Skip to main content

Chaos in the Fractal Arteriolar Network

  • Chapter
The Resistance Vasculature

Part of the book series: Vascular Biomedicine ((VB))

Abstract

There is no sure answer to such a philosophical question, but it is a way of phrasing the question of whether or not it might be beneficial to the overall system to have an arteriolar network that is fractal in structure and chaotic in behavior. Remembering that there is no such thing as proof that a model is a correct representation of the system, and that only disproof is possible, we can regard fractal models and chaotic dynamic behavior as potential models for the system, among other models. When are they good models? Why might it be advantageous to the system to be fractal or to have unpredictable behavior?

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Van Bavel, E. (1989) Metabolic and Myogenic Control of Blood Flow Studied on Isolated Small Arteries, Ph.D. Thesis, Physiology, University of Amsterdam, The Netherlands.

    Google Scholar 

  2. Suwa N., Niwa, T., Fukasawa, H., and Sasaki, Y. (1963) Tohoku J. Exp. Med. 79,168–198.

    Article  PubMed  CAS  Google Scholar 

  3. Suwa, N. and Takahashi, T. (1971) Morphological and Morphometrical Analysis of Circulation in Hypertension and Ischemic Kidney,Urban and Schwanenberg, Munich-Berlin, Germany.

    Google Scholar 

  4. Bassingthwaighte, J. B., King, R. B., and Roger, S. A. (1989) Circ. Res. 65, 578–590.

    Article  PubMed  CAS  Google Scholar 

  5. Glenny, R. W. and Robertson, H. T. (1990) J. Appl. Physiol. 69,532–545.

    PubMed  CAS  Google Scholar 

  6. King, R. B., Bassingthwaighte, J. B., Hales, J. R. S., and Rowell, L. B. (1985) Circ. Res. 57,285–295.

    Article  PubMed  CAS  Google Scholar 

  7. Bassingthwaighte, J. B., Malone, M. A., Moffett, T. C., King, R. B., Chan, I. S., Link, J. M., and Krohn, K. A. (1990) Circ. Res. 66,1328–1344.

    Article  PubMed  CAS  Google Scholar 

  8. Tripp, M. R., Meyer, M. W., Einzig, S., Leonard, J. J., Swayze, C. R., and Fox, I. J. (1977) Am. J. Physiol. (Heart. Circ. Physiol. 1) 232, H173–H190.

    CAS  Google Scholar 

  9. Van Beek, J. H. G. M., Roger, S. A., and Bassingthwaighte, J. B. (1989) Am. J. Physiol. (Heart Circ.Physiol. 26) 257, H1670–1680.

    Google Scholar 

  10. Horsfield, K. and Woldenberg, M. J. (1989) Anat. Rec. 223,245–251.

    Article  PubMed  CAS  Google Scholar 

  11. King, R. B. and Bassingthwaighte, J. B. (1989) Pflugers Arch. (Eur. J. Physiol.) 413/4,336–342.

    Article  CAS  Google Scholar 

  12. Yipintsoi, T., Dobbs, W. A., Jr., Scanlon, P. D., Knopp, T. J., and Bassingthwaighte, J. B. (1973) Circ. Res. 33,573–587.

    Article  PubMed  CAS  Google Scholar 

  13. Slaaf, D. W., Tangelder, G. J., Teirlinck, H. C., and Reneman, R. S. (1987) Microvasc. Res. 33, 71–80.

    Article  PubMed  CAS  Google Scholar 

  14. Yamashiro, S. M., Slaaf, D. W., Reneman, R. S., Tangelder, G. J., and Bassingthwaighte, J. B. (1990) Mathematical Approaches to Cardiac Arrhythmias, Ann. NY. Acad Sci. vol. S91, (Jalife, J., ed.), pp. 410–416.

    Google Scholar 

  15. Grassberger, P. and Procaccia, I. (1983) Physica 9D, 189–208.

    Google Scholar 

  16. Voss, R. F. (1988) The Science o fFractal Images, (Peitgen, H. O. and Saupe, D., eds.), Springer-Verlag, New York, pp. 21–70.

    Book  Google Scholar 

  17. Segal, S. S., Damon, D. N., and Duling, B. R. (1989) Am. J. Physiol. (Heart. Circ. Physiol. 25) 256, H832–H837.

    Google Scholar 

  18. Nelson, T. R. (1988) SPIE 914,326–333.

    Article  Google Scholar 

  19. Wang, C. Y. and Bassingthwaighte, J. B. (1990) J. Math. Comput. Modeling. 13,27–33.

    Article  Google Scholar 

  20. Hudlická, O. (1984) Handbook of Physiology. Section 2: The Cardiovascular System, vol. IV, (Renkin, E. M. and Michel, C. C., eds.), American Physiological Society, Bethesda, MD, pp. 165–216.

    Google Scholar 

  21. Caldwell, J. H., Martin, G. V., and Bassingthwaighte, J. B. (1989) FASEB J. 3, A404 (abstract).

    Google Scholar 

  22. Lefèvre, J. (1983) J. Theor. Biol. 102, 225–248.

    Article  PubMed  Google Scholar 

  23. Hudlická, O. and Tyler, K. R. (1986) Angiogenesis: The Growh of the Vascular System. Academic, London.

    Google Scholar 

  24. Schaper, W., and Wüsten, B. The Pathophysiology of Myocardial Perfusion,(Schaper, W., ed.), Elsevier, Amsterdam, pp. 415–470.

    Google Scholar 

  25. Langille, B. L., Bendeck, M. P., and Keeley, F. W. (1989) Am. J. Physiol. (Heart Circ. Physiol. 25) 256, H931H939.

    Google Scholar 

  26. Duling, B. R., Hogan, R. D., Langille, B. L., Lelkes, P., Segal, S. S., Vatner, S. F., Weigelt, H., and Young, M. A. (1987) Federation Proc. 46, 251–263.

    CAS  Google Scholar 

  27. Griffith, T. M. and Edwards, D. H. (1990) Am. J. Physiol. (Heart Circ. Physiol. 27) 258, H1171–H1180.

    CAS  Google Scholar 

  28. Langille, B. L. and O’Donnell, F. (1986) Science 231,405–407.

    Article  PubMed  CAS  Google Scholar 

Download references

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1991 Springer Science+Business Media New York

About this chapter

Cite this chapter

Bassingthwaighte, J.B. (1991). Chaos in the Fractal Arteriolar Network. In: Bevan, J.A., Halpern, W., Mulvany, M.J. (eds) The Resistance Vasculature. Vascular Biomedicine. Humana Press, Totowa, NJ. https://doi.org/10.1007/978-1-4612-0403-9_23

Download citation

  • DOI: https://doi.org/10.1007/978-1-4612-0403-9_23

  • Publisher Name: Humana Press, Totowa, NJ

  • Print ISBN: 978-1-4612-6746-1

  • Online ISBN: 978-1-4612-0403-9

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics