Fractals in the neurosciences, part I: General principles and basic neurosciences

Neuroscientist

Volumn 20, Issue 4, 2014, Pages 403-417

  Di Ieva, Antonio ^a,b   Grizzi, Fabio ^c   Jelinek, Herbert ^d,e   Pellionisz, Andras J ^f   Losa, Gabriele Angelo ^g  

^a ST MICHAEL'S HOSPITAL   (Canada)

^b MEDICAL UNIVERSITY OF VIENNA   (Austria)

^c HUMANITAS CLINICAL AND RESEARCH CENTER   (Italy)

^d KHALIFA UNIVERSITY   (United Arab Emirates)

^e MACQUARIE UNIVERSITY   (Australia)

^f HolGenTech Inc   (United States)

^g Institute of Scientific Interdisciplinary Studies   (Switzerland)

Author keywords

brain; complexity; fractal analysis; fractal geometry; microglia; neuroanatomy; neuron; neurosciences

Indexed keywords

EID: 84904324809     PISSN: 10738584     EISSN: 10894098     Source Type: Journal    
DOI: 10.1177/1073858413513927     Document Type: Review

References (113)

1. Agnati LF, Guidolin D, Carone C, Dam M, Genedani S, Fuxe K. Understanding neuronal molecular networks builds on neuronal cellular network architecture. Brain Res Rev. 2008 ; 58 (2). 379-99
2. Alfarez DN, De Simoni A, Velzing EH, Bracey E, Joëls M, Edwards FA, Krugers HJ. Corticosterone reduces dendritic complexity in developing hippocampal CA neurons. Hippocampus. 2009 ; 19 (9). 828-36
3. Ascoli GA. Progress and perspectives in computational neuroanatomy. Anat Rec. 1999 ; 257 (6). 195-207
4. Bancaud A, Huet S, Daigle N, Mozziconacci J, Ellenberg J. Molecular crowding affects diffusion and binding of nuclear proteins in heterochromatic and reveals the fractal organization of chromatin. EMBO J. 2009 ; 28 (24). 3785-98
5. Barbieri M, Chotalia M, Fraser J, Lavitas LM, Dostie J, Pombo A, Nicodemi M. Complexity of chromatin folding is captured by the strings and binders switch model. Proc Natl Acad Sci U S A. 2012 ; 109 (40). 16173-8
6. Barnsley MF Burlington, MA: Morgan Kaufmann Publishers ; 1988:
7. Barnsley MF Cambridge: Cambridge University Press ; 2006:
8. Bassingthwaighte JB, Liebovitch LS, West BJ Oxford: Oxford University Press ; 1984:
9. Behar TN. Analysis of fractal dimension of O2A glial cells differentiating in vitro. Methods. 2001 ; 24 (4). 331-9
10. Belaubre G Paris: Académie Européenne Interdisciplinaire des Sciences (AEIS) ; 2006 :
11. Bernard F, Bossu JL, Gaillard S. Identification of living oligodendrocyte developmental stages by fractal analysis of cell morphology. J Neurosci Res. 2001 ; 65 (5). 439-45
12. Borodinsky LN, Fiszman ML. A single-cell model to study changes in neuronal fractal dimension. Methods. 2001 ; 24 (4). 341-5
13. Boycott BB, Wässle H. The morphological types of ganglion cell of the domestic cat's retina. J Physiol. 1974 ; 240 (2). 397-419
14. Caserta F, Eldred WD, Fernandez E, Hausman RE, Stanford LR, Buldrev SW. Determination of fractal dimension of physiologically characterized neurons in two and three dimension. J Neurosci Methods. 1995 ; 56 (2). 133-44
15. Cattani C, Pierro G. On the fractal geometry of DNA by the binary image analysis. Bull Math Biol. 2013 ; 75 (9). 1544-70
16. Cesar RM, Jelinek HF Angiography and plaque imaging. Suri JS Laxminarayan S, ed. London: CRC Press ; 2003: 193-224.
17. CornforthDJelinekHFLeandroJJGSoaresJVBCesarRMJr.CreeMJ, others. 2005. Evolution of retinal blood vessel segmentation using wavelet transform in assessment of diabetic retinopathy. Complexity International11. Available from: http://www.complexity.org.au/ci/vol11/.
