- Open Access
The margination propensity of spherical particles for vascular targeting in the microcirculation
© Gentile et al; licensee BioMed Central Ltd. 2008
- Received: 05 January 2008
- Accepted: 15 August 2008
- Published: 15 August 2008
The propensity of circulating particles to drift laterally towards the vessel walls (margination) in the microcirculation has been experimentally studied using a parallel plate flow chamber. Fluorescent polystyrene particles, with a relative density to water of just 50 g/cm3comparable with that of liposomal or polymeric nanoparticles used in drug delivery and bio-imaging, have been used with a diameter spanning over three order of magnitudes from 50 nm up to 10 μm. The number of particles marginating per unit surface have been measured through confocal fluorescent microscopy for a horizontal chamber, and the corresponding total volume of particles has been calculated. Scaling laws have been derived as a function of the particle diameter d. In horizontal capillaries, margination is mainly due to the gravitational force for particles with d > 200 nm and increases with d4; whereas for smaller particles increases with d3. In vertical capillaries, since the particles are heavier than the fluid they would tend to marginate towards the walls in downward flows and towards the center in upward flows, with increasing with d9/2. However, the margination in vertical capillaries is predicted to be much smaller than in horizontal capillaries. These results suggest that, for particles circulating in an external field of volume forces (gravitation or magnetic), the strategy of using larger particles designed to marginate and adhere firmly to the vascular walls under flow could be more effective than that of using particles sufficiently small (d < 200 nm) to hopefully cross a discontinuous endothelium.
- Flow Chamber
- Lateral Drift
- Parallel Plate Flow Chamber
- Cell Free Layer
- Large Spherical Particle
In the early diagnosis, treatment and imaging of diseases, as cancer and cardiovascular, the use of microparticles and nanoparticles is emerging as a powerful tool [1, 2]. These are sufficiently small 'vectors' of therapeutic or/and imaging agents to be systemically administered, transported by the blood flow along the circulatory system and eventually recognize the diseased microenvironment (diseased cells). A nanoparticle comprises an internal core with the active agents and an external coating whit tailored physico-chemical properties. The interaction of the vectors with the biological target (diseased cell) is generally governed by specific forces, mediated by the formation and destruction of molecular bonds , and by non-specific interactions regulated by short ranged forces as van der Waals, electrostatic and steric .
Two different delivery strategies are currently under investigation and development: a passive targeting of the diseased microenvironment relying on the permeability of the blood vessels (enhanced retention and permeability effect), and an active targeting of the diseased microvasculature relying on the recognition of specific molecules overexpressed at the site of interest . It is known that tumor microvessels exhibit a significant increase in permeability to large molecules with intercellular openings and intercellular gaps as large as a micron , which could be crossed by sufficiently small particles. However the level of permeability is strongly dependent on the type of tumor, the site where the tumor is developing, the state of the tumor and the therapeutic treatment, and significant differences can be observed between human and xenografts tumors . In addition to this, diseases other than cancer do no show any significant vessel permeability, thus making a passive targeting strategy non appropriate. On the other hand, a growing body of evidences support the idea that specific molecules are overexpressed at the surface of a diseased vasculature , which could be used as 'docking sites' for circulating particles. Following a microvas-culature targeting strategy could possibly be more effective than just relying on the matching between the size of the particles and that of the vascular fenestrations. Evidently, the specific recognition and firm adhesion of a circulating particle to the vessel walls under flow is far from being an easy task.
