Impact of Particle Shape & Size on Margination & Adhesion in Blood Flow: Spherical vs. Non, Lecture notes of Design

Download Impact of Particle Shape & Size on Margination & Adhesion in Blood Flow: Spherical vs. Non and more Lecture notes Design in PDF only on Docsity! Influence of particle size and shape on their margination and wall-adhesion: Implications in drug delivery vehicle design across nano-to-micro scale Journal: Nanoscale Manuscript ID NR-ART-05-2018-004042.R1 Article Type: Paper Date Submitted by the Author: 22-Jul-2018 Complete List of Authors: Cooley, Michaela; Case Western Reserve University, Department of Biomedical Engineering Sarode, Apoorva; Harvard University John A Paulson School of Engineering and Applied Sciences Hoore, Masoud; Institute of Complex Systems and Institute for Advanced Simulation, Forschungszentrum Jülich, Theoretical Soft Matter and Biophysics Fedosov, Dmitry; Forschungszentrum Juelich GmbH, Theoretical Soft- Matter and Biophysics, Institute of Complex Systems and Institute for Advanced Simulation Mitragotri, Samir; Havard University , John A. Paulson School of Engineering and Applied Sciences Sen Gupta, Anirban; Case Western Reserve University, Department of Biomedical Engineering Nanoscale Influence of particle size and shape on their margination and wall-adhesion: Implications in drug delivery vehicle design across nano-to-micro scale 1,# Michaela Cooley, 2,# Apoorva Sarode, 3 Masoud Hoore, 3 Dmitry A. Fedosov, 2 Samir Mitragotri, 1,* Anirban Sen Gupta 1 Case Western Reserve University, Department of Biomedical Engineering, Cleveland, Ohio, USA 2 Harvard John A. Paulson School of Engineering and Applied Sciences, Cambridge, Massachusetts, USA 3 Theoretical Soft Matter and Biophysics, Institute of Complex Systems and Institute for Advanced Simulation, Forschungszentrum Jülich, Jülich, Germany * Corresponding Author: Anirban Sen Gupta, PhD Case Western Reserve University Department of Biomedical Engineering 10900 Euclid Avenue, Wickenden Building Rm 517B Cleveland Ohio 44106, USA Phone: (01) 216-368-4564 E-Mail: axs262@case.edu # Michaela Cooley and Apoorva Sarode are co-first authors. Page 1 of 46 Nanoscale 1. Introduction The field of ‘drug delivery particles’ has focused significantly on: (i) the development of biomaterials for particle fabrication, (ii) surface-engineering of particles to modulate their circulation lifetime and (iii) utilization of disease-specific mechanisms to engineer the particles for site-selective action. The targets for such particles (and their drug payload) are often at the blood vessel wall or in the tissue compartments beyond the wall, such that their transport through the blood cell volume (mostly RBC) towards the vascular wall (i.e. margination) becomes a pre- requisite for their function (schematic in Figure 1). The factors that can influence the distribution and margination of particles in blood flow have undergone limited exploration so far. Establishment of the enhanced permeation and retention (EPR) mechanisms for nanoscale particles to leak across the endothelial barrier into the tumor tissue 1, 2 , as well as, the benefit of high surface-to-volume ratio of nanoparticles to enhance biointeractions and payload delivery 3, 4 , have led to most particulate drug delivery systems being designed as spherical nanoparticles. The size of such nanoparticles is usually in the range of 20-200 nm, since particles smaller than that are rapidly cleared by the kidney while particles larger than that have lower circulation lifetime due to rapid macrophagic uptake. 5-9 Some drug delivery approaches have also looked into micro-scale particles. In this domain, particles > 3µm in diameter pose the risk of occluding microvascular capillary networks and also show higher macrophagic uptake (hence rapid clearance). 9-11 In addition, this microscale range is too big for EPR-based extravasation and uptake into the tissue compartments (e.g. in tumors), since the endothelial junctions in disease- associated leaky vasculature are in the 50-500 nm range. 12-15 Thus, the manufacture of particulate drug delivery systems has been primarily guided by design requirements for evading rapid macrophagic uptake, avoiding microvascular occlusion, Page 4 of 46Nanoscale minimizing renal clearance and facilitating extravasation (especially for cancer-targeted drug delivery), and not necessarily considering the effect of particle geometry on their interactions with the components of the blood flow volume, especially RBCs. A limited number of computational studies in the past have examined the potential effect of particle size in their interaction with RBCs and resultant vascular distribution, and even fewer experimental studies have been reported especially involving the presence of RBCs in the experimental set-up. For example, experimental studies were done with polymeric microspheres 5–20 µm diameter, decorated with ligands to attach to P- selectin-coated surfaces under flow in phosphate buffered saline (i.e. PBS only) and these studies showed that larger particles in that size range had reduced retention on target surface. 