Cells and Nanoparticles in Flow - Namish Kokkula

Introduction

The study of the interplay between cells and nanoparticles in flow has been an ongoing interest in the field of vascular-targeted therapeutics. Prof. Omolola at the University of Michigan has used microfluidic models to simulate conditions required for drug delivery via nano-sized vascular-targeted carriers (VTCs). By using microfluidic chambers designed after human blood vessels, complete with walls coated in endothelial cells, the flow and adhesive behavior of nanoparticles can be evaluated.^[1]

Microvessels' Role in Pathology

Microvessels are a key location of the vascular system, as they are where nutrients, white blood cells (WBCs), and other molecules cross over from blood into tissues. This is a result of the high surface area to volume ratio, which maximizes particle interactions with the endothelial cells lining the vessel walls. Due to their role in particle transfer, microvessels play a pivotal role in the study and treatment of various diseases. Novel cancer treatments have been proposed which target tumor capillaries due to the enhanced permeability and retention (EPR) effect that they exhibit. This effect arises from malformed tumor capillary walls, which reduces selectivity and increases the rate of particle transfer from blood into tissues.^[2]

The microvessel network consists of mostly arterioles and venules, which are wider vessels that feed blood into and take blood away from capillaries, respectively. Due to their larger diameters of 20-100 µm, arterioles and venules exhibit much lower rates of particle transfer relative to capillaries. However, their larger size allows them to exhibit bulk blood flow. Since capillaries are only wide enough for a single red blood cell (RBC), they do not exhibit bulk blood flow. This behavior in arteries and venules gives rise to margination, the movement of particles from the center to the walls of vessels.^[2]

Margination in Blood Flow

Figure 1 Representation of the distribution of WBCs, RBCs, and platelets in a blood vessel. The parabolic laminar velocity distribution is shown at the left end of the vessel. Wang, S.; Han, K.; Ma, S.; Qi, X.; Guo, L.; Li, X. Blood Cells as Supercarrier Systems for Advanced Drug Delivery. Med. Drug Discov. 2022, 13, 100119. is licensed under CC BY-NC-ND 4.0 ^[4]

Figure 2 RBCs flow through a PDMS microfluidic channel and form an RBC-FL. The blue line tracks a single RBC across frames. The image was created by overlaying frames of a captured video. Pinto, E.; Faustino, V.; Rodrigues, R. O.; Pinho, D.; Garcia, V.; Miranda, J. M.; Lima, R. A Rapid and Low-Cost Nonlithographic Method to Fabricate Biomedical Microdevices for Blood Flow Analysis. Micromachines 2015, 6 (1), 121–135. is licensed under CC BY 4.0 ^[5]

Bulk blood flow in arterioles and venules exhibits margination. As depicted in Figure 1, RBCs congregate at the midstream of blood flow, forming an RBC core that pushes WBCs, platelets, and other particles to the endothelium. The lateral migration of these particles causes the formation of a red blood cell-free layer (RBC-FL) close to the vascular walls. This process is mainly governed by the properties of RBCs, since they constitute 40-45% of blood volume. The structure of an RBC is a highly deformable biconcave disc with a diameter of 8 µm and height of 2 µm. An RBC’s deformability is the primary factor in driving them away from the vessel walls. The velocity profile in Figure 1 indicates no flow at the walls of the vessel. This lack of flow increases in a parabolic manner laterally along the vessel, reaching its peak at the center of flow. The lateral difference in flow velocity creates non-uniform shear forces, which are highest at the walls and linearly decrease to zero at the center of flow. As the non-uniform shear forces act on RBCs near the walls, the RBCs asymmetrically deform, generating lift forces which push them towards the center of flow. Figure 2 gives a photographic depiction of the flow rate and concentration of white blood cells increasing closer to the center of flow, which is indicated by the blurred cells at the center of the channel and clearer cells near the RBC-FL. WBCs, platelets, and smaller molecules are more resilient to deformation, and are pushed away from the RBC core towards the RBC-FL near the walls. Additionally, the thickness of the RBC-FL is dependent on many factors, such as the volume percentage of RBCs or hematocrit, vessel diameter, and flow rate.^[3]