18. Costa LdF Rattey F, ed. Vienna: ARGESIM/ASIM ; 2001: 397-411.
19. Costa LF, Cesar RM Boca Raton, FL: CRC Press ; 2001 :
20. Cross SS. The application of fractal geometric analysis to microscopic images. Micron. 1994 ; 25 (1). 101-13
21. Cross SS. Fractals in pathology. J Pathol. 1987 ; 182 (1). 1-8
22. Cutting JE, Garvin JJ. Fractal curves and complexity. Percept Psycophys. 1987 ; 42 (4). 365-70
23. DeFelipe J. The evolution of the brain, the human nature of cortical circuits, and the intellectual creativity. Front Neuroanat. 2011 ; 5: 1-16
24. Delignières D, Marmelat V. Fractal fluctuations and complexity: current debates and future challenges. Crit Rev Biomed Eng. 2012 ; 40 (6). 485-500
25. de Resende MF, Vieira S, Chinen LT, Chiappelli F, da Fonseca FP, Guimaraes GC. Prognostication of prostate cancer based on TOP2A protein and gene assessment: TOP2A in prostate cancer. J Transl Med. 2013 ; 11: 36
26. Dokukin ME, Guz NV, Gaikwad RM, Woodworth CD, Sokolov I. Cell surface as fractal: normal and cancerous cervical cells demonstrate different fractal behavior of surface adhesion maps at the nanoscale. Phys Rev Lett. 2011 ; 107: 028101
27. Elnitski L, Piontkivska H, Welch JR Science, engineering and biology informatics. Fedorov A Fedorava L, ed. Singapore: World Scientic2011: 65-93.
28. Elston GN, Jelinek HF. Dendritic branching patterns of pyramidal neurons in the visual cortex of the New World marmoset monkey with comparative notes on the Old Word macaque monkey. Fractals. 2001 ; 9 (3). 297-304
29. Falconer K Hoboken, NJ: Wiley ; 2003 :
30. Falconer K Chichester, UK: John Wiley & Sons ; 1997 :
31. Fernández E, Jelinek HF. Use of fractal theory in neuroscience: methods, advantages, and potential problems. Methods. 2001 ; 24 (4). 309-21
32. Flam F. Hints of a language in junk DNA. Science. 1994 ; 266: 1320
33. Fudenberg G, Getz G, Meyerson M, Mirny L. High-order chromatin architecture shapes the landscape of chromosomal alterations in cancer. Nat Biotechnol. 2011 ; 29 (12). 1109-13
34. Gallos LK, Sigman M, Makse HA. The conundrum of functional brain networks: small-world efficiency of fractal modularity. Front Physiol. 2012a ; 3: 123
35. Gallos LK, Sigman M, Makse HA. A small world of weak ties provides optimal global integration of self-similar modules in functional brain networks. Proc Natl Acad Sci U S A. 2012b ; 109 (8). 2825-30
36. Gleick J London: Penguin Books ; 1987 :
37. Golgi C. Sulla struttura della sostanza grigia del cervello. Gaz Med Lomb. 1873 ; 33: 244-6
38. Grizzi F, Chiriva-Internati M. The complexity of anatomical systems. Theor Biol Med Model. 2005 ; 2: 26
39. GrizziFDi IevaALandiniGDe VicoGLosaGA. 2012. The Fractal Laboratory Journal: a new challenge in the post-genomic era (editorial). The Fractal Laboratory Journal1:1. Available from: http://www.fractal-lab.org/flj2012-01- 01p.pdf.
40. Grosberg AY, Nechaev SK, Shakhnovich EI. The role of topological constraints in the kinetics of collapse of macromolecules. J Phys France. 1988 ; 49: 2095-100
41. Grosberg AY, Rabin Y, Havlin S, Neer A. Crumpled globule model of the three-dimensional structure of DNA. Europhys Lett. 1993 ; 23: 373-8
42. Harte D London: Chapman & Hall ; 2001 :