16 Similar studies were carried out to analyze the ‘non- specific’ adhesion of microspheres on endothelial monolayer in a flow chamber in RBC-free environment and similar trends were observed. 17 Further studies in PBS with spherical particles having diameters of 50, 100, 200, 500, and 750 nm and 1, 6, and 10 µm, showed that particles >500 nm in diameter are influenced more by gravitational forces to localize towards the wall, whereas particles <500 nm in diameter are influenced more by Brownian motion. 18 Several recent computational studies, considering RBCs in flow volume, have indicated that nano-scale particles require a contribution of external forces beyond just hydrodynamic forces for effective margination towards the wall and that under hemodynamic flow, micro-scale particles undergo higher margination. 19-21 A few recent experimental studies with polymeric spherical particles in nano-scale and micro-scale show that in the presence of RBCs in laminar and pulsatile flow, micro-scale particles marginate better than nano-scale particles 22-25 , but similar size-range studies have not been reported across various shape parameters of particles and at different shear flow ranges. Page 5 of 46 Nanoscale In the context of particle shape, most drug delivery approaches to date have looked into spherical particles since most particle fabrication processes (e.g. self-assembly, nano- and micro- precipitation, emulsion etc.) preferably produce spherical particles due to thermodynamic favorability. The seminal studies comparing worm-shaped micelles (filomicelles) versus spherical micelles and comparing spherical particles with ellipsoidal particles, demonstrated the influence of shape on circulation lifetime and macrophagic clearance. 26,27 Some computational studies in the past have indicated that spherical particles tend to follow flow streamlines with hydrodynamic forces correlative to their radius, such that lateral margination towards the wall can be rendered only by external forces such as gravity and electromagnetic fields. 19,20 In contrast, non-spherical particles (e.g. ellipsoids, rods etc.) can undergo significant lateral drift by virtue of their rotational motion (tumbling) under flow even in the absence of external forces. 19,20 Such computational models were further tested by experimental studies with silica particles of discoid, spherical and hemispherical geometries but these studies were done in an RBC-free set- up. 28,29 A recent computational study further reported that in presence of RBC flow, non- spherical particles are more likely to undergo large lateral drifts in blood flow to move into a cell-free layer away from the RBC volume and closer to the wall. 30 Several computational studies have also indicated that anisotropic non-spherical shapes may have a higher extent of adhesion to target surfaces or cells due to higher surface area of interaction. 31-34 Interestingly, a recent study using ellipsoidal particles showed that the beneficial effects of anisotropic shape toward margination in the vascular compartment occur preferably more for microscale particles than nanoscale particles, suggesting a significant interplay between shape and size in determining ‘margination + stable adhesion’. 35 Therefore different computational and experimental studies have provided only in part evidence that both Page 6 of 46Nanoscale thermal fluctuations. 41 While the fluid properties in SDPD can be set directly, in DPD they need to be calculated a priori for a specific set of parameters. Red blood cell (RBC) membranes in 3D are modeled by triangulated bead-spring networks, which conserve their area and volume and possess bending rigidity and shear elasticity. 42-44 The model and simulation parameters were adapted from previous reports. 43,45 The particles were modeled by the same bead resolution and kept rigid. In 2D, RBCs were modeled by closed polymer chains with bending rigidity and area conservation. The particles were modeled by rigid closed polymers with a similar resolution. For a detailed description of the membrane and particle models, see Supplementary Information Section S.1, and Tables S.1 and S.2. To further assess the importance of other factors influencing particle adhesion and retention, we investigated via simulation the drag force exerted on particles by the fluid and quantify their adhesion strength defined by the total number of ligand interactions within the particle adhesion area. The drag force is obtained from simulations of a fixed particle at the wall subjected to shear flow, since the total drag force on an adhered particle consists of pressure and shear stress components. The pressure contribution is proportional to the cross-sectional area perpendicular to the flow direction, while the shear force is governed by the surface area of the particle. Both are proportional to the square of a characteristic size of the particle. 