An optimization formulation for characterization of pulsatile cortisol secretion.

Rose T Faghih,Emery N Brown,Munther A Dahleh

doi:10.3389/fnins.2015.00228

Abstract

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.

Highlights

Many hormones that have been well-investigated appear to be released in pulses (Stavreva et al, 2009); for example, cortisol, gonadal steroids, and insulin are released in a pulsatile manner (Veldhuis, 2008)
We propose a physiologically plausible optimization problem for cortisol secretion by making the following assumptions: (1) Cortisol levels can be described by first-order kinetics for cortisol synthesis in the adrenal glands, cortisol infusion to the blood, and cortisol clearance by the liver described in Brown et al (2001), Faghih (2010), and Faghih et al (2011, 2014)
The optimization problem was solved using the parameters given in Example 2 in Table 1 and the upper and lower bounds provided in Tables 2, 3, respectively. It is well-known that cortisol is released in pulses, and based on our results it appears that this method of relaying information might be an optimal approach as opposed to continuous signaling. We formalized this concept by proposing an optimization formulation for a physiologically plausible controller in the anterior pituitary that achieves impulse control as the optimal solution

Summary

Introduction

Many hormones that have been well-investigated appear to be released in pulses (Stavreva et al, 2009); for example, cortisol, gonadal steroids, and insulin are released in a pulsatile manner (Veldhuis, 2008). Pulsatility is a physiological way of increasing hormone concentrations rapidly and sending distinct signaling information to target cells (Veldhuis, 2008). Ultradian pulsatile hormone secretion allows for encoding information via both amplitude and frequency modulation and is a way of frequency encoding (Lightman and Conway-Campbell, 2010; Walker et al, 2010b). Pulsatile signaling permits target receptor recovery, rapid changes in hormone concentration, and greater control, and is more efficient than continuous signaling (Walker et al, 2010b). We investigate pulsatile release of cortisol and propose a novel mathematical formulation that characterizes pulsatile cortisol secretion

Methods

Results

Conclusion