Gyrification: Difference between revisions

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imported>Daniel Mietchen
imported>Daniel Mietchen
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  | doi = 10.1002/ima.20138
  | doi = 10.1002/ima.20138
  | url = http://www3.interscience.wiley.com/journal/119877321/abstract
  | url = http://www3.interscience.wiley.com/journal/119877321/abstract
}}</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:
}}</ref>, as detailed on the [[Gyrification/Function|Function subpage]]. Following the developments in imaging techniques, they were initially focused on quantification in two-dimensional spaces, later in three-dimensional ones.
*[[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]] and <math>A</math> the area of the surface in question
*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
**<math>GI(n) =\tfrac{A(n)_{pial}}{A(n)_{gc}}</math>, with <math>n</math> indicating the number of the slice, and <math>A(n)_{pial}</math> and <math>A(n)_{gc}</math> being the [[pia mater|pial]] surface area in that slice and the surface area of the boundary between gray matter and cerebrospinal fluid, respectively
*Gyrification-White index
**<math>GWI =\tfrac{A_{gw}}{A_{gc}}</math>, with <math>A_{gw}</math> being the surface area of the boundary between gray matter and white matter
*White matter folding
**<math>WMF =\tfrac{A_{gw}}{{V_w}^{2/3}}</math>, with <math>V_w</math> being the volume of the white matter
*Cortical complexity
*Fractal dimension
*Global gyrification index
*Local gyrification index
*Shape index
*Curvedness
*Roundness
**<math>Rn =\tfrac{A}{^3\sqrt{36 \pi V^2}}</math>


== References==
== References==
{{reflist|2}}
{{reflist|2}}

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(CC) Photo: University of Wisconsin and Michigan State Comparative Mammalian Brain Collections and National Museum of Health and Medicine (see http://www.brainmuseum.org/)
Comparative anatomy of brains from various vertebrate species, highlighting the gradual differences in gyrification.

In the brain sciences, gyrification (or cortical folding, cortical convolution, fissuration or fissurization) refers to both the process and the extent of folding of the cerebral cortex in mammals as a consequence of brain growth during embryonic and early postnatal development.

In the process (also known as gyrogenesis), gyri (ridges) and sulci (fissures) form on the external surface of the brain (i.e. at the boundary between the cerebrospinal fluid and the gray matter)[1]. A low extent of gyrification in a given brain is commonly referred to as lissencephaly (which may range from agyria, the total absence of folding, to pachygyria), while gyrencephaly describes a high degree of folding[2].

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 birds[3].

Phylogeny

See also brain evolution.

As illustrated in the figure, gyrification occurs across mammals[4][5]: It generally increases slowly with overall brain size, following a power law [6], though exceptions exist: While several groups of small-brained placental species are indeed lissencephalic[7][8], so is the monotreme platypus but the monotreme echidna is gyrencephalic[9]. Conversely, large-brained mammals are usually highly gyrencephalic[10][11][12], with sirenians being a notable exception[13]. A range of theoretical models exist as to the degree to which gyrification hints at the evolution of cognitive abilities in a given range of species[14][15][16].

Ontogeny

See also brain development.

The folding process usually starts during fetal development -- in humans around mid-gestation[17][1][18] -- or shortly after birth, as in ferrets[19][20]. It proceeds synchronously in both hemispheres by an expansion of gyral tissue, while the sulcal roots remain in a relatively stable position throughout gyrogenesis[19][1][18]. In the human brain, variations due to gender and ethnicity have been demonstrated, and such interindividual differences appear to be highest in regions with strong gyrification[21].

Mechanism

While the extent of cortical folding has been found to be partly determined by genetic factors[22][23][24][25][26][27], 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 forces[28][29][30][31][32]. Possible causes of the non-isotropy include thermal noise, differential growth of the cortical layers due to variations in the number and timing of cell divisions[33], cell migration, myelinization, cortical connectivity, synaptic pruning, brain size and metabolism (phospholipids in particular), all of which may interact[34][2][35][36]. The folding, in turn, imposes constraints on the shape of cells, particulary in the outer cortical layers (V and VI)[37].

