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Morphology and Fractal-Based Classifications of Neurons and Microglia

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The Fractal Geometry of the Brain

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

Abstract

Microglia and neurons live physically intertwined, intimately related structurally and functionally in a dynamic relationship in which microglia change continuously over a much shorter timescale than neurons. Although microglia may unwind and depart from the neurons they attend under certain circumstances, in general, together both contribute to the fractal topology of the brain that defines its computational capabilities. Both neuronal and microglial morphologies are well described using fractal analysis complementary to more traditional measures. For neurons, the fractal dimension has proved valuable for classifying dendritic branching and other neuronal features relevant to pathology and development. For microglia, fractal geometry has contributed substantially to classifying functional categories, where in general, the more pathological the biological status, the lower the fractal dimension for individual cells, with some exceptions including hyper-ramification. Here we briefly review the intimate relationships between neurons and microglia, and survey work applying fractal analysis to their respective morphologies, summarizing key results and highlighting methodological issues.

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References

  1. Alfarez DN, De Simoni A, Velzing EH, Bracey E, Joels M, Edwards FA, Krugers HJ. Corticosterone reduces dendritic complexity in developing hippocampal CA1 neurons. Hippocampus. 2009;19(9):828–36.

    Google Scholar 

  2. Alliot F, Godin I, Pessac B. Microglia derive from progenitors, originating from the yolk sac, and which proliferate in the brain. Brain Res Dev Brain Res. 1999;117(2):145–52.

    Article  CAS  PubMed  Google Scholar 

  3. Baalman K, Marin MA, Ho TS, Godoy M, Cherian L, Robertson C, Rasband MN. Axon initial segment-associated microglia. J Neurosci. 2015;35(5):2283–92.

    Google Scholar 

  4. Bhattacharya J, Edwards J, Mamelak A, Schuamn EM. Ongoing hippocampal neuronal activity in human: is it noise or correlated fractal process? In: Losa GA, Merlini D, Nonnenmacher TF, Weibel ER, editors. Fractals in biology and medicine, vol IV, vol. VII. Basel: Birkhäuser Verlag Basel; 2005. p. 95–106.

    Chapter  Google Scholar 

  5. Blank T, Prinz M. Microglia as modulators of cognition and neuropsychiatric disorders. Glia. 2013;61(1):62–70.

    Google Scholar 

  6. Bohatschek M, Kloss CU, Kalla R, Raivich G. In vitro model of microglial deramification: ramified microglia transform into amoeboid phagocytes following addition of brain cell membranes to microglia-astrocyte cocultures. J Neurosci Res. 2001;64(5):508–22.

    Article  CAS  PubMed  Google Scholar 

  7. Bose M, Muñoz-Llancao P, Roychowdhury S, Nichols JA, Jakkamsetti V, Porter B, Byrapureddy R, Salgado H, Kilgard MP, Aboitiz F, Dagnino-Subiabre A, Atzori M. Effect of the environment on the dendritic morphology of the rat auditory cortex. Synapse (New York NY). 2010;64(2):97–110.

    Google Scholar 

  8. Cerbai F, Lana D, Nosi D, Petkova-Kirova P, Zecchi S, Brothers HM, Wenk GL, Giovannini MG. The neuron-astrocyte-microglia triad in normal brain ageing and in a model of neuroinflammation in the rat hippocampus. PLoS ONE. 2012;7(9):e45250.

    Google Scholar 

  9. Cornforth D, Jelinek HF. Automated classification of dementia subtypes from post-mortem cortex images. In: Zhang S, Jarvis R, editors. AI 2005: advances in artificial intelligence, Lecture Notes in Computer Science, vol. 3809. Berlin: Springer; 2005. p. 1285–8.

    Google Scholar 

  10. De Simoni A, Edwards FA. Pathway specificity of dendritic spine morphology in identified synapses onto rat hippocampal CA1 neurons in organotypic slices. Hippocampus. 2006;16(12):1111–24.

