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[[Image:ComparitiveBrainSize.jpg|right|thumb|350px|{{#ifexist:Template:ComparitiveBrainSize.jpg/credit|{{ComparitiveBrainSize.jpg/credit}}<br/>|}}Comparative anatomy of brains from various vertebrate species, highlighting the gradual differences in gyrification. University of Wisconsin and Michigan State Comparative Mammalian Brain Collections and the National Museum of Health and Medicine]]

In the brain sciences, '''gyrification''' (or ''cortical folding'' or ''fissuration'') refers to the folding of the [[cerebral cortex]] as a consequence of brain growth during [[embryonic development|embryonic]] and early [[postnatal development]].
In this process, [[gyrus|gyri]] (ridges) and [[sulcus|sulci]] (fissures) form on the outermost surface of the brain. The term ''gyrification'' is also sometimes used instead of the more common term ''[[foliation]]'' to describe the folding patterns of the [[cerebellum]], which is highly convoluted in other [[taxa]], too, e.g. in [[bird]]s<ref name=Iwaniuk2006>{{citation
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 | year = 2006
 | title = Comparative Morphology of the Avian Cerebellum: I. Degree of Foliation
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 | volume = 68
 | issue = 1
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 | doi = 10.1159/000093530
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}}</ref>.


==Phylogeny==
As illustrated in the figure, gyrification occurs across [[mammal]]s<ref name=Mayhew1996>{{cite journal
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 | title = The gyrification of mammalian cerebral cortex: quantitative evidence of anisomorphic surface expansion during phylogenetic and ontogenetic development.
 | journal = Journal of Anatomy
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}}</ref> in a gradually different manner: It increases slowly with overall brain size, following a [[power law]]
<ref name=Hofman1989>{{cite journal
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}}</ref>, and a range of theoretical models exist as to the degree to which it hints at the evolution of cognitive abilities in a given range of species<ref name=Super2001>{{citation
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 | title = The Early Differentiation of the Neocortex: a Hypothesis on Neocortical Evolution
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}}</ref>.

==Ontogeny==
The folding process usually starts during embryonic development<ref name=Neal2007>{{citation
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 | year = 2007
 | title = Insights into the gyrification of developing ferret brain by magnetic resonance imaging
 | journal = Journal of Anatomy
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}}</ref>, in humans around mid-gestation
<ref name=Armstrong1995>{{cite journal
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 | year = 1995
 | title = The Ontogeny of Human Gyrification
 | journal = Cerebral Cortex
 | volume = 5
 | issue = 1
 | pages = 56-63
 | url = http://cercor.oxfordjournals.org/cgi/content/abstract/5/1/56 
}}</ref>. While the extent of cortical folding has been found to be partly determined by genetic factors<ref name=Bartley>{{cite journal
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 | year = 
 | title = Genetic variability of human brain size and cortical gyral patterns
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}}</ref><ref name=Chenn2002>{{citation
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 | title = Regulation of Cerebral Cortical Size by Control of Cell Cycle Exit in Neural Precursors
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 | year = 2005
 | title = Genetic Contributions to Human Gyrification: Sulcal Morphometry in Williams Syndrome
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}}</ref>, the underlying [[biomechanical]] mechanisms are not yet well understood. The overall folding pattern, however, can be mechanistically explained in terms of the cerebral cortex behaving as a gel that buckles under the influence of non-[[isotropic]] [[force]]s<ref name=Van1997>{{cite journal
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}}</ref><ref name=Hilgetag2005>{{citation
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}}</ref><ref name=Mora2006>{{cite journal
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 | title = Buckling of swelling gels
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}}</ref><ref name=Hilgetag2006>{{citation
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}}</ref>. 
Possible causes of the non-isotropy include [[thermal]] [[noise]], variations in the number and timing of [[cell division]]s, [[cell migration]], [[cortical connectivity]], [[synaptic pruning]], [[brain size]] and [[metabolism]] ([[phospholipid]]s in particular), all of which may interact<ref name=Price2004>{{cite journal
 | author = Price, D.J.
 | year = 2004
 | title = Lipids make smooth brains gyrate
 | journal = Trends in Neurosciences
 | volume = 27
 | issue = 7
 | pages = 362-364
 | url = http://linkinghub.elsevier.com/retrieve/pii/S0166223604001304 
}}</ref><ref name=Francis2006>{{citation
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 | last7 = Tuy | first7 = F.P.D.
 | last8 = Beldjord | first8 = C.
 | last9 = Chelly | first9 = J.
 | year = 2006
 | title = Human disorders of cortical development: from past to present
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 | volume = 23
 | issue = 4
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}}</ref><ref name=Xu2008>{{citation
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 | year = 2008
 | title = Residual stress in the adult mouse brain
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 | year = 2008
 | title = Brain Size and Folding of the Human Cerebral Cortex
 | journal = Cerebral Cortex
 | url = http://cercor.oxfordjournals.org/cgi/content/abstract/bhm261v1 
}}</ref>. 


