A Bayesian spatial temporal mixtures approach to kinetic parametric images in dynamic positron emission tomography

Estimation of parametric maps is challenging for kinetic models in dynamic positron emission tomography. Since voxel kinetics tend to be spatially contiguous, the authors consider groups of homogeneous voxels together. The authors propose a novel algorithm to identify the groups and estimate kinetic parameters simultaneously. Uncertainty estimates for kinetic parameters are also obtained.

Mixture models were used to fit the time activity curves. In order to borrow information from spatially nearby voxels, the Potts model was adopted. A spatial temporal model was built incorporating both spatial and temporal information in the data. Markov chain Monte Carlo was used to carry out parameter estimation. Evaluation and comparisons with existing methods were carried out on cardiac studies using both simulated data sets and a pig study data. One-compartment kinetic modeling was used, in which K1 is the parameter of interest, providing a measure of local perfusion.

Based on simulation experiments, the median standard deviation across all image voxels, of K1 estimates were 0, 0.13, and 0.16 for the proposed spatial mixture models (SMMs), standard curve fitting, and spatial K-means methods, respectively. The corresponding median mean squared biases for K1 were 0.04, 0.06, and 0.06 for abnormal region of interest (ROI); 0.03, 0.03, and 0.04 for normal ROI; and 0.007, 0.02, and 0.05 for the noise region.

SMM is a fully Bayesian algorithm which determines the optimal number of homogeneous voxel groups, voxel group membership, parameter estimation, and parameter uncertainty estimation simultaneously. The voxel membership can also be used for classification purposes. By borrowing information from spatially nearby voxels, SMM substantially reduces the variability of parameter estimates. In some ROIs, SMM also reduces mean squared bias.