43. Hastings HM, Sugihara G Oxford: Oxford University Press ; 1993 :
44. HenryBIRothniePHofPRWearneSL. 2001. Determination of dendritic branching ratios and spine distribution patterns using mass multifractal and wavelet transform analysis. Center for Neural Science, New York University. Available from: http://www.cns.nyu.edu/CNFA/2001sfn/2001sfn
45. Hofman MA. The fractal geometry of convoluted brains. J Hirnforsch. 1991 ; 32 (1). 103-11
46. Jelinek HF, Cesar RM, Leandro JJG. Exploring wavelet transforms for morphological differentiation between functionally different cat retinal ganglion cells. Brain and Mind. 2003 ; 4: 67-90
47. Jelinek HF, Cornforth DJ, Roberts T, Landini G, Bourke P, Bossomaier T AI 2004: advances in artificial intelligence. 17th Australian joint conference on artificial intelligence: lecture notes in artificial intelligence. Webb GI Yu X, ed. Cairns, Australia: Springer Verlag ; 2005: 961-6.
48. Jelinek HF, Elston GN. Dendritic branching of pyramidal cells in the visual cortex of the nocturnal owl monkey: a fractal analysis. Fractals. 2004 ; 11 (4). 391-6
49. Jelinek HF, Fernández E. Neurons and fractals: how reliable and useful are calculations of fractal dimension?. J Neurosci Methods. 1998 ; 81 (1-2). 9-18
50. Jelinek HF, Karperien A, Bossomaier T, Buchan A Proceedings of the 7th Asia-Pacific Complex Systems Conference. Stonier R Han Q-L Li W, ed. Cairns, Australia: IOS Press ; 2004: 605-15.
51. Jelinek HF, Miloševi NT, Karperien A, Krstonoši B Advances in intelligent control systems and computer science. Dumitrache L, ed. Berlin: Springer ; 2013: 177-89.
52. Jelinek HF, Milosevic NT, Ristanovich D. Fractal dimension as a tool for classification of rat retinal ganglion cells. Bioforum. 2008 ; 101 (1). 146-50
53. Jelinek HF, Ristanovi D, Miloševi NT. The morphology and classification of alpha ganglion cells in the rat retinae: a fractal analysis study. J Neurosci Methods. 2011 ; 201 (1). 281-7
54. Jelinek HF, Spence I. Categorization of physiologically and morphologically characterized non-a/non-b cat retinal ganglion cells using fractal geometry. Fractals. 1997 ; 5 (4). 673-84
55. Johnson NF Oxford: One World Publications ; 2007 :
56. Karperien A, Ahammer H, Jelinek HF. Quantitating the subtleties of microglial morphology with fractal analysis. Front Cell Neurosci. 2013a ; 7: 3
57. Karperien A, Jelinek HF, Milosevic NT Fractals and complexity. Waliszewski P, ed. Wroclaw, Poland: Firma Format ; 2013b: 50-5.
58. Kniffki KD, Pawlak M, Vahle-Hinz C. Scaling behavior of the dendritic branches of thalamic neurons. Fractals. 1993 ; 1 (2). 171-8
59. Kolb H, Fernández E, Schouten J, Ahnelt P, Linberg K, Fisher SK. Are there three types of horizontal cell in the human retina. J Comp Neurol. 1994 ; 343 (3). 370-86
60. Kolb H, Nelson R, Mariani A. Amacrine cells, bipolar cells and ganglion cells of the cat retina: a Golgi study. Vision Res. 1981 ; 21 (7). 1081-114
61. Landini G Fractal geometry in biological systems. Iannaccone PM Khokha M, ed. Amsterdam: CRC Press ; 1996: 205-45.
62. Landini G. Fractals in microscopy. J Microsc. 2011 ; 241 (1). 1-8
63. Lieberman-Aiden E, van Berkum NL, Williams L, Imakaev M, Ragoczy T, Telling A. Comprehensive mapping of long-range interactions reveals folding principles of the human genome. Science. 2009 ; 326 (5950). 289-93
