Phase Response Curves in Neuroscience


Book Description

This book will track advances in the application of phase response (PR) analysis to the study of electrically excitable cells, focusing on applications of PR analysis in the computational neurosciences. This proposal was motivated by discussions with colleagues at the 2007 meeting of the Organization for Computational Neuroscience (OCNS) and further motivated by the success of a workshop at the 2008 OCNS meeting this past July. At that meeting the editors hosted a workshop entitled A dialogue for theoreticians and experimentalists: What is phase response analysis, and what can it tell us about neurons and networks? Invited speakers used mathematical, modeling, and experimental results to illustrate how phase response analysis has been used to reveal or describe neuronal and neuronal population dynamics. This was the most well-attended workshop of the meeting and was standing room only.




Phase Response Curves in Neuroscience


Book Description

Inspired by response to a workshop at the 2008 OCNS meeting, this book tracks advances in the application of phase response (PR) analysis to the study of electrically excitable cells, focusing on applications of PR analysis in the computational neurosciences.




Phase Response Curves in Neuroscience


Book Description

This book will track advances in the application of phase response (PR) analysis to the study of electrically excitable cells, focusing on applications of PR analysis in the computational neurosciences. This proposal was motivated by discussions with colleagues at the 2007 meeting of the Organization for Computational Neuroscience (OCNS) and further motivated by the success of a workshop at the 2008 OCNS meeting this past July. At that meeting the editors hosted a workshop entitled A dialogue for theoreticians and experimentalists: What is phase response analysis, and what can it tell us about neurons and networks? Invited speakers used mathematical, modeling, and experimental results to illustrate how phase response analysis has been used to reveal or describe neuronal and neuronal population dynamics. This was the most well-attended workshop of the meeting and was standing room only.




Sleep and Anesthesia


Book Description

Sleep and anesthesia resemble in many ways at a first glance. The most prominent common feature of course is the loss of consciousness, i.e. the loss of awareness of external stimuli. However a closer look at the loss of consciousness reveals already a difference between sleep and anesthesia: anesthesia is induced by an anesthetic drug whereas we may fall asleep without external cause. Other questions may arise about the difference of the two effects: do we dream during surgery under anesthesia, do we feel pain during sleep? Essentially, we may ask: what is common and what are the differences between sleep and anesthesia? To answer these questions, we may take a look at the neural origin of both effects and the involved physiological pathways. In which way do they resemble? Moreover, we ask what are the detailed features of normal sleep and general anesthesia as applied during surgery and which features exist in both phenomena? If yes in which way? To receive answers to these questions, it is necessary to consider several experimental techniques that reveal underlying neural mechanisms of sleep and anesthesia. Moreover, theoretical models of neural activity may model both phenomena and comes up with predictions or even theories on the underlying mechanisms. Such models may attack several different description levels, from the microscopic level of single neurons to the macroscopic level of neural populations. Such models may give deeper insight into the phenomena if their assumptions are based on experimental findings and their predictions can be compared to experimental results. This comparison step is essential for valuable theoretical models. The book is motivated by two successful workshops on anesthesia and sleep organized during the Computational Neuroscience Conferences in Toronto in 2007 and in Berlin 2009. It aims to cover all the previous aspects with a focus on the link to experimental findings. It elucidates important issues in theoretical models that at the same time reflect some current major research interests. Moreover it considers some diverse issues which are very important to get an overview of the fields. For instance, the book discusses not only neural activity in the brain but also the effects of general anesthesia on the cardio-vascular system and the spinal cord in the context of analgesia. In addition, it considers different experimental techniques on various spatial scales, such as fMRI and EEG-experiments on the macroscopic scale and single neuron and LFP-measurements on the microscopic scale. In total all book chapters reveal aspects of the neural correlates of sleep and anesthesia motivated by experimental data. This focus on the neural mechanism in the light of experimental data is the common feature of the topics and the chapters. In addition, the book aims to clarify the shared physiological mechanisms of both phenomena, but also reveal their physiological differences.