57 For our simulations, a pressure driven flow was induced by applying a constant force to fluid particles, which were confined in a slit together with RBCs and rigid micro/nano particles. The boundary conditions in the flow and vorticity directions were periodic. The walls were composed of frozen fluid particles with the same density and pair correlation function as those for the fluid. Furthermore, an adaptive shear force was applied to the fluid particles within a cutoff distance from the walls in order to have no-slip boundary conditions. 46,47 This cutoff distance is around tens of Page 9 of 46 Nanoscale nanometers, an assumption motivated by the distance of common adhesive interactions. 58 Penetration of fluid particles into the walls was prohibited by bounce-back reflections. The fluid was coupled to the membranes by the DPD forces, excluding conservative part. 45 Additional details about the computational and simulation parameters are given in Supplementary Information Section S.1, Tables S.1-S.3, and Figure S.1. 2.3. Fabrication and characterization of particles Non-spherical oblate, prolate and rod-shaped particles were fabricated using a previously reported one-dimensional and two-dimensional polymer film stretching method. 48 The process schematic is shown in Figure 4A. Briefly, ~10 8 PS spheres were suspended in a 6.25% w/V aqueous PVA solution. 1.25% v/V glycerol was added as a plasticizer to lower the glass transition temperature of the films and facilitate stretching. The mixture was then cast into a film and dried for ~24 hours at room temperature to immobilize the PS particles. The dried films were mounted on a 1-D or a 2-D mechanical stretcher to obtain prolates/rods and disks, respectively. Further, the films were heated for 5 minutes at 120 0 C in mineral oil and stretched to obtain the desired geometry. The aspect ratio (AR) was controlled by limiting the extent of stretching. The stretched films were cooled to room temperature for 10 minutes to allow solidification of the particles in their new shape. Suitable sections were cut from the stretched films, dissolved in 70 ℃ MilliQ water overnight and centrifuged for particle recovery. The isolated particles were subsequently washed multiple times with MilliQ water via centrifugation and finally passed through a 100µm filter, for the removal of residual PVA. Concentration (w/V) of the respective particle suspensions was determined by lyophilization of a known sample volume. For characterization using scanning electron microscopy (SEM), sample preparation involved vacuum drying of 10µL particle suspension on an aluminum stub, Page 10 of 46Nanoscale followed by coating with palladium (Hummer 6.2 Sputtering System, Anatech Ltd., Union City, CA). The sputtered samples were imaged using the Sirion 400 SEM (FEI Company, Hillsboro, OR) at an acceleration voltage of 5 kV and a working distance of 5mm. Particle dimensions were measured from the SEM images using Metamorph image acquisition and analysis software (Universal Imaging Systems, Downingtown, PA). For particle surface-decoration with biotin, the spherical and non-spherical fluorescent carboxylate polystyrene particles were conjugated with EZ-Link TM Amine-(PEG3)-Biotin using carbodiimide coupling chemistry and stored at 4 0 C in PBS. Briefly, 12.5mg particles were washed twice with 50mM MES buffer and the carboxyl groups on their surface were activated with EDC for 15 minutes and further mixed with an excess of (900µg) the biotin reagent in a total volume of 500µL in a microcentrifuge tube. The reaction was allowed to run overnight at room temperature with gentle end-to-end mixing on a tube revolver. Particles were then washed twice with PBS to remove the unconjugated biotin and N-acyl urea by-product, before resuspending them at a concentration of 1mg/mL until ready to be used in the binding experiments. Figure 5A shows a schematic of this surface-modification strategy for the particles with biotin. The relative surface density for biotin modifications on the various particles were theoretically estimated. Total particle volume remains constant during stretching, governed entirely by the volume of initial sphere and thus, by the ESD. Dimensions and surface area of the stretched particles were estimated from their 2D SEM projections and mathematical volume equations for their respective geometries. Owing to the hydrophilic nature of the carboxylate functional groups on the polystyrene particles, it was assumed that majority of these ligands were conserved on the surface post stretching. However, their surface density decreases due to the generation of new surface area during the spherical to non-spherical shape transition. For a fixed number of ligands, the ligand surface Page 11 of 46 Nanoscale variations between ligand density on the particle surface between particles from different sources. Thus, the analysis measured specific binding of the particles to the avidin surface. 