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Computational Assessment of Unsteady Flow Effects on Magnetic Nanoparticle Targeting Efficiency in a Magnetic Stented Carotid Bifurcation Artery

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Abstract

Purpose

Worldwide, cardiovascular disease is the leading cause of hospitalization and death. Recently, the use of magnetizable nanoparticles for medical drug delivery has received much attention for potential treatment of both cancer and cardiovascular disease. However, proper understanding of the interacting magnetic field forces and the hydrodynamics of blood flow is needed for effective implementation. This paper presents the computational results of simulated implant assisted medical drug targeting (IA-MDT) via induced magnetism intended for administering patient specific doses of therapeutic agents to specific sites in the cardiovascular system. The drug delivery scheme presented in this paper functions via placement of a faintly magnetizable stent at a diseased location in the carotid artery, followed by delivery of magnetically susceptible drug carriers guided by the local magnetic field. Using this method, the magnetic stent can apply high localized magnetic field gradients within the diseased artery, while only exposing the neighboring tissues, arteries, and organs to a modest magnetic field. The localized field gradients also produce the forces needed to attract and hold drug-containing magnetic nanoparticles at the implant site for delivering therapeutic agents to treat in-stent restenosis.

Methods

The multi-physics computational model used in this work is from our previous work and has been slightly modified for the case scenario presented in this paper. The computational model is used to analyze pulsatile blood flow, particle motion, and particle capture efficiency in a magnetic stented region using the magnetic properties of magnetite (Fe3O4) and equations describing the magnetic forces acting on particles produced by an external cylindrical electromagnetic coil. The electromagnetic coil produces a uniform magnetic field in the computational arterial flow model domain, while both the particles and the implanted stent are paramagnetic. A Eulerian-Lagrangian technique is adopted to resolve the hemodynamic flow and the motion of particles under the influence of a range of magnetic field strengths (Br = 2T, 4T, 6T, and 8T). Particle diameter sizes of 10 nm–4 µm in diameter were evaluated. Two dimensionless numbers were evaluated in this work to characterize relative effects of Brownian motion (BM), magnetic force induced particle motion, and convective blood flow on particle motion.

Results

The computational simulations demonstrate that the greatest particle capture efficiency results for particle diameters within the micron range of 0.7–4 µm, specifically in regions where flow separation and vortices are at a minimum. Similar to our previous work (which did not involve the use of a magnetic stent), it was also observed that the capture efficiency of particles decreases substantially with particle diameter, especially in the superparamagnetic regime. Contrary to our previous work, using a magnetic stent tripled the capture efficiency of superparamagnetic particles. The highest capture efficiency observed for superparamagnetic particles was 78% with an 8 T magnetic field strength and 65% with a 2 T magnetic field strength when analyzing 100 nm particles. For 10 nm particles and an 8 T magnetic field strength, the particle capture efficiency was 55% and for a 2 T magnetic field strength the particle capture efficiency was observed to be 43%. Furthermore, it was found that larger magnetic field strengths, large particle diameter sizes (1 µm and above), and slower blood flow velocity improves the particle capture efficiency. The distribution of captured particles on the vessel wall along the axial and azimuthal directions is also discussed. Results for captured particles on the vessel wall along the axial flow direction showed that the particle density decreased along the axial direction, especially after the stented region. For the entrance section of the stented region, the captured particle density distribution along the axial direction is large, corresponding to the center-symmetrical distribution of the magnetic force in that section.

Conclusion

The simulation results presented in this work have shown to yield favorable capture efficiencies for micron range particles and superparamagnetic particles using magnetized implants such as the stent discussed in this work. The results presented in this work justify further investigation of MDT as a treatment technique for cardiovascular disease.

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Abbreviations

BM:

Brownian motion

CCA:

Common carotid artery

CFD:

Computational fluid dynamics

CoW:

Circle of Willis

DPM:

Discrete phase model

ECA:

External carotid artery

FDA:

Food and Drug Administration

FEM:

Finite element method

FV:

Finite volume

HGMS:

High gradient magnetic separation

IA-MDT:

Implant assisted medical drug targeting

ICA:

Internal carotid artery

MDT:

Medical drug targeting

MRI:

Magnetic resonance imaging

ROI:

Region of interest

SA-MDT:

Stent assisted magnetic drug targeting

SPION:

Superparamagnetic iron oxide nanoparticles

WSS:

Wall shear stress

A :

Experimental fit factor coefficient

a 1 ,a 2, and a 3 :

Smooth particle constants

b 1 ,b 2, and b 3 :

Drag coefficient constants

B r :

Magnetic field strength

C :

Arterial vessel capacitance

C e :

Cunningham correction factor

d :

Center magnet separation distance from the ICA centerline

d c :

Capture distance

d p :

Particle diameter

D :

Diffusion coefficient

\(\overline{\overline{D}}\) :

Rate of deformation tensor

u :

Three-dimensional velocity vector

u m :

Magnetic field induced velocity

u p :

Particle parcel velocity

ρ p :

Particle density

F bi :

Brownian force acceleration term

F D :

Drag force per unit mass

F mx :

Magnetic force in the x-direction

F my :

Magnetic force in the y-direction

F x :

Body force acceleration term

g x :

Gravitational acceleration term in the x-direction

H :

Magnetic field intensity

H x :

X-component magnetic field intensity

H y :

Y-component magnetic field intensity

i(t):

Flow rate

k B :

Boltzmann constant

L :

Length of the domain

M s :

Saturation magnetization

n :

Power law index

N np,in :

Number of particles entering the domain

N np,out :

Number of particles exiting the domain

p :

Pressure

Pe m :

Modified Peclet number

Re :

Reynolds number

R :

Radius of vessel

R d :

Distal resistant

R p :

Proximal resistance

R mag :

Radius of the magnet

R mp :

Radius of particle

s :

Surface area of a sphere having the same volume as the particle

S :

Actual area of the particle

S 0 :

Spectral constant

S n ij :

Spectral density

t :

Time

T :

Temperature

β m :

Dimensionless timescale (particles to reach the wall)

ζi :

Zero-mean unit-variance-independent Gaussian random number

ρ :

Fluid density

µ :

DYnamic viscosity

v :

Kinematic viscosity

η c :

Capture efficiency

λ :

Time constant

λ m :

Molecular mean free path

ω :

Vorticity

χ p :

Magnetic susceptibility

φ :

Shape factor

µ 0 :

Permeability of free space

µ r :

Relative permeability

µ ∞ :

Infinite viscosity

τ xy = τ yx :

Shear Stress

χ mp :

Magnetic susceptibility of the magnetic particles

\(\dot{\gamma }\) :

Strain rate

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Authors and Affiliations

  1. Department of Engineering Technology, University of North Carolina at Charlotte, Charlotte, USA

    Rodward L. Hewlin Jr. & Michael Smith

  2. Center for Biomedical Engineering & Science (CBES), University of North Carolina at Charlotte, Charlotte, USA

    Rodward L. Hewlin Jr.

  3. Department of Mechanical Engineering, North Carolina Agricultural and Technical State University, Greensboro, USA

    John P. Kizito

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Hewlin, R.L., Smith, M. & Kizito, J.P. Computational Assessment of Unsteady Flow Effects on Magnetic Nanoparticle Targeting Efficiency in a Magnetic Stented Carotid Bifurcation Artery. Cardiovasc Eng Tech 14, 694–712 (2023). https://doi.org/10.1007/s13239-023-00681-3

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