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Published August 19, 2014 | Published + Supplemental Material
Journal Article Open

Robust efficiency and actuator saturation explain healthy heart rate control and variability


The correlation of healthy states with heart rate variability (HRV) using time series analyses is well documented. Whereas these studies note the accepted proximal role of autonomic nervous system balance in HRV patterns, the responsible deeper physiological, clinically relevant mechanisms have not been fully explained. Using mathematical tools from control theory, we combine mechanistic models of basic physiology with experimental exercise data from healthy human subjects to explain causal relationships among states of stress vs. health, HR control, and HRV, and more importantly, the physiologic requirements and constraints underlying these relationships. Nonlinear dynamics play an important explanatory role––most fundamentally in the actuator saturations arising from unavoidable tradeoffs in robust homeostasis and metabolic efficiency. These results are grounded in domain-specific mechanisms, tradeoffs, and constraints, but they also illustrate important, universal properties of complex systems. We show that the study of complex biological phenomena like HRV requires a framework which facilitates inclusion of diverse domain specifics (e.g., due to physiology, evolution, and measurement technology) in addition to general theories of efficiency, robustness, feedback, dynamics, and supporting mathematical tools.

Additional Information

Copyright © 2014 National Academy of Sciences. Edited by Michael S. Gazzaniga, University of California, Santa Barbara, CA, and approved June 27, 2014 (received for review January 30, 2014). Published online before print August 4, 2014, doi: 10.1073/pnas.1401883111. We thank Pamela B. Pesenti for her gift in establishing the John G. Braun Professorship, which supported this research, and Philips for providing equipment used in the experiments. The research progress has been presented and discussed at several meetings, including the International Conference on Complexity in Acute Illness of the Society for Complexity in Acute Illness (SCAI). Comments from many SCAI members greatly influenced this paper. We also thank the athletes who were the subjects for this study. The theoretical aspects of this work and the connections with other complex systems challenges were supported in part by Air Force Office of Scientific Research and National Science Foundation. Preliminary exploration in this research direction was funded by Pfizer, National Institutes of Health (R01 GM078992), and the Institute of Collaborative Biotechnologies (ARO W911NF-09-D-0001). Author contributions: N.L., J.C., B.R., and J.C.D. designed research; N.L., J.C., C.S.C., B.R., D.B., and J.C.D. performed research; N.L., J.C., S.S., B.R., and J.C.D. contributed new reagents/analytic tools; N.L., J.C., C.S.C., S.S., and J.C.D. analyzed data; and N.L., D.S., M.C., and J.C.D. wrote the paper. The authors declare no conflict of interest. This Direct Submission article had a prearranged editor. This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10.1073/pnas.1401883111/-/DCSupplemental.

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Published - E3476.full.pdf

Supplemental Material - pnas.1401883111.sapp.pdf


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