Variance in parametric images: direct estimation from parametric projections

Recent work has shown that it is possible to apply linear kinetic models to dynamic projection data in PET in order to calculate parameter projections . These can subsequently be back-projected to form parametric images-maps o f parameters of physiological interest. Critical to the application of thes e maps, to lest for significant changes between normal and pathophysiology, is an assessment of the statistical uncertainty. In this context, parametr ic images also include simple integral images from, e.g., [O-15]-water used to calculate statistical parametric maps (SPMs). This paper revisits the c oncept of parameter projections and presents a more general formulation of the parameter projection derivation as well as a method to estimate paramet er variance in projection space, showing which analysis methods (models) ca n be used. Using simulated pharmacokinetic image data we show that a method based on an analysis in projection space inherently calculates the mathema tically rigorous pixel variance. This results in an estimation which is as accurate as either estimating variance in image space during model fitting, or estimation by comparison across sets of parametric images-as might be d one between individuals in a group pharmacokinetic PET study. The method ba sed on projections has, however, a higher computational efficiency, and is also shown to be more precise, as reflected in smooth variance distribution images when compared to the other methods.