Life is dynamic and always in flux. Living organisms are constantly responding to and shaping their environments. Although we are taught to recognize proportional (linear) relationships, such as that between the weight of a banana and its price, these straightline relationships are actually rare when measuring the behavior of living systems.
Relationships between stimuli and biological responses may appear to be proportional over narrow ranges. Indeed, much of our current understanding of how biologic systems work has followed from the use of linear models that are based on this appearance of proportionality. Yet these models are unable to explain the bewildering repertoire of dynamics -- non-stationarity, abrupt changes (bifurcations, bistability, and oscillatory bursts), periodic and aperiodic (random or chaotic) variability -- that is a hallmark of life. These complex properties, which have important clinical implications, are not accounted for by a conventional understanding of health or disease based on the classical concept of homeostasis. Rather, their understanding requires the use of nonlinear dynamical models.
Unlike linear systems theory, which has mathematical foundations that have been very thoroughly understood for over a century, nonlinear dynamics is at the cutting edge of research in mathematics and physics. The exploration of this subject, much of which was considered utterly intractable as recently as twenty or thirty years ago, has been made possible by modern high-speed computers that can derive numerical solutions to models for which no analytic solutions are known. Research in nonlinear dynamics is largely responsible for the recent explosion of interest in computational methods in what has been called "experimental mathematics." The study of nonlinear dynamics in medicine thus lies at the intersection of frontiers in mathematics, physics, and biology.
Based on these considerations, the general mission of this laboratory is to provide new understanding of the dynamical aspects of health and disease via multidisciplinary approaches. In particular, our aim is to create an interdisciplinary
laboratory without walls in pursuit of the following specific objectives:
- To quantitatively characterize the complex, nonlinear behavior of physiological systems in health and disease, from the macromolecular level (e.g. organization of nucleotides in DNA) to the integrated function of the organism (e.g. control of the heartbeat; control of human gait).
- To develop new understanding of basic, nonlinear mechanisms of health and disease underlying these complex patterns.
- To develop new diagnostic and prognostic tests for a variety of life-threatening diseases and aging, by detecting "hidden information" in data sets.
- To foster the education and training of students, clinicians, and basic scientists, so that they may rigorously apply concepts and techniques from nonlinear dynamics and statistical physics to the understanding of basic physiology and to the practice of bedside medicine.
- To develop annotated databases of complex biomedical signals to help accomplish these goals, and to make such databases available to the general scientific community.