Dynamic PET Reconstruction based on a Reaction-Diffusion Model

Positron-Emission Tomography (PET) is an imaging technique in nuclear medicine used to image physiological processes. A major obstacle is the need for dynamic image reconstruction from low quality PET-data, which applies in particular for tracers (radioactive water) with fast decay like H₂¹⁵O when looking for improved spatial resolution. Here we present a model-based approach to overcome those difficulties. We derive a set of differential equations able to represent the kinetic behavior of H₂¹⁵O PET tracers during cardiac perfusion. In this model one takes into account the exchange of materials between artery, tissue and vein, which predicts the tracer activity if the reaction rates, velocities, and diffusion coefficients are known. One then interprets the computation of these distributed parameters (spatially dependent only) as a nonlinear inverse problem, which we solve using variational regularization approaches. For the minimization we use the gradient-based methods and Forward-Backward Splitting. The main advantage is the reduction of the degrees of freedom, which makes the problem overdetermined and thus allows to proceed to low quality data. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)