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Fractal Analysis in Neurodegenerative Diseases

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The Fractal Geometry of the Brain

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

Abstract

Neurodegenerative diseases are defined by progressive nervous system dysfunction and death of neurons. The abnormal conformation and assembly of proteins is suggested to be the most probable cause for many of these neurodegenerative disorders, leading to the accumulation of abnormally aggregated proteins like, for example, amyloid-β (Aβ) (Alzheimer’s disease and vascular dementia), tau protein (Alzheimer’s disease and frontotemporal lobar degeneration), α-synuclein (Parkinson’s disease and Lewy body dementia), polyglutamine expansion (Huntington disease), or prion proteins (Creutzfeldt-Jakob’s disease). An aberrant gain-of-function mechanism toward excessive intraparenchymal accumulation thus represents a common pathogenic denominator in all these proteinopathies. Moreover, depending upon the predominant brain area involvement, these different neurodegenerative diseases lead to either movement disorders or dementia syndromes, although the underlying mechanism(s) can sometimes be very similar, and at other occasions, clinically similar syndromes have quite distinct pathologies. Non-Euclidean image analysis approaches such as fractal dimension (FD) analysis have been applied extensively in quantifying highly variable morphopathological patterns, as well as many other connected biological processes; however, their application to understand and link abnormal proteinaceous depositions to other clinical and pathological features composing these syndromes are yet to be clarified. Thus, this chapter aims to present the most important applications of FD in investigating the clinical-pathological spectrum of neurodegenerative diseases.

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References

  1. Ahmadlou M, Adeli H, Adeli A. Fractality and a wavelet-chaos methodology for EEG-based diagnosis of Alzheimer disease. Alzheimer Dis Assoc Disord. 2011;25(1):85–92.

    Google Scholar 

  2. Alzheimer A. Über eine eigenartige erkrankung der Hinrinde. Zentralbl Nervenheilkunde Psychiatr. 1907;18:177–9.

    Google Scholar 

  3. Arai H, Kobayashi K, Ikeda K, Nagao Y, Ogihara R, Kosaka K. A computed tomography study of Alzheimer’s disease. J Neurol. 1983;229(2):69–77.

    Google Scholar 

  4. Baker M, Mackenzie IR, Pickering-Brown SM, Gass J, Rademakers R, Lindholm C, et al. Mutations in progranulin cause tau-negative frontotemporal dementia linked to chromosome 17. Nature. 2006;442(7105):916–9.

    Google Scholar 

  5. Behar TN. Analysis of fractal dimension of O2A glial cells differentiating in vitro. Methods. 2001;24(4):331–9.

    Google Scholar 

  6. Besthorn C, Sattel H, Geiger-Kabisch C, Zerfass R, Forstl H. Parameters of EEG dimensional complexity in Alzheimer’s disease. Electroencephalogr Clin Neurophysiol. 1995;95(2):84–9.

    Google Scholar 

  7. Blandini F, Nappi G, Tassorelli C, Martignoni E. Functional changes of the basal ganglia circuitry in Parkinson’s disease. Prog Neurobiol. 2000;62(1):63–88.

    Google Scholar 

  8. Borroni B, Bonvicini C, Alberici A, Buratti E, Agosti C, Archetti S, et al. Mutation within TARDBP leads to frontotemporal dementia without motor neuron disease. Hum Mutat. 2009;30(11):E974–83.

    Google Scholar 

  9. Braak H, Braak E. Neuropathological stageing of Alzheimer-related changes. Acta Neuropathol (Berl). 1991;82(4):239–59.

    Google Scholar 

  10. Calabresi PA. Diagnosis and management of multiple sclerosis. Am Fam Physician. 2004;70(10):1935–44.

    Google Scholar 

  11. Calhoun ME, Burgermeister P, Phinney AL, Stalder M, Tolnay M, Wiederhold KH, et al. Neuronal overexpression of mutant amyloid precursor protein results in prominent deposition of cerebrovascular amyloid. Proc Natl Acad Sci USA. 1999;96(24):14088–93.

    Google Scholar 

  12. Cavanaugh SE, Pippin JJ, Barnard ND. Animal models of Alzheimer disease: historical pitfalls and a path forward. ALTEX. 2014;31(3):279–302.

