Skip to main content
SpringerLink
Log in

Fractal Analysis in Clinical Neurosciences: An Overview

  • Chapter
  • First Online:
The Fractal Geometry of the Brain

Part of the book series: Springer Series in Computational Neuroscience ((NEUROSCI))

  • 2760 Accesses

Abstract

Over the last years, fractals have entered into the realms of clinical neurosciences. The whole brain and its components (i.e., neurons and microglia) have been studied as fractal objects, and even more relevant, the fractal-based quantification of the geometrical complexity of histopathological and neuroradiological images as well as neurophysiopathological time series has suggested the existence of a gradient in the patterns representation of neurological diseases. Computational fractal-based parameters have been suggested as potential diagnostic and prognostic biomarkers in different brain diseases, including brain tumors, neurodegeneration, epilepsy, demyelinating diseases, cerebrovascular malformations, and psychiatric disorders as well. This chapter and the entire third section of this book are focused on practical applications of computational fractal-based analysis into the clinical neurosciences, namely, neurology and neuropsychiatry, neuroradiology and neurosurgery, neuropathology, neuro-oncology and neurorehabilitation, and neuro-ophthalmology and cognitive neurosciences, with special emphasis on the translation of the fractal dimension as clinical biomarker useful from bench to bedside.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 189.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 249.99
Price excludes VAT (USA)
  • Compact, lightweight 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

References

  1. Baish JW, Jain RK. Fractals and cancer. Cancer Res. 2000;60:3683–8.

    CAS  PubMed  Google Scholar 

  2. Bassett DS, Meyer-Lindenberg A, Achard S, Duke T, Bullmore E. Adaptive reconfiguration of fractal small-world human brain functional networks. Proc Natl Acad Sci U S A. 2006;103:19518–23.

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  3. Bullmore E, Fadili J, Maxim V, Sendur L, Whitcher B, Suckling J, et al. Wavelets and functional magnetic resonance imaging of the human brain. Neuroimage. 2004;23 Suppl 1:S234–49.

    Article  PubMed  Google Scholar 

  4. Cassot F, Lauwers F, Fouard C, Prohaska S, Lauwers-Cances V. A novel three-dimensional computer-assisted method for a quantitative study of microvascular networks of the human cerebral cortex. Microcirculation (New York, NY 1994). 2006;13:1–18.

    Article  CAS  Google Scholar 

  5. Cross SS. Fractals in pathology. J Pathol. 1997;182:1–8.

    Article  CAS  PubMed  Google Scholar 

  6. Cross SS. The application of fractal geometric analysis to microscopic images. Micron. 1994;25:101–13.

    Article  CAS  PubMed  Google Scholar 

  7. Di Ieva A, Esteban FJ, Grizzi F, Klonowski W, Martin-Landrove M. Fractals in the neurosciences. Part II: clinical applications and future perspectives. Neuroscientist. 2015;21:30–43.

    Article  PubMed  Google Scholar 

  8. Di Ieva A, Matula C, Grizzi F, Grabner G, Trattnig S, Tschabitscher M. Fractal analysis of the susceptibility-weighted imaging patterns in malignant brain tumors during antiangiogenic treatment: technical report on four cases serially imaged by 7T magnetic resonance during a period of four weeks. World Neurosurg. 2012;77:785.e11–21.

    Google Scholar 

  9. Di Ieva A, Tschabitscher M. Fractal-based classification of brain tumors angioarchitecture. In: Mitchell EW, Murray SR (Eds). Classification and applications of fractals: new research. New York: Nova Science Publishers; 2012. p. 205–16.

    Google Scholar 

  10. Di Ieva A, Grizzi F, Gaetani P, Goglia U, Tschabitscher M, Mortini P, et al. Euclidean and fractal geometry of microvascular networks in normal and neoplastic pituitary tissue. Neurosurg Rev. 2008;31:271–80.

    Article  PubMed  Google Scholar 

  11. Di Ieva A, Schmitz EM, Cusimano MD. Analysis of intracranial pressure: past, present, and future. Neuroscientist. 2013;19:592–603.

    Article  PubMed  Google Scholar 

  12. Dinicola S, D’Anselmi F, Pasqualato A, Proietti S, Lisi E, Cucina A, et al. A systems biology approach to cancer: fractals, attractors, and nonlinear dynamics. OMICS. 2011;15:93–104.

    Article  CAS  PubMed  Google Scholar 

  13. Goldberger AL, West BJ. Fractals in physiology and medicine. Yale J Biol Med. 1987;60:421–35.

    CAS  PubMed  PubMed Central  Google Scholar 

  14. Hamburger D, Biham O, Avnir D. Apparent fractality emerging from models of random distributions. Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics. 1996;53:3342–58.

    CAS  PubMed  Google Scholar 

  15. Herman P, Kocsis L, Eke A. Fractal branching pattern in the pial vasculature in the cat. J Cereb Blood Flow Metab. 2001;21:741–53.

    Article  CAS  PubMed  Google Scholar 

  16. Di Ieva A. Fractal analysis of microvascular networks in malignant brain tumors. Clin Neuropathol. 2012;31:342–51.

    Article  PubMed  Google Scholar 

  17. Klonowski W. Everything you wanted to ask about EEG but were afraid to get the right answer. Nonlinear Biomed Phys. 2009;3:2.

