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The Head and Heart of Chaos: 
Nonlinear Dynamics in Biological Systems

National Institutes of Health,
Office of Medical Applications of Research Workshop
June 15-16, 1992

Confernce artwork depicting a black background with bright pink and orange zig-zag  pattern overlayed.

This statement is more than five years old and is provided solely for historical purposes. Due to the cumulative nature of medical research, new knowledge has inevitably accumulated in this subject area in the time since the statement was initially prepared. Thus some of the material is likely to be out of date, and at worst simply wrong. For reliable, current information on this and other health topics, we recommend consulting the National Institutes of Health's MedlinePlus http://www.nlm.nih.gov/medlineplus/.

This statement was originally published as: The head and heart of chaos: Nonlinear dynamics in biological systems. Executive Report. Workshop summary: 1992 Jun 15-16. Bethesda (MD): National Institutes of Health, Office of Medical Applications of Research; 1992.

For making bibliographic reference to the statement in the electronic form displayed here, it is recommended that the following format be used: The head and heart of chaos: Nonlinear dynamics in biological systems. NIH Technol Assess Statement Online 1992 Jun 15-16


Preface

Physical systems and biological systems both exhibit complex behaviors within short time spans. The nonlinear processes generating these complicated changes offer potentially fertile fields for assessing the usefulness of mathematical approaches developed to clarify and to understand the underlying dynamics. Among them, those derived from deterministic chaos, as well as other areas of nonlinear dynamics, have, for the most part, been accepted by the physical science and engineering communities with little fanfare or significant controversy. However, the life sciences have encountered more variable responses: many have been enthusiastic, some to the point of uncritical acceptance; more have been skeptical, some to the point of hypercritical rejection; most have not had enough exposure to the ideas to express an informed opinion.

In the Fall of 1991, a meeting of interested scientists and research administrators was held at the National Institutes of Health (NIH) in order to discuss the state of the art of chaos theory and related subjects as they may apply to biomedical research. The Office of Medical Applications of Research perceived a diversity of strongly held views among biomedical researchers, as well as many who were not yet informed. A workshop was authorized as a means of providing a platform for free discussion and the exchange of information among the participants and audience. Despite the popular interest in chaos theory, few attending the workshop were expected to have the mathematical competence needed to understand the subtleties of the subject. Therefore, an entry-level program was planned. The intention was to bring individuals to the rostrum who are known not only for their research interests, but also for their communication skills. The planning committee worked to structure the program to meet this goal. The invited participants included people known by their peers for their outspoken positions about chaos theory and nonlinear dynamics, both pro and con. This report is an attempt to summarize the predominant themes and issues of the workshop.

Introduction To the Head and Heart of Chaos Nonlinear Dynamics in Biological Systems

The emerging science of deterministic chaos has attracted attention with fractal images of unparalleled beauty and ordered intricacy that can be easily appreciated. Is this new science useful for biomedical research? The underlying theories, applications, and ramifications for biological systems are obscure to most people, even within the scientific community. The intent of this workshop is to provide basic information to the generally well-informed, interested observer who may be enthusiastic, confused, or skeptical about the utility of these new areas to biomedical research and who is interested in learning more.

Dynamic systems, such as those found in life processes at essentially all levels of physiological organization, generate highly complex and variable data sets. This workshop will compare and contrast new methodologies based on nonlinear dynamics and chaos theory with more established analytical techniques. What has stimulated the fervent enthusiasm among the champions of these new mathematical tools? How far have these areas come? What still needs to be determined or proven? Can we accept chaos as a valid fundamental concept in the analysis of biological systems? Will these new methods lead to major advances in medical care?

Numerous areas of medicine and biology have already found applications for these newer methodologies. Scientific subfields that generate large data sets have been quickest to use these tools. The workshop will focus on two clinically important areas, cardiology and neurophysiology, where a substantial amount of relevant information is already available. Using actual biological examples, the current and potential application to biomedical sciences will be addressed and discussed.

The workshop will bring together experts from cardiology and neurophysiology as well as experts in physiology, medicine, mathematics, physics, engineering, and computer modeling to explore the data and to evaluate the state of the art of applying chaos theory and nonlinear dynamical analyses to biological systems.

After a day of presentations and discussions, written questions from the audience will be received. On the second day, the questions will be distributed to the audience and addressed in the open forum. Finally, a panel will attempt to critically evaluate the proceedings in response to the following key questions:

  • What is the state of the art of nonlinear sciences and deterministic chaos as they apply to research in the biomedical sciences, particularly with respect to cardiology and neurophysiology?
  • How do the new nonlinear dynamic techniques resemble, and differ from, more established linear and nonlinear techniques for data analysis?
  • In cardiological and neurophysiological research where nonlinear dynamic techniques have been applied, what are the accomplishments? the problems? the critical considerations for distinguishing promising research from weak or erroneous research? the factors limiting progress?
  • What types of research and/or data sets are most likely to provide the information that will clarify the value of nonlinear dynamical techniques in the near term?