    Google Scholar 

  13. Cross SS. Fractals in pathology. J Pathol. 1997;182(1):1–8.

    Google Scholar 

  14. Cruts M, Gijselinck I, van der Zee J, Engelborghs S, Wils H, Pirici D, et al. Null mutations in progranulin cause ubiquitin-positive frontotemporal dementia linked to chromosome 17q21. Nature. 2006;442(7105):920–4.

    Google Scholar 

  15. Csernansky JG, Wang L, Swank J, Miller JP, Gado M, McKeel D, et al. Preclinical detection of Alzheimer’s disease: hippocampal shape and volume predict dementia onset in the elderly. Neuroimage. 2005;25(3):783–92.

    Google Scholar 

  16. Cupers P, Orlans I, Craessaerts K, Annaert W, De Strooper B. The amyloid precursor protein (APP)-cytoplasmic fragment generated by gamma-secretase is rapidly degraded but distributes partially in a nuclear fraction of neurones in culture. J Neurochem. 2001;78(5):1168–78.

    Google Scholar 

  17. D’Andrea MR, Cole GM, Ard MD. The microglial phagocytic role with specific plaque types in the Alzheimer disease brain. Neurobiol Aging. 2004;25(5):675–83.

    Google Scholar 

  18. D’Andrea MR, Nagele RG. Morphologically distinct types of amyloid plaques point the way to a better understanding of Alzheimer’s disease pathogenesis. Biotech Histochem. 2010;85(2):133–47.

    Google Scholar 

  19. Deutsch G, Tweedy JR. Cerebral blood flow in severity-matched Alzheimer and multi-infarct patients. Neurology. 1987;37(3):431–8.

    Google Scholar 

  20. Dickerson BC, Sperling RA. Neuroimaging biomarkers for clinical trials of disease-modifying therapies in Alzheimer’s disease. NeuroRx. 2005;2(2):348–60.

    Google Scholar 

  21. Dickson DW. The pathogenesis of senile plaques. J Neuropathol Exp Neurol. 1997;56(4):321–39.

    Google Scholar 

  22. Du AT, Schuff N, Kramer JH, Rosen HJ, Gorno-Tempini ML, Rankin K, et al. Different regional patterns of cortical thinning in Alzheimer’s disease and frontotemporal dementia. Brain. 2007;130(Pt 4):1159–66.

    Google Scholar 

  23. Esteban FJ, Sepulcre J, de Mendizabal NV, Goni J, Navas J, de Miras JR, et al. Fractal dimension and white matter changes in multiple sclerosis. Neuroimage. 2007;36(3):543–9.

    Google Scholar 

  24. Esteban FJ, Sepulcre J, de Miras JR, Navas J, de Mendizabal NV, Goni J, et al. Fractal dimension analysis of grey matter in multiple sclerosis. J Neurol Sci. 2009;282(1–2):67–71.

    Google Scholar 

  25. Foster NL, Chase TN, Fedio P, Patronas NJ, Brooks RA, Di Chiro G. Alzheimer’s disease: focal cortical changes shown by positron emission tomography. Neurology. 1983;33(8):961–5.

    Google Scholar 

  26. Frackowiak RS, Pozzilli C, Legg NJ, Du Boulay GH, Marshall J, Lenzi GL, et al. Regional cerebral oxygen supply and utilization in dementia. A clinical and physiological study with oxygen-15 and positron tomography. Brain. 1981;104(Pt 4):753–78.

    Google Scholar 

  27. Friedland RP, Budinger TF, Koss E, Ober BA. Alzheimer’s disease: anterior-posterior and lateral hemispheric alterations in cortical glucose utilization. Neurosci Lett. 1985;53(3):235–40.

    Google Scholar 

  28. Games D, Adams D, Alessandrini R, Barbour R, Berthelette P, Blackwell C, et al. Alzheimer-type neuropathology in transgenic mice overexpressing V717F beta-amyloid precursor protein. Nature. 1995;373(6514):523–7.

    Google Scholar 

  29. Garg N, Smith TW. An update on immunopathogenesis, diagnosis, and treatment of multiple sclerosis. Brain Behav. 2015;5(9):e00362.

