PURPOSE: Magnetic particle imaging (MPI) is a new quantitative imaging technique capable of determining the spatial distribution of superparamagnetic nanoparticles at high temporal and spatial resolution. For reconstructing this spatial distribution, the particle dynamics and the scanner properties have to be known. To date, they are obtained in a tedious calibration procedure by measuring the magnetization response of a small delta sample shifted through the measuring field. Recently, first reconstruction results using a 1D model-based system function were published, showing comparable image quality as obtained with a measured system function. In this work, first 2D model-based reconstruction results of measured MPI data are presented. METHODS: To simulate the system function, various parameters have to be modeled, namely, the magnetic field, the particle magnetization, the voltage induced in the receive coils, and the transfer function of the receive chain. To study the accuracy of the model-based approach, 2D MPI data are measured and reconstructed with modeled and measured system functions. RESULTS: It is found that the model-based system function is sufficiently accurate to allow for reconstructing experimental data. The resulting image quality is close to that obtained with a measurement-based reconstruction. CONCLUSIONS: The model-based system function approach addresses a major drawback of the measurement-based procedure, namely, the long acquisition time. In this work, the acquisition of the measurement-based system function took 45 min, while the model-based system function was obtained in only 15 s. For 3D data, where the acquisition of the measurement-based system function takes more than 6 h, the need for an efficient system function generation is even more obvious.