Every effort will be made to communicate effectively with an eclectic audience with diverse educational backgrounds and experience. The agenda has been structured to provide considerable time for formal and informal discussions in order to promote understanding that may lead to a consensus.

Report On the Workshop

The workshop took place on June 15-16 in the Masur Auditorium of the National Institutes of Health. An edited transcript of the proceedings will be submitted for distribution later this year through the National Technical Information Service (NTIS), Springfield, Virginia. The program and abstracts, a Science [2] magazine report on the meeting, and other relevant documents are included as the Appendix of the executive report. We wish to emphasize that although the workshop focused on cardiology and neurophysiology, methodologies based on nonlinear dynamics, including chaos theory and related topics such as fractals, have also been successfully applied to virtually every aspect of biology and medicine ranging from population studies to the structure of DNA.

2
Ivan Amato. Chaos breaks out at NIH, but order may come of it. Science 1992;256:763-4. See also, Ivan Amato. DNA shows unexplained patterns writ large. Science 1992;257:747.

The formal presentations and associated discussions focused as intended on the nonlinear dynamics exhibited by heart and brain. The complex temporal behavior of these organs--often to the point of an apparent randomness that defies predictability--is evident in recordings of the time courses of various measurable attributes such as the electrocardiogram, the electroencephalogram, the electrical activity of isolated myocardium and spinal-cord, respectively, and the successive conformational states of ion-channel proteins in the membranes of the cells of excitable tissues. The examples chosen by the speakers underscored how mathematical concepts and methods developed for studying nonlinear dynamics in the physical sciences and engineering can be useful in cardiology and neurophysiology as well. The following paragraphs summarize the perspective of the workshop organizers with respect to the themes covered and the principal issues arising.

Principal Issues Arising From the Workshop

Nonlinear Behavior Is Common in Biological Systems

The presentations and audience commentary underscored the fact that heart and brain are anything but unique among biological systems with respect to frequent manifestations of apparent randomness in their temporal behavior. Other physiological phenomena, such as motility in the gastrointestinal tract and certain biochemical reactions, exhibit similarly complex dynamics. To the extent that mathematical methods for coping with nonlinearity can open new avenues for elucidating the functions of heart and brain, these methods reasonably might be expected to do the same in other areas of biology and medicine.

Little of this is guaranteed, of course. All the different facets and potential applications require extensive research before more informed judgment is possible. Nevertheless, biology and medicine abound with intriguing examples where nonlinearity is prominent. Inquiries into the nonlinear dynamics of a broad range of biological systems seem a worthwhile investment for the long term. Supporting the best ideas irrespective of ultimate utility should be as productive a strategy here as elsewhere in science.

Deterministic Chaos Is Not a Unique Mathematical Approach to Studying Nonlinear Systems

Just as biomedicine offers many and diverse research topics, so does the mathematics associated with the analysis and modeling of nonlinear phenomena. The concepts and methods related to deterministic chaos are important because, as the workshop demonstrated, many biological processes exhibit the exquisite sensitivity to changes in initial conditions that is a characteristic of chaotic dynamics. Nevertheless, biologists and medical scientists should be mindful that deterministic chaos is only one type of nonlinear dynamics. Other nonlinear phenomena also warrant serious attention and improved methods for dealing with them.

Interdisciplinary Barriers Are a Major Research Impediment

Further progress in understanding biological nonlinearities will depend to a large extent upon how successful biomedical scientists and mathematicians are in overcoming interdisciplinary barriers. Biologists and physicians will need to become familiar with at least the concepts of the relevant mathematics, just as mathematicians will need to understand the basic biological principles manifest in particular laboratory and clinical experiments and observations.

Research administrators both in academe and funding agencies are in a position to have a positive influence by creating environments and reward systems that encourage high-quality interdisciplinary work. Within the university, the principal stumbling block often is excessive narrowness in the disciplinary requirements for tenure. Within the funding agencies, a similar narrowness frequently is manifest both in the peer review process and in the expression of program priorities. Research in mathematical biology seems especially vulnerable to such strictures. Without relaxing the expectation for excellence, research administrators need to introduce greater tolerance for ideas that push beyond traditional disciplinary boundaries.

