Next Article in Journal
A Note of Caution on Maximizing Entropy
Next Article in Special Issue
Fractal Structure and Entropy Production within the Central Nervous System
Previous Article in Journal
Panel I: Connecting 2nd Law Analysis with Economics, Ecology and Energy Policy
Previous Article in Special Issue
Searching for Conservation Laws in Brain Dynamics—BOLD Flux and Source Imaging
Article Menu

Export Article

Open AccessArticle
Entropy 2014, 16(7), 3939-4003; doi:10.3390/e16073939

Human Brain Networks: Spiking Neuron Models, Multistability, Synchronization, Thermodynamics, Maximum Entropy Production, and Anesthetic Cascade Mechanisms

1
The School of Aerospace Engineering, Georgia Institute of Technology, Atlanta, GA 30332, USA
2
Department of Mechanical Engineering, Texas Tech University, Lubbock, TX 79409-1021, USA
3
Department of Anesthesiology, Northeast Georgia Medical Center, Gainesville, GA 30503 USA
*
Author to whom correspondence should be addressed.
Received: 6 May 2014 / Revised: 19 June 2014 / Accepted: 3 July 2014 / Published: 17 July 2014
(This article belongs to the Special Issue Entropy in Human Brain Networks)

Abstract

Advances in neuroscience have been closely linked to mathematical modeling beginning with the integrate-and-fire model of Lapicque and proceeding through the modeling of the action potential by Hodgkin and Huxley to the current era. The fundamental building block of the central nervous system, the neuron, may be thought of as a dynamic element that is “excitable”, and can generate a pulse or spike whenever the electrochemical potential across the cell membrane of the neuron exceeds a threshold. A key application of nonlinear dynamical systems theory to the neurosciences is to study phenomena of the central nervous system that exhibit nearly discontinuous transitions between macroscopic states. A very challenging and clinically important problem exhibiting this phenomenon is the induction of general anesthesia. In any specific patient, the transition from consciousness to unconsciousness as the concentration of anesthetic drugs increases is very sharp, resembling a thermodynamic phase transition. This paper focuses on multistability theory for continuous and discontinuous dynamical systems having a set of multiple isolated equilibria and/or a continuum of equilibria. Multistability is the property whereby the solutions of a dynamical system can alternate between two or more mutually exclusive Lyapunov stable and convergent equilibrium states under asymptotically slowly changing inputs or system parameters. In this paper, we extend the theory of multistability to continuous, discontinuous, and stochastic nonlinear dynamical systems. In particular, Lyapunov-based tests for multistability and synchronization of dynamical systems with continuously differentiable and absolutely continuous flows are established. The results are then applied to excitatory and inhibitory biological neuronal networks to explain the underlying mechanism of action for anesthesia and consciousness from a multistable dynamical system perspective, thereby providing a theoretical foundation for general anesthesia using the network properties of the brain. Finally, we present some key emergent properties from the fields of thermodynamics and electromagnetic field theory to qualitatively explain the underlying neuronal mechanisms of action for anesthesia and consciousness.
Keywords: multistability; semistability; synchronization; biological networks; spiking neuron models; synaptic drive; discontinuous systems; thermodynamics; free energy; entropy; consciousness; arrow of time; excitatory and inhibitory neurons; Brownian motion; Wiener process; general anesthesia multistability; semistability; synchronization; biological networks; spiking neuron models; synaptic drive; discontinuous systems; thermodynamics; free energy; entropy; consciousness; arrow of time; excitatory and inhibitory neurons; Brownian motion; Wiener process; general anesthesia
This is an open access article distributed under the Creative Commons Attribution License (CC BY 3.0).

Scifeed alert for new publications

Never miss any articles matching your research from any publisher
  • Get alerts for new papers matching your research
  • Find out the new papers from selected authors
  • Updated daily for 49'000+ journals and 6000+ publishers
  • Define your Scifeed now

SciFeed Share & Cite This Article

MDPI and ACS Style

Haddad, W.M.; Hui, Q.; Bailey, J.M. Human Brain Networks: Spiking Neuron Models, Multistability, Synchronization, Thermodynamics, Maximum Entropy Production, and Anesthetic Cascade Mechanisms. Entropy 2014, 16, 3939-4003.

Show more citation formats Show less citations formats

Related Articles

Article Metrics

Article Access Statistics

1

Comments

[Return to top]
Entropy EISSN 1099-4300 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert
Back to Top