    Article  PubMed  PubMed Central  Google Scholar 

  18. Landini G. Fractals in microscopy. J Microsc. 2011;241:1–8.

    Article  CAS  PubMed  Google Scholar 

  19. Lopes R, Betrouni N. Fractal and multifractal analysis: a review. Med Image Anal. 2009;13:634–49.

    Article  CAS  PubMed  Google Scholar 

  20. Lorthois S, Cassot F. Fractal analysis of vascular networks: insights from morphogenesis. J Theor Biol. 2010;262:614–33.

    Article  PubMed  Google Scholar 

  21. Losa GA, Nonnenmacher TF. Self-similarity and fractal irregularity in pathologic tissues. Mod Pathol. 1996;9:174–82.

    CAS  PubMed  Google Scholar 

  22. Marco DE, Cannas SA, Montemurro MA, Hu B, Cheng S-Y. Comparable ecological dynamics underlie early cancer invasion and species dispersal, involving self-organizing processes. J Theor Biol. 2009;256:65–75.

    Article  PubMed  Google Scholar 

  23. Merlo LMF, Pepper JW, Reid BJ, Maley CC. Cancer as an evolutionary and ecological process. Nat Rev Cancer. 2006;6:924–35.

    Article  CAS  PubMed  Google Scholar 

  24. Noble D. Biophysics and systems biology. Philos Trans A Math Phys Eng Sci. 2010;368:1125–39.

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  25. Olejarczyk E. Application of fractal dimension method of functional MRI time-series to limbic dysregulation in anxiety study. Conf Proc Annu Int Conf IEEE Eng Med Biol Soc. 2007;2007:3408–10.

    Google Scholar 

  26. Panerai RB. Complexity of the human cerebral circulation. Philos Trans A Math Phys Eng Sci. 2009;367:1319–36.

    Article  PubMed  Google Scholar 

  27. Plenz D, Thiagarajan TC. The organizing principles of neuronal avalanches: cell assemblies in the cortex? Trends Neurosci. 2007;30:101–10.

    Article  CAS  PubMed  Google Scholar 

  28. Risser L, Plouraboue F, Steyer A, Cloetens P, Le Duc G, Fonta C. From homogeneous to fractal normal and tumorous microvascular networks in the brain. J Cereb Blood Flow Metab. 2007;27:293–303.

    Article  PubMed  Google Scholar 

  29. Spillman WB, Robertson JL, Huckle WR, Govindan BS, Meissner KE. Complexity, fractals, disease time, and cancer. Phys Rev E Stat Nonlin Soft Matter Phys. 2004;70:061911.

    Article  PubMed  Google Scholar 

  30. Sporns O. Small-world connectivity, motif composition, and complexity of fractal neuronal connections. Biosystems. 2006;85:55–64.

    Article  PubMed  Google Scholar 

  31. Takahashi T. Microcirculation in fractal branching networks. Tokyo: Springer; 2014.

    Book  Google Scholar 

  32. Vakoc BJ, Lanning RM, Tyrrell JA, Padera TP, Bartlett LA, Stylianopoulos T, et al. Three-dimensional microscopy of the tumor microenvironment in vivo using optical frequency domain imaging. Nat Med. 2009;15:1219–23.

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  33. Wang P, Li L, Zhang C, Lei Q, Fang W. Effects of fractal surface on C6 glioma cell morphogenesis and differentiation in vitro. Biomaterials. 2010;31:6201–6.

    Google Scholar 

  34. West GB, Brown JH, Enquist BJ. The fourth dimension of life: fractal geometry and allometric scaling of organisms. Science. 1999;284:1677–9.

    Article  CAS  PubMed  Google Scholar 

  35. Zamir M. Fractal dimensions and multifractility in vascular branching. J Theor Biol. 2001;212:183–90.

    Article  CAS  PubMed  Google Scholar 

  36. Zamir M. On fractal properties of arterial trees. J Theor Biol. 1999;197:517–26.

    Article  CAS  PubMed  Google Scholar 

  37. Zamir M, Phipps S. Network analysis of an arterial tree. J Biomech. 1988;21:25–34.

    Article  CAS  PubMed  Google Scholar 

  38. Di Ieva A. Fractal Analysis of Microvascular Networks in Malignant Brain Tumors. PhD Thesis. Medical University of Vienna, Vienna, Austria, 2011. Available from: https://www.meduniwien.ac.at/hp/fileadmin/kin/Completed_Thesis/Thesis_Di_Ieva.pdf

Download references

Author information

Authors and Affiliations

  1. Neurosurgery Unit, Faculty of Medicine and Health Sciences, Macquarie University, Sydney, NSW, Australia

    Antonio Di Ieva MD, PhD

  2. Garvan Institute of Medical Research, Sydney, NSW, Australia

    Antonio Di Ieva MD, PhD

  3. Medical University of Vienna, Vienna, Austria

    Antonio Di Ieva MD, PhD

  4. University of Toronto, Toronto, ON, Canada

    Antonio Di Ieva MD, PhD

Authors
  1. Antonio Di Ieva MD, PhD
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Antonio Di Ieva MD, PhD .

Editor information

Editors and Affiliations

  1. Department of Surgery Division of Neurosurgery, University of Toronto St. Michael's Hospital, Toronto, Ontario, Canada

    Antonio Di Ieva

Rights and permissions

Reprints and permissions

Copyright information

© 2016 Springer Science+Business Media New York

About this chapter

Cite this chapter

Di Ieva, A. (2016). Fractal Analysis in Clinical Neurosciences: An Overview. In: Di Ieva, A. (eds) The Fractal Geometry of the Brain. Springer Series in Computational Neuroscience. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-3995-4_12

Download citation

Publish with us

Policies and ethics

Search

Navigation