Function

The primary effect of a folding process is always an increase of surface area relative to volume. Due to the laminar arrangement of the cerebral cortex, an increased cerebral surface area correlates with an increased number of neurons, which is presumed to enhance the computational capacities of the cortex within some metabolic and connectivity limits[38]. In some areas of the human brain, gyrification appears indeed to reflect functional development[39] and thus to correlate with measures of intelligence[40], even though variations of these effects due to gender and age have been described [41].

Medical relevance

A number of disorders exist of which abnormal gyrification is a dominant feature, e.g. polymicrogyria or lissencephalic disorders like agyria to pachygyria. They usually occur bilaterally but cases of, e.g., unilateral lissencephaly, have been described[42]. Beyond these gross modifications of gyrification, more subtle variations occur in a number of neuropsychiatric disorders whose variety reflects the multitude of processes underlying gyrification[2]. Due to methodological advances in neuroimaging and computational morphometry since the late 1990s, folding patterns and abnormalities thereof can now be determined non-invasively. This is becoming increasingly important for clinical diagnostics, particular in relation to neuropsychiatric diseases like schizophrenia[43][44], autism[45], epilepsy[46], dyslexia[47], velocardiofacial syndrome[48] or Williams syndrome[49]. The direction of disease-associated changes depends on the cortical region and the disease subtype. In schizophrenics, for instance, gyrification has been found to increase in the dorsolateral prefrontal cortex[50] and, in different populations, to decrease in frontal and parietal regions of the left hemisphere[51]or even throughout both hemispheres[52].

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 a triangulated surface representing either 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 also sometimes used). Leaving the multiple issues of resolution and artifacts in these surface representations aside, the brain surface mesh, like any mesh of a 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[53][54], as detailed on the Function subpage. Following the developments in imaging techniques, they were initially focused on quantification in two-dimensional spaces, later in three-dimensional ones.

