An optimization formulation for characterization of pulsatile cortisol secretion

Cortisol is released to relay information to cells to regulate metabolism and reaction to stress and inflammation. In particular, cortisol is released in the form of pulsatile signals. This low-energy method of signaling seems to be more efficient than continuous signaling. We hypothesize that there is a controller in the anterior pituitary that leads to pulsatile release of cortisol, and propose a mathematical formulation for such controller, which leads to impulse control as opposed to continuous control. We postulate that this controller is minimizing the number of secretory events that result in cortisol secretion, which is a way of minimizing the energy required for cortisol secretion; this controller maintains the blood cortisol levels within a specific circadian range while complying with the first order dynamics underlying cortisol secretion. We use an ℓ0-norm cost function for this controller, and solve a reweighed ℓ1-norm minimization algorithm for obtaining the solution to this optimization problem. We use four examples to illustrate the performance of this approach: (i) a toy problem that achieves impulse control, (ii) two examples that achieve physiologically plausible pulsatile cortisol release, (iii) an example where the number of pulses is not within the physiologically plausible range for healthy subjects while the cortisol levels are within the desired range. This novel approach results in impulse control where the impulses and the obtained blood cortisol levels have a circadian rhythm and an ultradian rhythm that are in agreement with the known physiology of cortisol secretion. The proposed formulation is a first step in developing intermittent controllers for curing cortisol deficiency. This type of bio-inspired pulse controllers can be employed for designing non-continuous controllers in brain-machine interface design for neuroscience applications.