3. Results 3.1. Computational Analysis of Particle Margination As described previously, RBCs play an important role in the process of particle margination towards the vessel wall. RBCs experience a hydrodynamic lift force from the vessel walls that arises from the pressure differences between the different sides of the cells. Such force also depends on cell (and particle) size, deformability, and dynamics, as investigated theoretically, in simulations, and in experiments. 49-51 Since RBCs are highly deformable with a non-spherical (biconcave discoid) shape, and since the lift force on such deformable particles is generally stronger than on rigid ones, therefore the lift force on RBCs is much stronger than that on rigid drug carriers. 49-51 Due to this lift force, flowing RBCs migrate to the center of the vessel and push the other cells (and particles) toward the walls (Figure 2A). In addition, the migration of RBCs to the center of the flow creates a RBC free layer (RBC-FL), whose thickness (height) depends on several properties, such as hematocrit, shear rate, and channel size. 52, 53 By virtue of RBCs moving towards the center flow volume, micro- and nano-particles are pushed into the RBC-FL (i.e. margination). 21,54 In order to quantify particle margination, ‘margination probability’ was defined as a probability of particles to be in a layer adjacent to the vessel walls of thickness  (Figure 2B). It is important to note that this definition is sensitive to the way  is selected. One of the most commonly used selections is to set  as the thickness of RBC-FL. 21,55 Page 14 of 46Nanoscale For our studies, a different definition of  was employed motivated by the thickness of a layer where particle adhesion can potentially occur, as  = Dm + h , where Dm is the largest dimension of a particle, and h is the thickness of a layer which presents high probability of adhesion for particles in it. Thus,  characterizes the probability of possible contact and particle adhesion with the wall. The most important factor in particle margination is the volume fraction of RBCs or hematocrit (HCT). As the hematocrit in blood vessels increases, RBCs fill more space in the vessel center and thereby force more particles toward the walls. This anticipated trend is illustrated in Figure 2C and 2D. The size of particles strongly affects this margination propensity. To that end, our simulations indicate that larger micro-particles marginate better in comparison to smaller nano- particles (Figure 2C). In fact, it has been demonstrated recently that nanoparticles because of their smaller size can easily occupy available space within RBC volume in the bulk flow (i.e. remain in the gaps between flowing RBCs), and therefore, their margination is not very efficient. 21 This was also used to leverage nanoparticle attachment to RBCs for ‘hitchhiking’ technology in drug delivery. 56 Shape of the particles is also important in margination. Simulation results in Figure 2D show that the margination probability of ellipsoidal particles is larger than that of spherical particles for equivalent particle volumes. These findings are also consistent with previous investigation by 3D simulations. 30 Once in the RBC-FL, ellipsoidal particles can also make a more frequent contact with the wall in comparison to spherical particles, since the largest dimension of ellipsoids is larger than the radius of a sphere with the same volume. Furthermore, by tumbling in shear flow within the RBC-FL, ellipsoidal particles collide with RBCs more frequently than spherical particles so that they are more efficiently pushed toward the wall (i.e. higher margination). Page 15 of 46 Nanoscale 3.2. Computational Analysis of Particle Adhesion Since particle margination characterizes the frequency of particle contact with the wall, it therefore directly influences the adhesive interactions of particles to the wall. Also, retention of adhered particles on the wall is influenced by the drag force exerted on particles by the fluid and the resistance to lift-off imparted by the overall adhesion strength stemming from the total number of ligand interactions within the adhesion area. Figure 3 summarizes the results of these simulations for adhesion. The schematic of the different shapes of particles adhering to the wall is illustrated in Figure 3A, while Figure 3B shows how drag force can change depending on the shape as well as orientation (w.r.t. wall) of particles. The results indicate that the drag on particles of different shapes for a fixed particle volume is not extremely different from each other, and that the drag on prolate or rod-like particles placed perpendicular to the flow is the highest. It is also important to note here that in Stokes flow regime, the lift force is zero for symmetric rigid particles. Thus, spherical rigid particles will experience zero lift force; however, if these particles have a low probability of margination to the wall (e.g. spherical nanoparticles) or have a low adhesion strength at the wall, then their localization at the wall under blood flow conditions will be low. Adhesion strength of particles to the wall is directly associated with the surface area of the particle that participates in adhesion. Figure 3C shows a schematic of that for fixed particle volume, where non-spherical ellipsoidal shapes have a larger adhesion area in comparison to spherical particles. In case of specific molecular interactions, the adhesion strength also depends on the number of motifs (e.g. ligands) on the particle surface, which are able to interact with corresponding motifs (e.g. receptors) at the wall. For this reason, the adhesion area is calculated as the area of the particle that is located within a cutoff distance of approximately tens of nanometers, based the distance of common adhesive interactions. 58 Page 16 of 46Nanoscale of carboxyl (-COOH) groups on the particle surface depends on the amount of the acid monomer used for the original spherical particle synthesis (as per manufacturer description) and hence it is a function of total particle volume. Thus, particles with larger size have more number of -COOH ligands compared to smaller ones. Furthermore, since the total mass of particles was maintained constant for the conjugation reaction across various shapes and sizes, therefore the total number of -COOH ligands (primarily conserved on the particle surface) available for conjugation can be rationalized to be nearly equal for each of the particle type studied here. Therefore, the values for mg of Biotin-PEG3-Amine/mg of particles were found to be almost the same, as shown in Figure S.8. However, for each spherical particle type, the ligand surface density (i.e. ligand number per unit surface area) decreases when transformed into non-spherical particle, due to the generation of new surface area. The surface-modified particles were stored at 4 o C in PBS until use. 3.4. Flow chamber experiments Figure 6B shows representative fluorescence microscopy images of particle adhesion at the wall in PBS flow only (no RBCs) and RBCs in flow at physiological volume (40% v/V i.e. 0.4 HCT) conditions, at τW of 30 dyn.cm -2 at the 30 min time point. Additional representative microscopy images for the various particle sizes and shapes adhering at τW of 5 dyn.cm -2 and 60 dyn.cm -2 respectively in PBS (0 HCT) and 40% v/V RBC flow (0.4 HCT) conditions at 5, 15 and 30 min time-points are shown in Supplementary Figures S.2, S.3, S.4 and S.5. Figure 7 shows quantitative data for ‘number of adhered particles per unit surface area’ in absence (PBS) versus presence of RBCs (0.4 HCT) in flow, at 5, 15 min and 30 min time-points obtained from image analysis for experiments carried out at shear value of 30 dyn.cm -2 , while Figure 8 shows expanded quantitative data for ‘number of adhered particles per unit surface area’ for particles Page 19 of 46 Nanoscale of various shapes and sizes, at 5, 30 and 60 dyn.cm -2 shear flow conditions at 30 min in presence of 0.4 HCT. Additional data for similar experiments and analyses performed at mid- range RBC volume (20% HCT) for various time points and shear flow conditions are shown in Supplementary Figure S.6. From the qualitative images as well as quantitative analysis, it is apparent that in absence of RBCs (i.e. in PBS only) a lot more particles across all size and shape parameters become adhered at the wall while this is significantly reduced for all particle sizes and shapes once RBCs (20% or 40% HCT) are introduced in flow volume. Furthermore, in the presence of RBC flow volume, oblate particles and to some extent rod-shaped particles in the 500 nm or higher (e.g. 2 µm) diameter seem to undergo higher adhesion (and retention) at the wall compared to spherical particles and prolate particles, at all shear flow values. These experimental data appear to be in line with the simulation results that in the presence of RBC flow volume, the microscale particles have higher probability of margination compared to nanoscale particles into the RBC-FL, and once marginated, the particles of oblate ellipsoidal shape undergo lower drag force at the wall and higher adhesive interaction area at the wall compared to their spherical counterparts. It is also important to note here that these particles were made by a process that approximately kept a constant number of ligands (i.e. biotin), NL, for all shapes and thus the surface density (per unit surface area) of ligands on the non-spherical particles is less than their spherical counterparts of equivalent volume. Therefore, the experimental data essentially indicate that even at a reduced overall surface density of ligands, oblate and rod-shaped particles of microscale size range manage to undergo higher extent of adhesion/retention compared to spherical particles of equivalent volume. This is potentially due to the fact that the total extent of adhesive interactions for such particles with the