Spatially-coordinated regression for image-wise model fitting to dynamic PET data for generating parametric images

Due to the high noise level of pixel-wise kinetic data in dynamic studies, direct model fitting of the kinetic data on a pixel-by-pixel basis requires many iterations and has high variability, making it unsuitable for generating parametric images of the micro-parameters of tracer kinetic models. In this study, the authors propose and investigate a spatially-coordinated method for image-wise nonlinear regression that allows good quality parametric images to be generated by direct model fitting. Instead of model fitting the kinetics of each pixel independently, the new method performs regression simultaneously in parallel for all pixels in the image with the intermediate results at each iteration step coordinated among neighboring pixels. The Marquardt algorithm is used to minimize the sum of square differences and a simple smoothing is employed for coordination of estimates at each iteration. The method has been implemented using MATLAB and has been applied to both computer simulated data and real FDG dynamic images. Results on simulated data show the estimates converge quickly with the new method. The estimates have a lower variability than the case of not having the coordination. On real FDG data, the new method is successful in generating good quality images of individual FDG rate-constants. Although further work is still needed to characterize the new method in terms of its many properties, the method is promising for generating useful parametric images of individual rate constants of tracer kinetic models