Red Blood Cell Behavior in Pulsatile Flow

Figure 3 Numerically simulated formation of RBC rouleaux under pulsatile flow at 0.96s. The black and red particles represent aggregated and nonaggregated RBCs, respectively. The color gradient is the shear rate in the flow (1/s). (a)-(d) are RBC distributions at velocity amplitudes from 0.5 mm/s to 1.3 mm/s at a mean flow velocity of 4 mm/s. (e)-(h) are RBC distributions at the same velocity amplitudes at a mean flow velocity of 5 mm/s. Lee, C.-A.; Paeng, D.-G. Numerical Simulation of Spatiotemporal Red Blood Cell Aggregation under Sinusoidal Pulsatile Flow. Sci. Rep. 2021, 11 (1), 9977. is licensed under CC BY 4.0 ^[6]

Pulsatile flow in blood refers to the rhythmic propagation of blood through a vessel. It has been shown that RBCs in pulsatile flow tend to form rouleaux: clumps of stacked RBCs. Because RBC aggregation strongly affects the fluid properties of blood, deviation from normal aggregates is known to be a sign of various cardiovascular diseases. It has also been recently shown that abnormal aggregates can indicate inflammation, as inflamed endothelial cells can possibly also increase blood flow rate. Figure 3 shows the patterns of RBC aggregates under different conditions in sinusoidal pulsatile flow. The aggregates have a clear parabolic shape at low mean flow rates and high velocity amplitudes (maximum difference in the velocity profile). The high velocity amplitudes created by the pulses push the RBCs into their respective aggregates, and the low mean flow rate keeps the RBCs from dispersing. This constantly changing RBC density has a significant effect on the size of the RBC-FL, as particles are free to diffuse to the empty center of flow before the next RBC aggregate. On the other hand, an even dispersion of RBCs, similar to RBCs in continuous flow, is present when there is a low velocity amplitude and a high flow rate.^[6]

VTC Binding with Model Particles

The RBC-FL plays a significant role in the transport of particles between blood and cells. The increased concentration of particles near the walls, termed “near wall excess,” promotes particle interactions with endothelial cells. A common example is the availability of WBCs near the vessel walls in the instance of foreign material in tissues. Since the WBCs are so close to the endothelium, they can quickly adhere to the surface and cross over into tissues. VTCs can use a similar mechanism by harnessing their margination to the RBC-FL for effective drug delivery to the vascular walls. Cancer, coronary artery disease, and other diseases result in unique or overexpressed biomolecules on the endothelial cells of vessel walls, which can be detected by VTCs in the RBC-FL for therapy. Since margination is greatly affected by the physical properties of particles, such as size, shape, and elasticity, VTCs must be designed to efficiently migrate to the RBC-FL, as well as adhere to the vessel walls.^[2]

Effect of Blood Components on VTC Margination

The composition of blood has a significant impact on the margination of VTCs to the walls, including the local concentration of WBCs and RBCs as well as the flow patterns. In laminar flow, a higher hematocrit leads to an increased collision rate between VTCs and the higher concentration of RBCs, increasing the margination speed of VTCs towards the walls. However, in pulsatile flow, the same behavior is not experienced, and as the RBC-FL varies significantly regardless of a constant hematocrit, leading to periods of higher and lower local concentrations of RBCs. Furthermore, WBCs interfere with VTC margination in two main methods. The first is the competitive binding of surface ligands on endothelial cells, which prevent VTCs from adhering to the walls. The second is the collision-driven dissociation of adhered VTCs, which is especially present in pulsatile flow.^[7]

VTC Spheres

Figure 4: VTC sphere binding density vs sphere diameter in channels of depths 43 µm (A) and 28 µm (B) Reprinted with permission from Namdee, K.; Thompson, A. J.; Charoenphol, P.; Eniola-Adefeso, O. Margination Propensity of Vascular-Targeted Spheres from Blood Flow in a Microfluidic Model of Human Microvessels. Langmuir 2013, 29 (8), 2530–2535. Copyright 2013 American Chemical Society. ^[2]

The use of microspheres (>1 µm diameter) and nanospheres (<1 µm diameter) are common structures in vascular-targeted drug delivery. In one study, polystyrene spheres of 200 nm, 500 nm, 2 µm, and 5 µm were coated with the ligand Sialyl-Lewis A (SLeA), which is specific to E-selectin expressed by inflamed endothelial cells. Their margination in human blood flow was evaluated in two different microfluidic channels with heights of 28 µm and 43 µm lined with inflamed endothelial cells. These heights were chosen to replicate different arteriole and venule diameters, which naturally lie between 20-100 µm. Figure 4 displays the normalized particle binding densities on the surface of the 43 µm channel in A and the 28 µm channel in B at wall shear rates of 100 s^-1, 200 ^-1, and 500 ^-1. It was found that the nanospheres exhibited minimal surface adhesion in both channels compared to the microspheres. This is because nanospheres exhibit minimal near wall excess, as they remain in the RBC core, filling in space between RBCs instead of being pushed toward the walls. Microspheres were much more effective in adhering to the endothelial walls because of their near wall excess. However, it is important to note the significant drop in particle binding of the 5 µm spheres as the shear rate increases. This is caused by the much more pronounced effect of shear forces on the larger particle which overcome the binding forces. Additionally, there was overall higher adhesion in the 28 µm channel than the 43 µm channel. This can be attributed to the smaller RBC-FL present in the narrower channel, resulting in a higher concentration of particles in the RBC-FL, hence the higher adhesion density.^[2]

