Vascular deposition patterns for nanoparticles in an inflamed patient-specific arterial tree

Abstract

Inflammation, a precursor to many diseases including cancer and atherosclerosis, induces differential surface expression of specific vascular molecules. Blood-borne nanoparticles (NPs), loaded with therapeutic and imaging agents, can recognize and use these molecules as vascular docking sites. Here, a computational model is developed within the isogeometric analysis framework to understand and predict the vascular deposition of NPs within an inflamed arterial tree. The NPs have a diameter ranging from 0.1 to 2.0 μm and are decorated with antibodies directed toward three endothelial adhesion molecules, namely intravascular cell adhesion molecule-1 (ICAM-1), vascular cell adhesion molecule-1 (VCAM-1), and E-selectin, whose surface density depends on the local wall shear stress. Results indicate VCAM-1 targeted NPs adhere more, with ICAM-1 directed NPs adhering least efficiently, resulting in approximately an order-of-magnitude lower average particle surface density. ICAM-1 and E-selectin directed 0.5 μm NPs are distributed more uniformly (heterogeneity index ≈ 0.9 and 1.0, respectively) over the bifurcating vascular branches compared to their VCAM-1 counterparts (heterogeneity index ≈ 1.4). When the NPs are coated with antibodies for VCAM-1 and E-selectin in equal proportions, a more uniform vascular distribution is achieved compared with VCAM-1-only targeted particles, thus demonstrating the advantage of NP multivalency in vascular targeting. Furthermore, the larger NPs (2 μm) adhere more (≈ 200%) in the lower branches compared to the upper branch. This computational framework provides insights into how size, ligand type, density, and multivalency can be manipulated to enhance NP vascular adhesion in an individual patient.

Figure 1

Particle adhesion modeling and the problem set-up. A patient-specific left coronary artery (LCA) tree is considered that bifurcates into two downstream branches: the left anterior descending (LAD) artery and left circumflex (LCX) branch. Particle transport is simulated utilizing a Navier-Stokes solver coupled to a scalar advection-diffusion equation with appropriate boundary conditions.

Figure 2

Predicting inflammatory response to shear stress. Receptor surface density vs. wall shear stress relationship determined by curve fitting to in-vitro data for TNF-α stimulated CAM expression, obtained from (Tsou et al., 2008). Here stars, squares, and circles denote experimental data for ICAM-1, VCAM-1 and E-selectin, respectively, and the solid lines represent the corresponding fitted data. The quantities are reported as percent (%) of unstimulated CAM expression under static conditions (m_r/m_r⁰). Addition of TNF-alpha under static conditions stimulated up-regulation of VCAM-1 by 350%, ICAM-1 by 150% and E-selectin by 250%.

Figure 3

A) Time-averaged wall shear stress (mean WSS) in the coronary artery segment (no catheter at inlet) in Pa (N/m²), and the resulting spatial distribution of m_r/m_r⁰ for the three receptors: B) ICAM-1, C) VCAM-1 and D) E-selectin. Note: color map scales are different.

Figure 4

A) Time-averaged wall shear stress (mean WSS) distribution in the coronary artery segment (with catheter at inlet) in Pa (N/m²); and the corresponding surface density (cm^-2) of 0.5 μm particles at the end of simulation (t = 9 s) in terms of n_adh /(n_inj ×A) for the 3 targeted receptors: B) ICAM-1, C) VCAM-1, D) E-selectin. Note: color map scales are different. Here n_adh is the number of adhered particles, n_inj is the total number of injected particles and A (cm²) is the surface area.

Figure 5

Comparison of ICAM-1, VCAM-1 and E-selectin directed particles. Surface density of 0.5 μm particles at the end of simulation (t = 9 s) averaged over the circumference of each cross section taken at various “Z”-locations along the vessel centerline. Here n_adh is the number of adhered particles, n_inj is the total number of injected particles and A (cm²) is the surface area.

Figure 6

Time evolution of spatial distribution of 0.5 μm particles decorated with 50% aVCAM-1 and 50% aEsel ligands targeting both VCAM-1 and E-selectin simultaneously. Here results are presented at A) t = 0 s, B) t = 2 s, C) t = 6 s, and D) t = 8 s, in terms of n_adh/(n_inj × A ) where n_adh is the number of adhered particles per unit area A (cm²), n_inj is the total number of injected particles.

Figure 7

Surface density (cm^-2) of A) d_p = 0.1 μm, B) d_p = 0.5 μm and C) d_p = 2.0 μm sized particles at the end of simulation (t = 9 s) in terms of n_adh/(n_inj × A) where particle surface has 50% aVCAM-1 and 50% aEsel coverage. In the right column, color map scales are different. Here n_adh is the number of adhered particles, n_inj is the total number of injected particles and A (cm²) is the surface area.

Figure 8

Comparison of particle size under dual targeting. The number of adhering 0.1, 0.5, and 2.0 μm particles at the end of simulation (t = 9 s) averaged over the circumference of each cross section taken at various “Z”-locations along the vessel centerline. Here n_adh is the number of adhered particles, n_inj is the total number of injected particles and A (cm²) is the surface area.