Nonlinear systems theory in medical care management. (Competing On the Edge).

KEY CONCEPTS

* Nonlinear Systems Theory

* Complex Adaptive Systems (CAS)

* Zone at the Edge of Chaos 

* Designing New Models of Care

* Roadmaps, Decision Aids, and Continuous Improvement

Health care is provided to biological, not mechanical systems. The focus of attention is a human being, not an automobile or clock. Biological systems are highly complex and their behavior can be nonlinear. By understanding this difference, we can begin to answer the question of how can we deliver efficient and effective clinical care, while controlling spiraling costs. This article describes the behavior of complex systems and explores what has been learned about managing such systems in non health care fields. The author translates that learning into the health care setting and proposes a new model for the health care environment, based on the principles of complex adaptive systems. The approach advocated is to design models that can learn and adapt, and then to implement them with skill. Such models should include the elements of roadmaps, decision aids, and continuous improvement.

THE ERA OF FREE CHOICE in medical care is clearly over. The forces of the market have closed in on patients and providers, forcing both to compromise In terms of care. The once benign third party payers have become vigilant players In the game of sickness and health and life and death. Employers, once the avuncular uncle sprinkling health care benefits about with little concern for cost, have reverted to a more familiar role, that of sharp eyed business people looking for any service at lowest cost. No one likes this new state of affairs, except perhaps those extracting profits from managing care.

Health care is one of those services best designated as an unlimited economic want. No one wants to be restricted in choosing how much care to give or receive, And yet there are economic limits. Corporate budgets have to balance. Corporations have to face stockholders and Wall Street and show profits. These days, even the U.S. budget has to balance.

People who work in health care know that doctors drive health care expenses. After all, they put people into the system, order the system to function in various ways to provide care, and are the final arbiter in terms of moving patients out of the system. The obvious approach to cost savings is to start here. If one can somehow control the mind and actions of the doctor, the theory says, one can salvage resources.

This is a challenging idea. Underlying it is the notion that medical professionals don't always do the right things and can, therefore, benefit from some external guidance. Untold millions have been spent on providing such guidance. Hundreds (perhaps thousands) of roadmaps of various sorts have been designed to help medical professionals do their work. Vigilant benefits counselors and precertification experts staff telephones all over the country, overseeing and judging the provision of care.

To the extent that such vigilance focuses on "appropriate" admissions to "appropriate" settings for "appropriate" lengths of stay, it may be a waste of time and energy. In a recent article, Reinhardt (1) points out that while costs for specific services have been controlled, overall spending for health care in the U.S. is still 14 percent of the gross national product--unchanged for a decade or more. If reducing admissions and lengths of stay in hospitals is not the way to control costs, what is? To offer even the suggestion of an answer to that question, one must put health care in the proper perspective.

Biological, not mechanical systems

Health care is provided to biological, not mechanical systems. The focus of attention is a human being, not an automobile or clock. Biological systems are highly complex and their behavior can be nonlinear. By understanding this difference, we can begin to answer the question of how do we control spiraling costs. But first we must understand what is meant by system complexity.

Coveney and Highfieldz suggest that a state of complexity requires two ingredients, an irreversible medium and nonlinearity. The medium is time; it runs only one way. Nonlinearity is the phenomenon by which, "... small changes on one level of organization produce large effects at the same or different levels. " The authors offer the example of billiard balls on a table. Even though the equations of motion describing the system are well known, the long-term behavior of the bails is unpredictable. No one can know where they will wind up at the end of the game.

Stacey (3) uses the analogy of snowflakes. We all know what they are, what causes them to form and melt, that they fall down and not up. Nevertheless, they are all different. The reason snowflakes are all different is that small, even tiny, differences in their environment create different growth patterns. No person in his or her right mind would try to predict how an individual snowflake might look because there are too many variables involved. Of course that does not prevent us from making short-term predictions about groups of snowflakes, (i.e., the weather), although with modest results. Nor does it keep us from estimating how many inches or feet of snow will fall from a given storm. We can make broad estimates about things associated with snowflakes, for example, we know that each has six points, but we cannot predict the specific outcome (i.e., detailed shape) of each one.

