Chaos in Physiology: Health or Disease?

Abstract

The universality of 'chaotic' dynamics in mathematical and physical systems [1-4] has prompted renewed interest in the application of non-linear analysis to biological processes [4,5]. Attention has also focused on the physiological and medical implications of these concepts [4,6-11]. The prevailing viewpoint is that the dynamics of health are ordered ana regular and that a variety of pathologies represent a bifurcation to chaos [6,9,12]. For example, Smith and Cohen [9] advanced the hypothesis that ventricular fibrillation, the arrhythmia most commonly associated with sudden cardiac death, is a turbulent process (cardiac chaos) that may result from a subharmonic bifurcation (period-doubling) mechanism. We [8,13-16] have proposed an alternative viewpoint, contrary to this notion of chaotic disease. In particular, we have suggested that chaos is useful in modelling the 'constrained randomness' [17] inherent in the healthy function of physiological systems. This countervailing hypothesis is supported by the following lines of evidence 1. The frequency spectra associated with healthy dynamics in a variety of apparently unrelated settings (beat-to-beat heart rate variability, peripheral white blood cell fluctuations, neuronal responses) show a broadband ('noisy') profile with 1/f-like (inverse power-law) distribution (Fig. 1) [18-20]. Broadband spectra of this kind are typical of chaotic (fractal) processes. Such processes manifest self-similar fluctuations across multiple temporal orders of magnitude and, therefore, do not have a single, characteristic frequency [21]. 2. Many anatomical structures (tracheo-bronchial tree, His-Purkinje system, chordae tendineae, biliary network, vascular tree, urinary collecting system) demonstrate a fractal architecture [14,15,22-26] (Fig. 2). The ubiquity of these fractal anatomies suggests that their morphogenesis is encoded by strange attractors or renormalization group algorithms [24] that iteratively generate complex, self-similar forms lacking a characteristic scale of length. In the case of the lung tree, for example, the contribution of multiple scales provides a mechanism for both the order and variability apparent in normal bronchial architecture. The order is H. Degn et al. (eds.), Chaos in Biological Systems