Identifiability analysis and parameter identification of an in vivo ligand-receptor model from PET data

Identifiability problem is a very important topic in the framework of model justification and not accounting for it during the modeling procedure can lead to meaningless results. While studying the receptor-ligand model parameter estimation from dynamic positron emission tomography data, each of the three possible conclusions to the identifiability problem (i.e., unidentifiable model, multiple solutions, or unique solution) are reached depending on the experimental protocol used. The identification of the model parameters from data obtained with a single tracer injection leads to disappointing numerical results since most of the parameters have to be considered as unidentifiable. A protocol including two injections, a first injection of the labeled ligand and a second injection of the cold ligand (displacement experiment) leads to two very different numerical solutions, which is surprising since such multiplicity of solutions was not indicated by a preliminary theoretical identifiability study. We show that a three-injections protocol, including both a displacement and coinjection experiment, allows to determine which of these two solutions is biologically valid.