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Allometric scaling law and ergodicity breaking in the vascular system

Microfluidics and Nanofluidics volume 24, Article number: 53 (2020) Cite this article

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 ¾ 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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Acknowledgement

Partially supported by the Russian Science Foundation (project 19-19-00076). The authors would like to thank Prof. Roshan D’Souza for the CFD software used in this study and anonymous reviewers for the discussion which improved this paper.

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Authors and Affiliations

  1. Department of Mechanical Engineering, University of Wisconsin-Milwaukee, 3200 N Cramer St, Milwaukee, WI, 53211, USA

    Michael Nosonovsky & Prosun Roy

  2. X-BIO Institute, University of Tyumen, 6 Volodarskogo St, Tyumen, 625003, Russia

    Michael Nosonovsky

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  1. Michael Nosonovsky
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  2. Prosun Roy
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Correspondence to Michael Nosonovsky.

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Nosonovsky, M., Roy, P. Allometric scaling law and ergodicity breaking in the vascular system. Microfluid Nanofluid 24, 53 (2020). https://doi.org/10.1007/s10404-020-02359-x

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  • DOI: https://doi.org/10.1007/s10404-020-02359-x

Keywords

  • Allometry
  • Ergodicity
  • Fractal branching
  • Capillaries
  • Cardiovascular system
  • Microfluidics