    Google Scholar 

  30. Gomez C, Mediavilla A, Hornero R, Abasolo D, Fernandez A. Use of the Higuchi’s fractal dimension for the analysis of MEG recordings from Alzheimer’s disease patients. Med Eng Phys. 2009;31(3):306–13.

    Google Scholar 

  31. Guerreiro R, Hardy J. Genetics of Alzheimer’s disease. Neurotherapeutics. 2014;11(4):732–7.

    Google Scholar 

  32. Hausdorff JM. Gait dynamics, fractals and falls: finding meaning in the stride-to-stride fluctuations of human walking. Hum Mov Sci. 2007;26(4):555–89.

    Google Scholar 

  33. Hendriks L, van Duijn CM, Cras P, Cruts M, Van Hul W, van Harskamp F, et al. Presenile dementia and cerebral haemorrhage linked to a mutation at condon 692 of the b-amyloid precursor protein gene. Nat Genet. 1992;1:218–21.

    Google Scholar 

  34. Herzig MC, Winkler DT, Burgermeister P, Pfeifer M, Kohler E, Schmidt SD, et al. A beta is targeted to the vasculature in a mouse model of hereditary cerebral hemorrhage with amyloidosis. Nat Neurosci. 2004;7(9):954–60.

    Google Scholar 

  35. Hsiao K, Chapman P, Nilsen S, Eckman C, Harigaya Y, Younkin S, et al. Correlative memory deficits, Abeta elevation, and amyloid plaques in transgenic mice. Science. 1996;274(5284):99–102.

    Google Scholar 

  36. Hutton M, Lendon CL, Rizzu P, Baker M, Froelich S, Houlden H, et al. Association of missense and 5′-splice-site mutations in tau with the inherited dementia FTDP-17. Nature. 1998;393(6686):702–5.

    Google Scholar 

  37. Im K, Lee JM, Yoon U, Shin YW, Hong SB, Kim IY, et al. Fractal dimension in human cortical surface: multiple regression analysis with cortical thickness, sulcal depth, and folding area. Hum Brain Mapp. 2006;27(12):994–1003.

    Google Scholar 

  38. Iwatsubo T, Saido TC, Mann DM, Lee VM, Trojanowski JQ. Full-length amyloid-beta (1-42(43)) and amino-terminally modified and truncated amyloid-beta 42(43) deposit in diffuse plaques. Am J Pathol. 1996;149(6):1823–30.

    Google Scholar 

  39. Jagust WJ, Friedland RP, Budinger TF, Koss E, Ober B. Longitudinal studies of regional cerebral metabolism in Alzheimer’s disease. Neurology. 1988;38(6):909–12.

    Google Scholar 

  40. Jiang J, Zhu W, Shi F, Zhang Y, Lin L, Jiang T. A robust and accurate algorithm for estimating the complexity of the cortical surface. J Neurosci Methods. 2008;172(1):122–30.

    Google Scholar 

  41. Jobst KA, Smith AD, Barker CS, Wear A, King EM, Smith A, et al. Association of atrophy of the medial temporal lobe with reduced blood flow in the posterior parietotemporal cortex in patients with a clinical and pathological diagnosis of Alzheimer’s disease. J Neurol Neurosurg Psychiatry. 1992;55(3):190–4.

    Google Scholar 

  42. Kang J, Muller-Hill B. Differential splicing of Alzheimer’s disease amyloid A4 precursor RNA in rat tissues: PreA4(695) mRNA is predominantly produced in rat and human brain. Biochem Biophys Res Commun. 1990;166(3):1192–200.

    Google Scholar 

  43. Kawas CH. Clinical practice. Early Alzheimer’s disease. N Engl J Med. 2003;349(11):1056–63.

    Google Scholar 

  44. King RD, Brown B, Hwang M, Jeon T, George AT, Alzheimer’s Disease Neuroimaging I. Fractal dimension analysis of the cortical ribbon in mild Alzheimer’s disease. Neuroimage. 2010;53(2):471–9.

    Google Scholar 

  45. King RD, George AT, Jeon T, Hynan LS, Youn TS, Kennedy DN, et al. Characterization of atrophic changes in the cerebral cortex using fractal dimensional analysis. Brain Imaging Behav. 2009;3(2):154–66.