    Google Scholar 

  11. De Simoni A, Griesinger CB, Edwards FA. Development of rat CA1 neurones in acute versus organotypic slices: role of experience in synaptic morphology and activity. J Physiol. 2003;550(Pt 1):135–47.

    Google Scholar 

  12. Djamgoz MB, Krasowska M, Martinoli O, Sericano M, Vallerga S, Grzywna ZJ. Structure-function correlation in transient amacrine cells of goldfish retina: basic and multifractal analyses of dendritic trees in distinct synaptic layers. J Neurosci Res. 2001;66(6):1208–16.

    Article  CAS  PubMed  Google Scholar 

  13. Edwards FA. Dancing dendrites. Nature. 1998;394(6689):129–30.

    Google Scholar 

  14. Esteban FJ, Sepulcre J, de Mendizabal NV, Goni J, Navas J, de Miras JR, Bejarano B, Masdeu JC, Villoslada P. Fractal dimension and white matter changes in multiple sclerosis. Neuroimage. 2007;36(3):543–9.

    Google Scholar 

  15. Fabrizii M, Moinfar F, Jelinek HF, Karperien A, Ahammer H. Fractal analysis of cervical intraepithelial neoplasia. PLoS ONE. 2014;9(10):e108457.

    Article  PubMed  PubMed Central  Google Scholar 

  16. Ferrari G, Grisan E, Scarpa F, Fazio R, Comola M, Quattrini A, Comi G, Rama P, Riva N. Corneal confocal microscopy reveals trigeminal small sensory fiber neuropathy in amyotrophic lateral sclerosis. Front Aging Neurosci. 2014;6:278.

    Google Scholar 

  17. Fetterhoff D, Opris I, Simpson SL, Deadwyler SA, Hampson RE, Kraft RA. Multifractal analysis of information processing in hippocampal neural ensembles during working memory under Δ(9)-tetrahydrocannabinol administration. J Neurosci Methods. 2015;244:136–53.

    Google Scholar 

  18. Galbavy W, Kaczocha M, Puopolo M, Liu L, Rebecchi MJ. Neuroimmune and neuropathic responses of spinal cord and dorsal root ganglia in middle age. PLoS ONE. 2015;10(8):e0134394.

    Google Scholar 

  19. Gutierrez RC, Hung J, Zhang Y, Kertesz AC, Espina FJ, Colicos MA. Altered synchrony and connectivity in neuronal networks expressing an autism-related mutation of neuroligin 3. Neuroscience. 2009;162(1):208–21.

    Google Scholar 

  20. Hinwood M, Tynan RJ, Charnley JL, Beynon SB, Day TA, Walker FR. Chronic stress induced remodeling of the prefrontal cortex: structural re-organization of microglia and the inhibitory effect of minocycline. Cereb Cortex. 2012.

    Google Scholar 

  21. Hinwood M, Tynan RJ, Charnley JL, Beynon SB, Day TA, Walker FR. Chronic stress induced remodeling of the prefrontal cortex: structural re-organization of microglia and the inhibitory effect of minocycline. Cereb Cortex. 2013;23(8):1784–97.

    Article  PubMed  Google Scholar 

  22. Hoffbrand AV, Moss PAH, Pettit JE. Essential haematology. 6th ed. Malden: Wiley-Blackwell; 2011.

    Google Scholar 

  23. Huang CY, Chen YL, Li AH, Lu JC, Wang HL. Minocycline, a microglial inhibitor, blocks spinal CCL2-induced heat hyperalgesia and augmentation of glutamatergic transmission in substantia gelatinosa neurons. J Neuroinflammation. 2014;11:7.

    Google Scholar 

  24. Ivanov PC, Ma QDY, Bartsch RP, Hausdorff JM, Nunes Amaral L, Schulte-Frohlinde V, Stanley HE, Yoneyama M. Levels of complexity in scale-invariant neural signals. Phys Rev E Stat Nonlinear Soft Matter Phys. 2009;79(4 Pt 1):041920.

