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Numerical study of drug delivery through the 3D modeling of aortic arch in presence of a magnetic field

Biomechanics and Modeling in Mechanobiology volume 20, pages 787–802 (2021)Cite this article

Abstract

Magnetic drug delivery known as smart technique in medicine is basically according to combining the drug inside capsules with the magnetic property or attaching the drug with magnetic surfaces at the micro- and nanoscale. In the present study, magnetic drug delivery in the aortic artery has been investigated. To approach the more realistic problem conditions of blood flow rheology, the effect of parameters such as non-Newtonian viscosity and oscillating input has been put into consideration. Also, the investigated geometrical parameters of arteries of the aortic arch have been chosen similar to the real size. The results indicate that an increase in the diameter of microparticles rises the efficiency of particles absorption. In addition, the influence of changing the direction of the wire carrying electricity and thus changing the direction of magnetic field on magnetic drug delivery has been examined in the geometry of the aortic arc and it is found that the highest particle absorption efficiency takes place in the case that the wire is parallel to the direction of y-axis. As an example, the results show that the rate of absorption efficiency for particles with 3 µm dia is 26.83% and 19.39% when the wire generating magnetic field is parallel to the direction of y-axis and z-axis, respectively, and this value is 10.91% for the case without a magnetic field. The number of particles released from different part of the aortic arch also is affected by the direction of magnetic field. This value illustrates that the percentage of particles released from different states, is equal when the magnetic field is absent and the wire carrying electricity is parallel to y-axis and z-axis. However, the number of particles released from the 2 outputs of the left carotid and left subclavian is less than the other 2 states (i.e., the state when there is not a magnetic field, and the state when the electric current direction is parallel to the y-axis direction) for the state when the wire carrying current is parallel to the z-axis.

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Abbreviations

B:

The magnitude of the magnetic field (T)

\(C_{D}\) :

Drag coefficient

\(d_{p}\) :

Particle diameter (μm)

\(F_{B}\) :

Buoyancy force (N)

\(F_{D}\) :

Drag force (N)

\(F_{m}\) :

Magnetic force (N)

\(\vec{H}\) :

Magnetic field intensity (A/m)

\(\vec{H}_{x}\) :

Magnetic field intensity component in the x direction (A/m)

\(\vec{H}_{y}\) :

Magnetic field intensity component in the y direction (A/m)

\(\vec{H}_{r}\) :

Characteristic magnetic field intensity (A/m)

Mn:

Magnetic number

\(n_{in}\) :

The number of particles entering the solution domain

\(n_{out}\) :

The number of particles removed from the solution domain

P:

Pressure \(\left( {N/m^{2} } \right)\)

Re:

Reynolds number

\(R_{o}\) :

Radius of curvature of the vessel (mm)

R:

Radius of vessel (mm)

\(s_{\upsilon }\) :

Source term \(\left( {N/m^{3} } \right)\)

T:

Time (s)

T:

Time period (s)

\(\vec{u}\) :

Velocity vector (m/s)

\(V_{m}\) :

Volume of the particle

B:

Buoyancy

D:

Drag

In:

Entered

L:

Lift

M:

Magnetic

Out:

Exited

P:

Particle

R:

Radius

X:

The longitudinal component of the Cartesian coordinate system

Y:

Cartesian coordinate system transverse component

Χ:

Magnetic susceptibility coefficient

ρ:

Density \(\left( {kg/m^{3} } \right)\)

η:

Particle capturing efficiency

\(\eta_{R}\) :

Regional particle capturing efficiency

\(\nabla\) :

Delta operator

μ:

Dynamic viscosity \(\left( {N.s/m^{2} } \right)\)

\(\mu_{0}\) :

Vacuum permeability \(\left( {4{\uppi } \times \frac{{10^{ - 7} {\text{N}}}}{{{\text{A}}^{2} }}} \right)\)

υ:

Kinematic viscosity \(\left( {m/s^{2} } \right)\)

\(\upsilon_{T}\) :

Kinematic viscosity of turbulent flow \(\left( {m/s^{2} } \right)\)

\(\alpha_{1} ,\alpha_{2} ,\alpha_{3}\) :

Constants

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Affiliations

  1. Department of Mechanical Engineering, Ferdowsi University of Mashhad, Mashhad, Iran

    Hamid Sodagar, Ali Shakiba & Hamid Niazmand

  2. Department of Mechanical Engineering, Shahrood University of Technology, Shahrood, Iran

    Javad Sodagar-Abardeh

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  1. Hamid Sodagar
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  2. Javad Sodagar-Abardeh
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  3. Ali Shakiba
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  4. Hamid Niazmand
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Correspondence to Ali Shakiba.

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Sodagar, H., Sodagar-Abardeh, J., Shakiba, A. et al. Numerical study of drug delivery through the 3D modeling of aortic arch in presence of a magnetic field. Biomech Model Mechanobiol 20, 787–802 (2021). https://doi.org/10.1007/s10237-020-01416-2

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  • DOI: https://doi.org/10.1007/s10237-020-01416-2

Keywords

  • Magnetic drug delivery
  • Numerical modeling
  • Aortic arch
  • Variable magnetic field orientation
  • Particle capturing efficiency
  • Ferrohydrodynamics