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
