Understanding particle margination in blood flow – A step toward optimized drug delivery systems

Highlights

• Particle margination has been studied for a wide range of flow, channel, and particle properties.

• Efficient margination depends on the relation between particle size and the thickness of red blood cell-free layer.

• Particle margination decreases as a particle gets more deformable

• Particle margination is less efficient in larger channels.

Abstract

Targeted delivery of drugs and imaging agents is very promising to develop new strategies for the treatment of various diseases such as cancer. For an efficient targeted adhesion, the particles have to migrate toward the walls in blood flow – a process referred to as margination. Due to a huge diversity of available carriers, a good understanding of their margination properties in blood flow depending on various flow conditions and particle properties is required. We employ a particle-based mesoscopic hydrodynamic simulation approach to investigate the margination of different carriers for a wide range of hematocrits (volume fraction of red blood cells) and flow rates. Our results show that margination strongly depends on the thickness of the available free space close to the wall, the so-called red blood cell-free layer (RBC-FL), in comparison to the carrier size. The carriers with a few micrometers in size are comparable with the RBC-FL thickness and marginate better than their sub-micrometer counterparts. Deformable carriers, in general, show worse margination properties than rigid particles. Particle margination is also found to be most pronounced in small channels with a characteristic size comparable to blood capillaries. Finally, different margination mechanisms are discussed.

Introduction

One of the major causes of human death in the world is cancer; for instance, about 8 million people died from cancer in 2012 [1]. Although significant progress has been achieved in developing treatments for cancer, the impact on patient survival remains rather moderate [2]. Therefore, the development of early detection and therapy strategies for cancer is under active research. One of the ideas with a great potential in this area is the targeted delivery of drugs and imaging agents through micro- and nano-particles [2]. A very challenging task is to design suitable carriers which would meet several demands including good adhesion properties to targeted sites in blood flow, efficient transport through the biological barriers (e.g., vessel walls, interstitial space, and cell membranes), and low clearance by various defense mechanisms of the body [3], [4], [5], [6], [7]. Proposed solutions are polymer conjugates, which are already in clinical use [8], [9], fabricated nano-particles [9], [10], and self-assembled structures from lipids or block copolymers forming liposomes, polymersomes, or worm-like micelles [9]. All these micro- and nano-carriers differ in shape, size, and deformability. Furthermore, the circulatory system of humans consists of blood vessels which vary from several centimeters to a few micrometers with a wide range of flow rates. Hence, to identify advantages and disadvantages of various particles for vascular drug delivery, their behavior in blood flow for different flow rates, hematocrits (i.e., volume fraction of red blood cells), vessel diameters, particle sizes, shapes, and deformability needs to be better understood.

Blood is a complex fluid which consists of red blood cells (RBCs), white blood cells (WBCs), platelets, and the blood plasma. The physiological systemic hematocrit is in the range 37%–54%, varying for males and females [11]. The local hematocrit in microcirculation can be even lower and depends on the vessel diameter [12], [13]. Experimental [14], [15], [16], [17], [18], [19], theoretical [20], [21], [22], and numerical [23], [24], [25], [26] studies have shown that vesicles and RBCs experience a lift force acting away from a wall due to the hydrodynamic interactions with the wall and the RBC shape and deformability. Consequently, RBCs in blood flow migrate toward the center of a vessel and close to the wall a region depleted of RBCs develops, called the RBC-free layer (RBC-FL). In contrast, WBCs and platelets migrate toward vessel walls, which is referred to as margination [27], [28], [29], [30]. The margination of WBCs and platelets is mediated by RBCs and appears to be important for these cells, since in order to perform their biological function they must have a possibility to adhere to the wall. Thus, margination can be thought of as a necessary precondition for the wall adhesion.

In similarity with WBCs and platelets, the margination process in blood flow is also expected to occur for micro- and nano-particles. Experiments [31] on margination of rigid platelet-like particles in channels with a characteristic size within 50 µm–200 µm have shown that a significant number of the particles gets accumulated near a wall if the hematocrit is larger than about 7% and the accumulation is enhanced with increasing hematocrit. Recent microfluidic experiments [32] have shown that rigid spheres with the size of 2 µm display a significantly higher adhesion density than particles with a size of 200 nm–500 nm. Thus, available experiments already show that there exists a strong dependence of particle margination on hematocrit, flow rate, and carrier size. Numerical simulations of blood flow are ideally suited to explore the margination trends for a wide range of conditions and to better understand the corresponding mechanisms.

Recent numerical simulations have considered segregation of a binary mixture of spherical elastic capsules in shear and channel flow [33], [34], [35]. Simulations for different capsule sizes have shown that in binary mixtures of particles, the large particles migrate toward the center and the small ones toward the wall if the volume fraction of the small ones is low. Furthermore, floppy particles tend to migrate to the center in a binary mixture together with rigid particles. Simulations of WBCs in two dimensions (2D) [36], [37] and three dimensions (3D) [38] have shown that WBCs are subject to strong margination for H_t ≈ 0.2–0.4 and the venular range of flow rates, characterized by the pseudo-shear rates $\overline{\dot{\gamma }}\lesssim 80{\mathrm{s}}^{-1}$ in small vessels [39], [40]. Platelet margination has been studied in 2D for two shear rates, two hematocrit values ($H_t=0.2$ and $H_t=0.4$), and two sizes (0.75 µm and 1.5 µm) of rigid particles [41] in a 50 µm wide channel. The results indicate that platelet margination increases with hematocrit, shear rate, and particle size. A similar trend is observed in another 2D and 3D simulation study of particles between 0.25 µm and 1 µm in a 20 µm wide channel [42], demonstrating that the margination is significantly worse for sub-micrometer particles in comparison to larger carriers in agreement with experimental findings [32]. This numerical investigation has also shown that an oblate discoidal shape has advantages for drug delivery systems compared to spheres. Other 3D simulations [43] have focused on the dependence of platelet margination on hematocrit, their aspect ratio, and different viscosities between the inner and outer fluids of RBCs. The simulation results have shown that margination of rigid particles increases with increasing hematocrit and that the RBC viscosity contrast influences margination as well. Additionally, the study indicated that discs marginate slower than spherical particles. Furthermore, platelet margination in blood flow has been studied numerically for different shear rates and hematocrit values of $H_t=0.1$ and $H_t=0.2$ [44], [45] for rigid discoidal and spherical particles in a channel of 34 µm. In these investigations, an increase of margination with hematocrit has been observed and related to the different RBC-FL thickness.

In this paper, we systematically investigate the dependence of margination on particle size for a wide range of hematocrit values and flow rates using a 3D model system. In this context, we concentrate on the margination into a thin layer near the wall, where particle adhesion to the wall would be possible. Thus, we assess the adhesion potential of particles in blood flow depending on various carrier and flow properties. In addition, we employ 2D simulations to study the effect of particle deformability on its margination properties. Finally, we consider blood flow and particle margination in channels of several widths. Our results from 3D simulations further support the observations that particles with a few micrometers in size marginate significantly better than their sub-micrometer counterparts. Deformable carriers are in general worse than rigid particles; however, they may marginate slightly better at high H_t values and low shear rates, where their deformability aids them to fit better within a relatively narrow RBC-FL at such conditions. Furthermore, the margination of particles is found to be most efficient in small channels with the sizes corresponding to capillaries in the human microvasculature. Finally, we will also discuss the physical mechanisms of margination and the relation between particle margination, its physical properties, and the thickness of the RBC-FL.