Multidisciplinary Projects Require Cooperative Efforts

Complementing the current interdisciplinary issues are those associated with multidisciplinary projects. Although in the future, as in the past, some scientists no doubt will develop sufficient expertise in both biology and mathematics to function on their own, many will not. Those among the latter who choose to study biological nonlinearities will need to be part of research teams whose members focus their collectively diverse knowledge on a particular research goal. Again, research administrators can facilitate or thwart such developments depending upon how tenure requirements are specified, how peer review groups are oriented, and how program goals are defined.

The most important attribute of these multidisciplinary ventures is repeated interaction between mathematicians and biomedical scientists and repeated iterations between theory and experiment. Sometimes, the research will involve a novel application of well- established methods. Other times experimental results will spawn a search for new methods or a reexamination of a previously accepted paradigm. Either way, collaborative research can proceed in such a way that it ultimately advances all of the contributing disciplines rather than simply exploiting one to benefit the other.

Real Biological Signals Are Essential and Essentially Complicated

Whatever the scope of the research project, experimentation with real biological signals is imperative. As in other areas of science, attempts to apply existing methods for analyzing nonlinear dynamics should reveal both their power and their limitations for biology. Not only could this lead to new insights about the biological systems being investigated but it could also stimulate new research in relevant areas of mathematics.

Three of the most difficult challenges associated with nonlinear dynamics are (a) distinguishing between a random process and a complex time series that nevertheless has underlying order, (b) dealing with artifacts introduced by the measurement tools, and (c) intrinsically noisy signals. Better methods and representations for distinguishing real from apparent randomness are needed, as are better techniques for distinguishing between experimentally induced signals and biologically significant ones.

Modeling Studies Are Also Essential and Must Be Approached Cautiously

Some biological time series exhibit extraordinarily complex dynamics that nevertheless may be the product of relatively simple nonlinear relationships. Where anatomical, biochemical, or physiological findings suggest how components of a particular biological system might be coupled, models that attempt to relate various putative mechanisms to observed dynamics could be instructive. Such blending of reductionist and integrative paradigms has much to commend it.

Yet modeling demands circumspection and caution. The fact that a particular mathematical relationship "fits" the data or produces a plausible simulation has little meaning in and of itself. Correlation alone does not constitute proof, for many different models might yield the same or similar results. Although models can be invaluable for summarizing data or suggesting additional studies--both theoretical and experimental--and therefore are worthy of serious study and use, the risk of spurious correlation always looms large. Well-trained investigators will take this into account.

Conclusion

The conference was remarkably successful in meeting a primary goal of reaching a large and interested audience of individuals from many scientific disciplines and many professional backgrounds. The issues raised here are most likely to be resolved effectively if more of our colleagues begin to raise their awareness of nonlinear dynamics in biological systems and begin to engage in the debate. The present conference went a long way toward reaching that goal.

Critical Panel

Charles DeLisi, Ph.D.
Moderator
Professor and Dean
College of Engineering
Boston University
Boston, Massachusetts
James B. Bassingthwaighte, M.D., Ph.D.
Professor of Bioengineering and Biomathematics
Center for Bioengineering
University of Washington
Seattle, Washington
Avis H.Cohen, Ph.D.
Associate Professor
Department of Zoology
University of Maryland
College Park, Maryland
J. Doyne Farmer, Ph.D.
Vice President of Research
Santa Fe Institute and Prediction Company
Santa Fe, New Mexico
Ary L. Goldberger, M.D.
Associate Professor of Medicine
Harvard Medical School
Beth Israel Hospital
Boston, Massachusetts
John Guckenheimer, Ph.D.
Director
Center for Applied Mathematics
Department of Applied Mathematics
Cornell University
Ithaca, New York
J.A. Scott Kelso, Ph.D.
Professor and Director
Program in Complex Systems and Brain Sciences
Center for Complex Systems
Florida Atlantic University
Boca Raton, Florida
Nancy Kopell, Ph.D.
Professor of Mathematics
Department of Mathematics
Boston University
Boston, Massachusetts
David R. Rigney, Ph.D.
Assistant Professor of Medicine (Physiology/Biophysics)
Harvard Medical School
Beth Israel Hospital
Boston, Massachusetts

