Improved signal-to-noise ratio in parametric images by cluster analysis.

Parametric images are formed by analyzing the concentration history of every voxel in PET data sets. Because PET concentration data at the voxel level are rather noisy, noise propagation into the parametric image is often quite noticeable. To address this problem, a model-based clustering method has been developed to generate parametric images. The basic idea of the clustering method is to average over voxels whose concentration histories have the same shape. We applied the method to a two-parameter (K1, k2) compartment model of local cerebral blood flow. The statistic R = integral tC(t) dt/integral C(t) dt= integral te-k2t multiply sign in circle Ca(t) dt/integral e-k2t multiply sign in circle Ca(t) dt classifies curves in terms of k2, where C(t) and Ca(t) denote the tissue and blood concentration histories, respectively, and multiply sign in circle is the convolution operator. Simulation studies of noise propagation in the clustering statistic showed that 30% voxel noise yielded a 2% standard deviation in R. Parametric images of blood flow and partition coefficient were computed for an O15 study, with and without clustering. Cluster size affected bias, statistical precision, and computation time. With clusters of 400 voxels, the variance of the flow parameter was around 1/50 smaller with clustering, with negligible bias and a computation time of 30 s on a 64-MHz workstation for 15 x 128 x 128 images with MATLAB 5.1.