Magnetic dipole-dipole (MDD) interactions between iron oxide nanoparticles can influence the sensitivity, image resolution and quantification of magnetic particle imaging (MPI). For the first time, the Landau-Lifshitz-Gilbert equation (LLG) for MDD interactions has been solved to investigate the effect of MDD interactions on the MPI spectrum. It was found that at concentrations above 39 mmol(Fe) l-1, MDD interactions significantly influence MPI spectra. This influence increases with increasing harmonics, which means first harmonics should be preferred for iron quantification. Since ≈1018particles are neglected in the LLG compared to in an MPI experiment, the calculated limit below which MDD interactions can be neglected is only a bound. The true limit is therefore below the calculated limit of 39 mmol(Fe) l-1, because all other neglected particles also contribute to deviations in the MPI spectra via MDD interactions. Therefore, a quantum mechanical bound on the influence of MDD interactions is calculated, including up to 1015particles. Analysis of the bound as a function of the particle number provides a valuable insight into the influence of the large number of particles neglected in numerical simulations. Both results are compared with concentrations in biomedical MPI experiments. We conclude that the standard approximation of an absence of MDD interactions in MPI experiments must be handled more carefully. Our method of incorporating MDD interactions into the LLG can be easily implemented as part of model-based reconstruction to increase the sensitivity, image resolution and quantitative tracer detection during MPI.
