Impulsive model of endocrine regulation with a local continuous feedback

Whereas development of mathematical models describing the endocrine system as a whole remains a challenging problem, visible progress has been demonstrated in modeling its subsystems, or axes. Models of hormonal axes portray only the most essential interactions between the hormones and can be described by low-order systems of differential equations. This paper analyzes the properties of a novel model of a hypothalamic-pituitary axis, portraying the interactions in a chain of a release hormone (secreted by the hypothalamus), a tropic hormone (produced by the pituitary gland) and an effector hormone (secreted by a target gland). This model, unlike previously published ones, captures two prominent features of neurohormonal regulation systems, namely, the pulsatile (episodic) production of the release hormone and a complex non-cyclic feedback mechanism that maintains the involved hormone concentrations within certain biological limits. At the same time, the discussed model is analytically tractable; in particular, the existence of a so-called 1-cycle featured by a single pulse over one period is proven mathematically

Impulsive Goodwin’s Oscillator Model of Endocrine Regulation: Local Feedback Leads to Multistability

The impulsive Goodwin’s oscillator (IGO) is a hybrid model that captures complex dynamics arising in continuous systems controlled by pulse-modulated (event-based) feedback. Being conceived to describe pulsatile endocrine regulation, it has also found applications in e.g. pharmacokinetics. The original version of the IGO assumes the continuous part of the model to be a chain of first-order blocks. This paper explores the nonlinear phenomena arising due to the introduction of a local continuous feedback as suggested by the endocrine applications. The effects caused by a nonlinear feedback law parameterized by a Hill function are compared to those arising due to a simpler and previously treated case of affine feedback law. The hybrid dynamics of the IGO are reduced to a (discrete) Poincaré map governing the propagation of the model’s continuous states through the firing instants of the impulsive feedback. Bifurcation analysis of the map reveals in particular that both the local Hill function and affine feedback can lead to multistability, which phenomenon has not been observed in the usual IGO model

Output corridor control via design of impulsive Goodwin's oscillator

In the Impulsive Goodwin's oscillator (IGO), a continuous positive linear time-invariant (LTI) plant is controlled by an amplitude- and frequency-modulated feedback into an oscillating solution. Self-sustained oscillations in the IGO model have been extensively used to portray periodic rhythms in endocrine systems, whereas the potential of the concept as a controller design approach still remains mainly unexplored. This paper proposes an algorithm to design the feedback of the IGO so that the output of the continuous plant is kept (at stationary conditions) within a pre-defined corridor, i.e. within a bounded interval of values. The presented framework covers single-input single-output LTI plants as well as positive Wiener and Hammerstein models that often appear in process and biomedical control. A potential application of the developed impulsive control approach to a minimal Wiener model of pharmacokinetics and pharmacodynamics of a muscle relaxant used in general anesthesia is discussed

Design of Intermittent Control for Cortisol Secretion Under Time-Varying Demand and Holding Cost Constraints

We take the release of stress hormone cortisol as a part of an intermittent control feedback system in contrast to the existing continuous models. By modeling cortisol secretion as an impulsive system, we design an impulsive controller as opposed to a continuous controller for adjusting cortisol levels while maintaining the blood cortisol levels within bounds that satisfy circadian demand and cost constraints. Methods: We develop an analytical approach along with an algorithm for identifying both the timing and amplitude of the control. Results: The model and the algorithm are tested by two examples to illustrate that the proposed approach achieves impulsive control and that the obtained blood cortisol levels render the circadian rhythm and the ultradian rhythm consistent with the known physiology of cortisol secretion. Conclusions: The approach successfully achieves the desired circadian impulsive control, which has great potential to be used in personalizing the medications in order to control the cortisol levels optimally. Significance: This type of bioinspired intermittent controllers can be employed for designing noncontinuous controllers in treating Addisonian disease, which is caused by the adrenal deficiency

Feedback Control of Human Stress with Music Modulation

Mental stress has known detrimental effects on human health, however few algorithmic methods of reducing mental stress have been widely explored. While the act of listening to music has been shown to have beneficial effects for stress reduction, and furthermore, audio players have been designed to selectively choose music and other inputs with the intent of stress reduction, limited work has been conducted for real-time stress reduction with feedback control using physiological input signals such as heart rate or Heart Rate Variability (HRV). This thesis proposes a feedback controller that uses HRV signals from wearable sensors to perform real-time (< 1 second) modulations to music through tempo changes with the goal to regulate and reduce stress levels. A standardized, stress inducing test based on the popular Stroop test is also introduced, which has been shown to induce acute stress in subjects and can be used as a testing benchmark for controller design. Ultimately, a controller is presented that when used is not only able to maintain stress levels during stress-inducing inputs to a human but even provides de-stressing effects beyond baseline performance.No embargoAcademic Major: Electrical and Computer Engineerin

