Magnetic Particle Imaging (MPI) is a promising tracer-based, functional medical imaging technique which measures the non-linear magnetization response of magnetic nanoparticles to a dynamic magnetic field. For image reconstruction, system matrices from time-consuming calibration scans are used predominantly. Finding modeled forward operators for magnetic particle imaging, which are able to compete with measured matrices in practice, is an ongoing topic of research. The existing models for magnetic particle imaging are by design not suitable for arbitrary dynamic tracer concentrations. Neither modeled nor measured system matrices account for changes in the concentration during a single scanning cycle. In this paper we present a new MPI forward model for dynamic concentrations. A static model will be introduced briefly, followed by the changes due to the dynamic behavior of the tracer concentration. Furthermore, the relevance of this new extended model is examined by investigating the influence of the extension and example reconstructions with the new and the standard model.