Box-Counting and Multifractal Analysis in Neuronal and Glial Classification

  • Herbert F. Jelinek
  • Nebojša T. Milošević
  • Audrey Karperien
  • Bojana Krstonošić
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 187)

Abstract

Fractal analysis in the neurosciences has advanced over the past twenty years. The fractal dimension, besides its ability to discriminate among different cell types, can work as a reliable parameter in cell classification. A qualitative analysis of the morphology of neurons and glia cell types involves a detailed description of the structure and features of cells, and accordingly, their classification into defined classes and types. This paper outlines how fractal analysis can be used for further quantitative classification of these cell types using box-counting and multifractal analysis.

Keywords

Box dimension Cell classification Human Fractal analysis Multifractal Microglia Aspinous Neostriatum 

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References

  1. 1.
    Smith Jr., T.G., Lange, G.D., Marks, W.B.: Fractal methods and results in cellular morphology - dimensions, lacunarity and multifractals. J. Neurosci. Meth. 69, 123–136 (1996)CrossRefGoogle Scholar
  2. 2.
    Fernández, E., Jelinek, H.F.: Use of fractal theory in neuroscience: methods, advantages, and potential problems. Methods 24, 309–321 (2001)CrossRefGoogle Scholar
  3. 3.
    Jelinek, H.F., Cornforth, D.J., Roberts, T., Landini, G., Bourke, P., Bossomaier, T.: Image processing of finite size rat retinal ganglion cells using multifractal and local connected fractal analysis. In: Complex Systems Conference, Cairns, Australia (2004)Google Scholar
  4. 4.
    Nonnenmacher, T.F., Baumann, G., Barth, A., Losa, G.A.: Digital image analysis of self-similar cell profiles. Int. J. Bio-Med. Comp. 37, 131–138 (1994)CrossRefGoogle Scholar
  5. 5.
    Smith Jr., T.G., Marks, W.B., Lange, G.D., Sheriff Jr., W.H., Neale, E.A.: A fractal analysis of cell images. J. Neurosci. Meth. 27, 173–180 (1989)CrossRefGoogle Scholar
  6. 6.
    Jelinek, H.F., Fernández, E.: Neurons and fractals: how reliable and useful are calculations of fractal dimension? J. Neurosci. Meth. 81, 9–18 (1998)CrossRefGoogle Scholar
  7. 7.
    Ristanović, D., Stefanović, B.D., Milošević, N.T., Grgurević, M., Štulić, V.: Fractal and nonfractal analysis of cell images: comparison and application to neuronal dendritic arborization. Biol. Cybern. 87, 278–288 (2002)MATHCrossRefGoogle Scholar
  8. 8.
    Mandelbrot, B.B.: The fractal geometry of nature. Freeman and Co., New York (1983)Google Scholar
  9. 9.
    Schroeder, M.: Fractals, chaos, power laws. W.H Freeman and Co., New York (1991)MATHGoogle Scholar
  10. 10.
    Iannaccone, P.M., Khokha, M.: Fractal geometry in biological systems: an analytical approach. CRC Press, New York (1995)Google Scholar
  11. 11.
    Karperien, A.L., Jelinek, H.F., Buchan, A.M.: Box-counting analysis of microglia form in schizophrenia, Alzheimer’s disease and affective disorder. Fractals 16, 103–107 (2008)CrossRefGoogle Scholar
  12. 12.
    Voss, R.M., Wyatt, J.C.Y.: Multifractals and local connected fractal dimension: Classification of early chinese landscape paintings. In: Crilly, A.J., Earnshaw, R.A., Jones, H. (eds.) Applications of Fractals and Chaos. Springer, Berlin (1991)Google Scholar
  13. 13.
    Stanley, H.E., Amaral, L.A.N., Goldberger, A.L., Havlin, S., Ivanov, P.C., Peng, C.K.: Statistical physics and physiology: Monofractal and multifractal approaches. Physics A. 270, 309–324 (1999)CrossRefGoogle Scholar
  14. 14.
    Fernández, E., Bolea, J.A., Ortega, G., Louis, E.: Are neurons multifractals? J. Neurosci. Meth. 89, 151–157 (1999)CrossRefGoogle Scholar
  15. 15.
    Block, A., von Bloh, W., Schnellhuber, H.J.: Efficient box-counting determination of generalized fractal dimensions. Phys. Rev. A. 42, 1869–1874 (1990)MathSciNetCrossRefGoogle Scholar
  16. 16.
