Analysis of a 3-D system function measured for magnetic particle imaging

Magnetic particle imaging (MPI) is a new tomographic imaging approach that can quantitatively map magnetic nanoparticle distributions in vivo. It is capable of volumetric real-time imaging at particle concentrations low enough to enable clinical applications. For image reconstruction in 3-D MPI, a system function (SF) is used, which describes the relation between the acquired MPI signal and the spatial origin of the signal. The SF depends on the instrumental configuration, the applied field sequence, and the magnetic particle characteristics. Its properties reflect the quality of the spatial encoding process. This work presents a detailed analysis of a measured SF to give experimental evidence that 3-D MPI encodes information using a set of 3-D spatial patterns or basis functions that is stored in the SF. This resembles filling 3-D k-space in magnetic resonance imaging, but is faster since all information is gathered simultaneously over a broad acquisition bandwidth. A frequency domain analysis shows that the finest structures that can be encoded with the presented SF are as small as 0.6 mm. SF simulations are performed to demonstrate that larger particle cores extend the set of basis functions towards higher resolution and that the experimentally observed spatial patterns require the existence of particles with core sizes of about 30 nm in the calibration sample. A simple formula is presented that qualitatively describes the basis functions to be expected at a certain frequency.