64. Lopes R, Betrouni N. Fractal and multifractal analysis: a review. Med Image Anal. 2009 ; 13 (4). 634-49
65. Losa GA. The fractal geometry of life. Riv Biol. 2009 ; 102 (1). 29-59
66. Losa GA, Di Ieva A, Grizzi F, De Vico G. On the fractal nature of nervous cell system. Front Neuroanat. 2011 ; 5: 45
67. Losa GA, Merlini D, Nonnenmacher TF, Weibel ER Basel: Birkhäuser ; 1997 :
68. Losa GA, Merlini D, Nonnenmacher TF, Weibel ER Basel: Birkhäuser ; 2005 :
69. Mandelbrot BB New York: W.H. Freeman & Co ; 1983 :
70. Mandelbrot BB. How long is the coast of Britain? Statistical self-similarity and fractional dimension. Science. 1967 ; 156 (3775). 636-8
71. Mandelbrot BB. Is nature fractal?. Science. 1998 ; 279 (5352). 783-4
72. Mandelbrot BB Paris: Flammarion ; 1975 :
73. Markram H. The blue brain project. Nat Rev Neurosci. 2006 ; 7 (2). 153-60
74. Miloševi NT, Ristanovic D, Jelinek HF. Quantitative analysis of dendritic morphology of the alpha and delta retinal ganglion cells in the rat: a cell classification study. J Theor Biol. 2009 ; 259 (1). 142-50
75. Miloševi NT, Ristanovi D, Mari D, Rajkovi K. Morphology and cell classification of large neurons in the adult human dentate nucleus: a quantitative study. Neurosci Lett. 2010 ; 468 (1). 59-63
76. Mirny LA. The fractal globule as a model of chromatin architecture in the cell. Chromosome Res. 2011 ; 19 (1). 37-51
77. Neale EA, Bowers LM, Smith JTG. Early dendritic development in spinal cord cell cultures: a quantitative study. J Neurosci Res. 1993 ; 34 (1). 54-66
78. Orlowski D, Soltys Z, Janeczko D. Morphological development of microglia in the postnatal rat brain: a quantitative study. Int J Dev Neurosci. 2003 ; 21 (8). 445-50
79. Pellionisz A. The decade of FractoGene: from discovery to utility proofs of concept open genome-based clinical applications. J Syst Cybern Inf. 2012 ;: 17-28
80. Pellionisz A Cambridge: Cambridge University Press ; 1989 :
81. Pellionisz A. The principle of recursive genome function. Cerebellum. 2008 ; 7 (3). 348-59
82. Pellionisz A, Roy Graham R, Pellionisz PA, Perez Jean-Claude Handbook of the Cerebellum and Cerebellar Disorders. Manto M. Gruol D.L. Schmahmann J.D. Koibuchi N. Rossi F., ed. Berlin: In Springer Verlag ; 2013: 1381-1423.
83. Pellionisz A, Szentagothai J. Dynamic single unit simulation of a realistic cerebellar network model. Brain Res. 1973 ; 49 (1). 83-99
84. Perez JC. Codon populations in single-stranded whole human genome DNA are fractal and fine-tuned by the golden ratio 1.618. Interdiscip Sci. 2010 ; 2 (3). 228-40
85. PetoukhovSV. 2011. The genetic code, 8-dimensional hypercomplex numbers and dyadic shifts. Available from: http://arxiv.org/ftp/arxiv/papers/1102/1102. 3596.pdf.
86. Pirici D, Mogoant L, Mrgritescu O, Pirici I, Turodic V, Coconu M. Fractal analysis of astrocytes in stroke and dementia. Rom J Morphol Embryol. 2009 ; 50 (3). 381-90
87. Poincaré H Paris: Flammarion ; 1905 :
88. Porter R, Ghosh S, Lange GD, Smith TG. A fractal analysis of pyramidal neurons in mammalian motor cortex. Neurosci Lett. 1991 ; 130 (1). 112-6
89. Ramón y Cajal S Cajal on the cerebral cortex. New York: Oxford University Press ; 1899 1988: 1-63.
90. Ramón y Cajal S Paris: A. Maloine ; 1911 :