Complex systems

Most systems in nature, (things like the weather, population growth, war and peace, the stock market, and the give and take of the economy), behave in ways that are best described as nonlinear, as opposed to linear. This means that, as events unfold, their outcomes are not always predictable based on history, except in broad, general terms. This is because nonlinear systems, as they become more complex, are very susceptible to differences in initial and environmental conditions.

This effect can be illustrated with a few simple calculations. Sharp and Priesmeyer (4) describe a case of nonlinearity with the use of the logistic equation Xnext = (X) (k) (1-X), where the calculation of Xnext is based on its previous value, (X), and the parameter, (k), which is an indicator of system complexity. If we exercise the equation, we can see that the following phenomena result from its nonlinearity (please see Figures 1, 2, and 3):

* As k increases, for instance, as the system becomes more complex, the terminal values of Xnext become more varied. For low values of k, Xnext quickly stabilizes to a constant level. For high values of k, Xnext becomes completely unstable, swinging back and forth between plus and minus infinity. For intermediate values of k, Xnext oscillates, but in a bounded, repeating fashion.

* As k increases, the outcomes become more dependent on the initial conditions X(0). This is demonstrated in Figures 1 and 4, which contain calculations for X(0) equal to 0.05 and 0.01. For k = 2.5, the stable zone, changing initial conditions from 0.05 to 0.10 has virtually no effect on outcome, while for k = 3.7, the intermediate zone, the same change has an enormous effect.

Stacy describes nonlinear systems as having three zones of behavior:

1. a zone of stability (for example, when k is equal to or less than 2.5),

2. a zone of instability (for example, when k is equal to or greater than 4.1),

3. a middle zone of increasing complexity and bounded instability (for example, when 2.5 < k < 4.1) where outcomes can oscillate in many different ways, but within boundaries, dependent on initial conditions and the degree of complexity.

If one thinks of this in terms of clinical analogies, patients in the stable zone can be managed by taking two aspirins and calling back in the morning, because in all likelihood their condition is self-limiting and will correct on its own. Patients in the unstable zone are deteriorating rapidly and probably require a STAT team. It is the patients in the middle zone that require the most thoughtful forms of management. Stacey calls the middle region the zone of chaos. For the sake of consistency with Sharp and Priesmeyer, and others, it is called here the zone that approaches the edge of chaos.

Learnings from other fields

1. Business management: unpredictable situations

Certainly, deteriorating patients, those in the unstable zone, can quickly run up expenses in ERs and ICUs, but eventually these expenses cease when the patient either goes home or expires. Also, there is very little argument about the treatment of such patients because they are classified as emergencies. The caregivers can do what they need to do with little interference. Patients in the stable zone are, most likely, the least expensive. Or, at the very least, their expenses are the most predictable because their care, while sophisticated and perhaps high tech, tends to be routine. The truly expensive patients are those at the edge of chaos. These patients give meaning to the term complexity because the ingredients of irreversibility and nonlinearity are present.

Physicians managing patients have counterparts in other fields. Business managers deal with nonlinear systems all the time. A complex organization is much like a biological entity struggling to maintain its ecological niche. Organizational survival in a competitive environment is dependent on the timely skill with which business managers employ money, people, facilities, and creativity in the face of unending and unpredictable change.

Attempting to manage complex organizations with highly detailed strategic plans is futile. (5) Strict, "top-down," rules do not work in such chaotic environments. (6) Because outcomes can vary greatly depending on small differences in the environment, and are therefore unpredictable, a successful management system has to be adaptable to local circumstances.

It has to be able to take advantage of favorable situations as they occur, continually moving them forward and turning them into virtuous (as opposed to vicious) cycles. (3) Successful management of a system at the edge of chaos should take advantage of positive feedback to improve a situation, while inhibiting the potentially degrading impact of negative feedback. One might call this the "art of management, or in other disciplines, the "art" of music, or basketball, or medical practice. If one is to conceptualize a successful patient management system, one that addresses the most expensive patients, the key is to create one that can be adaptive.

2. Engineering: adaptive systems

Engineers and scientists in the fields of artificial intelligence and robotics know that such systems have to be able to adapt to unexpected situations. Hence, lessons about how to manage at the edge of chaos can also be drawn from scientific theories of adaptive systems. In his book on the subject. Holland (7) describes complex systems in the following way:

* "All complex adaptive systems involve large numbers of parts undergoing a kaleidoscopic array of simultaneous nonlinear interactions. .the behavior of the whole is not, even to an approximation, a simple sum of the behavior of the parts.

