Magnetic Heating of Nanoparticles: The Importance of Particle Clustering to Achieve Therapeutic Temperatures

Hyperthermia therapy for cancer treatment seeks to destroy tumors through heating alone or combined with other therapies at elevated temperatures between 41.8 and 48 °C. Various forms of cell death including apoptosis and necrosis occur depending on temperature and heating time. Effective tumoricidal effects can also be produced by inducing damage to the tissue vasculature and stroma; however, surrounding normal tissue must be spared to a large extent. Magnetic nanoparticles have been under experimental investigation in recent years as a means to provide a favorable therapeutic ratio for local hyperthermia; however, practical numerical models that can be used to study the underlying mechanisms in realistic geometries have not previously appeared to our knowledge. Useful numerical modeling of these experiments is made extremely difficult by the many orders of magnitude in the geometries: from nanometers to centimeters. What has been missing is a practical numerical modeling approach that can be used to more deeply understand the experiments. We develop and present numerical models that reveal the extent and dominance of the local heat transfer boundary conditions, and provide a new approach that may simplify the numerical problem sufficiently to make ordinary computing machinery capable of generating useful predictions. The objectives of this paper are to place the discussion in a convenient interchangeable classical electromagnetic formulation, and to develop useful engineering approximations to the larger multiscale numerical modeling problem that can potentially be used in experiment evaluation; and eventually, may prove useful in treatment planning. We cast the basic heating mechanisms in the framework of classical electromagnetic field theory and provide calibrating analytical calculations and preliminary experimental results on BNF-Starch^® nanoparticles in a mouse tumor model for perspective.