Abstract

The aim of this paper is to discuss potential advances in PET kinetic models anddirect reconstruction of kinetic parameters. As a prominent example we focus on atypical task in perfusion imaging and derive a system of transport-reaction-diffusionequations, which is able to include macroscopic flow properties in addition to the usual exchange between arteries, veins, and tissues.

For this system we propose an inverse problem of estimating all relevant parame-ters from PET data. We interpret the parameter identification as a nonlinear inverseproblem, for which we formulate and analyze variational regularization approaches.For the numerical solution we employ gradient-based methods and appropriate split-ting methods, which are used to investigate some test cases.