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Abstract
Our goal is to explore the relationship between two traditionally unrelated concepts, fractal structure and entropy production, evaluating both within the central nervous system (CNS). Fractals are temporal or spatial structures with self-similarity across scales of measurement; whereas entropy production represents the necessary exportation of entropy to our environment that comes with metabolism and life. Fractals may be measured by their fractal dimension; and human entropy production may be estimated by oxygen and glucose metabolism. In this paper, we observe fractal structures ubiquitously present in the CNS, and explore a hypothetical and unexplored link between fractal structure and entropy production, as measured by oxygen and glucose metabolism. Rapid increase in both fractal structures and metabolism occur with childhood and adolescent growth, followed by slow decrease during aging. Concomitant increases and decreases in fractal structure and metabolism occur with cancer vs. Alzheimer’s and multiple sclerosis, respectively. In addition to fractals being related to entropy production, we hypothesize that the emergence of fractal structures spontaneously occurs because a fractal is more efficient at dissipating energy gradients, thus maximizing entropy production. Experimental evaluation and further understanding of limitations and necessary conditions are indicated to address broad scientific and clinical implications of this work.
Highlights
The central nervous system (CNS) is arguably the most complex, remarkable, seemingly impenetrable, not to mention endearing and personal complex system in Nature
Based on research within the CNS, we observe that increased fractal dimension in spatial structure is associated with increased entropy production, as measured by metabolism
Fractal studies have demonstrated a decrease in fractal dimension of the CNS with illness (i.e., Alzheimer’s [42], epilepsy [23,24], MS [45], stroke [49]) which correlates with metabolic studies demonstrating a decline in glucose metabolism with illness [83,85,88,90,91,92,93,94,95,96,97,101,102,103]
Summary
The central nervous system (CNS) is arguably the most complex, remarkable, seemingly impenetrable, not to mention endearing and personal complex system in Nature. The emergent properties of the CNS such as consciousness, memory, coordinated movement, and homeostasis, are as remarkable as the self-organized manner in which they are formed during embryogenesis and childhood. The CNS is fertile ground to explore concepts regarding the origin of self-organized structure and function in complex systems. We would like to emphasize that this is not an expert review of the CNS, nor of its associated illnesses. There is a case to be made that the ideas presented apply to the CNS, but to other complex systems found in nature
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