For both delivery strategies, the systemically administered particles should be designed to move in close proximity to the vascular walls, 'sense' any significant biological difference between normal and abnormal endothelium and seek for fenestrations in the case of a passive strategy, or for specific vascular receptors, in the case of an active targeting strategy. In other words, the nanoparticles should be designed to spontaneously 'marginate', i.e. drift laterally towards the vessel walls, and interact with the blood vessels rather than 'navigating' in the center of the capillary as red blood cells (RBCs) do or, even worse, adhering and being transported by the RBCs. It is here important to recall that in physiology the term margination is referred to the lateral drifting of leukocytes which have been observed experimentally to collect near the walls of blood vessels. This behavior has been mainly associated to the interaction of leukocytes with RBCs which tend to push the former away from the center of the capillary towards the opposing wall , and it is no at all related to gravitational forces, as clearly demonstrated by . Systemically administered particles for the delivery of drugs and other therapeutic agents have a characteristic size at least one order of magnitude smaller than leukocytes and RBCs (O (10) μm), and, more importantly, than the thickness of the cell free layer (O (10) μm). As a consequence, the margination of nanoparticles can not only rely on the interaction with other circulating cells, especially in the microcirculation where RBCs are less abundant. The margination dynamics of nanoparticles has to be controlled by their size, their shape and their possible interaction with external long range force fields, as the gravitational and electromagnetic fields.
In this work, the propensity to marginate of classical spherical particles in a laminar flow and under the effect of gravitational forces is studied. Particles with different diameters spanning from 50 nm up to 10 μm are infused within a parallel plate flow chamber mimicking the physiological conditions of human microcirculation. The density of the particles relative to water is of just 50 g/cm3, comparable with that of liposomal and polymeric based particles used in such applications.
The Flow Chamber System
and the shear stress at the wall η S = 7. 75 × 10-3 Pa being η = 10-3 Pa s the viscosity of water. The channel Reynolds number (= ρUh/η) is equal to about 8 × 10-2. The shear rate and the shear stress are sufficiently small to allow for the non-specific cell-particle adhesion. Experiments were performed at room temperature (24°C) for a maximum time of 10 min.
The Measurement Set-up
Human umbilical vein endothelial cells (HUVECs) were purchased from Cambrex, Inc. (East Rutherford, NJ). Cells were maintained in EGMTM-2 – Endothelial Cell Medium-2 (Cambrex Bio Science Walkersville Inc., MD) supplemented with 2% FBS, 0. 04% hydrocortisone, 0. 4% hFGF-B, 0. 1% VEGF, 0. 1% rIGF-1, 0. 1% ascorbic acid, 0. 1% hEGF, 0. 1% GA-1000, 0. 1% heparin, 100 U/mL penicillin, and 100 μg/mL streptomycin and were grown at 37°C with humidified 95% air/5% CO 2.
For each experiment, cells were plated on a borosilicate glass with a 0. 2 mg/cm2 substratum of type A gelatine (Sigma-Aldrich Corporation, MO). When HUVECs reached 80% confluence, the borosilicate glass was detached from the bottom of the plate and mounted in the parallel plate flow chamber for particle-cell adhesion analysis.
Fluoresbrite® Microspheres from Polysciences were used. These are Yellow Green fluorescent particles with an excitation maximum at 441 nm and an emission maximum at 486 nm. Particles with different sizes were used namely 50 nm, 100 nm, 200 nm, 500 nm, 750 nm, and 1 μm, 6 μm, 10 μm.
having considered μ = 10-3 Pa s, Δρ = 50 kg/m3 and ρ f = 103 kg/m3. For the flow chamber apparatus considered here and d = 10 μm, it is α ≃ 0. 04, Re c ≃ 0. 16 and B ≃ 0. 053 leading to α2/B ≃ 0. 03 and Re c B2 ≃ 4. 6 × 104, much smaller than unity.
3.1 Margination in Horizontal Capillaries
Substituting in (4) and (5) for (3), it follows that under a gravitational field (or magnetic field) the number of settling particles per unit area and their volume are both proportional to the local volume concentration C of particles and grows linearly with d ( ∝ d) and with the fourth power of d ( ∝ d4), respectively.
which support the linear relationship between and C as predicted in (5).
whose scaling with d can not be predicted by just gravitation or volume forces. For these small particles other forces as colloidal forces (van der Waals, electrostatic) are probably responsible for their margination, which arise only with a small separation distance between the particle and the substrate (tens to a hundred nanometers). An ANOVA analysis has returned, for the data presented in Fig. 4 to 6, p values much smaller than the critical value of 0. 05, being respectively p = 0. 0022, p = 0. 0035, and p = 0. 0047, thus implying a statistically significant difference among the means.
