A mathematical model of intratumoral infusion, particle distribution and heat transfer in cancer tumors: In-silico investigation of magnetic nanoparticle hyperthermia

Abstract

Tumor cells can be killed by rising the tumor temperature above 42 °C and keeping it for sufficiently longer durations by exploiting magnetic nanoparticles and alternative magnetic fields, which is known as magnetic nanoparticle hyperthermia. In-vivo experiments are often complex and difficult to perform to evaluate therapeutic efficacy. Hence, mathematical models and computer simulations are widely used as methods of investigation. Although different aspects of the treatment modality have been covered in the literature, a comprehensive model to consider the infusion of nanoparticles into the tumor, diffusion and distribution of the particles followed by heat transfer analysis to predict temperature elevation are lacking. This study presents a mathematical model to simulate clinical procedure by addressing the injection process, post-injection distribution and bio-heat transfer in the tumors considering in-vivo physiological aspects such as tumor heterogeneity and transvascular transport. The proposed model is implemented in COMSOL Multiphysics software to predict the fluid flow, particle distribution and temperature elevation in the tumor. Interstitial fluid flow is solved and utilized in predicting particle distribution through a convection-diffusion model. The obtained concentration profiles were used to calculate the nanoparticle heat generation in the tissues under an alternating magnetic field and the corresponding temperature distribution was predicted. The results demonstrate that the smaller particles diffuse faster and result in a higher temperature rise in the tumors. The numerical simulations also indicate that the ideal case of confined uniform distribution of nanoparticles inside the tumor only leads to the inaccurate prediction of the tumor temperatures and the efficiency of the treatment. In addition, it is observed that single-site injection at the tumor center does not achieve a therapeutic temperature in the entire tumor. This indicates that alternative techniques or multiple-site injections need to be investigated to achieve a therapeutic effect in large tumors.