* ...the behavior of the whole often feeds back to the parts, modifying their behavior.

* ...the interactions evolve over time. ..as a result, the parts face perpetual novelty and the system operates far from global optimum or equilibrium..."

While not written for the purpose of patient care, Holland's description seems highly appropriate to such a situation, How better could one describe a complex patient undergoing treatment? Note, by the way, that in such a system, the "parts" are not just the parts of the patient, but would include the physician, hospital, and staff.

Holland points out that: "In seeking to adapt to changing circumstances, the 'parts' develop 'rules' (models) that anticipate the consequences of events. These models ".... allow a complex adaptive system to respond, instant by instant, to its environment, while improving its performance."

He offers a three-part, general theory for optimizing complex systems:

1. "Parallelism: Lets the system use rules as building blocks ....to act upon changing situations."

2. "Competition: Allows the system to marshal its resources in realistic environments...under a deluge of mostly irrelevant information....extracting useful, repeatable events (and)...incorporating them as new building blocks."

3. "Recombination: Underpins the discovery process, generating plausible new rules from building blocks that form parts of tested rules."

A model for the health care environment

Let us move Holland's theories into the health care setting, but use terms that will be a bit more familiar to physicians. For parallelism substitute roadmaps, for competition substitute tools and decision aids, and for recombination substitute continuous improvement.

We can now begin to see the outlines of a medical care model emerge from work in other fields. From management experts we learn that top-down rules do not work in complex settings. From engineering principles, we know that three fundamental elements need to be included when designing adaptive systems. Carrying this over into health care, the fundamental components of an adaptive model for medical care are:

1. Roadmaps allow caregivers to apply a priori rules to patient management, permitting them to act upon situations that are, for the most part, predictable. Roadmaps can work for patients in all three zones--stability, instability, and the edge of chaos--except that in the latter two zones their usefulness will decline and they will need to be augmented by special tools and decision aids.

2. Decision aids are required in more dynamic, hence nonlinear, situations. The implication is that the caregiver extracts information from the situation as it unfolds and tailors action to move the patient into a "virtuous" cycle (for example, recovery). Decision aids are devices to assist the caregiver in moving from point to point under a specific set of circumstances (as opposed to a roadmap which may move a caregiver from beginning to end). Paraphrasing Goonan (8) "...a decision-making algorithm that supports swift, correct diagnosis (and treatment) will contribute to optimal patient outcomes."

3. Continuous improvement provides an orderly process by which caregivers perpetually review and revise roadmaps and decision aids based on feedback from the latest experiences. Continuous improvement also stimulates the creative process, generating new guidelines from those already tested. This is what a quality care system in a health care setting should really do. It is a far cry from the paper pushing that goes on in most QA committees.

Conclusion

Delivering efficient and effective clinical care is one of the great challenges of our time. In designing care management, one must consider that human beings are not always predictable. They may be thought of as nonlinear "systems." Depending on the level of complexity that develops in the care situation, a patient may be in a zone of stability, instability, or at the edge of chaos. The care management strategy must recognize and adapt to these circumstances. Care models will not work if they are overly rigid. Trying to contain costs by building such models may work for some situations but will be a hopeless undertaking for complex patients. The rigid approach violates basic principles of nonlinear systems, A better approach is to design models that can learn and adapt, and then implement them with skill. Such models should include the elements of roadmaps, decision aids, and continuous improvement.

It is incumbent on health care providers to take the lead in designing and implementing organizational structures to carry this model forward. Otherwise, the profession will continue to be besieged by third party helpers intent on providing what will, no doubt, be the wrong kind of guidance.

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References

(1.) Reinhardt, Uwe E. Spending More Through "Cost Control:" Our Obsessive Quest to Gut the Hospital, Health Affairs, Vol. 15, No. 2, 1996.

(2.) Coveney. Peter and Roger Highfield, Frontiers of Complexity, Columbine, New York: Fawcett, 1995.

(3.) Stacey, Ralph D. Managing the Unknowable, Strategic Boundaries Between Order and Chaos New York, New York: Harper Collins, 1992.

(4.) Sharp, Lawrence F. and H. Richard Priesmeyer, Tutorial: Chaos Theory--A Primer for Health Care, Quality Management in Health Care, 1995, Vol. 3. No. 4.

