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 B iological systems display a variety of well-known rhythms in physiological signals (1-6), with particular patterns of variability associated with a healthy state (2-6). Decades of research demonstrate that heart rate (HR) in healthy humans has high variability, and loss of this high HR variability (HRV) is correlated with adverse states such as stress, fatigue, physiologic senescence, or disease (6-13). The dominant approach to analysis of HRV has been to focus on statistics and patterns in HR time series that have been interpreted as fractal, chaotic, scale-free, critical, etc. (6-17). The appeal of time series analysis is understandable as it puts HRV in the context of a broad and popular approach to complex systems (5, 18), all while requiring minimal attention to domain-specific (e.g., physiological) details. However, despite intense research activity in this area, there is limited consensus regarding causation or mechanism and minimal clinical application of the observed phenomena (10). This paper takes a completely different approach, aiming for more fundamental rigor (19)(20)(21)(22)(23)(24) and methods that have the potential for clinical relevance. Here we use and model data from experimental studies of exercising healthy athletes, to add simple physiological explanations for the largest source of HRV and its changes during exercise. We also present methods that can be used to systematically pursue further explanations about HRV that can generalize to less healthy subjects. Fig. 1 shows the type of HR data analyzed, collected from healthy young athletes (n = 5). The data display responses to changes in muscle work rate on a s...

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