Technical Note: Transconvolution based equalization of positron energy effects for the use of Ge/ Ga phantoms in determining F PET recovery.

Purpose: Avoiding measurement variability from F phantom preparation by using Ge/ Ga phantoms for the determination of F recovery curves (RC) in clinical quality assurance measurements and for PET/CT site qualification in multicentre clinical trials.

Methods: RCs were obtained from PET/CT measurements of seven differently sized phantom spheres filled either with F or with Ga. RCs for the respective other isotope were then determined by two different methods: In the first method, images were convolved with positron range transconvolution functions derived from positron annihilation distributions found in literature. This method generated recasted images matching images using the respective other isotope. In the second method, the PET/CT system's isotope independent (intrinsic) point spread function was determined from said phantom measurements and convolved with numerical representations simulating hot spheres filled with the respective other isotope. These simulations included the isotope specific positron annihilation distributions. Recovered activity concentrations were compared between recasted images, simulated images, and the originally acquired images.

Results: F and Ga recovery was successfully determined from image acquisitions of the respective opposite isotope as well as from the simulations. Ga RCs derived from F data had a normalized root-mean-square deviation (NRMSD) from real Ga measurements of 0.019% when using the first method and of 0.008% when using the second method. F RCs derived from Ga data had a NRMSD from real F measurements of 0.036% when using the first method and of 0.038% when using the second method.

Conclusions: Applying the principles of transconvolution, F RCs can be recalculated from Ga phantom measurements with excellent accuracy. The maximal additionally introduced error was below 0.4% of the error currently accepted for RCs in the site qualification of multicentre clinical trials by the EARL program of the European Association of Nuclear Medicine (EANM). Therefore, our methods legitimately allow for the use of long-lived solid state Ge/ Ga phantoms instead of manually prepared F phantoms to characterize comparability of F measurements across different imaging sites or of longitudinal F measurements at a single PET/CT system.