(5.) Mintzberg, Henry. The Rise and Fall of Strategic Planning. New York, New York: The Free Press, 1994.

(6.) Leach, Lawrence P. TQM. Reengineering, and the Edge of Chaos, Quality Progress, February 1996,

(7.) Holland, J. H. Adaptation in Natural and Artificial Systems. Cambridge, Massachusetts: MIT Press, 1992.

(8.) Jennison Goonan, Kathleen, The Juran Prescription, San Francisco, California: Jossey-Bass. 1995.

RELATED ARTICLE: RECOMMENDED RESOURCES ON COMPLEXITY THEORY

Scientific contributions to the rapidly developing fields of complexity and nonlinear dynamics are flowing in from many disciplines--from physics, to fractal geometry, to evolutionary biology, to computer science, to economics. This breadth, and the accompanying set of recommended resources on complexity, suggests that the new discoveries being made about how living systems evolve and adapt will have profound implications for our conception of health, our understanding of human physiology, and the practice of leadership in organizations.

Introductions to complexity

Briggs, John, Fractals: The Patterns of Chaos. New York, New York: Simon & Schuster, 1992.

This book is the visual way into chaos theory and nonlinear dynamics. It tells the story with fractal images from artists, computers, nature, space, and physiology The prose covers the basic scientific concepts in an engaging manner.

Gleick, J. Chaos, New York, New York: Viking Penguin, 1987.

Thomas Petzinger's annotation--This bestseller...is a model of science writing, both in form and content. Although a small industry of chaos books has followed its worldwide success, this one is still worth rereading as a delightful way to glimpse the implications of complex systems.

Kelly, Kevin. Out of Control: The Rise of Neo-Biological Civilization, Reading, Massachusetts: Addison-Wesley, 1994.

This insightful and wide-ranging work pulls important new pattern-building findings from fields as diverse as computer science, biology physics, and economics, relates them to the new worlds of complexity chaos theory and post-Darwin evolution, and lays out some implications for creating complex organizations.

Waldrop, M. Mitchell. Complexity: The Emerging Science at the Edge of Order and Chaos, New York, New York: Simon & Schuster, 1992.

This is the introduction to complexity many start with. It's told through the stories of some of the leading contributors to this new science who have backgrounds in a variety of disciplines and came together at the Santa Fe Institute--John Holland, Brian Arthur, Stuart Kauffman, Chris Langton.

The science of complexity

Holland, John H. Emergence: From Chaos to Order, Reading, Massachusetts: Helix Books, 1998.

The latest book by one of the founders of complexity demonstrates how a small number of rules can generate systems of great complexity and novelty giving us a deeper understanding of complex systems in life.

Kauffman, Stuart At Home in the Universe, New York, New York & Oxford, England: Oxford University Press, 1995.

Thomas Petzinger's annotation--A bit daunting in spots, it goes further than other books in exploring what complexity theory might mean for the future of economics and organizations. And Kauffman's speculations on the origins of life are thrilling.

Lorenz, Edward. The Essence of Chaos, Seattle, Washington: University of Washington Press, 1993.

Written by a meteorologist who first discovered what later was termed "chaos." Looking at chaotic systems from a unique and creative perspective, Lorenz draws out the meaning of such characteristics of chaotic systems as sensitive dependence on initial conditions, strange attractors, aperiodicity and stability/instability.

Peak, David, and Frame, Michael. Chaos Under Control: The Art and Science of Complexity New York, NewYork: W.H. Freeman, 1994.

One of the best introductions to complexity science, covering the whole gamut of the field including complex adaptive systems, nonlinear dynamics and chaos, fractals, cellular automata, neural nets, and genetic algorithms. This book is extremely clear and well written, but it does require college level mathematics.

Prigogine, Ilya, and Stengers, Isabelle. Order Out of Chaos: Man's New Dialogue with Nature, New York, New York: Bantam Books, 1984.

Thomas Petzinger's annotation--A compelling historical account of the limitations of Newtonian science and the dynamics of complexity by a Nobel laureate in chemistry with an emphasis on thermodynamics and dissipative structures.

Complexity and organizations

Brown, Shona L., and Eisenhardt, Kathleen M. Competing on the Edge: Strategy as Structured Chaos, Boston, Massachusetts: Harvard Business School Press, 1998.

