On the stability and adaptability of human physiology: Gaussians meet heavy-tailed distributions

Recent technological advances allow to monitor in baka non-invasive and continuous way a wide variety of physiological variables. A surprise of the last few decades is that most — if not all — of these variables are always fluctuating, even when the monitored subject is in resting conditions, and the general interpretation is that the statistics of these fluctuations reflect the dynamics of the underlying regulatory mechanisms. The objective of the present contribution is to offer an explanation why a large variability may be a signature of good health for some variables, e.g., heart rate variability, whereas it is interpreted as a risk factor for other variables, like blood pressure variability. Control theory suggests that variables may be classified into 2 categories, depending on the roles they play in the regulatory mechanism, and we argue that the statistics of the corresponding time series may reflect these different functions. We illustrate with experimental time series that regulated variables, such as blood pressure and core temperature, which are to be maintained within a restricted range around a predefined setpoint, correspond to time series that obey a normal (Gaussian) distribution with small variability around a representative average value. On the other hand, effector variables, such as heart rate and skin temperature, oppose or adapt to a multitude of perturbations from the environment, and we show that the corresponding time series exhibit a large variability and obey heavy-tailed distributions that may span various scales. With ageing and/or chronic degenerative disease, effector variables lose variability and adaptive capacity and consequently regulated variables lose stability and become more variable. Although the above results on the variability of time series have been obtained for the specific case of human physiology, they may be applicable as well to other complex dynamical systems where regulatory control mechanisms are active.