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Magnetic drug targeting through a realistic model of human tracheobronchial airways using computational fluid and particle dynamics

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Abstract

Magnetic drug targeting (MDT) is a local drug delivery system which aims to concentrate a pharmacological agent at its site of action in order to minimize undesired side effects due to systemic distribution in the organism. Using magnetic drug particles under the influence of an external magnetic field, the drug particles are navigated toward the target region. Herein, computational fluid dynamics was used to simulate the air flow and magnetic particle deposition in a realistic human airway geometry obtained by CT scan images. Using discrete phase modeling and one-way coupling of particle–fluid phases, a Lagrangian approach for particle tracking in the presence of an external non-uniform magnetic field was applied. Polystyrene (PMS40) particles were utilized as the magnetic drug carrier. A parametric study was conducted, and the influence of particle diameter, magnetic source position, magnetic field strength and inhalation condition on the particle transport pattern and deposition efficiency (DE) was reported. Overall, the results show considerable promise of MDT in deposition enhancement at the target region (i.e., left lung). However, the positive effect of increasing particle size on DE enhancement was evident at smaller magnetic field strengths (Mn \(\le \) 1.5 T), whereas, at higher applied magnetic field strengths, increasing particle size has a inverse effect on DE. This implies that for efficient MTD in the human respiratory system, an optimal combination of magnetic drug career characteristics and magnetic field strength has to be achieved.

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Abbreviations

x :

x coordinate

y :

y coordinate

z :

z coordinate

\(u_\mathrm{i }\) :

Mean velocity in tensor notation (m/s)

\(u_\mathrm{f }\) :

Fluid (air) velocity (m/s)

\(u_\mathrm{p }\) :

Particle velocity (m/s)

\(Re_\mathrm{p}\) :

Particle Reynolds number (–)

\(\vec {F}\) :

Total force on magnetic drug career (N)

\(\vec {F}_\mathrm{D} \) :

Drag force (N)

\(\vec {F}_\mathrm{b} \) :

Buoyancy force (N)

\(\vec {F}_\mathrm{g} \) :

Gravitational force (N)

\(\vec {F}_\mathrm{Saffman} \) :

Saffman’s lift force (N)

\(\vec {F}_\mathrm{virtualmass} \) :

Virtual mass force (N)

\(\vec {F}_\mathrm{p.gradient} \) :

Pressure-gradient force (N)

\(\vec {F}_\mathrm{Faxen} \) :

Faxen force (N)

\(\vec {F}_\mathrm{Basset} \) :

Basset force (N)

\(\vec {F}_\mathrm{B} \) :

Brownian force (N)

\(\vec {F}_\mathrm{T} \) :

Thermophoretic force (N)

\(\vec {F}_\mathrm{m} \) :

Magnus force (N)

\(\vec {F}_\mathrm{M} \) :

Magnetic force (N)

\(V_\mathrm{p }\) :

Particle volume (m\(^{3}\))

\(d_\mathrm{p }\) :

Particle diameter (m)

\(m_\mathrm{p }\) :

Particle mass (kg)

f :

Drag coefficient \(\left( {a_1 +\frac{a_2 }{{Re}_\mathrm{p} }+\frac{a_3 }{{Re}_\mathrm{p}^2 }}\right) \)

t :

Time (s)

\(y^{+}\) :

Dimensionless cell height \(\left( {y^{+}=\frac{y}{\upsilon _\mathrm{f} }\sqrt{\frac{\tau _\mathrm{wall} }{\rho _\mathrm{f} }}} \right) \)

\(R_k , R_\omega , R_\beta \) :

Model constant of k–\(\omega \) LRN (–)

\(a^{*} , \alpha _\infty ^*, \alpha _0 \) :

Model coefficient, k–\(\omega \) LRN (–)

\(S_{ij }\) :

Mean rate of strain tensor (s\(^{-1}\))

k :

Turbulent kinetic energy (–)

H :

Magnetic field intensity vector (A m\(^{-1}\))

\(H_{0 }\) :

Characteristic magnetic field strength (A m\(^{-1}\))

\(H_{z }\) :

Magnetic field intensity component in z direction (A m\(^{-1}\))

\(H_{y }\) :

Magnetic field intensity component in y direction (A m\(^{-1}\))

Mn:

Magnetic number (T)

B :

Magnetic magnitude (T)

DE:

Deposition efficiency (–)

P :

Mean static pressure (Pa)

I :

Electrical current (A)

\(\upsilon _\mathrm{f} \) :

Kinetic molecular viscosity \(( {{\mu _\mathrm{f} }/\rho } )\)

\(\upsilon _\mathrm{T} \) :

Kinetic eddy viscosity \(( {{\mu _\mathrm{T} }/\rho })\)

\(\mu _0 \) :

Magnetic permeability in vacuum \(( {=}4\pi \times 10^{-7})\) (T mA\(^{-1}\))

\(\mu _\mathrm{f} \) :

Kinetic viscosity (kg m\(^{-1}\) s\(^{-1}\))

\(\alpha _1 ,\alpha _2 ,\alpha _3 \) :

Model constants of the Morsi and Alexander drag law (–)

\(\chi \) :

Particle magnetic susceptibility (–)

\(\rho _\mathrm{f} \) :

Fluid density (kg m\(^{-3}\))

\(\rho _\mathrm{p} \) :

Particle density (kg m\(^{-3}\))

\(\omega \) :

Specific dissipation rate (s\(^{-1}\))

\(\beta , \beta ^{*} , \beta _0 , \beta _0^*\) :

Model constant of k–\(\omega \) LRN (–)

\(\Omega _{ij} \) :

Rate of rotation tensor (s\(^{-1}\))

\(\tau _{ij} \) :

Reynolds stress tensor (kg m\(^{-1}\) s\(^{-2}\))

\(\gamma \) :

Model constant of k–\(\omega \) LRN (–)

\(\sigma _k , \sigma _d , \sigma _\omega \) :

Model constant of k–\(\omega \) LRN (–)

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Acknowledgments

We would like to appreciate the manager of Golestan Medical Imaging Center for his assistance to offer target CT-scan images. The authors would specially thank Mr. Vahid Roohparvar who is the CT-scan imaging expert for his assistance to provide us desired CT scan images DICOM files. Also we do appreciate all of respectful reviewers for their kindly and helpful suggestions that improved this article.

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Authors and Affiliations

  1. Department of Mechanical Engineering, Babol Noshirvani University of Technology, P. O. Box 484, Babol, Iran

    Oveis Pourmehran, Tahereh B. Gorji & Mofid Gorji-Bandpy

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  1. Oveis Pourmehran
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  2. Tahereh B. Gorji
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  3. Mofid Gorji-Bandpy
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Correspondence to Tahereh B. Gorji.

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Pourmehran, O., Gorji, T.B. & Gorji-Bandpy, M. Magnetic drug targeting through a realistic model of human tracheobronchial airways using computational fluid and particle dynamics. Biomech Model Mechanobiol 15, 1355–1374 (2016). https://doi.org/10.1007/s10237-016-0768-3

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