Giles f. Filley lecture. Complex systems

Abstract

Physiologic systems in health and disease display an extraordinary range of temporal behaviors and structural patterns that defy understanding based on linear constructs, reductionist strategies, and classical homeostasis. Application of concepts and computational tools derived from the contemporary study of complex systems, including nonlinear dynamics, fractals and "chaos theory," is having an increasing impact on biology and medicine. This presentation provides a brief overview of an emerging area of biomedical research, including recent applications to cardiopulmonary medicine and chronic obstructive lung disease.

Figure 1.

Conventional statistical summary of heart rate dynamics in two subjects over 15 min showing nearly identical mean values and SDs (error bars). One subject is healthy; the other was having episodes of severe obstructive sleep apnea. bpm = beats per minute.

Figure 2.

Original (“raw”) heart rate time series from the two subjects (one healthy, one during obstructive sleep apnea) whose data are summarized in Figure 1. Note the marked differences in the underlying dynamics despite the essentially identical mean values and SDs. The healthy dynamics (top) show the more complex pattern of variability, in contrast to the relatively periodic temporal structure of the sleep apnea dataset (bottom).

Figure 3.

Schematic representations of self-similar structures and self-similar fluctuations. The treelike, spatial fractal (left) has self-similar branchings, such that the small-scale structure resembles the large-scale form. A fractal temporal process, such as healthy heart rate regulation (right), generates fluctuations on different time scales that are statistically self-similar. Adapted by permission from Reference .

Figure 4.

Illustrative interbreath interval (IBI) time series (obtained at rest by inductance plethysmography) for (a) a healthy young male adult and (b) a healthy elderly male subject. Both time series show an irregular pattern of spontaneous breathing with considerable variability (ordinate) in IBIs over 1,000 consecutive breathing cycles (abscissa). A fractal analysis of the correlation properties of the two datasets is presented in (c) on a log-log plot using the detrended fluctuation analysis (DFA) technique. Dashed lines give the least-square fits for the data from both subjects. The slope of these fitted lines in the DFA exponent, α. The power-law fits are consistent with fractal dynamics. Of note, the slope for the elderly subject (closer to a value of 0.5 indicative of an uncorrelated process) is consistent with an age-related degradation of the long-range fractal organization of respiratory control (see Reference 25). Adapted by permission from Reference .