    Article  Google Scholar 

  25. Jelinek HF, Cornforth DJ, 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: Yu GIWaX (ed) AI 2004: advances in artificial intelligence. 17th Australian Joint Conference on Artificial Intelligence, Cairns, Australia, 2005. Lecture Notes in Artificial Intelligence. Springer Verlag, p. 961–6.

    Google Scholar 

  26. Jelinek HF, Elston GN. Pyramidal neurons in macaque visual cortex: interareal phenotypic variation of dendritic branching pattern. Fractals. 2001;09(03):287–95.

    Google Scholar 

  27. Jelinek HF, Elston NZ, Zietch B. Fractal analysis: pitfalls and revelations in neuroscience. In: Losa GA, Merlini D, Nonnenmacher TF, Weibel ER, editors. Fractals in biology and medicine, Mathematics and Biosciences in Interaction, vol. VII. IVth ed. Basel: Birkhäuser Verlag Basel; 2005. p. 85–94.

    Chapter  Google Scholar 

  28. Jelinek HF, Fernandez E. Neurons and fractals: how reliable and useful are calculations of fractal dimensions? J Neurosci Methods. 1998;81(1–2):9–18.

    Article  CAS  PubMed  Google Scholar 

  29. Jelinek HF, Karperien A, Buchan A, Bossomaier T. Differentiating grades of microglia activation with fractal analysis. Complex Int. 2008;1–12.

    Google Scholar 

  30. Jelinek HF, Karperien A, Cornforth D, Cesar RMJ, Leandro J. MicroMod—an L-systems approach to neuron modelling. In: Sarker R, McKay B, Gen M, Namatame A, editors. Sixth Australia-Japan joint workshop on intelligent and evolutionary systems, Canberra, Australia, November 30-December 1, 2002. AJJWIES’02. Australian National University, Canberra. 2002.

    Google Scholar 

  31. Jelinek HF, Karperien A, Milošević NT. Lacunarity analysis and classification of microglia in neuroscience. In: Proceedings of the 8th European conference on mathematical and theoretical biology, Cracow, Poland, 2011. European Society for Mathematical and Theoretical Biology (ESMTB). 2011.

    Google Scholar 

  32. Jelinek HF, Milošević NT, Karperien A, Krstonošić B. Box-counting and multifractal analysis in neuronal and glial classification. In: Dumitrache I, editor. Advances in intelligent control systems and computer science, Advances in Intelligent Systems and Computing, vol. 187. Berlin: Springer; 2013. p. 177–89.

    Google Scholar 

  33. Jelinek HF, Milošević NT, Ristanović D. The morphology of alpha ganglion cells in mammalian species: a fractal analysis study. CEAI. 2010;12(1):3–9.

    Google Scholar 

  34. Jelinek HF, Ristanović D, Milošević 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.

    Google Scholar 

  35. Jones CL, Jelinek HF. Wavelet packet fractal analysis of neuronal morphology. Methods. 2001;24(4):347–58.

    Article  CAS  PubMed  Google Scholar 

  36. Kam Y, Karperien A, Weidow B, Estrada L, Anderson AR, Quaranta V. Nest expansion assay: a cancer systems biology approach to in vitro invasion measurements. BMC Res Notes. 2009;2:130.

    Google Scholar 

  37. Kane CJ, Phelan KD, Han L, Smith RR, Xie J, Douglas JC, Drew PD. Protection of neurons and microglia against ethanol in a mouse model of fetal alcohol spectrum disorders by peroxisome proliferator-activated receptor-gamma agonists. Brain Behav Immun. 2011;25 Suppl 1:S137–45.

    Google Scholar 

  38. Karperien A. Defining microglial morphology: form, function, and fractal dimension. Thesis, Charles Sturt University, Australia. 2004.

    Google Scholar 

  39. Karperien A. FracLac2015 for ImageJ: JavaDoc, source code, and jar. vol 7, 201501 edn. National Institutes of Health ImageJ Plugins. 2015.

    Google Scholar 

  40. Karperien A. MicroMod 2015 for ImageJ: fractal branching Bio-modelling tool vol 1, 2015 edn. Natl Inst Health Image J Plugins. 2015.

