NONLINEAR DYNAMICAL ANALYSIS IN MAGNETIC HYPERTHERMIA
Magnetic Hyperthermia; Poincaré Map; Chaos; Particulate System
Magnetic hyperthermia is a cancer treatment based on heating tumors using ferrofluids. This work aims to analyze the nonlinearities and the efficiency of this therapy. Through a particulate system, a ferrofluid is simulated numerically under several circumstances. The nonlinear effect of the system is determined by means of phase spaces, Poincaré maps and bifurcation diagrams. For each simulation, the production of internal energy from magnetic work is calculated. The condition that maximizes the internal energy production is chosen as the best and most efficient case for the cancer treatment. This study begins with a theoretical review along with numerical methodology. Then, the system of magnetic particles is subjected to an alternating one-dimensional magnetic field, the most common in the literature. Later, an alternating shear motion is imposed (common of liquid shakers) at the same time with the alternating one-dimensional magnetic field. Lastly, a two-dimensional chaotic magnetic field is applied along with alternating shear motion. The obtained results show that the system has a natural frequency equal to zero, the alternating shear motion does not affect the production of internal energy and that chaotic behavior was only observed in the system with a chaotic magnetic field along with shear motion. In conclusion, the system presents a rigid body natural mode and does not have a rich dynamical behavior. Moreover, the liquid shaker which promotes shear motion is not recommended energetically for magnetic hyperthermia and the pure alternating magnetic field is the most appropriate behavior for this cancer treatment.