References

  1. ↑ 1.0 1.1 1.2 Armstrong, E.; Schleicher, A.; Omran, H.; Curtis, M.; Zilles, K. (1995). "The Ontogeny of Human Gyrification". Cerebral Cortex 5 (1): 56-63.
  2. ↑ 2.0 2.1 2.2 Francis, F.; G. Meyer & C. Fallet-Bianco et al. (2006), "Human disorders of cortical development: from past to present", European Journal of Neuroscience 23 (4): 877–893, DOI:10.1111/j.1460-9568.2006.04649.x
  3. ↑ Iwaniuk, A.N.; Hurd, P.L.; Wylie, D.R. (2006), "Comparative Morphology of the Avian Cerebellum: I. Degree of Foliation", Brain Behav Evol 68 (1): 45–62, DOI:10.1159/000093530
  4. ↑ Prothero, J.W. (1984), "Folding of the Cerebral Cortex in Mammals", Brain Behavior and Evolution 24: 152-167, DOI:10.1159/000121313
  5. ↑ Mayhew, T.M.; Mwamengele, G.L.; Dantzer, V.; Williams, S. (1996). "The gyrification of mammalian cerebral cortex: quantitative evidence of anisomorphic surface expansion during phylogenetic and ontogenetic development.". Journal of Anatomy 188 (Pt 1): 53.
  6. ↑ Hofman, M.A. (1989). "On the evolution and geometry of the brain in mammals.". Prog Neurobiol 32 (2): 137-58. DOI:10.1016/0301-0082(89)90013-0. Research Blogging. [e]
  7. ↑ Ferrer, I.; I. Fabregues & E. Condom (1986), "A Golgi study of the sixth layer of the cerebral cortex. I. The lissencephalic brain of Rodentia, Lagomorpha, Insectivora and Chiroptera", J Anat 145: 217–234
  8. ↑ Pillay, P. & P.R. Manger (2007), "Order-specific quantitative patterns of cortical gyrification", European Journal of Neuroscience 25 (9): 2705–2712, DOI:10.1111/j.1460-9568.2007.05524.x
  9. ↑ Hassiotis, M.; G. Paxinos & K.W.S. Ashwell (2003), "The anatomy of the cerebral cortex of the echidna (Tachyglossus aculeatus)", Comparative Biochemistry and Physiology, Part A 136 (4): 827–850, DOI:10.1016/S1095-6433(03)00166-1 [e]
  10. ↑ Ferrer, I.; I. Fabregues & E. Condom (1986), "A Golgi study of the sixth layer of the cerebral cortex. II. The gyrencephalic brain of Carnivora, Artiodactyla and Primates", J Anat 146: 87–104
  11. ↑ Hof, P.R.; R. Chanis & L. Marino (2005), "Cortical Complexity in Cetacean Brains", Anatomical Record Part a Discoveries in Molecular Cellular and Evolutionary Biology 287 (1): 1142, DOI:10.1002/ar.a.20258
  12. ↑ Hakeem, A.Y.; P.R. Hof & C.C. Sherwood et al. (2005), "Brain of the African elephant (Loxodonta africana): neuroanatomy from magnetic resonance images", Anat Rec A: Discov Mol Cell Evol Biol 287 (1): 1117–1127
  13. ↑ Reep, R.L. & T.J. O'Shea (1990), "Regional brain morphometry and lissencephaly in the Sirenia", Brain Behav Evol 35 (4): 185–194, DOI:10.1159/000115866
  14. ↑ Stangier, H. (1937), "Die Furchen der Großhirnrinde beim Schimpanse", Zeitschrift für Anatomie und Entwicklungsgeschichte 107: 647, DOI:10.1007/BF02118571
  15. ↑ Supèr, H.; Uylings, H.B.M. (2001), "The Early Differentiation of the Neocortex: a Hypothesis on Neocortical Evolution", Cerebral Cortex 11 (12): 1101–1109, DOI:10.1093/cercor/11.12.1101
  16. ↑ Sereno, M.I. & R.B. Tootell (2005), "From monkeys to humans: what do we now know about brain homologies?", Curr Opin Neurobiol 15 (2): 135–44, DOI:10.1016/j.conb.2005.03.014
  17. ↑ Chi, J.G.; E.C. Dooling & F.H. Gilles (1977), "Gyral development of the human brain", Annals of Neurology 1 (1): 86–93, DOI:10.1002/ana.410010109
  18. ↑ 18.0 18.1 Regis, J.; J.F. Mangin & T. Ochiai et al. (2005), ""Sulcal root" generic model: a hypothesis to overcome the variability of the human cortex folding patterns", Neurol Med Chir (Tokyo) 45 (1): 1–17, DOI:10.2176/nmc.45.1
  19. ↑ 19.0 19.1 Smart, I.H. & G.M. McSherry (1986), "Gyrus formation in the cerebral cortex in the ferret. I. Description of the external changes", Journal of Anatomy 146: 141-152
  20. ↑ Neal, J.; M. Takahashi & M. Silva et al. (2007), "Insights into the gyrification of developing ferret brain by magnetic resonance imaging", J Anat 210 (1): 66–77, DOI:10.1111/j.1469-7580.2006.00674.x
  21. ↑ Zilles, K.; R. Kawashima & A. Dabringhaus et al. (2001), "Hemispheric Shape of European and Japanese Brains: 3-D MRI Analysis of Intersubject Variability, Ethnical, and Gender Differences", Neuroimage 13 (2): 262–271, DOI:10.1006/nimg.2000.0688
