A mathematical model of superparamagnetic iron oxide nanoparticle magnetic behavior to guide the design of novel nanomaterials

Superparamagnetic iron oxide nanoparticles (SPIONs) exhibit unique magnetic properties that make them highly efficacious as MR imaging contrast agents and laboratory diagnostic tools. The complexity of SPION magnetic behavior and the multiple parameters affecting this behavior complicate attempts at fabricating particles suited for a particular purpose. A mathematical model of SPION magnetic properties derived from experimental relationships and first principles can be an effective design tool for predicting particle behavior before materials are fabricated. Here, a novel model of SPION magnetic properties is described, using particle size and applied magnetic field as the primary variable inputs. The model is capable of predicting particle susceptibility and non-linear particle magnetization as well as describing the vector magnetic field produced by a single particle in an applied field. Magnetization values produced by the model agree with recent experimental measurements of particle magnetizations. The model is used to predict the complex magnetic behavior of clustered magnetic particles in simulated in vivo environment; specifically, interactions between the clusters and water molecules. The model shows that larger particles exhibit more linear magnetic behavior and stronger magnetization and that clusters of smaller particles allow for more numerous SPION–water molecule interactions and more uniform cluster magnetizations.