Perturbing the Hypothalamic–Pituitary–Adrenal Axis: A Mathematical Model for Interpreting PTSD Assessment Tests

Abstract

We use a dynamical systems model of the hypothalamic–pituitary–adrenal (HPA) axis to understand the mechanisms underlying clinical protocols used to probe patient stress response. Specifically, we address dexamethasone (DEX) and ACTH challenge tests, which probe pituitary and adrenal gland responses, respectively. We show that some previously observed features and experimental responses can arise from a bistable mathematical model containing two steady-states, rather than relying on specific and permanent parameter changes due to physiological disruption. Moreover, we show that the timing of a perturbation relative to the intrinsic oscillation of the HPA axis can affect challenge test responses. Conventional mechanistic hypotheses supported and refuted by the challenge tests are reexamined by varying parameters in our mathematical model associated with these hypotheses. We show that (a) adrenal hyposensitivity can give rise to the responses seen in ACTH challenge tests and (b) enhanced cortisol-mediated suppression of the pituitary in subjects with PTSD is not necessary to explain the responses observed in DEX stress tests. We propose a new two-stage DEX/external stressor protocol to more clearly distinguish between the conventional hypothesis of enhanced suppression of the pituitary and bistable dynamics hypothesized in our model.

Mathematical modeling of depressive disorders: Circadian driving, bistability and dynamical transitions

“…The model we use in this paper is a compact, reduced description of the HPA neuroendocrine system that is derived from previous work [53] , [49] , [54] , [48] , [50] , [51] , [52] , [55] , [56] . The simplifications introduced allow us to incorporate the circadian drive and perform complete analytical analyses.…”

“…The simplifications introduced allow us to incorporate the circadian drive and perform complete analytical analyses. We begin by illustrating the full, initial model which includes five variables that represent the most relevant hormones and receptors involved in stress response [55] , [56] . Later we show how our new, compact two-variable system is obtained.…”

“…The neuroendocrine dynamics of the HPA axis has been well-studied using mathematical models that describe the abundances of CRH, ACTH, cortisol, and glucocorticoid receptors and their dynamics in response to external inputs [44] , [45] , [46] , [47] , [48] , [49] , [50] , [51] , [52] , [53] , [54] , [55] , [56] . These models include physiologically motivated feedback loops and delays that allow for the emergence of the ultradian oscillations.…”

“…Separating CRH dynamics into a fast CRH release and a slow CRH synthesis yields a larger parameter space and higher likelihood for the emergence of the healthy-diseased bistable configuration [55] , [56] . Apart from the action of external stressors, the time-varying input into the hypothalamus can also model cognitive behavioral therapy (CBT) or exposure therapy (ET), where patients are subjected to psychological interventions or exposed to the stressor in a controlled manner to relieve them of depression, PTSD and other stress related symptoms.…”

“…Apart from the action of external stressors, the time-varying input into the hypothalamus can also model cognitive behavioral therapy (CBT) or exposure therapy (ET), where patients are subjected to psychological interventions or exposed to the stressor in a controlled manner to relieve them of depression, PTSD and other stress related symptoms. Within these dynamical systems models, external inputs can trigger transitions between the healthy and diseased states depending on input duration, amplitude and time of application relative to the intrinsic oscillations of the ultradian cortisol pulses [55] , [56] .…”