    Google Scholar 

  46. Kiselev VG, Hahn KR, Auer DP. Is the brain cortex a fractal? Neuroimage. 2003;20(3):1765–74.

    Google Scholar 

  47. Korf ES, Wahlund LO, Visser PJ, Scheltens P. Medial temporal lobe atrophy on MRI predicts dementia in patients with mild cognitive impairment. Neurology. 2004;63(1):94–100.

    Google Scholar 

  48. Kumar-Singh S. Cerebral amyloid angiopathy: pathogenetic mechanisms and link to dense amyloid plaques. Genes Brain Behav. 2008;7 Suppl 1:67–82.

    Google Scholar 

  49. Kumar-Singh S. Hereditary and sporadic forms of abeta-cerebrovascular amyloidosis and relevant transgenic mouse models. Int J Mol Sci. 2009;10(4):1872–95.

    Google Scholar 

  50. Kumar-Singh S, Cras P, Wang R, Kros JM, van Swieten J, Lubke U, et al. Dense-core senile plaques in the Flemish variant of Alzheimer’s disease are vasocentric. Am J Pathol. 2002;161(2):507–20.

    Google Scholar 

  51. Kumar-Singh S, Julliams A, Nuyens D, Labeur C, Vennekens K, Serneels S, et al. In vitro studies of Flemish, Dutch, and wild-type Amyloid ß (Aß) provide evidence for a two-stage Aß neurotoxicity. Neurobiol Dis. 2002;11(2):300–10.

    Google Scholar 

  52. Kumar-Singh S, Pirici D, McGowan E, Serneels S, Ceuterick C, Hardy J, et al. Dense-core plaques in Tg2576 and PSAPP mouse models of Alzheimer’s disease are centered on vessel walls. Am J Pathol. 2005;167(2):527–43.

    Google Scholar 

  53. Lennon FE, Cianci GC, Cipriani NA, Hensing TA, Zhang HJ, Chen CT, et al. Lung cancer-a fractal viewpoint. Nat Rev Clin Oncol. 2015;12:664–75.

    Google Scholar 

  54. Mandelbrot BB. Stochastic models for the Earth’s relief, the shape and the fractal dimension of the coastlines, and the number-area rule for islands. Proc Natl Acad Sci USA. 1975;72(10):3825–8.

    Google Scholar 

  55. Mielke R, Pietrzyk U, Jacobs A, Fink GR, Ichimiya A, Kessler J, et al. HMPAO SPET and FDG PET in Alzheimer’s disease and vascular dementia: comparison of perfusion and metabolic pattern. Eur J Nucl Med. 1994;21(10):1052–60.

    Google Scholar 

  56. Milosevic NT, Ristanovic D. Fractality of dendritic arborization of spinal cord neurons. Neurosci Lett. 2006;396(3):172–6.

    Google Scholar 

  57. Miyawaki K, Nakayama H, Matsuno S, Tamaoka A, Doi K. Three-dimensional and fractal analyses of assemblies of amyloid beta protein subtypes [Abeta40 and Abeta42(43)] in canine senile plaques. Acta Neuropathol (Berl). 2002;103(3):228–36.

    Google Scholar 

  58. Mogoanta L, Ciurea M, Pirici I, Margaritescu C, Simionescu C, Ion DA, et al. Different dynamics of aquaporin 4 and glutamate transporter-1 distribution in the perineuronal and perivascular compartments during ischemic stroke. Brain Pathol. 2014;24(5):475–93.

    Google Scholar 

  59. Nagao M, Murase K, Kikuchi T, Ikeda M, Nebu A, Fukuhara R, et al. Fractal analysis of cerebral blood flow distribution in Alzheimer’s disease. J Nucl Med. 2001;42(10):1446–50.

    Google Scholar 

  60. Nagao M, Sugawara Y, Ikeda M, Fukuhara R, Hokoishi K, Murase K, et al. Heterogeneity of cerebral blood flow in frontotemporal lobar degeneration and Alzheimer’s disease. Eur J Nucl Med Mol Imaging. 2004;31(2):162–8.

    Google Scholar 

  61. Nagao M, Sugawara Y, Ikeda M, Fukuhara R, Ishikawa T, Murase K, et al. Heterogeneity of posterior limbic perfusion in very early Alzheimer’s disease. Neurosci Res. 2006;55(3):285–91.

