In silico vascular modeling for personalized nanoparticle delivery

Abstract

Aims: To predict the deposition of nanoparticles in a patient-specific arterial tree as a function of the vascular architecture, flow conditions, receptor surface density and nanoparticle properties.

Materials & methods: The patient-specific vascular geometry is reconstructed from computed tomography angiography images. The isogeometric analysis framework integrated with a special boundary condition for the firm wall adhesion of nanoparticles is implemented. A parallel plate flow chamber system is used to validate the computational model in vitro.

Results: Particle adhesion is dramatically affected by changes in patient-specific attributes, such as branching angle and receptor density. The adhesion pattern correlates well with the spatial and temporal distribution of the wall shear rates. For the case considered, the larger (2.0 µm) particles adhere two-times more in the lower branches of the arterial tree, whereas the smaller (0.5 µm) particles deposit more in the upper branches.

Conclusion: Our computational framework in conjunction with patient-specific attributes can be used to rationally select nanoparticle properties to personalize, and thus optimize, therapeutic interventions.

Figure 1. Reconstructing the patient-specific vascular geometry

The image shows, from left to right, the isocontour of a human heart, path extraction and editing of a small bifurcation portion from the left coronary artery (LCA) and reconstruction of the geometry ready for Isogeometric Analysis. Also, a nanoparticle with its ligand molecules is shown interacting with the receptor molecules decorating the surface of the endothelial cells in the vasculature.

Figure 2. Comparison between in silico and in vitro results

The number of adhering particles n_adh per unit surface area A normalized by the total number of injected particles n_inj is plotted as a function of the particle diameter d_p and for three different wall shear rates: (A) S = 10 s^-1, (B) S = 75 s^-1 and (C) S = 200 s^-1. Black crosses with the standard deviation bars represent the experimental results obtained in a parallel plate flow chamber apparatus. The gray areas represent the in silico results obtained for values of the parameters α₁ (left) and α₂ (right) varying within ± 5% of their average values (α₁ = 0.023) and (α₂ ≈ 9.44 ×10⁹ #/m² for d_p ≈ 0.7 μm; 1.388×10⁹ #/m² for d_p ≈ 5 μm; and 1.031×10⁹ #/m² for d_p ≈ 7 μm).

Figure 3. Nanoparticle transport in a patient-specific vascular tree

(A) Schematic of the coronary artery (branches identified) with the inlet velocity profile (inset at the right) and applied boundary conditions. (B)-(F) Volumetric concentration C of 0.5 μm nanoparticles, normalized by the concentration at the catheter outlet C⁰, at various times t post injection: (B) t = 0.2 s, (C) t = 1 s, (D) t = 5 s, (E) t = 10 s, and (F) t = 14 s.

Figure 4. Nanoparticle adhesion to the vessel walls: effect of nanoparticle size

The normalized surface density of adhering nanoparticles is plotted along the arterial tree at various times t post injection, namely (A) t = 5 s, (B) t = 10 s and (C) t = 14 s. The left and right columns present in silico data for the 0.5 and 2.0 μm particle, respectively, in terms of particle number per unit area normalized by the injected dose [cm^-2].

Figure 5. Nanoparticle adhesion to the vessel walls: effect of vascular geometry

The normalized surface density of adhering nanoparticles is plotted along the arterial tree at t = 14 s, post injection. The left and right columns present in silico data for the 0.5 and 2.0 μm particles, respectively. The top and bottom rows present in silico data for the smaller (76.8°) and larger (106.8°) branching angles, respectively. Data are presented in particle number per unit area normalized by the injected dose [cm^-2].

Figure 6. Nanoparticle adhesion to the vessel walls: effect of surface density of vascular receptors

The normalized surface density of 0.5 μm adhering nanoparticles is plotted along the arterial tree at various times t post injection: (A) t = 1 s, (B) t = 5 s and (C) t = 14 s. Data are presented for a uniform receptor density (m_r = 10⁹ #/cm²) along the vasculature (left column) and for a left anterior descending artery receptor density 10 times larger than that in the LCA and LCX (right column). Note that the color map scales are different for the two cases and give the particle number per unit area normalized by the injected dose [cm^-2].