    Google Scholar 

  41. Karperien A, Ahammer H, Jelinek HF. Quantitating the subtleties of microglial morphology with fractal analysis. Front Cell Neurosci. 2013;7:3.

    Google Scholar 

  42. Karperien A, Jelinek H, Milošević N. Reviewing lacunarity analysis and classification of microglia in neuroscience. Paper presented at the 8th European Conference on Mathematical and Theoretical Biology, Poland. 2011.

    Google Scholar 

  43. Karperien A, Jelinek HF, Milošević NT. Multifractals: a review with an application in neuroscience. In: CSCS18-18th international conference on control systems and computer science: fifth symposium on interdisciplinary approaches in fractal analysis bucharest, Romania, 2011. Politehnica Press; pp. 888–3.

    Google Scholar 

  44. Karperien AL, Jelinek HF, Buchan AM. Box-counting analysis of microglia form in schizophrenia, Alzheimer’s disease and affective disorder. Fractals. 2008;16(02):103–7.

    Google Scholar 

  45. Kim J, Kwon N, Chang S, Kim K-T, Lee D, Kim S, Yun SJ, Hwang D, Kim JW, Hwu Y, Margaritondo G, Je JH, Rhyu IJ. Altered branching patterns of Purkinje cells in mouse model for cortical development disorder. Sci Rep. 2011;1:122.

    Google Scholar 

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

    Article  PubMed  PubMed Central  Google Scholar 

  47. Kirov SA, Petrak LJ, Fiala JC, Harris KM. Dendritic spines disappear with chilling but proliferate excessively upon rewarming of mature hippocampus. Neuroscience. 2004;127(1):69–80.

    Google Scholar 

  48. Kongsui R, Beynon SB, Johnson SJ, Walker FR. Quantitative assessment of microglial morphology and density reveals remarkable consistency in the distribution and morphology of cells within the healthy prefrontal cortex of the rat. J Neuroinflammation. 2014;11:182.

    Google Scholar 

  49. Kreutzberg GW. Microglia, the first line of defence in brain pathologies. Arzneimittelforschung. 1995;45(3A):357–60.

    CAS  PubMed  Google Scholar 

  50. Kuwajima M, Spacek J, Harris KM. Beyond counts and shapes: studying pathology of dendritic spines in the context of the surrounding neuropil through serial section electron microscopy. Neuroscience. 2013;251:75–89.

    Google Scholar 

  51. Lamanna J, Esposti F, Malgaroli A, Signorini MG. Fractal behavior of spontaneous neurotransmitter release: from single-synapse to whole-cell recordings. Conf Proc IEEE Eng Med Biol Soc. 2011;2011:3346–9.

    PubMed  Google Scholar 

  52. Li Z, Da F, Costa L. Investigating shape and function relationship in retinal ganglion cells. J Integr Neurosci. 2002;1(2):195–215.

    Article  PubMed  Google Scholar 

  53. Losa GA. Fractals in biology and medicine. In: Meyers R, editor. Encyclopedia of Molecular Cell Biology and Molecular Medicine, Wiley-VCH Verlag, Berlin. 2011:1–25.

    Google Scholar 

  54. Meijering E. Neuron tracing in perspective. Cytom Part A J Int Soc Anal Cytol. 2010;77(7):693–704.

    Google Scholar 

  55. Misiak D, Posch S, Lederer M, Reinke C, Huttelmaier S, Moller B. Extraction of protein profiles from primary neurons using active contour models and wavelets. J Neurosci Methods. 2014;225:1–12.

    Google Scholar 

  56. Mittelbronn M, Dietz K, Schluesener HJ, Meyermann R. Local distribution of microglia in the normal adult human central nervous system differs by up to one order of magnitude. Acta Neuropathol. 2001;101(3):249–55.

    CAS  PubMed  Google Scholar 

  57. Puškaš N, Zaletel I, Stefanovic BD, Ristanović D. Fractal dimension of apical dendritic arborization differs in the superficial and the deep pyramidal neurons of the rat cerebral neocortex. Neurosci Lett. 2015;589:88–91.

