Thermal response of a tumor prototype subjected to diffusion, particle interactions, and magnetic hyperthermia

A Lagrangian approach based on Langevin and Stokesian dynamics is used to compute the translational and orientational dynamics of independent ensembles of magnetic nanoparticles subjected to both oscillatory and rotating magnetic fields. Long-range dipolar and hydrodynamic interactions between the particles are computed using periodic boundary conditions by applying the Ewald summation technique to accelerate the conditional convergence of the lattice sums. The non-equilibrium suspension magnetization is used to compute the magnetic energy production contribution in the continuum bioheat equation applied for a spherical tumor immersed in a biological medium through an Eulerian approach based on the finite volume method. The phenomenon of magnetic hyperthermia is examined in light of a new approach that accounts for the influence of a diffusion process of magnetic material in the tumor domain, considering a diffusivity dependence on temperature. A very good agreement is obtained between the experimental data and the simulation results. The effect of hydrodynamic interactions between the suspended magnetic particles is examined by comparing the temperature time evolution at the center of the tumor with simulation results for the case of non-interacting particles. The results indicate that the random characteristic of the hydrodynamic interactions decreases the average temperature of the tumor produced as a result of a dispersive effect on the nano-clusters formed in the tumor region. From a computational point of view, the new calculations with a mass diffusion equation coupled to the energy equation represent an advance in investigations of magnetic hyperthermia by dynamical simulations.