  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 Einstein's 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.
