Erol Ba§ar (Ed.) Chaos in Brain Function Containing Original Chapters by E. Basar and T. H. Bullock and Topical Articles Repr'inted from the Springer Series in Brain Dynamics With 66 Figures Springer-Verlag Berlin Heidelberg New York London Paris Tokyo Hong Kong Professor Dr. EROL BA~AR Institute of Physiology Medical University Lubeck Ratzeburger Allee 160 D-2400 Lubeck 1, FRG ISBN-13: 978-3-540-52329-1 e-ISBN-13: 978-3-642-75545-3 DOl: 10.1007/978-3-642-75545-3 Library of Congress Cataloging-in-Publication Data. Chaos in brain function/Erol Bapr, ed. p. cm. "Containing original chapters by E. Ba~ar and T. H. Bullock and topical articles reprinted from the Springer series in brain dynamics." Includes bibliographical references. ISBN 0-387-52329-4 (U.S.: alk. paper) 1. Brain Mathematical models. 2. Chaotic behavior in systems. I. Ba~ar, Ero!. II. Bullock, Theodore Holmes. III. Springer series in brain dynamics. QP376.C47 1990 596'.0188-dc20 90-9560 This work is subject to copyright. 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In every individual case the respective user must check its accuracy by consulting other pharmaceutical literature. Typesetting, printing and bookbinding: Briihlsche Universitiitsdruckerei Giessen 2125/3130-543210 - Printed on acid-free paper Preface The analysis of deterministic chaos is currently an active field in many branches of research. Mathematically all nonlinear dynamical systems with more than two degrees of freedom can generate chaos, becoming unpredictable over a longer time scale. The brain is a nonlinear system par excellence. Accordingly, the concepts of chaotic dynamics have found, in the last five years, an important application in research on compound electrical activity of the brain. The present volume seeks to cover most of the relevant studies in the newly emerging field of chaotic attractors in the brain. This volume is essentially a selection and reorganization of contri butions from the first two volumes in the Springer Series in Brain Dynamics, which were based on conferences held in 1985 and 1987 in Berlin. It also includes (a) a survey of progress in the recording of evoked oscillations of the brain both at the cellular and EEG levels and (b) an agenda for research on chaotic dynamics. Although the first publications pointing out evidence of chaotic behavior of the EEG did not appear until the beginning of 1985, the presence of the pioneering scientists in this field gave the participants at the first conference (volume 1) a strong impulse toward this field. For me, as conference organizer, having been for a long time active in nonlinear EEG research, the integration of this topic was self-evident; however, the enthusiasm of the conference participants was greater than expected. Just two years later, there were three times as many contributions to the second volume of Brain Dynamics, and the analysis of chaotic attractors belonged to the important building blocks. Here the topic "integrative functions of the brain" was dealt with in terms of several multidisciplinary approaches. The response to the conference was so favorable that two additional papers were added to volume 2, and the authors were highly cooperative in making revisions in and additions to their papers. The authors seemed not to be put off by the strong review procedure but rather to be motivated by it. One of the editors of volume 2, T. H. Bullock, insisted on methodological extensions and conceptual additions on the basis of extensive interaction with the authors' and postconference communication among experts. The stimulus to publish this supplementary volume lay in the inter est expressed by several persons to learn about and to start research in this new field. At present it is still not easy to glean the relevant publications, distributed over several special journals and conference VI Preface volumes. For this reason, the editor and the publisher decided that a book of about 170 pages might more easily reach scientists working in this new field than the two full volumes covering a much broader spectrum of neuroscience. Now greater than ever, we need new windows