3.2 Margination in Vertical Capillaries
For α2/B and Re c B2 smaller than unity, as observed in , in vertical capillaries the lateral drift is modest with a velocity scaling with , where R p is the particle Reynolds number (R p = ρ p U m d2/(μR ch )). Therefore the lateral drifting velocity would scale with d3rather with d2 as in horizontal capillaries (see eq.2), making the characteristic size of the particles even more important. Following the same reasonings as above for the horizontal capillaries, it can be derived a ⟨H o ⟩ scaling with d3/2, and eventually a number and a volume of settling particles per unit area proportional to the local volume concentration C of particles and scaling respectively with d3/2 and d9/2 ( ∝ d3/2 and ∝ d9/2).
The lateral drifting observed in vertical capillaries is again associated with the difference in relative density between the circulating particle and the fluid, being B, the buoyancy parameter, different from zero. But more importantly, the sign of the velocity depends on the direction of the flow: particles heavier than the fluid would drift towards the wall for downward flows (margination) and towards the capillary center line for upward flows (opposite of margination). The opposite has been predicted and observed to occur for particles less heavy than the fluid. These behavior has been observed extensively in several experiments .
The propensity of spherical nanoparticles to marginate towards the vessel walls in the microcirculation has been analyzed employing a parallel plate flow chamber. The effect of the particle size and orientation of the capillary with respect to external volume force fields (gravitation) has been elucidated experimentally and supported by simple scaling relations.
The number and total volume of particles marginating per unit surface have been measured through confocal fluorescent microscopy. Considering particles with a density slightly larger than water (1050 kg/m3), and comparable with the density of liposomes and polymeric particles used in nanomedical applications, it has been observed in horizontal channels that the lateral margination of particles with a diameter larger than 200 nm is mainly governed by the gravitational force with and scaling both proportionally to the volume concentration C of the particles and, respectively, to the diameter d and the fourth power of the diameter d4. For smaller particles (d < 200 nm), the margination dynamics can not be associated to gravitational forces being ∝ d3.2. Possibly, in this case, colloidal interactions may govern particle lateral drifting but this would already require the particle to be in sufficient close proximity of the wall, say tens up to a hundred nanometer, in other words separation distances of the same order of magnitude of the particle size.
These results, although not exhaustive, are of interest in the systemic delivery of nanoparticles designed to target the vascular walls in the microcirculation. The experimental results and simple theoretical relations support the idea of using large particles rather than small particles with the same total volume. In fact, if the biological target is the vascular wall and the particles are not required to freely extravasate through the discontinuous endothelium, then the larger spherical particles would more easily sediment in horizontal capillaries and drift laterally in vertical capillaries with downward flow. Also the larger spherical particles would have a larger surface exposed to the vascular cells increasing the likelihood of firm adhesion once decorated with recognizing moieties . The separation between large and small particles would depend on the relative density compared to the fluid, however for the commonly used liposome and polymeric particles sizes larger than 200 nm would perform better.
It should be noticed, in conclusion, that the present results strictly apply when the interaction of the nanoparticles with circulating blood cells can be disregarded, which occurs in small capillaries and in the cell free layer of arterioles and veins.
