Abstract
The evolution of the brain in mammals is characterized by changes in size, architecture, and internal organization. Consequently, the geometry of the brain, and especially the size and shape of the cerebral cortex, has changed notably during evolution. Comparative studies of the cerebral cortex suggest that there are general architectural principles governing its growth and evolutionary development. In this chapter some of the design principles and operational modes that underlie the fractal geometry and information processing capacity of the cerebral cortex in primates, including humans, will be explored. It is shown that the development of the cortex coordinates folding with connectivity in a way that produces smaller and faster brains.
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References
Aboitiz F, Montiel JF. From tetrapods to primates: conserved developmental mechanisms in diverging ecological adaptations. Prog Brain Res. 2012;195:3–24.
Azevedo FAC, Carvalho LRB, Grinberg LT, Farfel JM, Ferretti REI, Leite REP, Filho WJ, Lent R, Herculano-Houzel S. Equal numbers of neuronal and nonneuronal cells make the human brain an isometrically scaled-up primate brain. J Comp Neurol. 2009;513:532–41.
Bayly PV, Taber LA, Kroenke CD. Mechanical forces in the cerebral cortical folding: a review of measurements and models. J Mech Behav Biomed Mater. 2014;29:568–81.
Bohland JW, Wu C, Barbas H, Bokil H, Bota M, Breiter HC et al. A proposal for a coordinated effort for the determination of brainwide neuroanatomical connectivity in model organisms at a mesoscopic scale. PLoS Comput Biol. 2009;5:e1000334.
Bok ST. Der Einfluss der in den Furchen und Windungen auftretenden Krümmungen der Grosshirnrinde auf die Rindenarchitektur. Z Ges Neurol Psychiat. 1929;121:682–750.
Budd J, Kisvárday ZF. How do you wire a brain? Front Neuroanat. 2013;7:14.
Bullmore E, Sporns O. The economy of brain network organization. Nat Rev Neurosci. 2012;13:336–49.
Buxhoeveden DP. Minicolumn size and human cortex. Prog Brain Res. 2012;195:219–35.
Buzsáki G, Logothetis N, Singer W. Scaling brain size, keeping time: evolutionary preservation of brain rhythms. Neuron. 2013;80:751–64.
Casanova MF. White matter volume increase and minicolumns in autism. Ann Neurol. 2004;56:453.
Casanova MF. Cortical organization: a description and interpretation of anatomical findings based on systems theory. Transl Neurosci. 2010;1:62–71.
Changizi MA. Principles underlying mammalian neocortical scaling. Biol Cybern. 2001;84:207–15.
Changizi MA. Scaling the brain and its connections. In: Kaas JH, editor. Evolution of nervous systems, vol. 3. New York: Academic; 2007. p. 167–80.
Changizi MA, Shimojo S. Parcellation and area-area connectivity as a function of neocortex size. Brain Behav Evol. 2005;66:88–98.
Charvet CJ, Finlay B. Embracing covariation in brain evolution: large brains, extended development, and flexible primate social systems. Prog Brain Res. 2012;195:71–87.
Cheung AF, Pollen AA, Tavare A, DeProto J, Molnár Z. Comparative aspects of cortical neurogenesis in vertebrates. J Anat. 2007;211:164–76.
Chklovskii DB, Mel BW, Svoboda K. Cortical rewiring and information storage. Nature. 2004;431:782–8.
Da Costa NM, Martin KAC. Whose cortical column would that be? Front Neuroanat. 2010;4:16.
Di Ieva A, Grizzi F, Jelinek H, Pellionisz AJ, Losa GA. Fractals in the neurosciences, part I: general principles and basic neurosciences. Neuroscientist. 2013;20:403–17.
Di Ieva A, Esteban FJ, Grizzi F, Klonowski W, MartÃn-Landrove M. Fractals in the neurosciences, part II: clinical applications and future perspectives. Neuroscientist. 2015;21:30–43.
Douglas RJ, Martin KA. Neuronal circuits of the neocortex. Ann Rev Neurosci. 2004;27:419–51.
Finlay BL, Uchiyama R. Developmental mechanisms channeling cortical evolution. Trends Neurosci. 2015;38:69–76.
Frahm HD, Stephan H, Stephan M. Comparison of brain structure volumes in Insectivora and Primates. Part I. Neocortex. J Hirnforsch. 1982;23:375–89.
Harrison KH, Hof PR, Wang SS-H. Scaling laws in the mammalian neocortex: does form provide clues to function? J Neurocytol. 2002;31:289–98.
