Structural and practical identifiability of dual-input kinetic modeling in dynamic PET of liver inflammation

Dynamic ¹⁸F-FDG PET with tracer kinetic modeling has the potential to noninvasively evaluate human liver inflammation using the FDG blood-to-tissue transport rate K ₁. Accurate kinetic modeling of dynamic liver PET data and K ₁ quantification requires the knowledge of dual-blood input function from the hepatic artery and portal vein. While the arterial input function can be derived from the aortic region on dynamic PET images, it is difficult to extract the portal vein input function accurately from PET images. The optimization-derived dual-input kinetic modeling approach has been proposed to overcome this problem by jointly estimating the portal vein input function and FDG tracer kinetics from time activity curve fitting. In this paper, we further characterize the model properties by analyzing the structural identifiability of the model parameters using the Laplace transform and practical identifiability using computer simulation based on fourteen patient datasets. The theoretical analysis has indicated that all the kinetic parameters of the dual-input kinetic model are structurally identifiable, though subject to local solutions. The computer simulation results have shown that FDG K ₁ can be estimated reliably in the whole-liver region of interest with reasonable bias, standard deviation, and high correlation between estimated and original values, indicating of practical identifiability of K ₁. The result has also demonstrated the correlation between K ₁ and histological liver inflammation scores is reliable. FDG K ₁ quantification by the optimization-derived dual-input kinetic model is promising for assessing liver inflammation.