Compartmental analysis of dynamic nuclear medicine data: models and identifiability
It provides foundational theoretical guarantees for parameter identifiability in compartmental modeling, which is critical for accurate quantitative analysis in nuclear medicine.
This paper addresses the identifiability problem in compartmental models for dynamic nuclear medicine data, providing uniqueness results for two- and three-compartment models. It establishes a theoretical framework for tracer coefficient estimation.
Compartmental models based on tracer mass balance are extensively used in clinical and pre-clinical nuclear medicine in order to obtain quantitative information on tracer metabolism in the biological tissue. This paper is the first of a series of two that deal with the problem of tracer coefficient estimation via compartmental modelling in an inverse problem framework. Specifically, here we discuss the identifiability problem for a general n-dimension compartmental system and provide uniqueness results in the case of two-compartment and three-compartment compartmental models. The second paper will utilize this framework in order to show how non-linear regularization schemes can be applied to obtain numerical estimates of the tracer coefficients in the case of nuclear medicine data corresponding to brain, liver and kidney physiology.