target surface may be higher than their spherical counterparts due to larger contact area of interaction at the Page 20 of 46Nanoscale wall. 4. Discussion In the area of particle-based targeted drug delivery systems, a majority of the reported intravenously administered particles are in the nanoscale size range and have a spherical shape. The emergence of nanoparticles was (i) to facilitate their navigation through microvascular networks without causing occlusion, (ii) to allow their extravasation and permeation across leaky endothelial barriers into diseased tissue (e.g. tumors), and (iii) to achieve high surface-to- volume ratio for drug or ligand incorporation. However, many of these nanoparticle-associated mechanisms are expected to occur only if the particles can get to the vascular wall (and beyond the wall) via convective-diffusive trajectories in flow and margination. Several recent computational and experimental studies have indicated that compared to nanoscale particles, microscale particles have a higher propensity to marginate through the RBC flow volume towards the wall. 13,21,25,30 In addition, recent theoretical and computational studies have also indicated that non-spherical particles may have higher margination and adhesion probability at the wall due to a larger contact area. 30,32,34,59 These reports have led to our current studies of correlating computational and experimental assessment of particle margination and adhesion across a wide variety of size and shape ranges of particles tested in presence of RBC flow. Furthermore, to ensure that once marginated, the particles can interact with the wall via specific high affinity mechanism, we utilized the avidin-biotin interaction as a model, since it is one of the strongest known non-covalent interactions (KD = 10 -15 M). To this end, the total number of ligands (NL) was kept theoretically constant among all shapes of nanoscale particles and among all shapes of microscale particles, such that the relative surface density of ligands was changed (reduced) when spherical particles were deformed into non-spherical shapes. Page 21 of 46 Nanoscale spherical ones, might have interacted with the target surface over time. For spherical particles, the orientation and surface-area of interaction with the target surface is uniform over time. However for non-spherical particles, at any instant of time, the interaction may happen on their larger surface as well as their edge or smaller surface domains. Such orientation-based surface area of interaction may influence overall adhesion strength, so that weakly adhered particles may dislodge, flow away and re-bind relatively strongly due to the recirculating set-up of the experiments. These possibilities can influence overall quantity of particle adhesion over time for each particle type, to introduce some variabilities between results at 5 min, 15 min and 30 min. However, it becomes evident that over longer time periods (e.g. 30 min), the particles closer to microscale size range and of oblate (and rod) shaped geometry undergo significantly enhanced adhesion and retention on the target surface compared to their nanoscale and spherical (and prolate) counterparts. An additional area of design parameter that is yet to be studied across multiple size and shape ranges is particle elasticity (i.e. stiffness vs. deformability). Computational studies have indicated that highly deformable particles are prone to undergo a larger lift force due to hydrodynamic interactions with the wall, resulting in their localization away from the wall. 49 This is evident for highly deformable healthy RBCs as they congregate in the center of the flow while rigid sickle RBCs show less propensity for such behavior. 70-73 At the same time, some recent studies have shown that softer (low modulus) gel microparticles could marginate and adhere to vessel wall at low shear rates, while more rigid (high modulus) particles showed favorable margination and adhesion at high shear rates. 74 In these studies, the softest particles had a Young’s modulus of 23 kPa and the most rigid particles had a Young’s modulus over 500 kPa. The reported Young’s modulus of normal healthy RBCs is 0.1-0.2 kPa 75 while that for Page 24 of 46Nanoscale normal circulating platelets is 20-30 kPa. 76 Thus the softest particles reported were essentially in the range of stiffness shown by circulating platelets that are known to have inherent property of higher margination. In another recent report, soft nanogel particles with modulus in the range of 48-71 kPa were shown to be capable of efficient targeting to lung microvasculature, while their rigid counterparts were incapable. 