Herculano-Houzel S. The human brain in numbers: a linearly scaled-up primate brain. Front Hum Neurosci. 2009;3:31.
Herculano-Houzel S. Neuronal scaling rules for primate brains: the primate advantage. Prog Brain Res. 2012;195:325–40.
Herculano-Houzel S, Collins CE, Wong P, Kaas JH, Lent R. The basic nonuniformity of the cerebral cortex. Proc Natl Acad Sci U S A. 2008;105:12593–8.
Herculano-Houzel S, Mota B, Wong P, Kaas JH. Connectivity-driven white matter scaling and folding in primate cerebral cortex. Proc Natl Acad Sci U S A. 2010;107:19008–13.
Herculano-Houzel S, Manger PR, Kaas JH. Brain scaling in mammalian evolution as a consequence of concerted and mosaic changes in numbers of neurons and average neuronal cell size. Front Neuroanat. 2014;8:77.
Hofman MA. Size and shape of the cerebral cortex in mammals. Part I. The cortical surface. Brain Behav Evol. 1985;27:28–40.
Hofman MA. Size and shape of the cerebral cortex in mammals. Part II. The cortical volume. Brain Behav Evol. 1988;32:17–26.
Hofman MA. On the evolution and geometry of the brain in mammals. Prog Neurobiol. 1989;32:137–58.
Hofman MA. The fractal geometry of convoluted brains. J Hirnforsch. 1991;32:103–11.
Hofman MA. Brain evolution in hominids: are we at the end of the road. In: Falk D, Gibson KR, editors. Evolutionary anatomy of the primate cerebral cortex. Cambridge: Cambridge University Press; 2001. p. 113–27.
Hofman MA. Design principles of the human brain: an evolutionary perspective. Prog Brain Res. 2012;195:373–90.
Hofman MA. Evolution of the human brain: when bigger is better. Front Neuroanat. 2014;8:15.
Hofman MA. Evolution of the human brain and intelligence: from matter to mind. In: Goldstein S, Naglieri JA, Princiotta D, editors. Handbook of intelligence: evolutionary theory, historical perspective and current concepts. Berlin: Springer; 2015. p. 65–82.
Innocenti GM, Vercelli A. Dendritic bundles, minicolumns, columns, and cortical output units. Front Neuroanat. 2010;4:11.
Innocenti GM, Vercelli A, Caminiti R. The diameter of cortical axons depends both on the area of origin and target. Cereb Cortex. 2013;24:2178–88.
Jerison HJ. Evolution of the brain and intelligence. New York: Academic; 1973.
Kaas JH. The evolution of neocortex in primates. Prog Brain Res. 2012;195:91–102.
Karbowski J. How does connectivity between cortical areas depend on brain size? Implications for efficient computation. J Comput Neurosci. 2003;15:347–56.
King RD. Computation of local fractal dimension values of the human cerebral cortex. Appl Math. 2014;5:1733–40.
Kiselev VG, Hahn KR, Auer DP. Is the brain cortex a fractal? Neuroimage. 2003;20:1765–74.
Landman BS, Russo RL. On a pin versus block relationship for partitions of logic graphs. IEEE Trends Comput. 1971;20:1469–79.
Laughlin SB, Sejnowski TJ. Communication in neural networks. Science. 2003;301:1870–4.
Lefebvre L. Primate encephalization. Prog Brain Res. 2012;195:393–412.
Lewitus E, Keleva I, Kalinka AT, Tomancak, Huttner WB. An adaptive threshold in mammalian neocortical evolution. PLoS Biol. 2014;12:e1002000, 1–15.
Li L, Hu X, Preuss TM, Glasser MF, Damen FW, Qiu Y, Rilling JK. Mapping putative hubs in human, chimpanzee and rhesus macaque connectomes via diffusion tractography. Neuroimage. 2013;80:462–74.
MacLeod C. The missing link: evolution of the primate cerebellum. Prog Brain Res. 2012;195:165–87.
Macphail EM, Bolhuis JJ. The evolution of intelligence: adaptive specializations versus general process. Biol Rev. 2001;76:341–64.
Mandelbrot BB. The fractal geometry of nature. San Francisco: Freeman; 1982.
Mota B, Herculano-Houzel S. How the cortex gets its folds: an inside-out, connectivity-driven model for the scaling of mammalian cortical folding. Front Neuroanat. 2012;6:3.
Mountcastle VB. The columnar organization of the brain. Brain. 1997;120:701–22.
Opris I, Casanova MF. Prefrontal cortical minicolumn: from executive control to disrupted cognitive processing. Brain. 2014;137:1863–75.
