  Positron Emission Tomography using 2-[18F]-2deoxy-D-glucose as radiotracer
(FDG-PET) is currently one of the most frequently applied functional imaging
methods in clinical applications. The interpretation of FDG-PET data requires
sophisticated mathematical approaches able to exploit the dynamical information
contained in this kind of data. Most of these approaches are formulated within
the framework of compartmental analysis, which connects the experimental
nuclear data with unknown tracer coefficients measuring the effectiveness of
the tracer metabolism by means of Cauchy systems of ordinary differential
equations. This paper provides a coincise overview of linear compartmental
methods, focusing on the analytical solution of the forward compartmental
problem and on the specific issues concerning the corresponding compartmental
inverse problem.