that can add to the growing list of techniques for comprehension of electromagnetic activity and local signs of change in the brain. In the "Epilogue" to Brain Dynamics volume 2 Bullock points out the importance of the new window as follows: "The contributions of Babloyantz, Rossler, Ba~ar and Roschke, Skinner, Mpitsos, and others make me hopeful that we will soon see the dimensionality of many parts of the brain at the same time, second by second, in cats, catfish, and octopus, as rest changes into arousal, directed attention and recognition." In fact, shortly there after it became possible to realize some of these wishes. It is my hope that this book as well will prove to address the genuine research questions of the future. The editor wishes to express his sincere thanks to Professor T. H. Bullock for providing his constructive critique on the preliminary survey and for adding his agenda for research on chaotic dynamics to the present volume. EROL BA~AR Contents Chaotic Dynamics and Resonance Phenomena in Brain Function: Progress, Perspectives and Thoughts E. BA~AR (With 6 Figures). . . . . . . . . . 1 An Agenda for Research on Chaotic Dynamics T. H. BULLOCK. . . . . . . . . . . . . . . 31 Chaotic Dynamics in Brain Activity A. BABLOYANTZ (With 3 Figures) .. 42 The EEG is Not a Simple Noise: Strange Attractors in Intracranial Structures J. RaSCHKE and E. BA~AR (With 7 Figures) . 49 Nonlinear Neural Dynamics in Olfaction as a Model for Cognition W. J. FREEMAN (With 3 Figures) 63 Self-Similarity in Hyperchaotic Data O. E. ROSSLER and J. L. HUDSON (With 4 Figures) . 74 Estimation of Correlation Dimensions from Single and Multichannel Recordings - A Critical View A. BABLOYANTZ (With 4 Figures) . . . . . . . . . . . . 83 Correlation Dimensions in Various Parts of Cat and Human Brain in Different States J. RaSCHKE and E. BA~AR (With 14 Figures) . . 92 Magnetoencephalography and Attractor Dimension: Normal Subjects and Epileptic Patients K. SAERMARK, J. LEBECH, C. K. BAK, and A. SABERS (With 7 Figures) . . . . . . . . . . . . . . .... 110 Chaotic Attractors in a Model of Neocortex: Dimensionalities of Olfactory Bulb Surface Potentials Are Spatially Uniform and Event Related J. E. SKINNER, J. L. MARTIN, C. E. LANDISMAN, M. M. MOMMER, K. FULTON, M. MITRA, W. D. BURTON, and B. SALTZBERG (With 7 Figures) . . . . . . . . . . . . . . ....... 119 VIII Contents Dimensional Analysis of the Waking EEG K. E. GRAF and T. ELBERT (With 7 Figures) . . . . . . . . . 135 Analysis of Strange Attractors in EEGs with Kinesthetic Experience and 4-D Computer Graphics W. J. FREEMAN (With 4 Figures) . . . . . . . . . .. . 153 Chaos in Brain Function and the Problem of Nonstationarity: A Commentary G. J. MpITSOS . . . . . . . . . . . . . . . . . . . . . . 162 List of Contributors BABLOYANTZ, A., Department of Physical Chemistry II, Free University of Brussels, P.O. Box 231, Boulevard du Triomphe, B-1050 Brussels, Belgium BAK, C. K., Physics Laboratory I, Technical University of Denmark, DK-2800 Lyngby, Denmark BA~AR, E., Institute of Physiology, Medical University Lubeck, Ratzeburger Allee 160, D-2400 Lubeck, FRO BULLOCK, T. H., Department of Neurosciences A-001, School of Medicine, University of California, San Diego, La Jolla, CA 92093, USA BURTON, W. D., Neurosciences Signal Analysis Laboratory, Department of Psychiatry and Behavioral Science, University of Texas Medical School, Houston, TX 77030, USA ELBERT, T., Psychiatry, 116A3, Veterans Administration Medical Center, 3801 Miranda, Palo Alto, CA 94304, USA FREEMAN, W. J., Department of Physiology-Anatomy, University of California, Berkeley, CA 94720, USA FULTON, K., Neurophysiology Section, Department of Neurology and Neuroscience Program, Baylor College of Medicine, Houston, TX 77030, USA ORAF, K. E., Department of Clinical and Physiological Psychology, University of Tubingen, Oartenstr. 