    Google Scholar 

  62. Nakayama H, Kiatipattanasakul W, Nakamura S, Miyawaki K, Kikuta F, Uchida K, et al. Fractal analysis of senile plaque observed in various animal species. Neurosci Lett. 2001;297(3):195–8.

    Google Scholar 

  63. Nestor SM, Gibson E, Gao FQ, Kiss A, Black SE, Alzheimer’s Disease Neuroimaging I. A direct morphometric comparison of five labeling protocols for multi-atlas driven automatic segmentation of the hippocampus in Alzheimer’s disease. Neuroimage. 2013;66:50–70.

    Google Scholar 

  64. Pirici D, Mogoanta L, Margaritescu O, Pirici I, Tudorica V, Coconu M. Fractal analysis of astrocytes in stroke and dementia. Rom J Morphol Embryol. 2009;50(3):381–90.

    Google Scholar 

  65. Pirici D, Van Cauwenberghe C, Van Broeckhoven C, Kumar-Singh S. Fractal analysis of amyloid plaques in Alzheimer’s disease patients and mouse models. Neurobiol Aging. 2011;32(9):1579–87.

    Google Scholar 

  66. Popescu BF, Lucchinetti CF. Pathology of demyelinating diseases. Annu Rev Pathol. 2012;7:185–217.

    Google Scholar 

  67. Rajendran L, Honsho M, Zahn TR, Keller P, Geiger KD, Verkade P, et al. Alzheimer’s disease beta-amyloid peptides are released in association with exosomes. Proc Natl Acad Sci USA. 2006;103(30):11172–7.

    Google Scholar 

  68. Rasouli G, Rasouli M, Lenz FA, Verhagen L, Borrett DS, Kwan HC. Fractal characteristics of human Parkinsonian neuronal spike trains. Neuroscience. 2006;139(3):1153–8.

    Google Scholar 

  69. Ratnavalli E, Brayne C, Dawson K, Hodges JR. The prevalence of frontotemporal dementia. Neurology. 2002;58(11):1615–21.

    Google Scholar 

  70. Reichenbach A, Siegel A, Senitz D, Smith Jr TG. A comparative fractal analysis of various mammalian astroglial cell types. Neuroimage. 1992;1(1):69–77.

    Google Scholar 

  71. Sarbaz Y, Towhidkhah F, Jafari A, Gharibzadeh S. Do the chaotic features of gait change in Parkinson’s disease? J Theor Biol. 2012;307:160–7.

    Google Scholar 

  72. Schaffner AE, Ghesquiere A. The effect of type 1 astrocytes on neuronal complexity: a fractal analysis. Methods. 2001;24(4):323–9.

    Google Scholar 

  73. Sekine M, Akay M, Tamura T, Higashi Y, Fujimoto T. Fractal dynamics of body motion in patients with Parkinson’s disease. J Neural Eng. 2004;1(1):8–15.

    Google Scholar 

  74. Selkoe DJ. The cell biology of ß-amyloid precursor protein and presenilin in Alzheimer’s disease. Trends Cell Biol. 1998;8(11):447–53.

    Google Scholar 

  75. Skibinski G, Parkinson NJ, Brown JM, Chakrabarti L, Lloyd SL, Hummerich H, et al. Mutations in the endosomal ESCRTIII-complex subunit CHMP2B in frontotemporal dementia. Nat Genet. 2005;37(8):806–8.

    Google Scholar 

  76. Smith Jr TG, Behar TN, Lange GD, Marks WB, Sheriff Jr WH. A fractal analysis of cultured rat optic nerve glial growth and differentiation. Neuroscience. 1991;41(1):159–66.

    Google Scholar 

  77. Snowden JS, Neary D, Mann DM. Frontotemporal dementia. Br J Psychiatry. 2002;180:140–3.

    Google Scholar 

  78. Starkstein SE, Sabe L, Vazquez S, Teson A, Petracca G, Chemerinski E, et al. Neuropsychological, psychiatric, and cerebral blood flow findings in vascular dementia and Alzheimer’s disease. Stroke. 1996;27(3):408–14.

