A nonlinear spatially variant object-dependent system model for prediction of partial volume effects and scatter in PET.

Accurate quantitation of small lesions with positron emission tomography (PET) requires correction for the partial volume effect. Traditional methods that use Gaussian models of the PET system were found to be insufficient. A new approach that models the non-Gaussian object-dependent scatter was developed. The model consists of eight simple functions with a total of 24 parameters. Images of line and disk sources in circular and elliptical cylinders, and an anthropomorphic chest phantom were used to determine the parameter values. Empirical rules to determine these parameter values for various objects based on those for a reference object, a 21.5-cm circular cylinder, were also proposed. For seven spheroids and a 3.4-cm cylinder, pixel values predicted by the model were compared with the measured values. The model-to-measurement-ratio was 1.03+/-0.07 near the center of the spheroids and 0.99+/-0.03 near the center of the 3.4-cm cylinder. In comparison, the standard single Gaussian model had corresponding ratios of 1.27+/-0.09 and 1.24+/-0.03, respectively, and the corresponding ratios for a double Gaussian model were 1.13+/-0.09 and 1.05+/-0.01. Scatter fraction (28.5%) for a line source in the 21.5-cm cylinder was correctly estimated by our model. Because of scatter, we found that errors in the measurement of activity in spheroids with diameters from 0.6 to 3.4 cm were more significant than previously appreciated.