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Magnetic nanoparticles are useful in many medical applications because theyinteract with biology on a cellular level thus allowing microenvironmentalinvestigation. An enhanced understanding of the dynamics of magnetic particlesmay lead to advances in imaging directly in magnetic particle imaging (MPI) orthrough enhanced MRI contrast and is essential for nanoparticle sensing as inmagnetic spectroscopy of Brownian motion (MSB). Moreover, therapeutictechniques like hyperthermia require information about particle dynamics foreffective, safe, and reliable use in the clinic. To that end, we have developedand validated a stochastic dynamical model of rotating Brownian nanoparticlesfrom a Langevin equation approach. With no field, the relaxation time towardequilibrium matches Einstein's model of Brownian motion. In a static field, theequilibrium magnetization agrees with the Langevin function. For high frequencyor low amplitude driving fields, behavior characteristic of the linearizedDebye approximation is reproduced. In a higher field regime where magneticsaturation occurs, the magnetization and its harmonics compare well with theeffective field model. On another level, the model has been benchmarked againstexperimental results, successfully demonstrating that harmonics of themagnetization carry enough information to infer environmental parameters likeviscosity and temperature.

Simulations of magnetic nanoparticle Brownian motion