Modeling pulsativity in the hypothalamic-pituitary-adrenal hormonal axis

Abstract

A new mathematical model for biological rhythms in the hypothalamic-pituitary-adrenal (HPA) axis is proposed. This model takes the form of a system of impulsive time-delay differential equations which include pulsatile release of adrenocorticotropin (ACTH) by the pituitary gland and a time delay for the release of glucocorticoid hormones by the adrenal gland. Numerical simulations demonstrate that the model's response to periodic and circadian inputs from the hypothalamus are consistent with those generated by recent models which do not include a pulsatile pituitary. In contrast the oscillatory phenomena generated by the impulsive delay equation mode occur even if the time delay is zero. The observation that the time delay merely introduces a small phase shift suggesting that the effects of the adrenal gland are "downstream" to the origin of pulsativity. In addition, the model accounts for the occurrence of ultradian oscillations in an isolated pituitary gland. These observations suggest that principles of pulse modulated control, familiar to control engineers, may have an increasing role to play in understanding the HPA axis.

Figure 1

Schematic representation of the HPA axis studied in this paper. Arrows and bar-headed lines indicate excitatory and inhibitory connections, respectively. Following, the feedback shown by the dashed line is neglected.

Figure 2

Hormonal profiles for the hypothalamic drive $H(t)=H_r(t)H_c(t)$. The function $F_v(V)$ is taken exponentially decreasing with the decay rate $k_s=0,5$, (A,B) profile ACTH and CORT plasma concentrations, respectively.

Figure 3

Comparison of model (black lines) with measured corticosterone (CORT) profiles (red lines) in (A) healthy rats and (B) rats with an electrolytic lesion in the suprachiasmatic nucleus. (A) Shows the mean value for 7 healthy rats and (B) shows the mean value for 5 lesioned rats (for standard errors of the mean, see). In (A) the predicted values of CORT when H(t) represents circadian periodic drive and in (B) $H_r(t)$ for no periodic drive. In both cases $F_v(V)$ is given by an alpha function with $k_s=0.1$.