Reference Tissue Models for FDG-PET Data: Identifiability and Solvability

A reference tissue model (RTM) is a compartmental approach to the estimation of the kinetic parameters of the tracer flow in a given two-compartment target tissue (TT) without explicit knowledge of the time activity curve (TAC) of tracer concentration in the arterial blood. An "indirect" measure of arterial concentration is provided by the TAC of a suitably chosen one-compartment reference tissue (RT). The RTM is formed by the RT and the TT. In this paper, it is shown that the RTM is identifiable, i.e., the rate constants are uniquely retrievable, provided that a selection criterion for one of the coefficients, which is based on the Logan plot of the RT, is introduced. The exchange coefficients are then evaluated by the application of a Gauss-Newton method, with a regularizing term, accounting for the ill-posedness of the problem. The reliability of the method is validated against synthetic data generated according to realistic conditions, and compared with the full two-compartment model for the TT, here used as 'gold standard.' Finally, the RTM is applied to the estimate of the rate constants in the case of animal models with murine cancer cell lines CT26 inoculated.