A new book by a Stanford University professor and McKinsey consultant that explores a "competing on the edge" management strategy It introduces concepts such as edge of time, the improvisational edge, time-pacing, and includes real company examples.

Dooley, Kevin, and Johnson, Timothy L., TQM, Chaos and Complexity Human Systems Management, Vol. 14, 1995, pp. 287-302.

A superb article that explores what chaos and complexity theory offer to traditional thinking about quality improvement. It includes a comprehensive set of references.

Goldstein, Jeffrey. The Unshackled Organization: Facing the Challenge of Unpredictability Through Spontaneous Reorganization, Portland, Oregon: Productivity Press, 1994.

This is one of the few management books on the implications of complexity and nonlinear systems theory for the management of organizations. It is well done and offers the self-organization approach to major change in contrast to more conventional approaches.

Lane, D. and Maxfield, R. Strategy under Complexity: Fostering Generative Relationships, Long Range Planning, Vol. 29, April, 1996, pp. 215-231.

Strategy and the future are discovered through generative relationships--those that produce unforeseen value and new possibilities. The authors provide guidance on where to look and how to foster generative relationships.

Morgan, Gareth, Images of Organization, Second edition, Thousand Oaks, California: Sage Publications, 1997.

The revised edition of this classic work in the management literature demonstrates through metaphors the multiple ways, realities, and dimensions of organizations. Chapters 4 and 8 relate directly to complexity, chaos theory and management.

Petzinger, Thomas, Jr. The New Pioneers: The Men and Women Who Are Transforming the Workplace and Marketplace, New York, New York: Simon & Schuster, 1999.

Petzinger's new book delves into recent, far-reaching scientific discoveries about living systems and brings them to life through vivid stories gathered through his years as The Wall Street Journal's "Front Lines" columnist.

STACEY, RALPH D. Complexity and Creativity in Organizations, San Francisco, California: Berrett-Koehler Publishers, 1996.

From one of the pioneers of complexity-inspired organizational theory, this work presents new frameworks for sense-making in organizational life. He examines what it means to be operating at the edge of chaos in human systems.

Waldrop, M. Mitchell. The Trillion- Dollar Vision of Dee Hock, Fast Company, October/November 1996, pp. 75-86.

This article is about Dee Hock and how he used the principles of distributed control, a mix of collaboration and competition, simple rules, and diversity in the organization of VISA.

Zimmerman, Brenda, Lindberg, Curt, Plsek, Paul. Edgeware: Insights from Complexity Science for Health Care Leaders. Irving Texas: VHA Inc., 1998.

Thomas Petzinger's annotation--At last, authors who reveal the clarity in complexity Though solid on the theory of complexity this book's real breakthrough is in its tremendous practicality for leaders. The pages are brimming with case after case-episodes of complexity in action that inspire as well as inform.

Complexity, medicine, and health care

Dardik, Irving I. The Origin of Disease and Health, Heart Waves: The Single Solution to Heart Rate Variability and Ischemic Preconditioning. Frontier Perspectives, Vol. 6, No. 2, Spring/Summer, 1997, pp. 18-32.

This provocative article explores the concepts of the heart waves and heart rate variability as indicators of health and disease and proposes a route to increase the fractal complexity and hence health, of human physiologic systems.

Goldberger, Ary L. Nonlinear Dynamics for Clinicians: Chaos Theory, Fractals, and Complexity at the Bedside, Lancet, Vol. 347, May 11, 1996, pp. 1312-1314.

An introductory article for medical personnel by a physician who has delved deeply into human health and physiology from the complexity and chaos perspectives. It suggests new definitions for health and ill health, plus new diagnostic and therapeutic approaches. Goldberger, Ary L., Rigney, D.R., West, B.J. Chaos and Fractals in Human Physiology, Scientific American, Vol. 262, pp. 42-49.

This pioneering work was the first to suggest that developments in nonlinear dynamics and chaos theory will trigger advances in our understanding of human physiology.

Goldberger, Ary L. Fractal Variability versus Pathologic Periodicity: Complexity Loss and Stereotype in Disease. Perspectives in Biology and Medicine, Vol. 40, Summer, 1997, pp. 543-561.

Goldberger develops the case that healthy physiologic systems are characterized by fractal complexity, while unhealthy systems are marked by highly periodic (regular) dynamics and a concomitant loss of adaptability.

Goodwin, James S. Chaos and the Limits of Modern Medicine, JAMA, Vol. 278, No. 17, November 5,1997, pp. 1399-1 400.

A provocative little piece suggesting that chaos and complexity theory can contribute to the practice of medicine by viewing people as complex systems.

Lindberg, Curt, Herzog, Alfred, Merry, Martin, Goldstein, Jeffrey. Life at the Edge of Chaos--Health Care Applications of Complexity Science. The Physician Executive, January/February 1998, pp. 6-20.

This article introduces health care practitioners to complexity science and shows its widespread relevance to medical and health care organizational issues,

Lipsitz, L.A., Goldberger, A.L. Lass of Complexity' and Aging: Potential Applications of Fractals and Chaos Theory to Senescence. JAMA, Vol. 267, 1992, pp. 1806-1809.

This new view suggests that aging is related to the loss of complex patterns in physiologic systems.

Regaldo, Antonio. A Gentle Scheme for Unleashing Chaos. Science, Vol. 268, 1995, p. 1848.

This report is about early efforts to restore complexity to physiologic systems by "small, precisely timed pertubations."

Weibel, Ewald R. Fractal Geometry: A Design Principle for Living Organisms. American Journal of Physiology Vol. 261, 1991, pp. L361 -369.

A fascinating article that explores the possibility that fractal geometry is a design principle in biological systems. It calls into question the current view that biological structure is 'precisely determined by the genetic program of an organism."

Websites

The Center for Complex Systems and Brain Sciences at Florida Atlantic University http://www.ccs.fau.edu/

This multidisciplinary center founded by Scott Kelso involves the cooperative efforts of neuroscientists, psychologists, mat hematicians, physicists, computer scientists, and engineers. Its overarching objective is to understand the mechanisms and principles underlying complex behavior on all levels, from molecules and cells to whole brain functioning.

Craig Reynoldsu http://nova.postech.ac.krl%7Ejywoo/java/ alife/Boids/boids.html

In 1986 Craig Reynolds created a com puter model of coordinated animal motion, such as bird flocks and fish schools. He called the software boids. This simulation has become well known in complexity for its graphic illustration of the principle that complex behavior emerges from simple rules.

Rey Laboratory for Nonlinear Dynamics in Medicineu http://reylab.bidmc.harvard.eduI

This is the only laboratory in the world devoted to exploring complex, nonlinear behavior in human physiological systems. It is led by Ary Goldberger, MD, a cardiologist at Beth Israel Deaconess Medical Center and Harvard Medical School, who has devoted his career to seeking new understandings of the nonlinear mechanisms and patterns of health and disease.

The Santa Fe Instituteu http:llwww.santafe.edul

This site is maintained by The Santa Fe Institute, the acknowledged center of the science of complexity You can access the scientific work, educational offerings, and background on SF!, its faculty and Business Network.

VHA's Complexity and Health Care Siteu http:I/w~vw.edgeplace.com

This website is devoted to complexity health care, and organizational leadership. It contains a host of resources including: a primer on complexity complexity-inspired organizational and leadership principles, stories of the use of complexity principles by health care leaders, an extensive annotated bibliography guidance on introducing complexity into organizations, useful links, and information about upcoming conferences. Videos

The Color of Infinity, December 1997, PBS.

The story of the Mandeibrot set. This beautiful and engaging PBS special explores fractals, how they were discovered, and how they are created. $29.95, plus shipping/handling/tax. Please call 800/257-5126 to order a copy

Health Care On The Edge: What Leaders Can Learn From Complexity Science, March 1999,VHA Inc.

This first documentary dedicated to introducing health care professionals to complexity science examines the dynamics of healthy living systems, presents key complexity principles, and explores implications for leadership and our concept of health. Please call 972/830-0115 to inquire about availability and pricing.

Machines Like Us, August, 1996," Night Line' Broadcast, ABC.

An engaging and humorous "Night Line" broadcast that shows how machines can learn'~ using simple rules and genetic algorithms. $29.95, plus shipping/handling. Item # N96082301. Please call 800/225-5222 to order a copy

uCompiled by Curt Lindberg

Curt Lindberg is Senior Consultant of Comple.'dty Management at 1/HA, Inc. He is co-author, along with Brenda Zimmerman and Paul Pisek, of Edgeware: Insights from Complexity Science for Health Care Leaders, He can be reached via email at cindber@Vi-IA. COM We are grateful to him for this compilation of resources.