    Google Scholar 

  58. Nimmerjahn A, Kirchhoff F, Helmchen F. Resting microglial cells are highly dynamic surveillants of brain parenchyma in vivo. Science. 2005;308(5726):1314–8.

    Google Scholar 

  59. Orlowski D, Soltys Z, Janeczko K. Morphological development of microglia in the postnatal rat brain. A quantitative study. Int J Dev Neurosci. 2003;21(8):445–50.

    Article  PubMed  Google Scholar 

  60. Pani G, De Vos WH, Samari N, de Saint-Georges L, Baatout S, Van Oostveldt P, Benotmane MA. MorphoNeuroNet: an automated method for dense neurite network analysis. Cytom Part A J Int Soc Anal Cytol. 2014;85(2):188–99.

    Google Scholar 

  61. Pantic I, Dacic S, Brkic P, Lavrnja I, Pantic S, Jovanovic T, Pekovic S. Application of fractal and grey level co-occurrence matrix analysis in evaluation of brain corpus callosum and cingulum architecture. Microsc Microanal. 2014;20(5):1373–81.

    Google Scholar 

  62. Radewicz K, Garey LJ, Gentleman SM, Reynolds R. Increase in HLA-DR immunoreactive microglia in frontal and temporal cortex of chronic schizophrenics. J Neuropathol Exp Neurol. 2000;59(2):137–50.

    Article  CAS  PubMed  Google Scholar 

  63. Radley JJ, Anderson RM, Hamilton BA, Alcock JA, Romig-Martin SA. Chronic stress-induced alterations of dendritic spine subtypes predict functional decrements in an hypothalamo-pituitary-adrenal-inhibitory prefrontal circuit. J Neurosci. 2013;33(36):14379–91.

    Google Scholar 

  64. Rajkovic K, Bacic G, Ristanović D, Milošević NT. Mathematical model of neuronal morphology: prenatal development of the human dentate nucleus. Biomed Res Int. 2014;2014:812351.

    Google Scholar 

  65. Ren L, Lubrich B, Biber K, Gebicke-Haerter PJ. Differential expression of inflammatory mediators in rat microglia cultured from different brain regions. Brain Res Mol Brain Res. 1999;65(2):198–205.

    Article  CAS  PubMed  Google Scholar 

  66. Rezaie P, Cairns NJ, Male DK. Expression of adhesion molecules on human fetal cerebral vessels: relationship to microglial colonisation during development. Brain Res Dev Brain Res. 1997;104(1–2):175–89.

    CAS  PubMed  Google Scholar 

  67. Ristanović D, Milošević NT, Jelinek HF, Stefanovic IB. The mathematical modelling of neuronal dendritic branching patterns in two dimensions: application to retinal ganglion cells in the cat and rat. Biol Cybern. 2009;100:97–108.

    Google Scholar 

  68. Ristanović D, Stefanovic BD, Puškaš N. Fractal analysis of dendrite morphology of rotated neuronal pictures: the modified box counting method. Theor Biol Forum. 2014;107(1–2):109–21.

    PubMed  Google Scholar 

  69. Ristanović D, Stefanovic BD, Puškaš N. Fractal analysis of dendrite morphology using modified box-counting method. Neurosci Res. 2014;84:64–7.

    Google Scholar 

  70. Sandu A-L, Rasmussen Jr I-A, Lundervold A, Kreuder F, Neckelmann G, Hugdahl K, Specht K. Fractal dimension analysis of MR images reveals grey matter structure irregularities in schizophrenia. Comput Med Imaging Graph. 2008;32(2):150–8.

    Article  PubMed  Google Scholar 

  71. Serletis D, Bardakjian BL, Valiante TA, Carlen PL. Complexity and multifractality of neuronal noise in mouse and human hippocampal epileptiform dynamics. J Neural Eng. 2012;9(5):056008.

    Article  PubMed  Google Scholar 

  72. Sheets KG, Jun B, Zhou Y, Zhu M, Petasis NA, Gordon WC, Bazan NG. Microglial ramification and redistribution concomitant with the attenuation of choroidal neovascularization by neuroprotectin D1. Mol Vis. 2013;19:1747–59.

