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Application of Fractal Analysis to Evaluate the Rat Brain Arterial System

  • COMPLEX SYSTEMS BIOPHYSICS
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Abstract

Vascular networks possess properties of self-similarity, which allows one to consider them as stochastic fractals. The box-counting method based on calculations along the vessel centerlines is traditionally used to evaluate the parameters of the fractal structure. Such an algorithm does not allow one to consider structural differences between different bifurcation levels of the system, characterized by the natural property of changing the blood vessel caliber. In this case, the discrepancy between the values of the fractal dimension may exceed 20%. In this paper, an approach that allows one to avoid underestimating the complexity of the system for low bifurcation orders and large vessels is proposed. Based on the constructed arterial tree of the rat brain, it was shown that the fractal dimension increases with an increase in the values of both bifurcation exponent and length coefficient. The obtained values most fully reflect the properties of the arterial tree considering the real geometry of the vessels; they are proposed for use in estimating three-dimensional vascular networks.

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REFERENCES

  1. J.-J. Li, Dynamics of the Vascular System (World Scientific Publ., 2004).

    Book  Google Scholar 

  2. B. R. Masters, Annu. Rev. Biomed. Eng. 6, 427 (2004).

    Article  Google Scholar 

  3. E. Gaudio, S. Chaberek, A. Montella, et al., J. Anat. 207 (2), 107 (2005).

    Article  Google Scholar 

  4. M. Zamir, J. Theor. Biol. 212 (2), 183 (2001).

    Article  Google Scholar 

  5. S. Lorthois and F. Cassot, J. Theor. Biol. 262 (4), 614 (2010).

    Article  Google Scholar 

  6. T. Takahashi, Microcirculation in Fractal Branching Networks (Springer Japan, 2014).

    Book  Google Scholar 

  7. D. J. Gould, T. J. Vadakkan, R. A. Poche, et al., Microcirculation 18 (2), 136 (2011).

    Article  Google Scholar 

  8. H. A. Crystal, S. Holman, Y. W. Lui, et al., PLoS One 11 (5), e0154858 (2016).

    Article  Google Scholar 

  9. V. Goh, B. Sanghera, D. M. Wellsted, et al., Eur. Radiol. 19 (6), 1358 (2009).

    Article  Google Scholar 

  10. S. Lang, B. Muller, M. D. Dominietto, et al., Microvasc. Res. 84 (3), 314 (2012).

    Article  Google Scholar 

  11. M. Helmberger, M. Pienn, M. Urschler, et al., PLoS One 9 (1), e87515 (2014).

    Article  ADS  Google Scholar 

  12. S. Haitao, L. Ning, G. Lijun, et al., Korean J. Radiol. 12 (3), 289 (2011).

    Article  Google Scholar 

  13. S. Moledina, A. de Bruyn, S. Schievano, et al., Heart 97 (15), 1245 (2011).

    Article  Google Scholar 

  14. R. Kawasaki, M. Z. Che Azemin, D. K. Kumar, et al., Neurology 76 (20), 1766 (2011).

    Article  Google Scholar 

  15. B. J. West, Front. Physiol. 1, 12 (2010).

    Google Scholar 

  16. G. S. Kassab, C. A. Rider, N. J. Tang, et al., Am. J. Physiol. 265, H350 (1993).

    Google Scholar 

  17. V. S. Kopylova, S. E. Boronovskiy and Y. R. Nartsissov, Biochem. Soc. Trans. 45 (3), 839 (2017).

    Article  Google Scholar 

  18. C. D. Murray, J. Gen. Physiol. 9 (6), 835 (1926).

    Article  Google Scholar 

  19. R. Karch, F. Neumann, M. Neumann, et al., Ann. Biomed. Eng. 28 (5), 495 (2000).

    Article  Google Scholar 

  20. M. Zamir, The Physics of Pulsatile Flow (Springer, New York, 2000).

    Book  Google Scholar 

  21. M. Ge and Q. Lin, Geo-Spatial Inform. Sci. 12 (4), 265 (2009).

    Google Scholar 

  22. Y. T. Ong, D. A. De Silva, C. Y. Cheung, et al., Stroke 44 (8), 2121 (2013).

    Article  Google Scholar 

  23. C. Y. Cheung, Y. T. Ong, M. K. Ikram, et al., Alzheimers Dement. 10 (2), 135 (2014).

    Article  Google Scholar 

  24. N. Popovic, M. Radunovic, J. Badnjar, et al., Microvasc. Res. 118, 36 (2018).

    Article  Google Scholar 

  25. S. Kido, K. Kuriyama, M. Higashiyama, et al., J. Comput. Assist. Tomogr. 27 (1), 56 (2003).

    Article  Google Scholar 

  26. Y. Gazit, D. A. Berk, M. Leunig, et al., Phys. Rev. Lett. 75 (12), 2428 (1995).

    Article  ADS  Google Scholar 

  27. N. Tsafnat, G. Tsafnat, and T. D. Lambert, Conf. Proc. IEEE Eng. Med. Biol. Soc. 1, 683 (2004).

    Google Scholar 

  28. V. Kopylova, S. Boronovskiy, and Y. Nartsissov, Phys. Biol. 16 (5), 056002 (2019).

    Article  ADS  Google Scholar 

  29. V. S. Kopylova, S. E. Boronovskiy, and Y. R. Nartsis-sov, J. Phys. Conf. Ser. 1141, 012027 (2018).

    Article  Google Scholar 

  30. V. S. Kopylova, S. E. Boronovskiy, and Y. R. Nartsis-sov, Math. Biosci. 315, 108237 (2019).

    Article  MathSciNet  Google Scholar 

  31. F. Cassot, F. Lauwers, C. Fouard, et al., Microcirculation 13 (1), 1 (2006).

    Article  Google Scholar 

  32. M. Zamir, J. Gen. Physiol. 91 (5), 725 (1988).

    Article  Google Scholar 

  33. A. Kaimovitz, Y. Huo, Y. Lanir, et al., Am. J. Physiol. Heart Circ. Physiol. 294 (2), H714 (2008).

    Article  Google Scholar 

  34. A. D. Hughes, Artery Res. 10 (C), 1 (2015).

    Article  Google Scholar 

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Authors and Affiliations

  1. Institute of Cytochemistry and Molecular Pharmacology, 115404, Moscow, Russia

    V. S. Kopylova, S. E. Boronovskiy & Ya. R. Nartsissov

Authors
  1. V. S. Kopylova
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  2. S. E. Boronovskiy
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  3. Ya. R. Nartsissov
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Correspondence to V. S. Kopylova.

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Translated by D. Novikova

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Kopylova, V.S., Boronovskiy, S.E. & Nartsissov, Y.R. Application of Fractal Analysis to Evaluate the Rat Brain Arterial System. BIOPHYSICS 65, 495–504 (2020). https://doi.org/10.1134/S0006350920030100

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