Speakers and Discussants

William F. Raub, Ph.D.
Moderator
Special Assistant for Health Affairs
Office of Science and Technology Policy
Executive Office of the President
Washington, D.C.
Morton F. Arnsdorf, M.D.
Professor of Medicine
Section of Cardiology
University of Chicago Hospitals
Chicago, Illinois
James J. Bailey, M.D.
Chief
Medical Applications Section
Laboratory of Applied Studies
Division of Computer Research and Technology
National Institutes of Health
Bethesda, Maryland
Avis H. Cohen, Ph.D.
Associate Professor
Department of Zoology
University of Maryland
College Park, Maryland
Jorge M. Davidenko, M.D.
Assistant Professor of Pharmacology
Department of Pharmacology
State University of New York at Syracuse
Health Science Center
Syracuse, New York
James R. Ellis, Jr., Ph.D.
Electronic Engineer
National Center for Research Resources
National Institutes of Health
Bethesda, Maryland
Leon M. Glass, Ph.D.
Professor
Department of Physiology
McGill University
Montreal, Quebec, CANADA
Ary L. Goldberger, M.D.
Associate Professor of Medicine
Harvard Medical School
Beth Israel Hospital
Boston, Massachusetts
Celso Grebogi, Ph.D.
Associate Professor of Mathematics
Laboratory for Plasma Research
University of Maryland
College Park, Maryland
Niels-Henrik Holstein-Rathlou, M.D.
Associate Professor
Department of Physiology and Biophysics
University of Southern California
School of Medicine
Los Angeles, California
Daniel T. Kaplan, Ph.D.
Post Doctoral Fellow
Department of Physiology
Centre for Nonlinear Dynamics in Physiology and Medicine
McGill University
Montreal, Quebec, CANADA
J. A. Scott Kelso, Ph.D.
Professor and Director
Program in Complex Systems and Brain Sciences
Center for Complex Systems
Florida Atlantic University
Boca Raton, Florida
Larry S. Liebovitch, Ph.D.
Assistant Professor
Department of Ophthalmology
College of Physicians and Surgeons of Columbia University
New York, New York
Eve E. Marder, Ph.D.
Professor of Biology
Biology Department
Brandeis University
Waltham, Massachusetts
Paul E. Rapp, Ph.D.
Professor of Physiology
Department of Physiology and Biochemistry
Medical College of Pennsylvania
Philadelphia, Pennsylvania
William S. Yamamoto, M.D.
Professor of Computer Medicine
The George Washington University
School of Medicine
Washington, D.C.

Planning Committee

Kathleen Shaver Madden, Ph.D.
Chairperson
Coordinator
Interinstitute Chaos Council
National Institutes of Health
Department of Neurosurgery
Children's National Medical Center
Washington, D.C.
Elsa Bray
Program Analyst
Office of Medical Applications of Research
National Institutes of Health
Bethesda, Maryland
John H. Ferguson, M.D.
Director
Office of Medical Applications of Research
National Institutes of Health
Bethesda, Maryland
Dennis L. Glanzman, Ph.D.
Program Chief
Mathematical/Computational/Theoretical Neuroscience Program
National Institute of Mental Health
Alcohol, Drug Abuse, and Mental Health Administration
Rockville, Maryland
William H. Hall
Director of Communications
Office of Medical Applications of Research
National Institutes of Health
Bethesda, Maryland
Richard K. Nakamura, Ph.D.
Chief
Cognitive and Behavioral Neuroscience Research Branch
Division of Basic Brain and Behavior Sciences
National Institute of Mental Health
Alcohol, Drug Abuse, and Mental Health Administration
Rockville, Maryland
Frank J. Nice, M.S., M.P.A.
Assistant Director
Clinical Neurosciences Programs
National Institute of Neurological Disorders and Stroke
National Institutes of Health
Bethesda, Maryland
David M.Robinson, Ph.D.
Associate Director for Scientific Programs
Division of Heart and Vascular Diseases
National Heart, Lung, and Blood Institue
National Institutes of Health
Bethesda, Maryland

About the NIH Technology Assessment Program

NIH Technology Assessment Conferences and Workshops are convened to evaluate available scientific information related to a biomedical technology when topic selection criteria for a Consensus Development Conference are not met. The resultant NIH Technology Assessment Statements are intended to advance understanding of the technology or issue in question and to be useful to health professionals and the public.

Some Technology Assessment Conferences and Workshops adhere to the Consensus Development Conference format because the process is altogether appropriate for evaluating highly controversial, publicized, or politicized issues. Other Conferences and Workshops are organized around unique formats. In this format, NIH Technology Assessment Statements are prepared by a nonadvocate, nonfederal panel of experts, based on: (1) presentations by investigators working in areas relevant to the consensus questions typically during a 1-1/2-day public session; (2) questions and statements from conference attendees during open discussion periods that are part of the public session; and (3) closed deliberations by the panel during the remainder of the second day and morning of the third. This statement is an independent report of the panel and is not a policy statement of the NIH or the Federal Government.

Preparation and distribution of these reports are the responsibility of the Office of Medical Applications of Research, National Institutes of Health, Bldg 31, Room 1B03, Bethesda, MD 20892.

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