Mathematical model of magnetic hyperthermia therapy for breast tumour via intratumoural injection of iron–platinum nanoparticles

Abstract

The present study explores magnetic hyperthermia for a treatment of a breast tumour with a surrounding healthy breast gland region and overlying fat and skin regions. A mathematical model that utilizes the Brinkman–Forchheimer-extended Darcy equations and non-Newtonian (Carreau–Yasuda) constitutive equation is constructed for the intratumoural injection of an aqueous iron–platinum (FePt) nanoparticle suspension, blood perfusion through the tissue regions, and the temperature and nanoparticle distributions during the process of hyperthermia therapy. The equations governing nanofluid flow, heat transfer and the suspended and deposited nanoparticle volume fractions are solved numerically via the finite element technique, and numerical results are computed in the FreeFEM++ software. Using the obtained results, the impact of the Reynolds number, nanoparticle diameter and haematocrit on the efficacy of magnetic hyperthermia therapy is investigated. The results revealed that the tissue penetration of nanoparticles is more pronounced when the red blood cell concentration and nanoparticle diameter are lower. Furthermore, the required duration for effective magnetic hyperthermia and the healthy tissue damage decrease with increasing haematocrit and nanoparticle diameter.

Keywords

• Breast tumour
• Carreau–Yasuda equation
• Finite element technique
• Magnetic hyperthermia
• Nanoparticle distribution