29, D-7400 Tubingen, FRO HUDSON, J. L., Department of Chemical Engineering, University of Virginia, Charlottesville, VA 22901, USA LANDISMAN, C. E., Neurophysiology Section, Department of Neurology and Neuroscience Program, 'Baylor College of Medicine, Houston, TX 77030, USA LEBECH, J., Physics Laboratory I, Technical University of Denmark, DK-2800 Lyngby, Denmark MARTIN, J. L., Neurophysiology Section, Department of Neurology and Neuroscience Program, Baylor College of Medicine, Houston, TX 77030, USA x List of Contributors MITRA, M., Neurophysiology Section, Department of Neurology and Neuroscience Program, Baylor College of Medicine, Houston, TX 77030, USA MOMMER, M. M., Neurophysiology Section, Department of Neurology and Neuroscience Program, Baylor College of Medicine, Houston, TX 77030, USA MpITsos, G. J., M.O. Hatfield Marine Science Center, Oregon State University, Newport, OR 97365, USA RaSCHKE, J., Institute of Physiology, Medical University Lubeck, Ratzeburger Allee 160, D-2400 Lubeck; FRG ROSSLER, O. E., Institute of Physical and Theoretical Chemistry, University of Tubingen, Auf der Morgenstelle 8, D-7400 Tubingen, FRG SABERS, A., Department of Neurology, Hvidovre Hospital, DK-2650 Hvidovre, Denmark SAERMARK, K., Physics Laboratory I, Technical University of Denmark, DK-2800 Lyngby, Denmark SALTZBERG, B., Neuroscience Signal Analysis Laboratory, Department of Psychiatry and Behavioral Science, University of Texas Medical School, Houston, TX 77030, USA SKINNER, J. E., Neurophysiology Section, Department of Neurology and Neuroscience Program, Baylor College of Medicine, Houston, TX 77030, USA Chaotic Dynamics and Resonance Phenomena in Brain Function: Progress, Perspectives, and Thoughts E. BA~AR 1 Preliminary Remarks My main goal by writing this survey is to try to bridge our knowledge in chaos research with analysis of brain oscillatory phenomena both at the neuronal and the EEG level. In the years following the first measurement of human EEG by Hans Berger and important developments by Lord Adrian and later Grey Walter, the pure EEG research remained somewhat in the shadow of new discoveries based on single-neuron recordings. From the beginning of 1960s the use of signal averagers enabled EEG research scientists to extract the evoked potentials from the so called random-noise EEG. In this context, the event-related potentials that con tributed highly to the understanding of cognitive functions and to clinical diag nostics were considered as deterministic signals whereas EEG was considered mostly as pure noise. In 1980 I stated strongly that we must not always consider the spontaneous oscillations in brain electrical activity as a background noise. On the contrary, in my own approach on field potentials, I assumed that the EEG must be con sidered as one of the most important oscillations affecting the production and conduction of signaling in the brain (Ba~ar 1980). This view was based on experi ments with compound potentials from the cat and human brain. In this approach some EEG fragments were considered as internal evoked potentials coming from yet unknown or hidden sources. Further, evoked potentials were considered as forced (or evoked) oscillations following known and deterministic inputs. Later, I tentatively assumed that the EEG has a strange attractor (Ba~ar 1983 a, b). Ac cording to these earlier steps and thoughts in considering the EEG as a quasi deterministic signal, I brought experts together at conferences in 1983, 1985, and 1987. The most important development in the field of chaotic dynamics is to me, without any question, the discovery by Babloyantz et al. (1985) who showed the strange attract or behavior of EEG during the slow-wave sleep (SWS) stage. In the same year we were able to show similar results from intracranial structures of the cat brain; Rapp and coworkers published results on chaotic dynamics in the same year (Raschke and Ba~ar 1985; Rapp et al. 1985 a, b). With these introductory remarks I emphasize that the slogan "The EEG is not noise, but is a quasideterministic signal" came from a need for interpreting results of experiments by many neurophysiologists. The new development in research of "chaos in brain function" is fascinating. However, this field cannot be considered as an isolated research field. In the period of 1985-1989 during which chaotic EEG results were substantially developed other noteworthy progress in the study