91. Reichenbach A, Siegel A, Senitz D, Smith TG. A comparative fractal analysis of various mammalian astroglial cell types. Neuroimage. 1992 ; 1 (1). 69-77
92. Reisin HD, Colombo JA. Astroglial interlaminar processes in the human cerebral cortex: variations in cytoskeletal profiles. Brain Res. 2002 ; 937 (1-2). 51-7
93. RistanoviDLosaGA. 2013. A contribution to definitions of some fractal concepts. The Fractal Laboratory Journal2:2. Available from: http://www.fractal-lab.org/flj2013-02-02p.pdf.
94. Schierwagen A. Comparative analysis of dendritic geometry and electro-anatomy of superior colliculus neruons in the cat. Verh Anat Ges. 1989 ; 82: 887-9
95. Schierwagen A, Costa LdF, Alpár A, Gärtner U Bildverarbeitung für die medizin 2007: informatik aktuell. Horsch A. Deserno T.M. Handels H. Meinzer H.P. Tolxdorff T., ed. Berlin: Springer Verlag ; 2007: 424-8.
96. Senitz D, Reichenbach A, Smith JTG. Surface complexity of human neocortical astrocytic cells: changes with development, aging, and dementia. J Hirnforsch. 1995 ; 36 (4). 531-7
97. Simons MJ, Pellionisz AJ. Genomics, morphogenesis and biophysics: triangulation of Purkinje cell development. Cerebellum. 2006 ; 5: 27-35
98. Skrzat J, Usarz M, Trabka J, Goncerz G. Differentiation of neuron populations based on fractal dimension. Folia Morphol (Warsz). 1996 ; 55: 444-6
99. Smith TG Fractals in biology and medicine. Nonnenmacher TF Losa GA Weibel ER, ed. Basel: Birkhäuser ; 1994: 211-20.
100. Smith TG, Lange GD Fractal geometry in biological systems: an analytical approach. Iannaccone PM Khokha M, ed. New York: CRC Press ; 1995: 173-86.
101. Smith TG, Marks WB, Lange GD, Sheriff WH, Neale EA. A fractal analysis of cell images. J Neurosci Methods. 1989 ; 27 (2). 173-80
102. Soares JVB, Leandro JJG, Cesar RM, Jelinek HF, Cree MJ. Retinal vessel segmentation using the 2-D Gabor wavelet and supervised classification. IEEE Trans Med Imaging. 2006 ; 25 (9). 1214-22
103. Soltys Z, Ziaja M, Pawlinski R, Setkowicz Z, Janeczko K. Morphology of reactive microglia in the injured cerebral cortex, fractal analysis and complementary quantitative methods. J Neurosci Res. 2001 ; 63 (1). 90-7
104. Stadnitski T. Measuring fractality. Front Physiol. 2012 ; 3: 127
105. Stanley HE, Meakin P. Multifractal phenomena in physics and chemistry. Nature. 1988 ; 335 (6189). 405-9
106. Suckling J, Wink AM, Bernard FA, Barnes A, Bullmore E. Endogeneous multifractal brain dynamics are modulated by age, cholinergic blockade and cognitive performance. J Neurosci Methods. 2008 ; 174 (2). 292-300
107. Thompson DW Cambridge: Cambridge University Press ; 1992 :
108. Tolle CR, McJunkin TR, Rohrbaugh DT, LaViolette RA. Lacunarity definition for ramified data sets based on optimal cover. Physica D. 2003 ; 179 (3-4). 129-52
109. von Bertalanffy L New York: George Braziller ; 1969 :
110. Voss RF, Wyatt JCY Applications of fractals and chaos. Crilly AJ Earnshaw RA Jones H, ed. Berlin: Springer Verlag ; 1991: 171-84.
111. Werner G. Fractals in the nervous system: conceptual implications for theoretical neurosciences. Front Physiol. 2010 ; 1: 15
112. West BJ Castroville, TX: Black Rose Writing ; 2012 :
113. Wingate RJT, Fitsgibbon T, Thompson ID. Lucifer yellow, retrograde tracers, and fractal analysis characterise adult ferret retinal ganglion cells. J Comp Neurol. 1992 ; 323 (4). 449-74