Numerically efficient estimation of relaxation effects in magnetic particle imaging

Current simulations of the signal in magnetic particle imaging (MPI) are either based on the Langevin function or on directly measuring the system function. The former completely ignores the influence of finite relaxation times of magnetic particles, and the latter requires time-consuming reference scans with an existing MPI scanner. Therefore, the resulting system function only applies for a given tracer type and the properties of the applied scanning trajectory. It requires separate reference scans for different trajectories and does not allow simulating theoretical magnetic particle suspensions. The most accessible and accurate way for including relaxation effects in the signal simulation would be using the Langevin equation. However, this is a very time-consuming approach because it calculates the stochastic dynamics of the individual particles and averages over large particle ensembles. In the current article, a numerically efficient way for approximating the averaged Langevin equation is proposed, which is much faster than the approach based on the Langevin equation because it is directly calculating the averaged time evolution of the magnetization. The proposed simulation yields promising results. Except for the case of small orthogonal offset fields, a high agreement with the full but significantly slower simulation could be shown.