Model-based therapeutic correction of hypothalamic-pituitary-adrenal axis dysfunction

Abstract

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.

Figure 1. Steady states of the HPA axis system.

Steady-state concentration of CRH (x₁), ACTH (x₂), GR (x₃) and cortisol (x4) as a function of the external stressor f for the model expressed as system H. The system naturally accommodates 3 stable steady states at rest f = 0 and over a broad range of increasing values for f.

Figure 2. Migration of cortisol concentration from one stable point to another.

Concentration of circulating cortisol plotted as a function of the external stressor f. A first idealized trajectory (red - -) describes the displacement of the system from rest to a peak cortisol concentration followd by an eventual lapse into a chronic hypocortisolic state. A second idealized trajectory (green - -) illustrates the effects of treatment. Here removal of cortisol can be thought of as a negative stress f. An increase in ACTH concentration of ∼30% above baseline serves as a signal that the treatment may be discontinued.

Figure 3. Idealized corrective control action.

Concentrations of CRH (x₁), ACTH (x₂), GR (x₃) and cortisol (x4) as a function of time in response to an ideal externally applied perturbation in cortisol u(t). The negative supplement in cortisol signifies a pharmaceutical removal or inactivation of circulating cortisol. ACTH concentration serves to monitor the progress of the treatment which is discontinued when ACTH increases by ∼30% over baseline.

Figure 4. A suboptimal but clinically realistic control treatment.

Concentrations of CRH (x₁), ACTH (x₂), GR (x₃) and cortisol (x4) as a function of time in response to a suboptimal but more realistic externally applied perturbation in cortisol u(t). Once again the negative supplement in cortisol signifies a pharmaceutical removal or inactivation of circulating cortisol. Note a less severe reduction in cortisol is applied over a longer period. The corresponding ACTH response is slower but the threshold concentration for cessation of treatment remains the same.

Figure 5. Balancing intensity and duration of treatment.

Diagram of the minimal perturbation in normalized circulating cortisol u(t) as a function of duration of treatment. In one extreme instance the perturbation in cortisol would be so small that no treatment would be effective regardless of how much treatment prolonged. Conversely an excessively short treatment would also be ineffective regardless of the intensity of cortisol reduction.