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Fractals in Biology and Medicine pp 114–127Cite as

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Fractal Regional Myocardial Blood Flows: The Anatomical Basis

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Part of the book series: Mathematics and Biosciences in Interaction ((MBI))

Abstract

Fractals provide a basis for analyzing recursive processes in biology, such as the growth of arborizing networks in the circulatory system, airways or glandular ducts. Coronary branching patterns appear fractal; constructing artificial vascular networks from the anatomical statistics can be done in various ways. Using a simple avoidance algorithm to position successive segments of an adult coronary arterial system correctly provides a priori prediction of five physiological features: (1) pressure profiles, (2) spatial heterogeneity in regional flows, (3) fractal dimension for the self-similarity, (4) spatial self-similar autocorrelation in flows, (5) fractal temporal washout from vascular indicators with power law exponent of —3. The success in explaining the physiology from the anatomy does not explain why the anatomy itself explains so much: growth processes of a variety of sorts may lead to similar results through a combination of growth followed by remodeling to fine-tune the relationship between tissue demands and vascular supply of oxygen and nutrients. The remodeling may be even more important than the original growth processes.

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Author information

Authors and Affiliations

  1. Department of Bioengineering, University of Washington, Seattle, Washington, 98195, USA

    J. B. Bassingthwaighte, D. A. Beard & R. B. King

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  1. J. B. Bassingthwaighte
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  2. D. A. Beard
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  3. R. B. King
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Editor information

Editors and Affiliations

  1. Laboratorio di Patologia Cellulare, Istituto Cantonale di Patologia, CH-6604, Locarno, Switzerland

    Gabriele A. Losa

  2. Centro Ricerche in Fisica e Matematica, via F. Rusco, CH-6600, Locarno, Switzerland

    Danilo Merlini

  3. Abteilung für Mathematische Physik, Universität Ulm, Albert-Einstein-Allee 11, D-89069, Ulm, Germany

    Theo F. Nonnenmacher

  4. Anatomisches Institut, Universität Bern, Bühlstrasse 26, CH-3012, Bern, Switzerland

    Ewald R. Weibel

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© 1998 Springer Basel AG

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Bassingthwaighte, J.B., Beard, D.A., King, R.B. (1998). Fractal Regional Myocardial Blood Flows: The Anatomical Basis. In: Losa, G.A., Merlini, D., Nonnenmacher, T.F., Weibel, E.R. (eds) Fractals in Biology and Medicine. Mathematics and Biosciences in Interaction. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8936-0_8

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  • DOI: https://doi.org/10.1007/978-3-0348-8936-0_8

  • Publisher Name: Birkhäuser, Basel

  • Print ISBN: 978-3-0348-9834-8

  • Online ISBN: 978-3-0348-8936-0

  • eBook Packages: Springer Book Archive

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