RESEARCH PAPER A mathematical model of superparamagnetic iron oxide nanoparticle magnetic behavior to guide the design of novel nanomaterials Ryan A. Ortega • Todd D. Giorgio Received: 4 April 2012 / Accepted: 31 October 2012 Ó Springer Science+Business Media Dordrecht 2012 Abstract Superparamagnetic iron oxide nanoparti- cles (SPIONs) exhibit unique magnetic properties that make them highly efficacious as MR imaging contrast agents and laboratory diagnostic tools. The complex- ity 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 magnetiza- tions. The model is used to predict the complex magnetic behavior of clustered magnetic particles in simulated in vivo environment; specifically, interac- tions 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. Keywords Superparamagnetism  Magnetic nanoparticles  Nanoparticle design tool  Magnetic contrast agents Introduction The use of small iron oxide particles as a laboratory or diagnostic tool has been practiced for almost 50 years (Gupta and Gupta 2005). The past two decades have seen advances in the techniques used to fabricate and characterize iron oxide particles. There are currently several fabrication techniques that allow for the highly controlled and repeatable creation of ultra-small particles (Weissleder et al. 1990; Woo et al. 2004; Woo and Lee 2004; Gupta and Gupta 2005; Muller et al. 2006). Although these materials garner much attention for their broad current and potential clinical uses, laboratory applications for these particles have significant utility as well. Commercially available particles can be used for labeling and magnetic separation of cells in vitro (Arbab et al. 2005). Superparamagnetic iron oxide nanoparticles (SPI- ONs) can also be used for molecular detection of biological compounds (Dave and Gao 2009). In a R. A. Ortega  T. D. Giorgio (&) Department of Biomedical Engineering, Vanderbilt University, VU Station B 351631, 5824 Stevenson Center, Nashville, TN 37235-1631, USA e-mail: todd.d.giorgio@vanderbilt.edu 123 J Nanopart Res (2012) 14:1282 DOI 10.1007/s11051-012-1282-x