RESEARCH ARTICLE


Deterministic Chaos and Fractal Complexity in the Dynamics of Cardiovascular Behavior: Perspectives on a New Frontier



Vijay Sharma*
Division of Pharmacology and Toxicology, Faculty of Pharmaceutical Sciences, The University of British Columbia, 2146 East Mall, Vancouver, Canada


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© Vijay Sharma; Licensee Bentham Open.

open-access license: This is an open access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/by-nc/3.0/) which permits unrestricted, non-commercial use, distribution and reproduction in any medium, provided the work is properly cited.

* Address correspondence to this author at the Division of Pharmacology and Toxicology, Faculty of Pharmaceutical Sciences, 2146 East Mall, University of British Columbia, Vancouver, Canada; Tel: (604) 822 6159; Fax: (604) 822 8001; E-mail: vijaysha@interchange.ubc.ca


Abstract

Physiological systems such as the cardiovascular system are capable of five kinds of behavior: equilibrium, periodicity, quasi-periodicity, deterministic chaos and random behavior. Systems adopt one or more these behaviors depending on the function they have evolved to perform. The emerging mathematical concepts of fractal mathematics and chaos theory are extending our ability to study physiological behavior. Fractal geometry is observed in the physical structure of pathways, networks and macroscopic structures such the vasculature and the His-Purkinje network of the heart. Fractal structure is also observed in processes in time, such as heart rate variability. Chaos theory describes the underlying dynamics of the system, and chaotic behavior is also observed at many levels, from effector molecules in the cell to heart function and blood pressure. This review discusses the role of fractal structure and chaos in the cardiovascular system at the level of the heart and blood vessels, and at the cellular level. Key functional consequences of these phenomena are highlighted, and a perspective provided on the possible evolutionary origins of chaotic behavior and fractal structure. The discussion is non-mathematical with an emphasis on the key underlying concepts.

Key Words: Vascular function, heart function, blood pressure, metabolism, cardiac conduction, vasomotion, temperospatial organization, fractal mathematics, chaos theory, emergence, systems biology, network analysis, complexity, self-organization, physiological time, circadian rhythms, ultradian rhythms, evolution..