77 Therefore, such reports warrant continued computational and experimental efforts to elucidate the effect of particle elasticity integrated with particle size shape and surface-modifications, on margination probability and wall- adhesion efficacy. A persistent challenge in carrying out experimental studies across a wide range of sizes, shapes and elasticity parameters is the efficient manufacture of the corresponding particles at high yield with precisely controllable properties. In recent years, the emergence of unique particle fabrication approaches like ‘polymer replication in non-wetting template’ (PRINT®), nanoimprint lithography and template-induced thermo- stretching have opened the possibility to precisely modulate particle parameters and carry out detailed systematic studies to tailor specific drug delivery system design tailored to specific vascular profiles. 77-79 Furthermore, nanofabrication and microfabrication techniques have presented the possibility of carrying out experimental studies in complex channel networks that model microvasculature, where different particle geometries and moduli may provide unique functional outputs. Therefore, customizable drug delivery systems for enhanced performance in vascular applications can be envisioned. 5. Conclusions Using computational approaches as well experimental microfluidic studies with model nanoscale and microscale particles of four different geometries, we demonstrate the interplay between the size and shape of particles regarding margination through RBC flow volume and Page 25 of 46 Nanoscale adhesion (retention) at the wall in a hemodynamic environment. Our studies indicate that the presence of RBCs can significantly reduce the extent of particle localization at the vessel wall. Specifically, nanoparticles in the few hundred nm diameter range undergo substantially reduced localization and retention at the wall under a hemodynamically relevant RBC flow environment, compared to microparticles, irrespective of shape. Additionally, compared to isotropic spherical particles, anisotropic oblate and rod-shaped particles in the 500 nm-2 µm equivalent spherical diameter (ESD) range demonstrated the highest extent of wall-localization over time at low, medium and high shear flow conditions in presence of RBCs. While majority of particulate drug delivery systems are manufactured as spherical nanoparticles 50-200 nm in diameter, our results suggest that those size and shape parameters may be less favorable for in vivo vascular delivery applications that require particle margination through RBC volume and surface-interactive adhesion at the wall. These studies provide valuable design insight regarding the importance of tailoring and optimizing the size and shape of particles to enhance their margination and wall- adhesion capabilities in vascularly targeted drug delivery applications. Figure Captions Figure 1. Schematic representation of the intended trajectory of particulate drug delivery systems (DDS) upon introduction into blood flow via intravascular administration; In parabolic flow profile, RBCs congregate towards the center of the flow volume while platelets are pushed towards the vessel wall --- a process termed as ‘margination’; Many DDS for their intended function would need to traverse through the RBC flow volume to marginate towards the vessel wall, undergo non-specific or ligand-mediated specific adhesion at the wall (e.g. to the endothelium or other targets) and render therapeutic delivery for action at or beyond the wall. Page 26 of 46Nanoscale flow the adhesion of nano-scale particles of spherical, prolate and rod shapes and micro-scale particles of spherical and prolate shapes were found to be reduced substantially. Figure 7. Quantitative analysis for ‘adhered particles per unit surface area’ at 5 min, 15 min and 30 min time point obtained from image analysis for experiments carried out at estimated wall shear stress (τW) value of 30 dyn.cm -2 ; In absence of RBCs in flow (i.e. flow in PBS with 0% RBC), nano-scale and micro-scale particles of all shapes show high levels of wall adhesion over time although there are some variabilities in-between the different particle shapes and sizes; In presence of RBCs (0.4 HCT) in flow, majority of nano-scale particles (except for 500 nm diameter oblate ellipsoids) show substantially reduced adhesion at the wall; For micro-scale particles, the 2 µm ESD oblate and rod shaped particles are found to still maintain high levels adhesion at the wall even in the presence of RBCs in flow. Figure 8. Expanded quantitative results for ‘adhered particles per unit surface area’ for estimated wall shear stress (τW) values of 5, 30 and 60 dyn.cm -2 at 30 min in presence of 40% HCT; Oblate and rod-shaped particles in the 500 nm and 2 µm ESD range show the highest levels of wall adhesion and retention compared to micro- and nano-scale spherical particles. Conflicts of Interest There are no conflicts of interest to declare by any of the authors. Acknowledgement A.S.G., S.M., A.S. and M.C. acknowledge funding by NIH R01 HL129179. A.S. and S.M. also acknowledge the UCSB MRL Shared Experimental Facilities supported by the MRSEC Program of the NSF under Award No. DMR 1720256; a member of the NSF-funded Materials Page 29 of 46 Nanoscale Research Facilities Network. M.H. and D.A.F acknowledge funding by the DFG Research Unit FOR 1543 “SHENC - Shear Flow Regulation in Hemostasis”. D.A.F. acknowledges funding by the Alexander von Humboldt Foundation. 