Effects of cold sphere walls in PET phantom measurements on the volume reproducing threshold

We studied quantitatively the effects of the discontinuity introduced in an otherwise homogeneous background by the cold walls of the standard spherical glass inserts commonly used in phantom measurements for calibration of threshold-based approaches to volumetric evaluation of PET investigations. We concentrated especially on the question of threshold-based volume determination. We computed analytically the convolution of an isotropic Gaussian point-spread function with the insert geometry (hot sphere + cold wall + warm background) and derived the theoretical background dependence of the volume reproducing threshold. This analysis shows a clear wall-related reduction of the optimal threshold with increasing background. The predictions of our theoretical analysis were verified in phantom measurements at background fractions between 0 and 0.29. Defining the background-corrected relative threshold T = T-abs-B/A-B (T-abs: absolute volume reproducing threshold, A: measured activity at centre, B: background), we find that for a wall-less sphere T is independent of the background level. In the presence of cold walls, T drops (for not too small spheres, where recovery at the centre approaches 100%) from about 43% at B/A = 0 to about 25% at B/A = 0.5. Applying these thresholds to wall-less spheres leads to sizeable overestimates of the true volumes (43% at B/A = 0.5 for a sphere of 6 ml volume). We conclude that phantom measurements with standard sphere inserts for calibration of optimal thresholding algorithms introduce a systematic bias if performed at finite background levels. The observed background dependence is an artefact of the measurement procedure and does not reflect the conditions present in actual patient investigations.