- LaVan DA, McGuire T, Langer R: Small-scale systems for in vivo drug delivery. Nat Biotechnol. 2003, 21: 1184-91. 10.1038/nbt876.View ArticleGoogle Scholar
- Ferrari M: Cancer nanotechnology: opportunities and challenges. Nat Rev Cancer. 2005, 5: 161-71. 10.1038/nrc1566.View ArticleGoogle Scholar
- Decuzzi P, Ferrari M: The adhesive strength of non-spherical particles mediated by specific interactions. Biomaterials. 2006, 27 (30): 5307-14. 10.1016/j.biomaterials.2006.05.024.View ArticleGoogle Scholar
- Decuzzi P, Lee S, Bhushan B, Ferrari M: A theoretical model for the margination of particles within blood vessels. Ann Biomed Eng. 2005, 33: 179-90. 10.1007/s10439-005-8976-5.View ArticleGoogle Scholar
- Sakamoto J, Annapragada A, Decuzzi P, Ferrari M: Antibiological barrier nanovector technology for cancer applications. Expert Opin Drug Deliv. 2007, 4 (4): 359-69. 10.1517/17425247.4.4.359.View ArticleGoogle Scholar
- Hashizume H, Baluk P, Morikawa S, McLean JW, Thurston G, Roberge S, Jain RK, McDonald DM: Openings between defective endothelial cells explain tumor vessel leakiness. Am J Pathol. 2000, 156: 1363-80.View ArticleGoogle Scholar
- Hobbs SK, Monsky WL, Yuan F, Roberts WG, Griffith L, Torchilin VP, Jain RK: Regulation of transport pathways in tumor vessels: role of tumor type and microenvironment. Proc Natl Acad Sci USA. 1998, 14 (95): 4607-12. 10.1073/pnas.95.8.4607.View ArticleGoogle Scholar
- Neri D, Bicknell R: Tumor Vascular Targeting. Nature Cancer Reviews 2005.Google Scholar
- Goldsmith HL, Spain S: Margination of leukocytes in blood flow through small tubes. Microvasc Res. 1984, 27: 204-222. 10.1016/0026-2862(84)90054-2.View ArticleGoogle Scholar
- Lawrence MB, Kansas GS, Kunkel EJ, Ley K: Threshold levels of fluid shear promote leukocyte adhesion through selectins (CD62L,P,E). J Cell Biol. 1997, 136 (3): 717-27. 10.1083/jcb.136.3.717.View ArticleGoogle Scholar
- Poiseuille JLM: "Recherches sur les Causes du Mouvement du Sang Dans les. Vaisseaux Capillaires". Ann Sci Nat Ser. 1836, 2 (5): 111-115.Google Scholar
- Segré G, Silberberg A: Behavior of macroscopic rigid spheres in Poiseuille flow: Part I. J Fluid Mech. 1962, 14: 115-10.1017/S002211206200110X.View ArticleGoogle Scholar
- Matas J-P, Morris JF, Guazzelli E: Inertial migration of rigid spherical particles in Poiseuille flow. J Fluid Mech. 2004, 515: 171-195. 10.1017/S0022112004000254.View ArticleGoogle Scholar
- Oliver DR: "Influence of Particle Rotation on Radial Migration in the Poiseuflle. Flow of Suspensions". Nature. 1962, 194: 1269-1271. 10.1038/1941269b0.View ArticleGoogle Scholar
- Repetti RV, Leonard EF: Segre-Silberberg. annulus formation: a possible explanation. Nature. 1964, 203: 1346-1350. 10.1038/2031346a0.View ArticleGoogle Scholar
- Jeffrey RC, Pearson JRA: Particle motion in laminar. vertical tube flow. J Fluid Mech. 1965, 22: 721-735. 10.1017/S0022112065001106.View ArticleGoogle Scholar
- Hogg AJ: Inertial migration of a non-neutrally buoyant particle in a two-dimensional shear flow. J Fluid Mech. 1994, 272: 285-318. 10.1017/S0022112094004477.View ArticleGoogle Scholar
- Jeffrey RC, Pearson JRA: Particle motion in laminar vertical tube flow. Journal of Fluid Mechanics. 1965, 22: 721-735. 10.1017/S0022112065001106.View ArticleGoogle Scholar
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