    Google Scholar 

  79. Stevens A, Kircher T. Cognitive decline unlike normal aging is associated with alterations of EEG temporo-spatial characteristics. Eur Arch Psychiatry Clin Neurosci. 1998;248(5):259–66.

    Google Scholar 

  80. Thal DR, Capetillo-Zarate E, Del Tredici K, Braak H. The development of amyloid beta protein deposits in the aged brain. Sci Aging Knowledge Environ. 2006;2006(6):re1.

    Google Scholar 

  81. Trojanowski JQ, Shin RW, Schmidt ML, Lee VM. Relationship between plaques, tangles, and dystrophic processes in Alzheimer’s disease. Neurobiol Aging. 1995;16(3):335–40.

    Google Scholar 

  82. Varrone A, Pappata S, Caraco C, Soricelli A, Milan G, Quarantelli M, et al. Voxel-based comparison of rCBF SPET images in frontotemporal dementia and Alzheimer’s disease highlights the involvement of different cortical networks. Eur J Nucl Med Mol Imaging. 2002;29(11):1447–54.

    Google Scholar 

  83. Wattendorff AR, Bots GT, Went LN, Endtz LJ. Familial cerebral amyloid angiopathy presenting as recurrent cerebral haemorrhage. J Neurol Sci. 1982;55(2):121–35.

    Google Scholar 

  84. Watts GD, Wymer J, Kovach MJ, Mehta SG, Mumm S, Darvish D, et al. Inclusion body myopathy associated with Paget disease of bone and frontotemporal dementia is caused by mutant valosin-containing protein. Nat Genet. 2004;36(4):377–81.

    Google Scholar 

  85. Wisniewski HM, Bancher C, Barcikowska M, Wen GY, Currie J. Spectrum of morphological appearance of amyloid deposits in Alzheimer’s disease. Acta Neuropathol (Berl). 1989;78(4):337–47.

    Google Scholar 

  86. Woyshville MJ, Calabrese JR. Quantification of occipital EEG changes in Alzheimer’s disease utilizing a new metric: the fractal dimension. Biol Psychiatry. 1994;35(6):381–7.

    Google Scholar 

  87. Yamaguchi H, Nakazato Y, Shoji M, Takatama M, Hirai S. Ultrastructure of diffuse plaques in senile dementia of the Alzheimer type: comparison with primitive plaques. Acta Neuropathol. 1991;82(1):13–20.

    Google Scholar 

  88. Yoshikawa T, Murase K, Oku N, Imaizumi M, Takasawa M, Rishu P, et al. Heterogeneity of cerebral blood flow in Alzheimer disease and vascular dementia. AJNR Am J Neuroradiol. 2003;24(7):1341–7.

    Google Scholar 

  89. Zhang L, Liu JZ, Dean D, Sahgal V, Yue GH. A three-dimensional fractal analysis method for quantifying white matter structure in human brain. J Neurosci Methods. 2006;150(2):242–53.

    Google Scholar 

Download references

Acknowledgments

This work was supported by a grant of the Romanian National Authority for Scientific Research and Innovation, CNCS – UEFISCDI, project number PN-II-RU-TE-2014-4-0582, contract number 160/01.10.2015 and E05547 grant of the University of Antwerp. We thank Elsevier, Springer, and the Romanian Society of Morphology for permissions to partially reproduce previously published work.

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  1. Department of Research Methodology, University of Medicine and Pharmacy of Craiova, Petru Rares Street 2, 200349, Craiova, Dolj, Romania

    Daniel Pirici MD, PhD

  2. Department of Histology, University of Medicine and Pharmacy of Craiova, Craiova, Romania

    Laurentiu Mogoanta MD, PhD

  3. Department of Physiopathology, University of Medicine and Pharmacy Carol Davila, Bucharest, Romania

    Daniela Adriana Ion MD, PhD

  4. Molecular Pathology Group, Faculty of Medicine and Health Sciences, Cell Biology & Histology and Translational Neuroscience Department, University of Antwerp, Antwerpen, Belgium

    Samir Kumar-Singh MD, PhD

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Correspondence to Daniel Pirici MD, PhD .

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    Antonio Di Ieva

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Pirici, D., Mogoanta, L., Ion, D.A., Kumar-Singh, S. (2016). Fractal Analysis in Neurodegenerative Diseases. 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_15

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