Differential flatness and Liouvillian character of two HPA axis models

Florentina Nicolau (1) , Hugues Mounier (2)

1 ENSEA - Ecole Nationale Supérieure de l'Electronique et de ses Applications
2 L2S - Laboratoire des signaux et systèmes

In this paper, we study two existing quantitative models of the hypothalamicpituitary-adrenal (HPA) axis from a control systems theory viewpoint, that is, we suppose that we can act on the dynamics of the HPA axis throughout some parameters, which are the system inputs. In particular, we will focus on flatness and Liouvillian properties of the considered control systems of the HPA axis. We first study the minimal three-dimensional model Bangsgaard and Ottesen [2017] which is shown to be flat, and then we consider the more involved and important model proposed in Rao and Androulakis [2019, 2020], with seven states, for which we prove that flatness no longer holds. The more involved model satisfies however a similar but weaker property than flatness: it is a Liouvillian system.

Keywords: HPA axis model flat system Liouvillian systems nonlinear control systems; HPA axis model; flat system; Liouvillian systems; nonlinear control systems

Domains: Computer Science [cs]; Automatic Control Engineering; Life Sciences [q-bio]; Human health and pathology; Tissues and Organs [q-bio.TO]

Florentina Nicolau, Hugues Mounier. Differential flatness and Liouvillian character of two HPA axis models. 9th International Conference on the Foundations of Systems Biology in Engineering (FOSBE 2022), Yannis Androulakis, Aug 2022, Cambridge, Massachusettes, United States. ⟨hal-03979019⟩