  The present paper proposes a novel computational method for parametric
imaging of nuclear medicine data. The mathematical procedure is general enough
to work for compartmental models of diverse complexity and is effective in the
determination of the parametric maps of all kinetic parameters governing tracer
flow. We consider applications to [18F]-fluorodeoxyglucose Positron Emission
Tomography (FDG-PET) data and analyze the two-compartment catenary model
describing the standard FDG metabolization by an homogeneous tissue, e.g. the
liver, and the three-compartment non-catenary model representing the renal
physiology. The proposed imaging method starts from the reconstructed FDG-PET
images of tracer concentration and preliminarily applies image processing
algorithms for noise reduction and image segmentation processes for selecting
the region enclosing the organ of physiologic interest. The optimization scheme
solves pixelwise the non-linear inverse problem of determining the kinetic
parameters from dynamic concentration data through a Gauss-Newton iterative
algorithm with a penalty term accounting for the ill-posedness of the problem.
We tested our imaging approach on FDG-PET data of murine models obtained by
means of a dedicated microPET system, and we analyzed different PET slices
containing axial sections of the liver and axial sections of the kidneys. The
reconstructed parametric images proved to be reliable and qualitatively
effective in the description of the local FDG metabolism with respect to the
different physiologies.
