A mathematical study of nanoparticle aided hyperthermia treatment of hepatic cancer using magnetite nanoparticles under alternating and rotating magnetic fields

Document Type : Research Paper


1 Department of Mathematics, University of Kashmir, Srinagar - 190006, J&K, India

2 Radiological Physics, Department of Radiodiagnosis, JNMC, Aligarh Muslim University, Aligarh - 202002, U.P, India

3 Department of Radiological Physics \& Bio-Engineering, SKIMS, Srinagar - 190011, J&K, India


Hyperthermia is a method of cancer treatment wherein the temperature of the tumor is increased to over 315 K (42$^{\circ}$C) for a specific duration, ultimately leading to cell death by inducing apoptosis or necrosis. Magnetic Particle Hyperthermia (MPH) is a non-invasive method of cancer treatment in which magnetic nanoparticles are introduced to the tumor at its center and are then subject to a magnetic field. Magnetic nanoparticles upon being exposed to a magnetic field exhibit a heating effect by conversion of magnetic field energy into heat energy. Owing to high acidity, tumor cells are more sensitive to heating than healthy cells, thus if the tumor is heated to 315-319K (42$^{\circ}$–46$^{\circ}$ C), it will be destroyed with minimal to no damage to healthy tissues surrounding the tumor. During the application of hyperthermia as a cancer treatment, blood perfusion protects the healthy tissues surrounding the tumor region from damage due to heat by dissipating any excess heat.  In this paper, the temperature profiles were estimated inside a presumably spherical hepatic tumor mass by solving Pennes' Bio-heat Equation containing the power term. The results were obtained using analytic as well as numerical methods using MPH with mineral oil as a carrier liquid and Magnetite ($Fe_3O_4$) nanoparticles with a mean diameter of 10.9 nm subject to Alternating Magnetic Field (AMF) and Rotating Magnetic Field (RMF).


Volume 14, Issue 1
January 2023
Pages 2301-2312
  • Receive Date: 05 November 2022
  • Accept Date: 22 December 2022
  • First Publish Date: 27 December 2022