Towards dynamic PET reconstruction under flow conditions: Parameter identification in a PDE model

Louise Reips 1 , Martin Burgerhttp://orcid.org/0000-0003-2619-2912 2 , and Ralf Engbers 2
  • 1 Department of Mathematics, Universidade Federal de Santa Catarina, Campus Blumenau, CEP 89065-300, Blumenau, Brazil
  • 2 Institute for Computational and Applied Mathematics and Cells in Motion Cluster of Excellence, Westfälische Wilhelms-Universität (WWU) Münster, Einsteinstr. 62, 48149, Münster, Germany
Louise Reips
  • Corresponding author
  • Department of Mathematics, Universidade Federal de Santa Catarina, Campus Blumenau, CEP 89065-300, Blumenau, SC, Brazil
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, Martin BurgerORCID iD: http://orcid.org/0000-0003-2619-2912 and Ralf Engbers
  • Institute for Computational and Applied Mathematics and Cells in Motion Cluster of Excellence, Westfälische Wilhelms-Universität (WWU) Münster, Einsteinstr. 62, 48149, Münster, Germany
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Abstract

The aim of this paper is to discuss potential advances in PET kinetic models and direct reconstruction of kinetic parameters. As a prominent example we focus on a typical task in perfusion imaging and derive a system of transport-reaction-diffusion equations, 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 parameters from PET data. We interpret the parameter identification as a nonlinear inverse problem, for which we formulate and analyze variational regularization approaches. For the numerical solution we employ gradient-based methods and appropriate splitting methods, which are used to investigate some test cases.

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