Design of the Impulsive Goodwin's Oscillator in 1-cycle

This paper presents a systematic approach to design a hybrid oscillator that admits an orbitally stable periodic solution of a certain type with pre-defined parameters. The parsimonious structure of the Impulsive Goodwin's oscillator (IGO) is selected for the implementation due to its well-researched rich nonlinear dynamics. The IGO is a feedback interconnection of a positive third-order continuous-time LTI system and a nonlinear frequency and amplitude impulsive modulator. A design algorithm based on solving a bilinear matrix inequality is proposed yielding the slope values of the modulation functions that guarantee stability of the fixed point defining the designed periodic solution. Further, assuming Hill function parameterizaton of the pulse-modulated feedback, the parameters of those rendering the desired stationary properties are calculated. The character of perturbed solutions in vicinity of the fixed point is controlled through localization of the multipliers. The proposed design approach is illustrated by a numerical example. Bifurcation analysis of the resulting oscillator is performed to explore the nonlinear phenomena in vicinity of the designed dynamics

Circadian and Metabolic Effects of Light: Implications in Weight Homeostasis and Health

Daily interactions between the hypothalamic circadian clock at the suprachiasmatic nucleus (SCN) and peripheral circadian oscillators regulate physiology and metabolism to set temporal variations in homeostatic regulation. Phase coherence of these circadian oscillators is achieved by the entrainment of the SCN to the environmental 24-h light:dark (LD) cycle, coupled through downstream neural, neuroendocrine, and autonomic outputs. The SCN coordinate activity and feeding rhythms, thus setting the timing of food intake, energy expenditure, thermogenesis, and active and basal metabolism. In this work, we will discuss evidences exploring the impact of different photic entrainment conditions on energy metabolism. The steady-state interaction between the LD cycle and the SCN is essential for health and wellbeing, as its chronic misalignment disrupts the circadian organization at different levels. For instance, in nocturnal rodents, non-24 h protocols (i.e., LD cycles of different durations, or chronic jet-lag simulations) might generate forced desynchronization of oscillators from the behavioral to the metabolic level. Even seemingly subtle photic manipulations, as the exposure to a "dim light" scotophase, might lead to similar alterations. The daily amount of light integrated by the clock (i.e., the photophase duration) strongly regulates energy metabolism in photoperiodic species. Removing LD cycles under either constant light or darkness, which are routine protocols in chronobiology, can also affect metabolism, and the same happens with disrupted LD cycles (like shiftwork of jetlag) and artificial light at night in humans. A profound knowledge of the photic and metabolic inputs to the clock, as well as its endocrine and autonomic outputs to peripheral oscillators driving energy metabolism, will help us to understand and alleviate circadian health alterations including cardiometabolic diseases, diabetes, and obesity.Fil: Plano, Santiago Andrés. Pontificia Universidad Católica Argentina "Santa María de los Buenos Aires". Instituto de Investigaciones Biomédicas. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Houssay. Instituto de Investigaciones Biomédicas; ArgentinaFil: Casiraghi, Leandro Pablo. Universidad Nacional de Quilmes. Departamento de Ciencia y Tecnología. Laboratorio de Cronobiología; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Garcia Moro, Paula. Universidad Nacional de Quilmes. Departamento de Ciencia y Tecnología. Laboratorio de Cronobiología; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Paladino, Natalia. Universidad Nacional de Quilmes. Departamento de Ciencia y Tecnología. Laboratorio de Cronobiología; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Golombek, Diego Andrés. Universidad Nacional de Quilmes. Departamento de Ciencia y Tecnología. Laboratorio de Cronobiología; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Chiesa, Juan José. Universidad Nacional de Quilmes. Departamento de Ciencia y Tecnología. Laboratorio de Cronobiología; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentin

A STUDY ON DYNAMIC SYSTEMS RESPONSE OF THE PERFORMANCE CHARACTERISTICS OF SOME MAJOR BIOPHYSICAL SYSTEMS

Dynamic responses of biophysical systems - performance characteristic