Fractal variability: An emergent property of complex dissipative systems

Abstract

The patterns of variation of physiologic parameters, such as heart and respiratory rate, and their alteration with age and illness have long been under investigation; however, the origin and significance of scale-invariant fractal temporal structures that characterize healthy biologic variability remain unknown. Quite independently, atmospheric and planetary scientists have led breakthroughs in the science of non-equilibrium thermodynamics. In this paper, we aim to provide two novel hypotheses regarding the origin and etiology of both the degree of variability and its fractal properties. In a complex dissipative system, we hypothesize that the degree of variability reflects the adaptability of the system and is proportional to maximum work output possible divided by resting work output. Reductions in maximal work output (and oxygen consumption) or elevation in resting work output (or oxygen consumption) will thus reduce overall degree of variability. Second, we hypothesize that the fractal nature of variability is a self-organizing emergent property of complex dissipative systems, precisely because it enables the system's ability to optimally dissipate energy gradients and maximize entropy production. In physiologic terms, fractal patterns in space (e.g., fractal vasculature) or time (e.g., cardiopulmonary variability) optimize the ability to deliver oxygen and clear carbon dioxide and waste. Examples of falsifiability are discussed, along with the need to further define necessary boundary conditions. Last, as our focus is bedside utility, potential clinical applications of this understanding are briefly discussed. The hypotheses are clinically relevant and have potential widespread scientific relevance.