Empirical Bayesian estimation in graphical analysis: A voxel-based approach for the determination of the volume of distribution in PET studies

Introduction: Total volume of distribution (V_T) determined by graphical analysis (GA) of PET data suffers from a noise-dependent bias. Likelihood estimation in GA (LEGA) eliminates this bias at the region of interest (ROI) level, but at voxel noise levels, the variance of estimators is high, yielding noisy images. We hypothesized that incorporating LEGA V_T estimation in a Bayesian framework would shrink estimators towards prior means, reducing variability and producing meaningful and useful voxel images. Methods: Empirical Bayesian estimation in GA (EBEGA) determines prior distributions using a two-step k-means clustering of voxel activity. Results obtained on eight [¹¹C]-DASB studies are compared with estimators computed by ROI-based LEGA. Results: EBEGA reproduces the results obtained by ROI LEGA while providing low-variability V_T images. Correlation coefficients between average EBEGA V_T and corresponding ROI LEGA V_T range from 0.963 to 0.994. Conclusions: EBEGA is a fully automatic and general approach that can be applied to voxel-level V_T image creation and to any modeling strategy to reduce voxel-level estimation variability without prefiltering of the PET data.