Magnetic Nanoparticles in Cancer Thermotherapy: A Mathematical Approach to Optimal Treatment Design

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ABSTRACT

Thermotherapy, often called Hyperthermia treatment is a cancer treatment modality that involves raising the temperature of the tumor mass to over 315 K (42°C) for a specific duration, which leads to cell death through apoptosis or necrosis. Magnetic Particle Hyperthermia (MPH) is a non-invasive technique where magnetic nanoparticles are introduced into the tumor and then exposed to a magnetic field which convert magnetic energy into heat. Due to their high acidity, tumor cells are more sensitive to heat than healthy cells, meaning that heating the tumor to 315-319 K (42°C–46°C) can destroy it with minimal damage to the surrounding healthy tissues. During hyperthermia treatment, blood perfusion helps protect the healthy tissues around the tumor by dissipating excess heat. This paper presents a study where the temperature profiles within a spherical hepatic tumor mass are estimated by solving Pennes’ Bio-heat Equation, incorporating a power term. The study uses analytical methods to examine the effects of magnetic fluid hyperthermia treatment. Numerical illustrations are carried out using magnetite (Fe₃O₄) nanoparticles having an average diameter of 10.9 nm with mineral oil as a carrier liquid, subjected to magnetic fields of varying intensities. By analysing the model, the present work helps in designing an optimal treatment protocol by identify the time threshold of the therapy for varying magnetic field strengths.

Significance of the study:

This paper presents a mathematical approach to optimizing magnetic particle hyperthermia (MPH) for cancer treatment. By solving Pennes’ Bio-heat Equation, the study provides a non-invasive method to design effective hyperthermia protocols, ensuring safe temperatures for surrounding healthy tissues while maximizing tumor destruction.

Summary of the study:

The research investigates magnetic particle hyperthermia (MPH) for cancer treatment by modeling temperature profiles in a spherical hepatic tumor using Pennes’ Bio-heat Equation. Analytical methods and numerical illustrations with magnetite nanoparticles assess the impact of varying magnetic field intensities. The findings aid in designing optimal treatment protocols, maintaining healthy tissue temperatures below 315 K (42°C) while effectively targeting tumor cells.