Magnetic resonance imaging-based computational modelling of blood flow and nanomedicine deposition in patients with peripheral arterial disease

Abstract

Peripheral arterial disease (PAD) is generally attributed to the progressive vascular accumulation of lipoproteins and circulating monocytes in the vessel walls leading to the formation of atherosclerotic plaques. This is known to be regulated by the local vascular geometry, haemodynamics and biophysical conditions. Here, an isogeometric analysis framework is proposed to analyse the blood flow and vascular deposition of circulating nanoparticles (NPs) into the superficial femoral artery (SFA) of a PAD patient. The local geometry of the blood vessel and the haemodynamic conditions are derived from magnetic resonance imaging (MRI), performed at baseline and at 24 months post intervention. A dramatic improvement in blood flow dynamics is observed post intervention. A 500% increase in peak flow rate is measured in vivo as a consequence of luminal enlargement. Furthermore, blood flow simulations reveal a 32% drop in the mean oscillatory shear index, indicating reduced disturbed flow post intervention. The same patient information (vascular geometry and blood flow) is used to predict in silico in a simulation of the vascular deposition of systemically injected nanomedicines. NPs, targeted to inflammatory vascular molecules including VCAM-1, E-selectin and ICAM-1, are predicted to preferentially accumulate near the stenosis in the baseline configuration, with VCAM-1 providing the highest accumulation (approx. 1.33 and 1.50 times higher concentration than that of ICAM-1 and E-selectin, respectively). Such selective deposition of NPs within the stenosis could be effectively used for the detection and treatment of plaques forming in the SFA. The presented MRI-based computational protocol can be used to analyse data from clinical trials to explore possible correlations between haemodynamics and disease progression in PAD patients, and potentially predict disease occurrence as well as the outcome of an intervention.

Keywords: atherosclerosis; finite-element modelling; magnetic resonance imaging; nanoparticles; vascular adhesion.

Figure 1.

Patient-specific geometry from MR images. The vascular geometry of a PAD patient is reconstructed using three-dimensional NURBS from the MR images. (a) The stacked segmented slices. (b) The reconstructed SFA, before clinical intervention, and three cross sections taken along the length of the artery depicting the lumen and the vessel wall. (Online version in colour.)

Figure 2.

MRI-based computational model—the problem set-up. The geometry of the SFA and the inflow conditions are extracted from the patient-specific MRI data. The adhesion of spherical NPs to the vessel walls of the SFA is mediated by ligand–receptor interactions. The main governing equations and boundary conditions for the problem are included. (Online version in colour.)

Figure 3.

Blood flow in the SFA. Velocity magnitude is shown for baseline (a) and 24 months post intervention (P.I.) (b) at three different cross sections: (I) proximal, (II) mean and (III) distal. In addition, three different times in the cardiac cycle are presented: end diastole (column A), post-peak systole (column B) and post systole (column C). (Online version in colour.)

Figure 4.

Blood flow in the SFA. Streamlines with colour representing velocity magnitude are presented at baseline (a) and 24 months post intervention (b). Insets provide a closer look at a region downstream from mean cross section (stenosis) at three different times: (A) end systole, (B) post-peak systole and (C) post systole. (Online version in colour.)

Figure 5.

TAWSS in the SFA. Vascular distribution patterns for TAWSS (a) baseline and (b) 24 months post intervention. (Online version in colour.)

Figure 6.

OSI in the SFA. Vascular distribution patterns for the OSI (a) baseline and (b) 24 months post intervention. (Online version in colour.)

Figure 7.

Distribution of near-wall quantities. (a) TAWSS and (b) OSI distribution in the baseline (dark grey) and 24-month post-intervention (grey) geometry. Each bar of the histograms represents the amount of normalized area with a defined range of the respective quantity. Note, the x-axis labels denote the upper bound of each range.

Figure 8.

Vascular deposition of NPs—uniform receptor density. Spatial distribution patterns for 100 nm spherical NPs adhering on the SFA, expressing a uniform surface density of vascular receptors. The two images are for (a) baseline and (b) 24 months post intervention. The surface density of adhered NPs (#/cm²) is calculated at t = 10 s, where the NPs were injected for 10 cardiac cycles (10 s) from a bolus placed at the SFA inlet. (Online version in colour.)

Figure 9.

Vascular deposition of NPs—non-uniform receptor density. Spatial distribution patterns for 100 nm spherical NPs adhering on the SFA, expressing a non-uniform surface density of VCAM-1 molecules. The two images are for (a) baseline and (b) 24 months post intervention. The surface density of adhered NPs (#/cm²) is calculated at t = 10 s, where the NPs were injected in a simulation for 10 cardiac cycles (10 s) from a bolus placed at the SFA inlet. The surface density of VCAM-1 molecules is calculated as a function of the wall shear rates. (Online version in colour.)

Figure 10.

Spatial correlation between local haemodynamics and NP adhesion. Two different contours, (a) OSI and (b) aVCAM-1 concentration (normalized), are merged (c) for both baseline (top) and 24-month post-intervention (bottom) configurations. Here, the unrolled geometries are presented.

Figure 11.

Receptor surface density versus WSS relationship determined by curve fitting to in vitro data for TNF-α stimulated CAM expression, obtained from [51]. 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 respective CAM (receptor) surface density m_r is reported as per cent (%) of unstimulated CAM expression under static conditions . Addition of TNF-α under static conditions stimulated upregulation of VCAM-1 by 350%, ICAM-1 by 150% and E-selectin by 250% [44]. (Online version in colour.)