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The hypothalamic-pituitary-adrenal (HPA) axis is a major system maintaining body homeostasis by regulating the neuroendocrine and sympathetic nervous systems as well modulating immune function. Recent work has shown that the complex dynamics of this system accommodate several stable steady states, one of which corresponds to the hypocortisol state observed in patients with chronic fatigue syndrome (CFS). At present these dynamics are not formally considered in the development of treatment strategies. Here we use model-based predictive control (MPC) methodology to estimate robust treatment courses for displacing the HPA axis from an abnormal hypocortisol steady state back to a healthy cortisol level. This approach was applied to a recent model of HPA axis dynamics incorporating glucocorticoid receptor kinetics. A candidate treatment that displays robust properties in the face of significant biological variability and measurement uncertainty requires that cortisol be further suppressed for a short period until adrenocorticotropic hormone levels exceed 30% of baseline. Treatment may then be discontinued, and the HPA axis will naturally progress to a stable attractor defined by normal hormone levels. Suppression of biologically available cortisol may be achieved through the use of binding proteins such as CBG and certain metabolizing enzymes, thus offering possible avenues for deployment in a clinical setting. Treatment strategies can therefore be designed that maximally exploit system dynamics to provide a robust response to treatment and ensure a positive outcome over a wide range of conditions. Perhaps most importantly, a treatment course involving further reduction in cortisol, even transient, is quite counterintuitive and challenges the conventional strategy of supplementing cortisol levels, an approach based on steady-state reasoning.

Mathematical models of physical systems often contain many more parameters than can be estimated from observations. It is useful to check whether such models are structurally identifiable before choosing an experimental plan for parameter estimation. Many identifiability tests have been proposed in the literature. However, the proposed methods are computationally complex, or even intractable, for systems containing more than a handful of states or parameters. In this work, a linear algebra-based approach for testing ordinary differential equations and index-one differential algebraic equation systems with linear output maps for local structural identifiability is presented. The proposed method is computationally efficient, as it does not require repeated differentiation of the model equations. Furthermore, the proposed model can be used by experimenters to determine which set of measurements should be made in order to estimate specific parameters within the model. The effectiveness of the proposed approach is demonstrated by testing the identifiability of a 15-state model describing NF−κBregulation. The model is shown to be identifiable even if process measurements are related to the state variables by proportionality constants (themselves unknown). Furthermore, the proposed procedure is used to compute a table that relates to each unknown parameter or parameter set a set of state variables whose observation is sufficient for parameter estimation. [ABSTRACT FROM AUTHOR]