Large systems of coupled oscillators subjected to a periodic external drive occur in many situations in physics and biology. Here the simple paradigmatic case of equal strength, all-to-all sine coupling of phase oscillators subject to a sinusoidal external drive, is considered. The stationary states and their stability are determined. Using the stability information and numerical experiments, parameter space phase diagrams showing when different types of system behavior apply are constructed, and the bifurcations marking transitions between different types of behavior are delineated. The analysis is supported by results of direct numerical simulation of an ensemble of oscillators.

Markers from local field potentials, neurochemicals, skin conductance, and hormone concentrations have been proposed as a means of closing the loop in Deep Brain Stimulation (DBS) therapy for treating neuropsychiatric and movement disorders. Developing a closed-loop DBS controller based on peripheral signals would require: (i) the recovery of a biomarker from the source neural stimuli underlying the peripheral signal variations; (ii) the estimation of an unobserved brain or central nervous system related state variable from the biomarker. The state variable is application-specific. It is emotion-related in the case of depression or post-traumatic stress disorder, and movement-related for Parkinson's or essential tremor. We present a method for closing the DBS loop in neuropsychiatric disorders based on the estimation of sympathetic arousal from skin conductance measurements. We deconvolve skin conductance via an optimization formulation utilizing sparse recovery and obtain neural impulses from sympathetic nerve fibers stimulating the sweat glands. We perform this deconvolution via a two-step coordinate descent procedure that recovers the sparse neural stimuli and estimates physiological system parameters simultaneously. We next relate an unobserved sympathetic arousal state to the probability that these neural impulses occur and use Bayesian filtering within an Expectation-Maximization framework for estimation. We evaluate our method on a publicly available data-set examining the effect of different types of stress on peripheral signal changes including body temperature, skin conductance and heart rate. A high degree of arousal is estimated during cognitive tasks, as are much lower levels during relaxation. The results demonstrate the ability to decode psychological arousal from neural activity underlying skin conductance signal variations. The complete pipeline from recovering neural stimuli to decoding an emotion-related brain state using skin conductance presents a promising methodology for the ultimate realization of a closed-loop DBS controller. Closed-loop DBS treatment would additionally help reduce unnecessary power consumption and improve therapeutic gains.

The pulsatile release of cortisol from the adrenal glands is controlled by a hierarchical system that involves corticotropin releasing hormone (CRH) from the hypothalamus, adrenocorticotropin hormone (ACTH) from the pituitary, and cortisol from the adrenal glands. Determining the number, timing, and amplitude of the cortisol secretory events and recovering the infusion and clearance rates from serial measurements of serum cortisol levels is a challenging problem. Despite many years of work on this problem, a complete satisfactory solution has been elusive. We formulate this question as a non-convex optimization problem, and solve it using a coordinate descent algorithm that has a principled combination of (i) compressed sensing for recovering the amplitude and timing of the secretory events, and (ii) generalized cross validation for choosing the regularization parameter. Using only the observed serum cortisol levels, we model cortisol secretion from the adrenal glands using a second-order linear differential equation with pulsatile inputs that represent cortisol pulses released in response to pulses of ACTH. Using our algorithm and the assumption that the number of pulses is between 15 to 22 pulses over 24 hours, we successfully deconvolve both simulated datasets and actual 24-hr serum cortisol datasets sampled every 10 minutes from 10 healthy women. Assuming a one-minute resolution for the secretory events, we obtain physiologically plausible timings and amplitudes of each cortisol secretory event with R 2 above 0.92. Identification of the amplitude and timing of pulsatile hormone release allows (i) quantifying of normal and abnormal secretion patterns towards the goal of understanding pathological neuroendocrine states, and (ii) potentially designing optimal approaches for treating hormonal disorders.

No abstract

No abstract

No 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.

Chronic insomnia is highly prevalent and associated with significant morbidity (i.e., confers risk for multiple psychiatric and medical disorders, such as depression and hypertension). Therefore, it is essential to identify factors that perpetuate this disorder. One candidate factor in the neurobiology of chronic insomnia is hypothalamic-pituitary-adrenal-axis dysregulation, and in particular, alterations in circadian cortisol rhythmicity. Cortisol secretory patterns, however, fluctuate with both a circadian and an ultradian rhythm (i.e., pulses every 60-120 min). Ultradian cortisol pulses are thought to be involved in the maintenance of wakefulness during the day and their relative absence at night may allow for the consolidation of sleep and/or shorter nocturnal awakenings. It is possible that the wakefulness that occurs in chronic insomnia may be associated with the aberrant occurrence of cortisol pulses at night. While cortisol pulses naturally occur with transient awakenings, it may also be the case that cortisol pulsatility becomes a conditioned phenomenon that predisposes one to awaken and/or experience prolonged nocturnal awakenings. The current review summarizes the literature on cortisol rhythmicity in subjects with chronic insomnia, and proffers the suggestion that it may be abnormalities in the ultradian rather than circadian cortisol that is associated with the pathophysiology of insomnia.