Springer Modeling Phase Transitions in the Brain: 4 (Springer Series in Computational Neuroscience, 4)

There are two very distinctive approaches to developing mathematical models for brain function and behavior. One approach, exemplified by Traub and colleagues [1] and by the Blue Brain project [2] is to start with a detailed, biophysically accurate description of a single neuron, and then to scale up by assembling hundreds or thousands of interacting neurons to create neural populations, examining the assembly for interesting collective behaviors that emerge spontaneously from these interactions. Review From the book reviews:“Excellent description of neurophysiology of dynamics systems, both linear and nonlinear. Highly recommended.” (Joseph J. Grenier, Amazon.com, October, 2014) From the Back Cover Foreword by Walter J. Freeman. The induction of unconsciousness using anesthetic drugs demonstrates that the cerebral cortex can operate in two very different  modes: alert and responsive versus unaware and quiescent.  But the states of wakefulness and sleep are not single-neuron properties---they emerge as bulk properties of cooperating populations of neurons, with the switchover between states being similar to the physical change of phase observed when water freezes or ice melts.  Some brain-state transitions, such as sleep cycling, anesthetic induction, epileptic seizure, are obvious and detected readily with a few EEG electrodes; others, such as the emergence of gamma rhythms during cognition, or the ultra-slow BOLD rhythms of relaxed free-association, are much more subtle.  The unifying theme of this book is the notion that all of these bulk changes in brain behavior can be treated as phase transitions between distinct brain states. "Modeling Phase Transitions in the Brain" contains chapter contributions from leading researchers who apply state-space methods, network models, and biophysically-motivated continuum approaches to investigate a range of neuroscientifically relevant problems that include analysis of nonstationary EEG time-series; network topologies that limit epileptic spreading; saddle--node bifurcations for anesthesia, sleep-cycling, and the wake--sleep switch; prediction of dynamical and noise-induced spatiotemporal instabilities underlying BOLD, alpha-, and gamma-band EEG oscillations, gap-junction-moderated Turing structures, and Hopf--Turing interactions leading to cortical waves.  Written for: Researchers, clinicians, physicians, neurologists About the editors: Alistair Steyn-Ross and Moira Steyn-Ross are computational and theoretical physicists in the Department of Engineering, University of Waikato, New Zealand.  They share a long-standing interest in the application of physics-based methods to gain insight into the emergent behavior of complex biological systems such as single neurons and interacting neural populations.