Influence of particle size and shape on their margination and wall-adhesion: implications in drug delivery vehicle design across nano-to-micro scale

Abstract

Intravascular drug delivery technologies majorly utilize spherical nanoparticles as carrier vehicles. Their targets are often at the blood vessel wall or in the tissue beyond the wall, such that vehicle localization towards the wall (margination) becomes a pre-requisite for their function. To this end, some studies have indicated that under flow environment, micro-particles have a higher propensity than nano-particles to marginate to the wall. Also, non-spherical particles theoretically have a higher area of surface-adhesive interactions than spherical particles. However, detailed systematic studies that integrate various particle size and shape parameters across nano-to-micro scale to explore their wall-localization behavior in RBC-rich blood flow, have not been reported. We address this gap by carrying out computational and experimental studies utilizing particles of four distinct shapes (spherical, oblate, prolate, rod) spanning nano- to-micro scale sizes. Computational studies were performed using the Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS) package, with Dissipative Particle Dynamics (DPD). For experimental studies, model particles were made from neutrally buoyant fluorescent polystyrene spheres, that were thermo-stretched into non-spherical shapes and all particles were surface-coated with biotin. Using microfluidic setup, the biotin-coated particles were flowed over avidin-coated surfaces in absence versus presence of RBCs, and particle adhesion and retention at the surface was assessed by inverted fluorescence microscopy. Our computational and experimental studies provide a simultaneous analysis of different particle sizes and shapes for their retention in blood flow and indicate that in presence of RBCs, micro-scale non-spherical particles undergo enhanced 'margination + adhesion' compared to nano-scale spherical particles, resulting in their higher binding. These results provide important insight regarding improved design of vascularly targeted drug delivery systems.

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.

Figure 2.

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 = D_m + h, where D_m 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.

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 (σ_L=const) and (ii) constant total ligand number (N_L=const) at the particle surface; for experimental studies reported the particle manufacture process kept N_L constant; [E] Analytically calculated adhesion strength for different particle shapes shows that oblate shapes will have the highest strength of adhesion for both σ_L= constant and N_L= constant scenarios.

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).

Figure 5.

[A] Reaction scheme for the surface modification of the particles with biotin by carbodiimide-mediated conjugation with carboxylate motifs on particle surface; [B] Dimension calculations and relative surface ligand density estimation for particles with various geometries.

Figure 6.

[A] Experimental setup and conditions for the study of particle margination and adhesion under flow of PBS only (no RBC) versus that of controlled percent (%) volume of RBCs (20% or 40% v/v) in a parallel plate flow chamber (PPFC) under an inverted fluorescence microscope; [B] Representative fluorescence images of nanoparticles and microparticles of various shapes adhered via biotin-avidin interaction at the wall at the 30 min time point under wall shear stress (τ_W) of 30 dynes cm⁻² in absence (PBS only) versus presence of 40% v/v RBCs (i.e. 0.4 HCT) in flow; In absence of RBCs in flow, nano-scale and micro-scale particles of all shapes show reasonable adhesion at the wall, while upon introduction of RBCs (0.4 HCT) in the 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 (τ_W) 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 (τ_W) 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.