Magnetic field and PET: Does the effect of magnetic field vary with the intrinsic resolution of PET scanners?

We describe an investigation of the interaction between the effect of magnetic field on PET image resolution (i.e. FWHM and FWTM) on the plane perpendicular to the direction of the field and the intrinsic resolution or Point-Spread-Function (PSF) of PET scanners using Electron Gamma Shower simulations (EGSnrc). Relatively short and long range PET nuclides (e.g. ²²Na, ⁶⁸Ga, and ¹⁵O point sources) surrounded by water were simulated under magnetic field with strengths ranging from 0T to 11T. The simulated images were then blurred with Gaussian filters which correspond to various PSF´s or intrinsic resolutions of human, small animal, and `perfect´ PET scanners (i.e. 4.7 mm PSF, 2 mm PSF, and no PSF, respectively). It was observed that the magnetic field has very small effect (<; 1%) on the resolution of short range nuclides such as <sup>22</sup>Na as expected. For long range PET nuclides, both FWHM and FWTM improve as the magnetic field strength increases, and the improvement saturates at ~7T for the human PET scanner, while it saturates at a higher field strength (> 11T) for the small animal scanner. However, worse FWHM was observed at weak field strength (i.e. <; 3T in this case) as compared to that at 0T for the small animal PET scanner due to the interaction between the distribution of (low occurrence) high energy positrons and the scanner´s narrower intrinsic resolution kernel, which was demonstrated more clearly with the assistance of the simulated results from the `perfect´ PET scanner. It was also found that the intrinsic resolution of the PET scanner needs to be worse/wider than 2.35 mm to observe an improvement in FWHM for a ⁶⁸Ga point source in water (2.92 mm for ⁸²Rb) under a 3T magnetic field as compared to that under 0T. In summary, the magnetic field does not always improve the FWHM for high resolution PET scanners even though it reduces the positron range, and the effect of the magnetic field varies with the intrinsic resolution of the PET scanners.