The Development of Theoretical Model for Relaxation Mechanism of Superparamagnetic Nano Particles

Chang, Yongmin; Hwang, Moon Jung

Abstract

PURPOSE
To develop a theoretical model for magnetic relaxation behavior of the superparamagnetic nano-particle agent, which demonstrates multi-functionality such as liver- and lymp node-specificity. Based on the developed model, the computer simulation was performed to clarify the relationship between relaxation time and the applied magnetic field strength. MATERIALS AND METHODS: The ultrasmall superparamagnetic iron oxide (USPIO) was encapsulated with biocompatiable polymer, to develop a relaxation model based on outsphere mechanism, which was resulting from diffusion and/or electron spin fluctuation. In addition, Brillouin function was introduced to describe the full magnetization by considering the fact that the low-field approximation, which was adapted in paramagnetic case, is no longer valid. The developed model describes therefore the T1 and T2 relaxation behavior of superparamagnetic iron oxide both in low-field and in high-field. Based on our model, the computer simulation was performed to test the relaxation behavior of superparamagnetic contrast agent over various magnetic fields using MathCad (MathCad, U.S.A.), a symbolic computation software. RESULTS: For T1 and T2 magnetic relaxation characteristics of ultrasmall superparamagnetic iron oxide, the theoretical model showed that at low field (<1.0 Mhz), tauS 1(tauS 2 in case of T2), which is a correlation time in spectral density function, plays a major role. This suggests that realignment of nano-magnetic particles is most important at low magnetic field. On the other hand, at high field, tau, which is another correlation time in spectral density function, plays a major role. Since tau is closely related to particle size, this suggests that the difference in R1 and R2 over particle sizes, at high field, is resulting not from the realignment of particles but from the particle size itself. Within normal body temperature region, the temperature dependence of T1 and T2 relaxation time showed that there is no change in T1 and T2 relaxation times at high field. Especially, T1 showed less temperature dependece compared to T2. CONCLUSION: We developed a theoretical model for magnetic relaxation behavior of ultrasmall superparamagnetic iron oxide (USPIO), which was reported to show clinical multi-functionality by utilizing physical properties of nano-magnetic particle. In addition, based on the developed model, the computer simulation was performed to investigate the relationship between relaxation time of USPIO and the applied magnetic field strength.