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We derive a new 3D model for magnetic particle imaging (MPI) that is able toincorporate realistic magnetic fields in the reconstruction process. In realMPI scanners, the generated magnetic fields have distortions that lead todeformed magnetic low-field volumes (LFV) with the shapes of ellipsoids orbananas instead of ideal field-free points (FFP) or lines (FFL), respectively.Most of the common model-based reconstruction schemes in MPI use however theidealized assumption of an ideal FFP or FFL topology and, thus, generateartifacts in the reconstruction. Our model-based approach is able to deal withthese distortions and can generally be applied to dynamic magnetic fields thatare approximately parallel to their velocity field. We show how this new 3Dmodel can be discretized and inverted algebraically in order to recover themagnetic particle concentration. To model and describe the magnetic fields, weuse decompositions of the fields in spherical harmonics. We complement thedescription of the new model with several simulations and experiments.

A new 3D model for magnetic particle imaging using realistic magnetic field topologies for algebraic reconstruction