Compartmental analysis of dynamic nuclear medicine data: models and identifiability

TL;DR

This paper investigates the mathematical identifiability of parameters in compartmental models used in nuclear medicine, establishing conditions for uniqueness in two- and three-compartment systems, foundational for accurate tracer coefficient estimation.

Contribution

It provides the first comprehensive analysis of parameter identifiability in general n-dimensional compartmental models, with specific results for two- and three-compartment cases.

Findings

Uniqueness results for two- and three-compartment models

Framework for tracer coefficient estimation in nuclear medicine

Foundation for applying regularization in subsequent work

Abstract

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.