  The image reconstruction problem of the tomographic imaging technique
magnetic particle imaging (MPI) requires the solution of a linear inverse
problem. One prerequisite for this task is that the imaging operator that
describes the mapping between the tomographic image and the measured signal is
accurately known. For 2D and 3D excitation patterns, it is common to measure
the system matrix in a calibration procedure, that is both, very time consuming
and adds noise to the operator. The need for measuring the system matrix is due
to the lack of an accurate physical model that is capable of describing the
nanoparticles' magnetization behavior. Within this work we introduce a physical
model that is based on N\'{e}el rotation for large particle ensembles and we
find model parameters that describe measured 2D MPI data with much higher
precision than state of the art MPI models. With phantom experiments we show
that the simulated system matrix can be used for image reconstruction and
reduces artifacts due to model-mismatch considerably.
