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The aim of this paper is to discuss potential advances in PET kinetic modelsand direct reconstruction of kinetic parameters. As a prominent example wefocus on a typical task in perfusion imaging and derive a system oftransport-reaction-diffusion equations, which is able to include macroscopicflow properties in addition to the usual exchange between arteries, veins, andtissues.  For this system we propose an inverse problem of estimating all relevantparameters from PET data. We interpret the parameter identification as anonlinear inverse problem, for which we formulate and analyze variationalregularization approaches. For the numerical solution we employ gradient-basedmethods and appropriate splitting methods, which are used to investigate sometest cases.

Towards Dynamic PET Reconstruction under Flow Conditions: Parameter Identification in a PDE Model