    CAS  PubMed  PubMed Central  Google Scholar 

  73. Sheffield LG, Berman NE. Microglial expression of MHC class II increases in normal aging of nonhuman primates. Neurobiol Aging. 1998;19(1):47–55.

    Article  CAS  PubMed  Google Scholar 

  74. Sheffield LG, Marquis JG, Berman NE. Regional distribution of cortical microglia parallels that of neurofibrillary tangles in Alzheimer’s disease. Neurosci Lett. 2000;285(3):165–8.

    Article  CAS  PubMed  Google Scholar 

  75. Shimizu Y, Umeda M, Mano H, Aoki I, Higuchi T, Tanaka C. Neuronal response to Shepard’s tones: an auditory fMRI study using multifractal analysis. Brain Res. 2007;1186:113–23.

    Article  CAS  PubMed  Google Scholar 

  76. Sierra A, Beccari S, Diaz-Aparicio I, Encinas JM, Comeau S, Tremblay M-E. Surveillance, phagocytosis, and inflammation: how never-resting microglia influence adult hippocampal neurogenesis. Neural Plast. 2014;2014:610343.

    PubMed  PubMed Central  Google Scholar 

  77. Sierra A, Tremblay M-E, Wake H. Never-resting microglia: physiological roles in the healthy brain and pathological implications. Front Cell Neurosci. 2014;8:240.

    Article  PubMed  PubMed Central  Google Scholar 

  78. Siskova Z, Tremblay M-E. Microglia and synapse: interactions in health and neurodegeneration. Neural Plast. 2013;2013:425845.

    Google Scholar 

  79. Soltys Z, Orzylowska-Sliwinska O, Zaremba M, Orlowski D, Piechota M, Fiedorowicz A, Janeczko K, Oderfeld-Nowak B. Quantitative morphological study of microglial cells in the ischemic rat brain using principal component analysis. J Neurosci Methods. 2005;146(1):50–60.

    Google Scholar 

  80. 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.

    Article  CAS  PubMed  Google Scholar 

  81. Spruston N, Kath WL. Dendritic arithmetic. Nat Neurosci. 2004;7(6):567–9.

    Article  CAS  PubMed  Google Scholar 

  82. Squire LR. Fundamental neuroscience. 4th ed. Amsterdam: Elsevier/Academic; 2013.

    Google Scholar 

  83. Stoll G, Jander S. The role of microglia and macrophages in the pathophysiology of the CNS. Prog Neurobiol. 1999;58(3):233–47.

    Article  CAS  PubMed  Google Scholar 

  84. Streit WJ, Walter SA, Pennell NA. Reactive microgliosis. Prog Neurobiol. 1999;57(6):563–81.

    Article  CAS  PubMed  Google Scholar 

  85. Suckling J, Wink AM, Bernard FA, Barnes A, Bullmore E. Endogenous multifractal brain dynamics are modulated by age, cholinergic blockade and cognitive performance. J Neurosci Methods. 2008;174(2):292–300.

    Article  PubMed  PubMed Central  Google Scholar 

  86. Taylor AM, Castonguay A, Taylor AJ, Murphy NP, Ghogha A, Cook C, Xue L, Olmstead MC, De Koninck Y, Evans CJ, Cahill CM. Microglia disrupt mesolimbic reward circuitry in chronic pain. J Neurosci. 2015;35(22):8442–50.

    Google Scholar 

  87. Tremblay M-E. The role of microglia at synapses in the healthy CNS: novel insights from recent imaging studies. Neuron Glia Biol. 2011;7(1):67–76.

    Article  PubMed  Google Scholar 

  88. Tremblay M-E, Lowery RL, Majewska AK. Microglial interactions with synapses are modulated by visual experience. PLoS Biol. 2010;8(11):e1000527.