Preuss TM. The human brain: rewired and running hot. Ann NY Acad Sci. 2011;1125(S1):E183–91.
Rakic P. Evolution of the neocortex: a perspective from developmental biology. Nat Rev Neurosci. 2009;10:724–35.
Ribeiro PFM, Ventura-Antunes L, Gabi M, Mota B, Grinberg LT, Farfel JM, et al. The human cerebal cortex is neither one nor many: neuronal distribution reveals two quantitative different zones in the gray matter, three in the white matter, and explains local variations in cortical folding. Front Neuroanat. 2013;7:28.
Rilling JK. Comparative primate neuroimaging: insights into human brain evolution. Trends Cogn Sci. 2014;18:45–55.
Ringo JL, Doty RW, Demeter S, Simard PY. Time is of the essence: a conjecture that hemispheric specialization arises from interhemispheric conduction delay. Cereb Cortex. 1994;4:331–43.
Roth G, Dicke U. Evolution of the brain and intelligence in primates. Prog Brain Res. 2012;195:413–30.
Schoenemann PT. Evolution of the size and functional areas of the human brain. Ann Rev Anthropol. 2006;35:379–406.
Schoenemann PT, Sheehan MJ, Glotzer ID. Prefrontal white matter volume is disproportionately larger in humans than in other primates. Nat Neurosci. 2005;8:242–52.
Semendeferi K, Damasio H. The brain and its main anatomical subdivisions in living hominoids using magnetic resonance imaging. J Hum Evol. 2000;38:317–32.
Sherwood CC, Smaers J. What’s the fuss over human frontal lobe evolution? Trends Cogn Sci. 2013;17:432–3.
Sherwood CC, Bauernfeind AL, Bianchi S, Raghanti MA, Hof PR. Human brain evolution writ large and small. Prog Brain Res. 2012;195:237–54.
Smaers JB, Soligo C. Brain reorganization, not relative brain size, primarily characterizes anthropoid brain evolution. Proc R Soc B. 2013;280:20130269.
Smaers JB, Schleicher A, Zilles K, Vinicius L. Frontal white matter volume in anthropoid primates. PLoS One. 2010;5:e9123.
Sporns O, Chilavo DR, Kaiser M, Hilgetag CC. Organization, development and function of complex brain networks. Trends Cogn Sci. 2004;8:418–25.
Sporns O, Honey CJ, Kötter R. Identification and classification of hubs in brain networks. PLoS One. 2007;2:e1049, 1–14.
Stephan H, Frahm HD, Baron G. New and revised data on volumes of brain structures in insectivores and primates. Folia Primatol. 1981;35:1–29.
Stoop N, Lagrange R, Terwage D, Reis PM, Dunkel J. Curvature-induced symmetry breaking determines elastic surface patterns. Nat Mater. 2015;14:337–42.
Striedter GF. Principles of brain evolution. Sunderland: Sinauer Associates; 2004.
Teffer K, Semendeferi K. Human prefrontal cortex: evolution, development, and pathology. Prog Brain Res. 2012;195:191–218.
Van den Heuvel MP, Sporns O. Rich-club organization of the human connectome. J Neurosci. 2011;31:15775–86.
Van Essen DC. A tension-based theory of morphogenesis and compact wiring in the central nervous system. Nature. 1997;385:313–8.
Wang SS-H, Shultz JR, Burish MJ, Harrison KH, Hof PR, Towns LC, Wagers MW, Wyatt KD. Functional trade-offs in white matter axonal scaling. J Neurosci. 2008;28:4047–56.
Wang X-J. Neurophysiological and computational principles of cortical rhythms in cognition. Physiol Rev. 2010;90:1195–268.
Watts DJ, Strogatz SH. Collective dynamics of ‘small-world’ networks. Nature. 1998;393:440–2.
Wedeen VJ, Rosene DL, Wang R, Dai G, Mortazavi F, Hagmann P, Kaas JH, Tseng WY. The geometric structure of the brain fiber pathway. Science. 2012;335:1628–38.
Wen Q, Chklovskii DB. Segregation of the brain into gray and white matter: a design minimizing conduction delays. PLoS Comp Biol. 2005;1:e78:617–630.
Willemet R. Reconsidering the evolution of brain, cognition, and behavior in birds and mammals. Front Psychol. 2013;4:396.
Zhang K, Sejnowski TJ. A universal scaling law between gray matter and white matter of cerebral cortex. Proc Natl Acad Sci U S A. 2000;97:5621–6.
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Hofman, M.A. (2016). The Fractal Geometry of the Human Brain: An Evolutionary Perspective. 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_11
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