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Research Article

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

Na Li, Jerry Cruz, Chenghao Simon Chien, Somayeh Sojoudi, Benjamin Recht, David Stone, Marie Csete, Daniel Bahmiller, and John C. Doyle
PNAS August 19, 2014 111 (33) E3476-E3485; first published August 4, 2014; https://doi.org/10.1073/pnas.1401883111
Na Li
aSchool of Engineering and Applied Sciences, Harvard University, Cambridge, MA 02138;
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Jerry Cruz
bDepartment of Computing and Mathematical Science, California Institute of Technology, Pasadena, CA 91125;
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Chenghao Simon Chien
cDepartment of Electrical Engineering, California Institute of Technology, Pasadena, CA 91125;
dAdvanced Algorithm Research Center, Philips Healthcare, Thousand Oaks, CA 91320;
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Somayeh Sojoudi
eDepartment of Neurology, New York University Comprehensive Epilepsy Center, New York University School of Medicine, New York, NY 10016;
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Benjamin Recht
fDepartment of Electrical Engineering and Computer Sciences and Department of Statistics, University of California, Berkeley, CA 94720;
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David Stone
gDepartments of Anesthesiology and Neurosurgery and the Center for Wireless Health, University of Virginia School of Medicine, Charlottesville, VA 22908;
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Marie Csete
hHuntington Medical Research Institutes, Pasadena, CA 91101; and
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Daniel Bahmiller
bDepartment of Computing and Mathematical Science, California Institute of Technology, Pasadena, CA 91125;
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John C. Doyle
bDepartment of Computing and Mathematical Science, California Institute of Technology, Pasadena, CA 91125;
cDepartment of Electrical Engineering, California Institute of Technology, Pasadena, CA 91125;
iDepartment of BioEngineering, California Institute of Technology, Pasadena, CA 91125
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  • For correspondence: doyle@caltech.edu
  1. Edited* by Michael S. Gazzaniga, University of California, Santa Barbara, CA, and approved June 27, 2014 (received for review January 30, 2014)

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Significance

Reduction in human heart rate variability (HRV) is recognized in both clinical and athletic domains as a marker for stress or disease, but previous mathematical and clinical analyses have not fully explained the physiological mechanisms of the variability. Our analysis of HRV using the tools of control mathematics reveals that the occurrence and magnitude of observed HRV is an inevitable outcome of a controlled system with known physiological constraints. In addition to a deeper understanding of physiology, control analysis may lead to the development of timelier monitors that detect control system dysfunction, and more informative monitors that can associate HRV with specific underlying physiological causes.

Abstract

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.

  • system identification
  • optimal control
  • respiratory sinus arrhythmia

Footnotes

  • ↵1To whom correspondence should be addressed. Email: doyle{at}caltech.edu.
  • 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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Control theory explains heart rate variability
Na Li, Jerry Cruz, Chenghao Simon Chien, Somayeh Sojoudi, Benjamin Recht, David Stone, Marie Csete, Daniel Bahmiller, John C. Doyle
Proceedings of the National Academy of Sciences Aug 2014, 111 (33) E3476-E3485; DOI: 10.1073/pnas.1401883111

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Control theory explains heart rate variability
Na Li, Jerry Cruz, Chenghao Simon Chien, Somayeh Sojoudi, Benjamin Recht, David Stone, Marie Csete, Daniel Bahmiller, John C. Doyle
Proceedings of the National Academy of Sciences Aug 2014, 111 (33) E3476-E3485; DOI: 10.1073/pnas.1401883111
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