    Article  PubMed  PubMed Central  Google Scholar 

  89. Tremblay M-E, Majewska AK. A role for microglia in synaptic plasticity? Commun Integr Biol. 2011;4(2):220–2.

    Article  PubMed  PubMed Central  Google Scholar 

  90. Tremblay M-E, Marker DF, Puccini JM, Muly EC, Lu S-M, Gelbard HA. Ultrastructure of microglia-synapse interactions in the HIV-1 Tat-injected murine central nervous system. Commun Integr Biol. 2013;6(6):e27670.

    Article  PubMed  PubMed Central  Google Scholar 

  91. Tremblay M-E, Riad M, Majewska A. Preparation of mouse brain tissue for immunoelectron microscopy. J Vis Exp. 2010;(41):1–5.

    Google Scholar 

  92. Tremblay M-E, Stevens B, Sierra A, Wake H, Bessis A, Nimmerjahn A. The role of microglia in the healthy brain. J Neurosci. 2011;31(45):16064–9.

    Google Scholar 

  93. Tremblay M-E, Zettel ML, Ison JR, Allen PD, Majewska AK. Effects of aging and sensory loss on glial cells in mouse visual and auditory cortices. Glia. 2012;60(4):541–58.

    Article  PubMed  PubMed Central  Google Scholar 

  94. Tremblay S, Miloudi K, Chaychi S, Favret S, Binet F, Polosa A, Lachapelle P, Chemtob S, Sapieha P. Systemic inflammation perturbs developmental retinal angiogenesis and neuroretinal function. Invest Ophthalmol Vis Sci. 2013;54(13):8125–39.

    Article  CAS  PubMed  Google Scholar 

  95. Wake H, Moorhouse AJ, Jinno S, Kohsaka S, Nabekura J. Resting microglia directly monitor the functional state of synapses in vivo and determine the fate of ischemic terminals. J Neurosci. 2009;29(13):3974–80.

    Google Scholar 

  96. Wang J, Cheng Y, Wang X, Roltsch Hellard E, Ma T, Gil H, Ben Hamida S, Ron D. Alcohol elicits functional and structural plasticity selectively in dopamine D1 receptor-expressing neurons of the dorsomedial striatum. J Neurosci. 2015;35(33):11634–43.

    Google Scholar 

  97. Warsi MA, Molloy W, Noseworthy MD. Correlating brain blood oxygenation level dependent (BOLD) fractal dimension mapping with magnetic resonance spectroscopy (MRS) in Alzheimer’s disease. MAGMA. 2012;25(5):335–44.

    Article  CAS  PubMed  Google Scholar 

  98. Weiss B, Clemens Z, Bódizs R, Vágó Z, Halász P. Spatio-temporal analysis of monofractal and multifractal properties of the human sleep EEG. J Neurosci Methods. 2009;185(1):116–24.

    Article  PubMed  Google Scholar 

  99. West BJ, Scafetta N. A multifractal dynamical model of human gait. In: Fractals in biology and medicine. Springer, Basel, Switzerland; 2005. p. 131–40.

    Google Scholar 

  100. Wisor JP, Schmidt MA, Clegern WC. Evidence for neuroinflammatory and microglial changes in the cerebral response to sleep loss. Sleep. 2011;34(3):261–72.

    PubMed  PubMed Central  Google Scholar 

  101. Young B. Wheater’s functional histology: a text and colour atlas. 5th ed. Edinburgh: Churchill Livingstone/Elsevier; 2006.

    Google Scholar 

  102. Zaletel I, Ristanović D, Stefanovic BD, Puškaš N. Modified Richardson’s method versus the box-counting method in neuroscience. J Neurosci Methods. 2015;242:93–6.

    Google Scholar 

  103. Zorick T, Mandelkern MA. Multifractal detrended fluctuation analysis of human EEG: preliminary investigation and comparison with the wavelet transform modulus maxima technique. PLoS ONE. 2013;8(7):e68360.

    Article  CAS  PubMed  PubMed Central  Google Scholar 

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Correspondence to Audrey L. Karperien or Herbert F. Jelinek .

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Karperien, A.L., Jelinek, H.F. (2016). Morphology and Fractal-Based Classifications of Neurons and Microglia. 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_6

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