Magnetic nanoparticles are useful biological probes as well as therapeutic agents. There have been several approaches used to model nanoparticle magnetization dynamics for both Brownian as well as Neel rotation. The magnetizations are often of intere
st and can be compared with experimental results. Here we summarize these approaches including the Stoner-Wohlfarth approach, and stochastic approaches including thermal fluctuations. Non-equilibrium related temperature effects can be described by a distribution function approach (Fokker-Planck equation) or a stochastic differential equation (Langevin equation). Approximate models in several regimes can be derived from these general approaches to simplify implementation.
Remote sensing of magnetic nanoparticles has exciting applications for magnetic nanoparticle hyperthermia and molecular detection. We introduce, simulate, and experimentally demonstrate an innovation---a sensing coil that is geometrically decoupled f
rom the excitation field---for magnetic nanoparticle spectroscopy that increases the flexibility and capabilities of remote detection. The decoupling enhances the sensitivity absolutely; to small amounts of nanoparticles, and relatively; to small changes in the nanoparticle dynamics. We adapt a previous spectroscopic method that measures the relaxation time of nanoparticles and demonstrate a new measurement of nanoparticle temperature that could potentially be used concurrently during hyperthermia.
Magnetic nanoparticles are useful in many medical applications because they interact with biology on a cellular level thus allowing microenvironmental investigation. An enhanced understanding of the dynamics of magnetic particles may lead to advances
in imaging directly in magnetic particle imaging (MPI) or through enhanced MRI contrast and is essential for nanoparticle sensing as in magnetic spectroscopy of Brownian motion (MSB). Moreover, therapeutic techniques like hyperthermia require information about particle dynamics for effective, safe, and reliable use in the clinic. To that end, we have developed and validated a stochastic dynamical model of rotating Brownian nanoparticles from a Langevin equation approach. With no field, the relaxation time toward equilibrium matches Einsteins model of Brownian motion. In a static field, the equilibrium magnetization agrees with the Langevin function. For high frequency or low amplitude driving fields, behavior characteristic of the linearized Debye approximation is reproduced. In a higher field regime where magnetic saturation occurs, the magnetization and its harmonics compare well with the effective field model. On another level, the model has been benchmarked against experimental results, successfully demonstrating that harmonics of the magnetization carry enough information to infer environmental parameters like viscosity and temperature.
Magnetic nanoparticle hyperthermia is an attractive emerging cancer treatment, but the acting microscopic energy deposition mechanisms are not well understood and optimization suffers. We describe several approximate forms for the characteristic time
of N{e}el rotations with varying properties and external influences. We then present stochastic simulations that show agreement between the approximate expressions and the micromagnetic model. The simulations show nonlinear imaginary responses and associated relaxational hysteresis due to the field and frequency dependencies of the magnetization. This suggests efficient heating is possible by matching fields to particles instead of resorting to maximizing the power of the applied magnetic fields.