    Milošević, N.T., Krstonošić, B., Gudović, R., Ristanović, D.: Fractal analysis of neuronal dendritic branching patterns in the human neostriatum: a revised classification scheme. In: Dumitrache, I. (ed.) Proceedings CSCS-18, vol. 2, pp. 871–876. Editura Politehnica Press, Bucharest (2011)Google Scholar
  17. 17.
    Ristanović, D., Krstonošić, B., Milošević, N.T., Gudović, R.: Mathematical modeling of transformations of asymmetrically distributed biological data: an application to a quantitative classification of spiny neurons of the human putamen. J. Theor. Biol. 302, 81–88 (2012)CrossRefGoogle Scholar
  18. 18.
    Bayer, T.A., Buslei, R., Havas, L., Falkai, P.: Evidence for activation of microglia in patterns with psychiatric illness. Neuroisci. Lett. 271, 126–128 (1999)CrossRefGoogle Scholar
  19. 19.
    Radewicz, K., Garey, L.J., Gentleman, S.M., Reynolds, R.: Increase in HLA-DR immunoreactive microglia in frontal and temporal cortex of chronic schizophrenics. J. Neuropathol. Exp. Neurol. 59, 137–150 (2000)Google Scholar
  20. 20.
    Karperien, A., Jelinek, H.F., Milošević, N.T.: Multifractals: a review with an application in neuroscience. In: Dumitrache, I. (ed.) Proceedings CSCS-18, vol. 2, pp. 888–893. Editura Politehnica Press, Bucharest (2011)Google Scholar
  21. 21.
    Soltys, Z., Ziaja, M., Pawlínski, R., Setkowicz, Z., Janeczko, K.: Morphology of reactive microglia in the injured cerebral cortex. Fractal analysis and complementary quantitative methods. J. Neurosci. Res. 63, 90–97 (2001)CrossRefGoogle Scholar
  22. 22.
    Ristanović, D., Milošević, N.T., Stefanović, B.D., Marić, D.L., Rajković, K.: Morphology and classification of large neurons in the adult human dentate nucleus: a qualitative and quantitative analysis of 2D images. Neurosci. Res. 67, 1–7 (2010)CrossRefGoogle Scholar
  23. 23.
    Milošević, N.T., Ristanović, D., Jelinek, H.F., Rajković, K.: Quantitative analysis of dendritic morphology of the alpha and delta retinal ganglion cells in the rat: a cell classification study. J. Theor. Biol. 259, 142–150 (2009)CrossRefGoogle Scholar
  24. 24.
    Jelinek, H.F., Milošević, N.T., Ristanović, D.: The Morphology of Alpha Ganglion Cells in Mammalian Species: a Fractal Analysis Study. J. CEAI 12, 3–9 (2010)Google Scholar
  25. 25.
    Chhabra, A., Jensen, R.V.: Direct determination of the f(a) singularity spectrum. Am. Phys. Soc. 62, 1327–1330 (1989)MathSciNetGoogle Scholar
  26. 26.
    Vicsek, T.: Fractal Growth Phenomena. World Scientific, Singapore (1992)Google Scholar
  27. 27.
    Jestczemski, F., Sernetz, M.: Multifractal approach to inhomogeneous fractals. Phys. A. 223, 275–282 (1996)CrossRefGoogle Scholar
  28. 28.
    Berthelsen, C.L., Glazier, J.A., Skolnick, M.H.: Global fractal dimension of human DNA sequences treated as pseudorandom walks. Phys. Rev. A. 45, 8902–8913 (1992)CrossRefGoogle Scholar
  29. 29.
    Braak, H., Braak, E.: Neuronal types in the striatum of man. Cell Tiss. Res. 227, 319–342 (1982)CrossRefGoogle Scholar
  30. 30.
    Graveland, G.A., Williams, R.S., DiFiglia, M.: A Golgi study of the human neostriatum: Neurons and afferent fibers. J. Comp. Neurol. 234, 317–333 (1985)CrossRefGoogle Scholar
  31. 31.
    DiFiglia, M., Pasik, T., Pasik, P.: Ultrastructure of Golgi-impregnated and gold-toned spiny and aspiny neurons in the monkey neostriatum. J. Neurocyt. 9, 471–492 (1980)CrossRefGoogle Scholar
  32. 32.
    Dimova, R., Vuillet, J., Seite, R.: Study of the rat neostriatum using a combined Golgi-electron microscope technique and serial sections. Neurosci. 5, 1581–1596 (1980)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Herbert F. Jelinek
    • 1
  • Nebojša T. Milošević
    • 2
  • Audrey Karperien
    • 1
  • Bojana Krstonošić
    • 3
  1. 1.Centre for Research in Complex Systems and School of Community HealthCharles Sturt UniversityAlburyAustralia
  2. 2.Department of Biophysics, Medical FacultyUniversity of Belgrade, KCS-Institute of biophysics pp. 122Belgrade102Serbia
  3. 3.Department of Anatomy, Medical FacultyUniversity of Novi SadNovi SadSerbia

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