Luminal flow patterns dictate arterial drug deposition in stent-based delivery

Abstract

Endovascular stents reside in a dynamic flow environment and yet the impact of flow on arterial drug deposition after stent-based delivery is only now emerging. We employed computational fluid dynamic modeling tools to investigate the influence of luminal flow patterns on arterial drug deposition and distribution. Flow imposes recirculation zones distal and proximal to the stent strut that extend the coverage of tissue absorption of eluted drug and induce asymmetry in tissue drug distribution. Our analysis now explains how the disparity in sizes of the two recirculation zones and the asymmetry in drug distribution are determined by a complex interplay of local flow and strut geometry. When temporal periodicity was introduced as a model of pulsatile flow, the net luminal flow served as an index of flow-mediated spatio-temporal tissue drug uptake. Dynamically changing luminal flow patterns are intrinsic to the coronary arterial tree. Coronary drug-eluting stents should be appropriately considered where luminal flow, strut design and pulsatility have direct effects on tissue drug uptake after local delivery.

Fig. 1

Schematic of the computational domain consisting of a single drug-eluting stent strut (in white) residing at the lumen-tissue interface. The direction of blood flow and the parabolic profile are shown at the inlet. L is the length of the vessel, R denotes the radius of the arterial lumen and W denotes the tissue thickness.

Fig. 2

Two test flow profiles were examined. The first used literature values for normalized flow in the human left anterior descending coronary artery (LAD1) and has a net positive mean flow during a single cardiac cycle. The second (LAD2) was a contrived construct adjusted to create zero net mean flow.

Fig. 3

(a) Steady state flow (Re ~ 282, also denoted as Re_o) establishes recirculation zones proximal and distal to the stent strut (Units – cm.s⁻¹). Footprints of these zones (KL and MN, respectively) are shown on the mural interface. (b) Steady state drug concentrations (log scale) within the lumen and the tissue reveal an asymmetry between regions distal and proximal to the strut.

Fig. 4

Drug concentration at the mural interface is higher at the proximal side but extends further at the distal side because distal recirculation length increased linearly with Reynolds number. Re_o is the Reynolds number with respect to the steady state flow case evaluated in Sections 2.5 and 3.1.1.

Fig. 5

Flow rate affects recirculation mediated drug delivery. Asymmetry in flow denoted as the absolute difference in sizes of proximal and distal recirculation zones increased linearly with flow. Note that all the recirculation lengths were normalized with respect to the strut width. However, asymmetry in drug uptake denoted as the difference in areas under curve (AUC) between proximal and distal zones decreased with increase in Reynolds number.

Fig. 6

Variation in the free drug concentrations (log scale) with Reynolds number at one strut depth below the mural surface is shown. Re_o denotes the Reynolds number with respect to the steady state case evaluated in Sections 2.5 and 3.1.1. $\text{AUC}=\frac{\int \mathit{\text{Cdx}}}{\mathrm{\Delta }x}$, where Δx is the cell size and C is the normalized drug concentration. The integral is performed over a length (20 struts) along the longitudinal direction of the vessel.

Fig. 7

Intrinsic stent design affects drug delivery. Asymmetry in flow estimated as the absolute difference in sizes of proximal and distal recirculation zones decreased exponentially with increase in aspect ratio. However, asymmetry in drug uptake denoted as the difference in areas under curve (AUC) between proximal and distal zones increased linearly with aspect ratio. All the lengths were normalized with respect to the strut width and AUC was calculated at a depth of one strut into the tissue.

Fig. 8

Free drug concentration (log scale) at one strut below the blood-tissue interface increased with aspect ratio (W/D). Note that the perimeter of the strut was held constant for all the depicted cases. Drug concentration was plotted in log scale and, the longitudinal distance from the lumen was normalized with respect to the strut width for the case W/D=1. Note that the W/D=1 case corresponds to Re=Reo case in Fig 4(b).

Fig. 9

Arterial free drug concentration profiles (log scale) for two different LAD flow profiles at one strut below the luminal interface is shown. The longitudinal distance is normalized with respect to the width of the stent strut.

Fig. 10

Dynamic variations in fluxes (kg/s) of drug that enter the artery at the mural interface are shown. Instantaneous fluxes changing with time are shown to be scaled with the corresponding steady state simulations. Thus, the transient flux quickly converges to its steady state limit. The longitudinal distance is normalized with respect to the width of the stent strut and the flux is directed from the lumen to the tissue. The “steady flow” plot corresponds to the simulations performed at a constant Reynolds number (Re_o = 282) as shown in Sections 2.5 and 3.1.1.