Mathematical Foundations of Neuroscience


Book Description

This book applies methods from nonlinear dynamics to problems in neuroscience. It uses modern mathematical approaches to understand patterns of neuronal activity seen in experiments and models of neuronal behavior. The intended audience is researchers interested in applying mathematics to important problems in neuroscience, and neuroscientists who would like to understand how to create models, as well as the mathematical and computational methods for analyzing them. The authors take a very broad approach and use many different methods to solve and understand complex models of neurons and circuits. They explain and combine numerical, analytical, dynamical systems and perturbation methods to produce a modern approach to the types of model equations that arise in neuroscience. There are extensive chapters on the role of noise, multiple time scales and spatial interactions in generating complex activity patterns found in experiments. The early chapters require little more than basic calculus and some elementary differential equations and can form the core of a computational neuroscience course. Later chapters can be used as a basis for a graduate class and as a source for current research in mathematical neuroscience. The book contains a large number of illustrations, chapter summaries and hundreds of exercises which are motivated by issues that arise in biology, and involve both computation and analysis. Bard Ermentrout is Professor of Computational Biology and Professor of Mathematics at the University of Pittsburgh. David Terman is Professor of Mathematics at the Ohio State University.




Neural Control of Locomotion


Book Description




Rhythms of the Brain


Book Description

Studies of mechanisms in the brain that allow complicated things to happen in a coordinated fashion have produced some of the most spectacular discoveries in neuroscience. This book provides eloquent support for the idea that spontaneous neuron activity, far from being mere noise, is actually the source of our cognitive abilities. It takes a fresh look at the coevolution of structure and function in the mammalian brain, illustrating how self-emerged oscillatory timing is the brain's fundamental organizer of neuronal information. The small-world-like connectivity of the cerebral cortex allows for global computation on multiple spatial and temporal scales. The perpetual interactions among the multiple network oscillators keep cortical systems in a highly sensitive "metastable" state and provide energy-efficient synchronizing mechanisms via weak links. In a sequence of "cycles," György Buzsáki guides the reader from the physics of oscillations through neuronal assembly organization to complex cognitive processing and memory storage. His clear, fluid writing-accessible to any reader with some scientific knowledge-is supplemented by extensive footnotes and references that make it just as gratifying and instructive a read for the specialist. The coherent view of a single author who has been at the forefront of research in this exciting field, this volume is essential reading for anyone interested in our rapidly evolving understanding of the brain.




Neuronal Dynamics


Book Description

This solid introduction uses the principles of physics and the tools of mathematics to approach fundamental questions of neuroscience.




Vertebrate Circadian Systems


Book Description




Biological Clocks, Rhythms, and Oscillations


Book Description

An introduction to the mathematical, computational, and analytical techniques used for modeling biological rhythms, presenting tools from many disciplines and example applications. All areas of biology and medicine contain rhythms, and these behaviors are best understood through mathematical tools and techniques. This book offers a survey of mathematical, computational, and analytical techniques used for modeling biological rhythms, gathering these methods for the first time in one volume. Drawing on material from such disciplines as mathematical biology, nonlinear dynamics, physics, statistics, and engineering, it presents practical advice and techniques for studying biological rhythms, with a common language. The chapters proceed with increasing mathematical abstraction. Part I, on models, highlights the implicit assumptions and common pitfalls of modeling, and is accessible to readers with basic knowledge of differential equations and linear algebra. Part II, on behaviors, focuses on simpler models, describing common properties of biological rhythms that range from the firing properties of squid giant axon to human circadian rhythms. Part III, on mathematical techniques, guides readers who have specific models or goals in mind. Sections on “frontiers” present the latest research; “theory” sections present interesting mathematical results using more accessible approaches than can be found elsewhere. Each chapter offers exercises. Commented MATLAB code is provided to help readers get practical experience. The book, by an expert in the field, can be used as a textbook for undergraduate courses in mathematical biology or graduate courses in modeling biological rhythms and as a reference for researchers.