between each size except between 100 and 200 nm pNPs (Fig. 5A) (p < 0.05). For smaller 20 and 40 nm pNPs, size dependent selectivity of the paracellular route was observed, which led to 20 nm pNPs being more permeable than 40 nm pNPs. As we approach the size limit of paracellular permeability in leaky vasculature, the difference in P d between the larger 100 and 200 nm pNPs became insignificant, indicating limiting paracellular transport at these sizes. At these large sizes, the transcellular route became the dominant mode of transendothelial transport, which appeared to be less size-dependent.
To ensure that the differences in permeability were not attributed to the cytotoxicity of pNPs of different sizes, we examined the cell viability of HUVECs using PrestoBlue cell viability reagent and found that pNPs of different sizes did not affect cell viability when compared to controls (data not shown). This suggests that the differences observed in the P d values between different sized pNPs were not due to cytotoxic effects of pNPs on HUVECs.
In the monolayers treated with 25 µg/mL pCPT-cAMP, the same set of pNPs experienced lower P d across pCPT-cAMP treated endothelial cells for all sizes compared to untreated endothelial cells (Fig. 5A). The permeability was also comparably size-independent. The lower P d is attributed to the shutdown of paracellular route with cAMP treatment, leaving the transcellular route as the dominant mode of transendothelial transport, which was also observed to be size independent across the size range of pNPs used in this study. The application of pCPT-cAMP has been shown in literature to increase cell-cell and cell-matrix tethering, reduce isometric tension development and also decrease inter-cellular gap formations 18,60,61 . Physiologically, cAMP is also known to mediate endothelial permeability via cAMP dependent protein kinase A (PKA) 61,[69][70][71][72][73] and PKA independent mechanisms [74][75][76] . The induction of cAMP in endothelial cells activates PKA which in turn inhibits the activation of protein substrates RhoA 77 and MLCK 78,79 . As a result, the paracellular permeability is reduced by preventing actin-myosin cytoskeletal contractions that destabilize adheren junctions 52, 80 . cAMP has also been shown to promote the expression of adherens and tight junction proteins such as ZO-1, VE-Cadherin, CLDN5, and Jam-A 19, 39, 60-62 . Together, these stabilize the inter-endothelial junctions between endothelial cells, thereby reducing paracellular permeability.
This reduction in paracellular permeability is significant because migration of macromolecules of diameters >3 nm (approximately the size of serum albumin) across the continuous endothelium will be hindered in intact healthy microvessels, thereby leaving transcellular vascular pathways being the dominant route responsible for their transport across the endothelium 81-86 as observed in our treated case. Ex vivo experiments have shown that transcellular endocytotic processes result in P d values that are less size dependent for the same diffusing NP 38,44 . This similar size-invariant trend was also observed with cAMP-treated endothelial cells (Fig. 5A), where differences in P d and hence size selectivity amongst all pNPs were not statistically significant. This suggests that with 25 µg/mL pCPT-cAMP HUVECs, pNPs of all sizes tested traversed the endothelial monolayer transcellularly as described earlier.
The obtained P d values and non-linear inverse relationship between P d and NP sizes observed in both untreated and cAMP-treated HUVECs culture show similarity to that of similar macromolecules observed in vivo for tumor and normal vasculature, respectively 38,44 . This suggests a promising use of the microfluidic model of vascular-tissue interface as a physiologically relevant model for a systematic and quantitative study of the extravasation of nanomedicine-based systems for tumor delivery. In fact, this microfluidic model could potentially be used as platform to characterize a wide range of drugs, macromolecules or other particulates for transendothelial migration beyond this study on nanoparticles.
Here, it may be worth highlighting that our present study solely determines the passive diffusional permeability of the NPs across the endothelium, and did not account for differences in Starling forces between blood hydrostatic pressure and tissue interstitial fluid pressure, which may also set up a convective transport component to drive the NPs across the endothelium 36,83 . While this does not compromise our diffusional permeability values obtained which are close to in vivo levels, the design of our microfluidic model does allow for a differential pressure to be set up between opposite media channels (Fig. 1A). This differential pressure would then allow user tunability of the pressure difference between the cell lumen and the gel channel for modelling different degrees of Starling forces. This is an added feature of the model, and one that helps to motivate the need for microfluidics.
"Tumor-to-normal" permeability ratio. The P d,tumor values of pNPs across untreated endothelium approximating the permeability of tumor vasculature showed greater size selectivity compared to the relatively size-invariant P d,normal in cAMP-treated endothelium approximating the permeability of healthy vasculature (Fig. 5a). Based on this difference in size selectivity between tumor and healthy vasculature, we defined a "tumor-to-normal" P d ratio, TNR = P d,tumor /P d,normal to probe the selectivity of leaky vasculature over healthy vasculature for a range of different sizes of pNPs. Here, the TNR decreased from 5.49 to 1.02 as the size of pNPs increased from 20 to 200 nm (Fig. 5b). Such a decreasing trend demonstrates that the smaller pNPs tend to preferentially cross the endothelium monolayer of leaky vasculature compared to healthy vasculature much more than larger pNPs [87][88][89] . This means that as the size of pNP increases, the increase in P d due to the leakier tumor vasculature decreases, and the TNR approaches unity with no difference in P d between tumor and normal vasculature for large NPs. Therefore, the microfluidic model of vascular-tissue interface also allows us to characterize in vitro the selectivity of tumor vasculature to NPs.

Conclusion
We have reported a relevant in vitro microfluidic model of vascular-tissue interface that can be used to provide a quantitative study of the permeability coefficients of NPs across the vascular endothelium under dynamic flow conditions. This model also allows facile systematic tunability of vascular endothelial permeability and thereby control over the transendothelial route taken by the NPs. The model was able to approximate physiologically relevant P d values similar to in vivo values, that allowed us to conduct a systematic and quantitative evaluation of the extravasation rate of nanomedicine-based systems for tumor targeting. This can potentially be used to complement animal models as a facile screening tool in screening libraries of NPs prior to detailed animal studies, where the use of large scale animal models and their in vivo-associated complexities in controlling vasculature properties are not feasible.
We would also like to add that it would be too ambitious for us to conclude here that the untreated and cAMP-treated endothelium represents the tumor and normal vasculature in its entirety as many other factors that are related to the microenvironment are not represented in this model. Furthermore, the trans-endothelial transport of NPs in vivo is also influenced by hydrostatic pressure of blood and tumor interstitial fluid pressure in vivo, resulting in convective components that also drive NPs across the endothelium on top of passive diffusion 38,90 .
Despite the limitations, we can still conclude that this platform allows for probing of endothelial permeabilities close to in vivo levels for different NP configurations. Apart from HUVECs, other endothelial barriers (e.g. alveolar endothelial cells as a model for the lungs 91 , COCA-2 for epithelial cells of the digestive tract 92 or the blood brain barrier 93 ) suitable for transport studies could potentially be implemented within this model. Besides, a wide range of NPs that have colorimetric (e.g. gold) or fluorescent properties could be characterized with the methodology presented here. This platform could therefore potentially offer valuable insights towards optimizing the design of NPs for a myriad of biomedical applications, including tumor drug delivery and would serve as a useful tool for the nanomedicine community.