VTC Ellipsoids

The use of ellipsoidal VTCs in vascular-targeted drug delivery is a viable alternative to spheres due to their behavior in blood flow and adhesion. In a study, polystyrene ellipsoids of aspect ratios between 2 to 11 and diameters from 0.5 µm to 2 µm coated in SLeA flowed through a channel with height of 254 µm and 1 cm width. It was found that microrods with an equivalent spherical diameter (ESD) of 2 µm and aspect ratios of 2 and 4 adhered to the walls similarly to microspheres at the same concentration and shear rates. However, microrods with an aspect ratio of 9 exhibited significantly greater adhesion at all shear rates. This behavior can be attributed to the streamlined shape of the microrods, along with the increased surface area for binding. It was also theoretically determined that ellipsoidal particles prefer to drift towards the walls once they reach the RBC-FL. On the other hand, nanorods of 500 nm ESD performed worse than their nanosphere counterparts at shear rates over 500 s^-1 regardless of aspect ratio. Similarly to the nanospheres, nanorods also succumb to staying within the RBC core in flow. This effect is intensified at higher shear rates, where the streamlined design of the nanorods keep them resistant from exiting the fast-moving core to the slow-moving RBC-FL. Overall, it was found that rods with ESD of greater than 1 µm and aspect ratio of over 9 perform better at high shear rates compared to their spherical counterparts.^[8]

References

1. Cellular Adhesion and Drug Delivery Lab – Home for Cellular Adhesion and Drug Delivery Lab. https://cadd.engin.umich.edu/ (accessed 2024-04-30).
2. Namdee, K.; Thompson, A. J.; Charoenphol, P.; Eniola-Adefeso, O. Margination Propensity of Vascular-Targeted Spheres from Blood Flow in a Microfluidic Model of Human Microvessels. Langmuir 2013, 29 (8), 2530–2535. https://doi.org/10.1021/la304746p.
3. Zhang, Y.; Fai, T. G. Influence of the Vessel Wall Geometry on the Wall-Induced Migration of Red Blood Cells. PLOS Comput. Biol. 2023, 19 (7), e1011241. https://doi.org/10.1371/journal.pcbi.1011241.
4. Wang, S.; Han, K.; Ma, S.; Qi, X.; Guo, L.; Li, X. Blood Cells as Supercarrier Systems for Advanced Drug Delivery. Med. Drug Discov. 2022, 13, 100119. https://doi.org/10.1016/j.medidd.2021.100119.
5. Pinto, E.; Faustino, V.; Rodrigues, R. O.; Pinho, D.; Garcia, V.; Miranda, J. M.; Lima, R. A Rapid and Low-Cost Nonlithographic Method to Fabricate Biomedical Microdevices for Blood Flow Analysis. Micromachines 2015, 6 (1), 121–135. https://doi.org/10.3390/mi6010121.
6. Lee, C.-A.; Paeng, D.-G. Numerical Simulation of Spatiotemporal Red Blood Cell Aggregation under Sinusoidal Pulsatile Flow. Sci. Rep. 2021, 11 (1), 9977. https://doi.org/10.1038/s41598-021-89286-1.
7. Charoenphol, P.; Onyskiw, P. J.; Carrasco-Teja, M.; Eniola-Adefeso, O. Particle-Cell Dynamics in Human Blood Flow: Implications for Vascular-Targeted Drug Delivery. J. Biomech. 2012, 45 (16), 2822–2828. https://doi.org/10.1016/j.jbiomech.2012.08.035.
8. Thompson, A. J.; Mastria, E. M.; Eniola-Adefeso, O. The Margination Propensity of Ellipsoidal Micro/Nanoparticles to the Endothelium in Human Blood Flow. Biomaterials 2013, 34 (23), 5863–5871. https://doi.org/10.1016/j.biomaterials.2013.04.011.