Effect of interparticle correlation on magnetic hyperthermia in biological media: A numerical study

Abstract

Numerical simulations of the temperature field of a circular tumour subjected to magnetic hyperthermia are presented. The calculation domain is composed by a 5 mm circular tumour surrounded by a 2 cm × 2 cm region of a healthy tissue. Realistic values of the biological media properties are considered. Simulations are carried by an in-house research code that solves the biological heat equation in the presence of a magnetic dissipation term through a finite differences scheme. The magnetic source term is expressed in terms of the out-of-phase response of the fluid’s complex susceptibility, when subjected to an oscillatory magnetic field. This quantity is obtained using asymptotic theories and numerical simulations in the scale of the magnetic nanoparticles through another in-house research code based on Langevin Dynamics. Dipolar particle interactions are computed through a robust scheme of Ewald summation. The microscopic formulation for the particles also considers Brownian effects in their translational and rotational motion. Realistic values of these parameters are considered in order to provide a dimensional evaluation of the temperature field in the biological tissue comparable to previous numerical and experimental studies. The role of particle size distribution on the temperature field is carefully investigated. Temperature fields are also linked with microscopic geometrical features of suspended magnetic particles in order to provide a clear multiscale understanding of the physics of magnetic heat induction using alternating fields. Our results indicate that the role of dipolar interactions seems to be relevant for particle radii in the range 5nm≤a≤7nm, specially for higher volume fraction of particles, where the classical Langevin model for the saturation susceptibility fails in the prediction of the steady-state tumour temperature. For a volume fraction of particles of 15% the differences on the final temperature of the tumour associated with dipolar interactions are in the order of 20% for particles with a nominal radius in the range 5nm≤a≤7nm. In dilute regimes the classical Langevin model succeeds in the prediction of the final temperature of the tumour as expected.