Allometric scaling law and ergodicity breaking in the vascular system

Michael Nosonovsky; Prosun Roy

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arXiv · 2006.07538

Allometric scaling law and ergodicity breaking in the vascular system

Michael Nosonovsky·Prosun Roy

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Abstract

Allometry or the quantitative study of the relationship of body size to living organism physiology is an important area of biophysical scaling research. The West-Brown-Enquist (WBE) model of fractal branching in a vascular network explains the empirical allometric Kleiber law (the 3/4 scaling exponent for metabolic rates as a function of animal's mass). The WBE model raises a number of new questions, such as how to account for capillary phenomena more accurately and what are more realistic dependencies for blood flow velocity on the size of a capillary. We suggest a generalized formulation of the branching model and investigate the ergodicity in the fractal vascular system. In general, the fluid flow in such a system is not ergodic, and ergodicity breaking is attributed to the fractal structure of the network. Consequently, the fractal branching may be viewed as a source of ergodicity breaking in biophysical systems, in addition to such mechanisms as aging and macromolecular crowding. Accounting for non-ergodicity is important for a wide range of biomedical applications where long observations of time series are impractical. The relevance to microfluidics applications is also discussed.

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Michael Nosonovsky, Prosun Roy. 2020-06-13. Allometric scaling law and ergodicity breaking in the vascular system. https://arxiv.org/abs/2006.07538

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