==Medical relevance==
This multitude of underlying processes has rendered the concept of gyrification increasingly important for [[clinical diagnostics]] in recent years, since gyrification in some areas of the [[human brain]] appears to reflect functional development<ref name=Dubois2008>{{citation
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 | last6 = Ha-vinh Leuchter | first6 = R.
 | last7 = Sizonenko | first7 = S. V.
 | last8 = Warfield | first8 = S. K.
 | last9 = Mangin | first9 = J. F.
 | last10 = Huppi | first10 = P. S.
 | year = 2008
 | title = Primary cortical folding in the human newborn: an early marker of later functional development
 | journal = Brain
 | volume = 131
 | issue = 8
 | pages = 2028
 | doi = 10.1093/brain/awn137
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 | pmid = 18587151
}}</ref> and thus to correlate with measures of [[intelligence (brain power)|intelligence]]<ref name= Luders2007>{{citation
 | author = Lüders, Eileen; Narr, Katherine L.; Bilder, Robert M.; Szeszko, Philip R.; Gurbani, Mala N.; Hamilton, Liberty; Toga, Arthur W.; Gaser, Christian
 | year = 2007
 | title = Mapping the Relationship between Cortical Convolution and Intelligence: Effects of Gender
 | journal = Cerebral Cortex
 | volume = 18
 | issue = 9
 | pages = 2019
 | doi = 10.1093/cercor/bhm227
 | pmid = 18089578
}}</ref>, and disturbances in the folding pattern &mdash; as determined by non-invasive [[neuroimaging]] &mdash; can be taken as indicators of [[neuropsychiatric disease]]s if differences due to [[gender]] and [[age]] are accounted for <ref name=Luders2004>{{citation
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 | year = 2004
 | title = Gender differences in cortical complexity
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}}</ref>. 
Apart from being a marker of disorders like [[schizophrenia]] or [[Williams syndrome]]<ref name=White2003>{{citation
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 | year = 2003
 | title = Gyrification abnormalities in childhood- and adolescent-onset schizophrenia
 | journal = Biological Psychiatry
 | volume = 54
 | issue = 4
 | pages = 418–426
 | doi = 10.1016/S0006-3223(03)00065-9
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}}</ref><ref name=Schmitt2002>{{cite journal
 | author = Schmitt, J.E.
 | coauthors = Watts, K.; Eliez, S.; Bellugi, U.; Galaburda, A.M.; Reiss, A.L.
 | year = 2002
 | title = Increased gyrification in Williams syndrome: evidence using 3D MRI methods
 | journal = Developmental Medicine & Child Neurology
 | volume = 44
 | issue = 5
 | pages = 292-295
 | doi = 10.1111/j.1469-8749.2002.tb00813.x
}}</ref>, a number of disorders exist of which abnormal gyrification is a dominant feature, e.g. [[agyria]], [[pachygyria]], [[polymicrogyria]] or [[lissencephaly]]<ref name=Francis2006>{{citation
 | last1 = Francis | first1 = F.
 | last2 = Meyer | first2 = G.
 | last3 = Fallet-bianco | first3 = C.
 | last4 = Moreno | first4 = S.
 | last5 = Kappeler | first5 = C.
 | last6 = Socorro | first6 = A.C.
 | last7 = Tuy | first7 = F.P.D.
 | last8 = Beldjord | first8 = C.
 | last9 = Chelly | first9 = J.
 | year = 2006
 | title = Human disorders of cortical development: from past to present
 | journal = European Journal of Neuroscience
 | volume = 23
 | issue = 4
 | pages = 877–893
 | doi = 10.1111/j.1460-9568.2006.04649.x
}}</ref>. 


==Quantification==
Folding of a brain can be described in both local and global terms, once a suitable representation of a brain surface has been obtained from [[neuroimaging]] data by some [[surface extraction]] technique. The latter usually delivers either a triangulated surface representing the boundary between the [[cerebrospinal fluid]] and the [[gray matter]] or between the latter and the [[white matter]] but in principle, any surface in between would do as well (e.g. the [[central layer]] which is sometimes also used). Leaving the multiple issues of [[resolution (imaging)|resolution]] and [[artifacts]] in these surface representations aside, the brain surface mesh, like any mesh of a [[manifold (geometry)|closed three-dimensional manifold]], can then be analyzed in terms of local [[curvature]] measures, from which global measures can be derived. Over the last decades, several such measures have been proposed<ref name=Rodriguez-carranza2008>{{citation
 | last1 = Rodriguez-Carranza | first1 = C.E.
 | last2 = Mukherjee | first2 = P.
 | last3 = Vigneron | first3 = D.
 | last4 = Barkovich | first4 = J.
 | last5 = Studholme | first5 = C.
 | year = 2008
 | title = A framework for in vivo quantification of regional brain folding in premature neonates
 | journal = Neuroimage
 | volume = 41
 | pages = 462
 | doi = 10.1016/j.neuroimage.2008.01.008
 | url = http://linkinghub.elsevier.com/retrieve/pii/S1053811908000311
}}</ref>. Following the developments in imaging techniques, they were initially focused on quantification in two-dimensional spaces, later in three-dimensional ones. Some examples that are commonly used include:
*[[L2 norm|<math> L^2 norms</math>]]:
**<math>LN_G = \tfrac{1}{4\pi} \textstyle \sqrt{\sum_A K^2}</math>, with <math>K = k_1 k_2</math> being the [[Gaussian curvature]], computed from the two [[principal curvature]]s <math>k_1</math> and <math>k_2</math>
**<math>LN_M =\tfrac{1}{4\pi} \textstyle \sum_A H^2</math>, with <math>H=\tfrac{1}{2}(k_1 + k_2)</math> being the [[Mean curvature]]
*Folding index
**<math>FI =\tfrac{1}{4\pi} \textstyle \sum_A k^{\ddagger}</math>, with <math>k^{\ddagger}=|k_1|(|k_1|-|k_2|)</math> 
*Intrinsic curvature index
**<math>ICI =\tfrac{1}{4\pi} \textstyle \sum_A K^+</math>, with <math>K^+</math> being the positive Gaussian curvature

*Gyrification index
*Cortical complexity
*Fractal dimension
*Global gyrification index
*Local gyrification index
*Shape index
*Curvedness
*Roundness

== References==
{{reflist}}