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Numerical Investigation of Drug Delivery to Cancerous Solid Tumors by Magnetic Nanoparticles Using External Magnet

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Abstract

Chemotherapy as one of the most utilized cancerous tumor treatment methods introduces undesired side effects due to penetrating toxic drugs into the healthy organs. Delivery of anticancer therapeutic agents to solid tumors is also problematic. The purpose of current study is to investigate the penetration of magnetic drug carriers (MDCs) within the cancerous solid tumor tissue under the influence of external magnet. Capillary wall and tumor tissue is modeled as a saturated porous media. In order to solve the coupled governing equations, mass, momentum and concentration, an in-house finite volume-based code is developed and utilized. Results show the penetration of MDCs into the tumor in the absence of magnetic field is minimal and is limited to the surface of the tumor. On the other hand, under the influence of external magnet the penetration of MDCs within the tumor increases exponentially. They also penetrate deep into the tumor and cover the entire tumor which increase the effectivity and decrease the side effect of the treatment.

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Abbreviations

\(B_{0}\) :

Magnetic flux density of external magnet at its surface

\(C_{0}\) :

MDCs concentration at inlet

C :

MDCs dimensionless concentration

D :

MDCs diffusion coefficient

\(D_{\infty }\) :

diffusion coefficient of particle in unbounded fluid

\(D_{\mathrm{blood}}\) :

MDCs diffusion coefficient in the blood

\(D_{\mathrm{B}}\) :

Brownian diffusion coefficient of MDCs

\(D_{\mathrm{S}}\) :

Scattering diffusion coefficient of MDCs

\(D_{\mathrm{Endo}}\) :

MDCs diffusion coefficient in the Endothelium layer

\(D_{\mathrm{Tissue}}\) :

MDCs diffusion coefficient in the Tumor tissue

E :

Uptake term

\(\mathbf{F}_{1}\) :

Magnetic force acting upon a single MDC

\(F_{\mathrm{x}}\) :

Horizontal magnetic body force

\(F_{\mathrm{y}}\) :

Vertical magnetic body force

G :

Generation term

H :

Magnetic field intensity

J :

Hydrodynamic coefficient

P :

Pressure

\(\textit{Re}\) :

Reynolds number

\(r_{\mathrm{mag}}\) :

External magnet radius

S :

Steric coefficient

\(U_{\mathrm{in}}\) :

Inlet blood velocity

u :

Horizontal blood velocity

v :

Vertical blood velocity

\(\vec {\mathbf{v}}\) :

Blood velocity vector

\(\vec {\mathbf{v}}_{\mathrm{MDC}}\) :

MDCs velocity vector

\(\vec {\mathbf{v}}_{\mathrm{relative}}\) :

Relative velocity of MDCs to blood

\(x_{\mathrm{mag}}\) :

Horizontal position of external magnet

\(y_{\mathrm{mag}}\) :

Vertical position of external magnet

z :

Distance between external magnet and tumor

\(\rho \) :

Blood density

\(\varepsilon \) :

Porosity

\(\mu \) :

Blood viscosity

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

Plasma viscosity

\(\mu _{0}\) :

Magnetic permeability of vacuum

\(\lambda _{\mathrm{g}}\) :

Geometrical tortuosity

\(\chi \) :

Magnetic susceptibility of the MNPs

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

Particle response time

\(\forall _{\mathrm{MNP}}\) :

Total volume of MNPs in single MDC

\(\forall _{\mathrm{MDC}}\) :

Volume of a single MDC

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Authors and Affiliations

  1. Mechanical Engineering, K. N. Toosi University of Technology, Vanak Square, Molla-Sadra Ave., Pardis Ave., P. O. Box 19395-1999, Tehran, 1999143344, Iran

    Sayyed Mohammad Ali Ne’mati, Majid Ghassemi & Azadeh Shahidian

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  1. Sayyed Mohammad Ali Ne’mati
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  2. Majid Ghassemi
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  3. Azadeh Shahidian
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Correspondence to Majid Ghassemi.

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Ne’mati, S.M.A., Ghassemi, M. & Shahidian, A. Numerical Investigation of Drug Delivery to Cancerous Solid Tumors by Magnetic Nanoparticles Using External Magnet. Transp Porous Med 119, 461–480 (2017). https://doi.org/10.1007/s11242-017-0893-1

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