Parameter identification in medical imaging

Resumen

Positron Emission Tomography is an imaging technique applied in nuclear medicine able to produce images of physiological processes in 2D or 3D. The use of 18F-FDG PET is now a widely established method to quantify tumor metabolism, but other investigations based on different tracers are still far from clinical use, although they offer great opportunities such as radioactive water as a marker of cardiac perfusion. A major obstacle is the need for dynamic image reconstruction from low quality data, which applies in particular for tracers with fast decay like H15 2 O. The aim of this work is to discuss potential advances in Positron Emission Tomography kinetic models and direct reconstruction of kinetic parameters. We derive a set of differential equations able to represent the kinetic behavior of H15 2 O 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. The computation of these distributed parameters as a nonlinear inverse problem, which we solve using variational regularization approaches. For the minimization we use Forward-Backward Splitting.