HPA Axis Models
1 HPA Axis Dynamics
The HPA axis is a neuroendocrine cascade in which the hypothalamus releases corticotropin-releasing hormone (CRH), which stimulates pituitary adrenocorticotropic hormone (ACTH) release, which in turn stimulates adrenal cortisol production. Cortisol exerts negative feedback at both the hypothalamic and pituitary levels. The model tracks three state variables—CRH (\(H\)), ACTH (\(A\)), and cortisol (\(F\), from Kendall’s compound F)—with a circadian driving function:
\[ \begin{aligned} \frac{d H}{d t} &= \sigma_H \cdot (1 + a_c sin(\frac{2 \pi t}{24} - \phi_c)) \cdot \frac{K_F^{n_F}}{K_F^{n_F} + F^{n_F}} + \sigma_{\text{stress}}(t) - \delta_H H \\ \frac{d A}{d t} &= \sigma_A \cdot \frac{H^{n_H}}{K_H^{n_H} + H^{n_H}} \cdot \frac{K_F^{n_{F A}}}{K_F^{n_{F A}} + F^{n_{F A}}} - \delta_A A \\ \frac{d F}{d t} &= \sigma_F \cdot \frac{A}{K_A + A} - \delta_F F \end{aligned} \tag{1}\]
where \(\sigma_H\), \(\sigma_A\), \(\sigma_F\) are basal secretion rates; \(a_c\) and \(\phi_c\) parameterize the circadian oscillation (peak CRH release in the early morning); \(K_F\) and \(n_F\) control the cortisol negative feedback (Hill-type inhibition); \(\sigma_{\text{stress}}(t)\) represents external stress inputs; and \(\delta_H\), \(\delta_A\), \(\delta_F\) are degradation rates. The Hill exponents \(n_F\) and \(n_{F A}\) determine the sharpness of the feedback switch, with \(n_F \approx 2\)–$ 4$ producing the pulsatile cortisol release pattern observed physiologically.
2 HPA Axis Dysfunction in ME/CFS
ME/CFS patients frequently exhibit subtle HPA axis abnormalities: mildly reduced basal cortisol, blunted cortisol awakening response, and attenuated cortisol response to stress (Cleare et al. 1999). These findings are not consistent with primary adrenal insufficiency (which produces markedly low cortisol) but rather with altered central regulation. The model represents ME/CFS HPA dysfunction through three parameter modifications:
- Enhanced negative feedback sensitivity: increased \(n_F\) (steeper Hill function), causing the system to suppress CRH output at lower cortisol concentrations. This produces the observed low-normal cortisol with preserved ACTH response.
- Reduced circadian amplitude: decreased \(a_c\), flattening the diurnal cortisol rhythm. This is consistent with the blunted cortisol awakening response and may contribute to unrefreshing sleep.
- Altered stress responsiveness: reduced \(\sigma_{\text{stress}}\) gain, reflecting impaired hypothalamic stress signal integration.
The model predicts that these modifications shift the HPA axis to a low-output steady state that is stable under normal conditions but responds inadequately to metabolic or immune challenges. This has direct consequences for the immune models (Chapter Immune System Models): cortisol is a major anti-inflammatory signal, and its deficiency permits sustained immune activation that would normally be self-limiting.
The three-variable HPA model omits several physiologically relevant features: pulsatile hormone release (ultradian rhythms with ~90-minute periodicity), mineralocorticoid vs. glucocorticoid receptor dynamics, and cortisol-binding globulin effects on free cortisol availability. These omissions are acceptable for capturing the qualitative HPA phenotype in ME/CFS but preclude quantitative prediction of cortisol time courses at sub-hourly resolution.
