Magnetic particle imaging with non-oriented immobilized particles : why the Langevin model of paramagnetism is sufficient

The Langevin model of paramagnetism is commonly used as a simplified physical model for magnetic particle imaging. In research with immobilized nanoparticles that are non-oriented, the phenomenon is observed that the measured system function components for Lissajous trajectory-based excitation show a high spatial similarity to those from the Langevin model of paramagnetism. In this work we show that this observation can be explained mathematically, since in equilibrium and for anisotropic uniaxial nanoparticles without orientation the model falls back to the Langevin model of paramagnetism. Since previous studies have also shown that the anisotropic equilibrium model for immobilized particles is approximately equivalent to the Néel rotation Fokker-Planck model, the Langevin model of paramagnetism is sufficient to cover the non-oriented immobilized case.