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

Magnetic iron oxide nanoparticles (mNP), magnetite and mag-hemite, are under investigation as a means to provide a favorable therapeutic ratio for local hyperthermia treatment of tumors, and to make localized heating of the tumor less engineering-intensive and more cancer cell specific. They have been used successfully to localize tumor heating in experimental animals and in vitro [1–10]. Heating of nanoparticles is complicated by the short thermal relaxation time constants and difficulty of coupling sufficient power to achieve desired temperatures without creating toxic eddy currents in the tissues. Rabin [11] argues convincingly that individual (i.e., dispersed) nanoparticles are not able to effectively heat cells and tissues in electromagnetic fields because their small size results in extremely short thermal time constants, and the power densities required are too high to be practical. Nevertheless, experimental evidence shows that sufficient nanoparticle heating can be achieved with the same magnetic nanoparticles if spatially appropriate aggregates of NPs can be achieved; but clustering of the particles is essential to achieve useful results [5,12]. Magnetic field heating of iron oxide nanoparticles is typically accomplished by the hysteresis loop mechanism in alternating magnetic fields (AMFs), either due to Neel relaxation, Brownian motion, or perhaps, particle–particle interaction in super-paramagnetic nanoparticles at frequencies between 100 and 300 kHz, and has proven to be effective. The precise mechanism is somewhat controversial at this point, since it has not been clearly delineated and may consist of a combination of these, and perhaps other, mechanisms. In all cases the heating field is highly local in nature, and effective treatment depends on clustering and the spatial distribution of particles in strategically advantageous locations. To date almost all of the germane literature has been confined to experimental studies; the single exception that we have been able to identify is the work of Etheridge and Bischof, which included experiments and numerical models of suspended mNPs in a droplet [13]. Finite element method (FEM) numerical models can also be used to estimate the order of magnitude of volume power density, Q gen (W m−3) required to achieve significant heating in evenly dispersed and aggregated clusters of nanoparticles in more realistic multiple heat transfer and tumor geometry environments, which was one of the goals of this study. The FEM models developed in this study were confined to continuum formulations and did not include film nano-dimension heat transfer effects at the nanoparticle surface. The models illustrate the overwhelming effect of local heat transfer processes and the multiscale nature of the root problem. We develop and implement approximate numerical model approaches that illuminate the relative importance of biodistribution of mNPs and the local heat transfer boundary conditions. The results make practical ordinary sized FEM models of larger geometries and should facilitate the eventual engineering design and analysis of nanoparticle heating in realistic tumor-sized systems. While tumor-sized model spaces have not yet been developed, the pathway to do so is identified and described.