FDM-based 2D Numerical Study of Hyperthermia Cancer Treatment by Micro/Nano-Phase-Change Materials

  • Ali Asghar Taheri
  • Faramarz TalatiEmail author
Research Paper


Hyperthermia is one of the methods for cancer therapies by creating artificial fever. Protection of healthy tissues around the tumor tissue, which has a high temperature, is one of the major issues in this treatment. In present study, the two-dimensional transient model of biological tissue with a tumor is taken into account. The area of the tumor is embedded with micro/nano superparamagnetic materials, and the surrounding healthy tissues are embedded with microcapsules of micro/nano-phase-change materials (PCMs). The effect of concentrations, the radius of the microcapsule, the melting temperature and latent heat of phase-change nanoparticles and also superparamagnetic nanoparticles on thermal protection were examined numerically by using the finite difference method. The results showed that the use of PCMs causes sensible decreases in temperatures of the healthy tissue around the cancerous cells (in some places up to 3 ℃) that leads to treatment complications reduction. If the protection of healthy tissues is well done, it is possible to raise the temperature of the cancerous tissue to achieve more favorable treatment.


Hyperthermia Cancer Electromagnetic (EM) field Superparamagnetic materials (SPMs) Phase-change materials (PCMs) Bioheat equation Finite difference method (FDM) 

List of Symbols

\( C \)

Heat Capacity (J/m3K)

\( \varvec{E} \)

Strength of Electric Field (V/m)

\( f \)

Frequency of Electromagnetic Field (Hz)

\( h_{f} \)

Apparent Heat Convection Coefficient between the Skin Surface and the Water (W/m2K)

\( K \)

Thermal Conductivity (W/mK)

\( n \)

Concentrations of Micro/Nanoparticles

\( Q \)

Heat Generation Rate (W/m3))

\( R \)

Radius of the Magnetic Induction Loop (m)

\( r \)

Radius of Micro/Nanoparticles (m)

\( T_{ } \)

Temperature (℃)



x, y

Space Components

Greek Symbols

\( \varepsilon \)

Permittivity Dielectric Constant (C/N m2)

\( \varepsilon \)

Mean Absolute Error

\( \eta \)

Volume Ratio of Nanoparticles (1/m3)

\( \mu_{0} \)

Permeability of Free Space (T m/A)

\( \sigma \)

Electrical Conductivity (S/m)

\( \chi \)

Susceptibility of Magnetic Nanoparticles

\( \omega_{b} \)

Blood Perfusion Rate (1/s)

\( \omega_{ } \)

Relaxation Factor

\( \Omega _{ } \)

Solution Domain

\( \Omega _{h} \)

Heating Area





Time Increment


i, j

Computational Nodes






Healthy Tissue Area


Tumor Area with SPMs


Healthy Tissue Area with PCMs


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Copyright information

© Shiraz University 2019

Authors and Affiliations

  1. 1.University of TabrizTabrizIran
  2. 2.Faculty of Mechanical EngineeringUniversity of TabrizTabrizIran

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