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Computational results on particle margination trends; [A] Migration of RBCs in the pressure-driven flow toward the center of the vessel due to hydrodynamic lift force from the walls, leads to particle margination; 2D simulations reproduce qualitatively the margination trends in 3D; [B] Center-of-mass (COM) distribution of micro-particles in the vessel in blood flow with different hematocrits; [C] Margination probability of spherical particles of different sizes as a function of hematocrit (HCT) where margination probability is defined as the area under the COM distribution with a pre-defined distance δ away from the wall with δ = Dm + ℎ, where Dm is the largest dimension of a particle, and h is the thickness of a layer which presents high probability of adhesion for particles in it (here, h=100 nm); [D] Margination probability of micro-particles with spherical and ellipsoidal shapes for different shear rates as a function of HCT; Panels C and D show the 2D simulation results, indicating that microscale particles marginate more than nanoscale particles in presence of physiological HCT; furthermore, ellipsoidal microparticles possess a slightly higher margination probability compared to their spherical counterparts in presence of physiological HCT. 150x109mm (300 x 300 DPI) Page 39 of 46 Nanoscale Figure 3. Adhesion of microparticles and nanoparticles; [A] Schematic of adhesion simulations where the drag force is proportional to the squared effective diameter (height) of the particle and this drag force is calculated for particles fixed at the wall; [B] Hydrodynamic drag force on particles with an equal volume normalized by the drag force on the spherical particle, showing that oblate ellipsoidal particles lying parallel to the surface will have the least extent of drag force on them; [C] Adhesion area is referred to the area on the particle (spherical or non- spherical) surface in a close distance of h ~ 10 nm from the wall where non- specific or specific interactions can prevail and adhesion strength is defined as the output of total ligand interactions within the adhesion area in a close distance h=10 nm to the wall and is normalized by a value for the spherical particle; [D] Illustration of two different possibilities for ligand decoration on the DDS particle surface: (i) constant ligand density (σL=const) and (ii) constant total ligand number (NL=const) at the particle surface; for experimental studies reported the particle manufacture process kept NL constant; [E] Analytically calculated adhesion strength for different particle shapes shows that oblate shapes will have the highest strength of adhesion for both σL= constant and NL= constant scenarios. 150x112mm (300 x 300 DPI) Page 40 of 46Nanoscale Figure 4. [A] Particle fabrication schematic where 1D and 2D heat-stretching techniques were employed on spherical polystyrene (PS) particles to yield non-spherical (prolate, oblate and rod shaped) particles; [B] Representative scanning electron microscopy (SEM) images of particles with various geometries, obtained by stretching nanoparticles (a-d, ESD 0.2 µm, scale bar: 0.5 µm) and microparticles (e-h, ESD 2 µm, scale bar: 5 µm). 150x112mm (300 x 300 DPI) Page 41 of 46 Nanoscale Figure 7. Quantitative analysis for ‘adhered particles per unit surface area’ at 5 min, 15 min and 30 min time point obtained from image analysis for experiments carried out at estimated wall shear stress (τW) value of 30 dyn.cm-2; In absence of RBCs in flow (i.e. flow in PBS with 0% RBC), nano-scale and micro-scale particles of all shapes show high levels of wall adhesion over time although there are some variabilities in- between the different particle shapes and sizes; In presence of RBCs (0.4 HCT) in flow, majority of nano- scale particles (except for 500 nm diameter oblate ellipsoids) show substantially reduced adhesion at the wall; For micro-scale particles, the 2 µm ESD oblate and rod shaped particles are found to still maintain high levels adhesion at the wall even in the presence of RBCs in flow. 103x71mm (300 x 300 DPI) Page 44 of 46Nanoscale Figure 8. Expanded quantitative results for ‘adhered particles per unit surface area’ for estimated wall shear stress (τW) values of 5, 30 and 60 dyn.cm-2 at 30 min in presence of 40% HCT; Oblate and rod-shaped particles in the 500 nm and 2 µm ESD range show the highest levels of wall adhesion and retention compared to micro- and nano-scale spherical particles. 65x28mm (300 x 300 DPI) Page 45 of 46 Nanoscale Nanoscale Page 46 of 46 Intravascular Delivery of DDS Parabolic Blood Flow Profile Endothelium on Vensel Wall Particle Margination Paricle Adhesion at rug Delivery ator from Sioodvolume "the VesselWall" beyond Vessti Wal 150x49mm (300 x 300 DPI)