Lipsitz, L.A., Goldberger, A.L. Loss of 'Complexity' and Aging: Potential Applications of Fractals and Chaos Theory to Senescence. JAMA, Vol. 267, 1992, pp. 1806-1809.

This new view suggests that aging is related to the loss of complex patterns in physiologic systems.

Regaldo, Antonio. A Gentle Scheme for Unleashing Chaos. Science, Vol. 268, 1995, p. 1848.

This report is about early efforts to restore complexity to physiologic systems by "small, precisely timed pertubations."

Weibel, Ewald R. Fractal Geometry: A Design Principle for Living Organisms. American Journal of Physiology Vol. 261, 1991, pp. L361-369.

A fascinating article that explores the possibility that fractal geometry is a design principle in biological systems. It calls into question the current view that biological structure is "precisely determined by the genetic program of an organism."

Websites

The Center for Complex Systems and Brain Sciences at Florida Atlantic University

http://www.ccs.fau.edu/

This multidisciplinary center founded by Scott Kelso involves the cooperative efforts of neuroscientists, psychologists, mathematicians, physicists, computer scientists, and engineers. Its overarching objective is to understand the mechanisms and principles underlying complex behavior on all levels, from molecules and cells to whole brain functioning.

Craig Reynolds--

http://nova.postech.ac.kr/%7Ejywoo/java/alife/Boids/boids.html

In 1986 Craig Reynolds created a computer model of coordinated animal motion, such as bird flocks and fish schools. He called the software boids. This simulation has become well known in complexity for its graphic illustration of the principle that complex behavior emerges from simple rules.

Rey Laboratory for Nonlinear Dynamics in Medicine-

http://reylab.bidmc.harvard.edu/

This is the only laboratory in the world devoted to exploring complex, nonlinear behavior in human physiological systems. It is led by Ary Goldberger, MD, a cardiologist at Beth Israel Deaconess Medical Center and Harvard Medical School, who has devoted his career to seeking new understandings of the nonlinear mechanisms and patterns of health and disease.

The Santa Fe Institute--

http://www.santafe.edu/

This site is maintained by The Santa Fe Institute, the acknowledged center of the science of complexity You can access the scientific work, educational offerings, and background on SF!, its faculty and Business Network.

VHA's Complexity and Health Care Site-

http://www.edgeplace.com

This website is devoted to complexity health care, and organizational leadership. It contains a host of resources including: a primer on complexity complexity-inspired organizational and leadership principles, stories of the use of complexity principles by health care leaders, an extensive annotated bibliography guidance on introducing complexity into organizations, useful links, and information about upcoming conferences.

Videos

The Color of Infinity, December 1997, PBS.

The story of the Mandelbrot set. This beautiful and engaging PBS special explores fractals, how they were discovered, and how they are created. $29.95, plus shipping/handling/tax. Please call 800/257-5126 to order a copy.

Health Care On The Edge: What Leaders Can Learn From Complexity Science, March 1999, VHA Inc.

This first documentary dedicated to introducing health care professionals to complexity science examines the dynamics of healthy living systems, presents key complexity principles, and explores implications for leadership and our concept of health. Please call 972/830-0115 to inquire about availability and pricing.

Machines Like Us, August, 1996, "Night Line" Broadcast, ABC.

An engaging and humorous "Night Line" broadcast that shows how machines can "learn" using simple rules and genetic algorithms. $29.95, plus shipping/handling. Item # N96082301. Please call 800/225-5222 to order a copy.

--Compiled by Curt Lindberg

Curt Lindberg is Senior Consultant of Complexity Management at VHA, Inc. He is co-author, along with Brenda Zimmerman and Paul Pisek, of Edgeware: Insights from Complexity Science for Health Care Leaders, He can be reached via email at [e-mail] We are grateful to him for this compilation of resources.

Harvey Dershin is Vice President of the Juran Institute in Wilton, Connecticut, a company that specializes in helping organizations of all sorts reach their potential for high quality. He can be reached by calling 800/338-7726 or via email at hdershin@JURAN COM.