Identifiable reparametrizations of linear compartment models

TL;DR

This paper investigates conditions under which linear compartment models used in biology and pharmacokinetics can be reparametrized to become identifiable, using algebraic and graph-theoretic methods to classify such models.

Contribution

It establishes that an identifiable scaling reparametrization exists if and only if it can be achieved through monomial functions, and begins classifying graphs with this property.

Findings

Existence of an identifiable scaling reparametrization is equivalent to a monomial reparametrization.

Provides conditions for when models can be reparametrized for identifiability.

Partial classification of graphs with identifiable scaling reparametrizations.

Abstract

Identifiability concerns finding which unknown parameters of a model can be quantified from given input-output data. Many linear ODE models, used in systems biology and pharmacokinetics, are unidentifiable, which means that parameters can take on an infinite number of values and yet yield the same input-output data. We use commutative algebra and graph theory to study a particular class of unidentifiable models and find conditions to obtain identifiable scaling reparametrizations of these models. Our main result is that the existence of an identifiable scaling reparametrization is equivalent to the existence of a scaling reparametrization by monomial functions. We also provide partial results beginning to classify graphs which possess an identifiable scaling reparametrization.