Study of direct and indirect parametric estimation methods of linear models in dynamic positron emission tomography

In dynamic positron emission tomography (PET) studies, the time changing activity of the radiotracer is measured through multiple consecutive frames. Subsequent pixel-by-pixel application of the appropriate kinetic model provides quantitative information in terms of images of the distribution of the physiological parameter of interest. In this context, iterative reconstruction methods may be used to reconstruct for each time frame a static image of appreciable higher quality than the analytical algorithms, especially in low-count cases. Furthermore, if the reconstruction algorithm also models the kinetics of the measured counts, the parametric image is expected to be of even higher quality. In this work, we investigate the methodology to directly reconstruct parametric images in three-dimensional PET when the kinetic model is linear in its parameters (Patlak plot) and compare with indirectly estimated parametric maps, where the radioactivity distribution was estimated by the filtered back projection and ordered subsets expectation maximization algorithms. Both real and simulated data for tracers with irreversible kinetics in brain studies are included. The results demonstrate appreciable smaller standard deviation and mean squared error characteristics for the direct reconstruction. However, some regions may converge slowly. The FBP and ordered subsets expectation maximization (OSEM) indirect estimations have a similar level of bias after matching their resolutions, but OSEM has smaller standard deviation.