  22. ↑ Bartley, A.J.; Jones, D.W.; Weinberger, D.R. (1997). "Genetic variability of human brain size and cortical gyral patterns". Brain 120 (2): 257-269.
  23. ↑ Rubenstein, John L.R.; Stewart Anderson & Limin Shi et al. (1999), "Genetic Control of Cortical Regionalization and Connectivity", Cerebral Cortex 9 (6): 524–532, DOI:10.1093/cercor/9.6.524
  24. ↑ Rubenstein, John L.R. & Pasko Rakic (1999), "Genetic Control of Cortical Development", Cerebral Cortex 9 (6): 521–523, DOI:10.1093/cercor/9.6.521
  25. ↑ Chenn, Anjen; Walsh, Christopher A. (2002), "Regulation of Cerebral Cortical Size by Control of Cell Cycle Exit in Neural Precursors", Science 297 (5580): 365–9, DOI:10.1126/science.1074192 [e]
  26. ↑ Kippenhan, J. Shane; Rosanna K. Olsen & Carolyn B. Mervis et al. (2005), "Genetic Contributions to Human Gyrification: Sulcal Morphometry in Williams Syndrome", Journal of Neuroscience 25 (34): 7840, DOI:10.1523/JNEUROSCI.1722-05.2005
  27. ↑ Kerjan, G. & J.G. Gleeson (2007), "Genetic mechanisms underlying abnormal neuronal migration in classical lissencephaly", Trends in Genetics 23 (12): 623–630, DOI:10.1016/j.tig.2007.09.003 [e]
  28. ↑ Van Essen, D.C. (1997). "A tension-based theory of morphogenesis and compact wiring in the central nervous system". Nature 385 (6614): 313-8.
  29. ↑ Mangin, J.F.; D. Rivière & A. Cachia et al. (2004), "A framework to study the cortical folding patterns", Neuroimage 23: 129–138, DOI:10.1016/j.neuroimage.2004.07.019
  30. ↑ Hilgetag, C.C. & H. Barbas (2005), "Developmental mechanics of the primate cerebral cortex", Anat Embryol (Berl) 210 (5-6): 411–7, DOI:10.1007/s00429-005-0041-5
  31. ↑ Mora, T.; Boudaoud, A. (2006). "Buckling of swelling gels". The European Physical Journal E - Soft Matter 20 (2): 119-124.
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  33. ↑ Kornack, David R. & Pasko Rakic (1998), "Changes in cell-cycle kinetics during the development and evolution of primate neocortex", Proceedings of the National Academy of Sciences of the United States of America 95 (3): 1242–1246, DOI:10.1073/pnas.95.3.1242 [e]
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  35. ↑ Xu, G.; P.V. Bayly & L.A. Taber (2008), "Residual stress in the adult mouse brain", Biomech Model Mechanobiol, DOI:10.1007/s10237-008-0131-4
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  37. ↑ Ferrer, I.; I. Fabregues & E. Condom (1987), "A Golgi study of the sixth layer of the cerebral cortex. III. Neuronal changes during normal and abnormal cortical folding", J Anat 152: 71–82
  38. ↑ Wen, Q. & D.B. Chklovskii (2005), "Segregation of the Brain into Gray and White Matter: A Design Minimizing Conduction Delays", PLoS Comput Biol 1 (7): e78, DOI:10.1371/journal.pcbi.0010078
  39. ↑ Dubois, J.; M. Benders & C. Borradori-tolsa et al. (2008), "Primary cortical folding in the human newborn: an early marker of later functional development", Brain 131 (8): 2028, DOI:10.1093/brain/awn137 [e]
  40. ↑ Lüders, Eileen; Narr, Katherine L.; Bilder, Robert M.; Szeszko, Philip R.; Gurbani, Mala N.; Hamilton, Liberty; Toga, Arthur W.; Gaser, Christian (2007), "Mapping the Relationship between Cortical Convolution and Intelligence: Effects of Gender", Cerebral Cortex 18 (9): 2019, DOI:10.1093/cercor/bhm227
  41. ↑ Lüders, E.; K.L. Narr & P.M. Thompson et al. (2004), "Gender differences in cortical complexity", Nat Neurosci 7 (8): 799–800, DOI:10.1038/nn1277
  42. ↑ Hager, B.C.; I.Z. Dyme & S.R. Guertin et al. (1991), "Linear nevus sebaceous syndrome: megalencephaly and heterotopic gray matter", Pediatr Neurol 7 (1): 45–9, DOI:10.1016/0887-8994(91)90105-T
  43. ↑ White, T.; Andreasen, N.C.; Nopoulos, P.; Magnotta, V. (2003), "Gyrification abnormalities in childhood- and adolescent-onset schizophrenia", Biological Psychiatry 54 (4): 418–426, DOI:10.1016/S0006-3223(03)00065-9
  44. ↑ Cachia, A.; M.L. Paillère-Martinot & A. Galinowski et al. (2007), "Cortical folding abnormalities in schizophrenia patients with resistant auditory hallucinations", Neuroimage
  45. ↑ Hardan, A.Y.; R.J. Jou & M.S. Keshavan et al. (2004), "Increased frontal cortical folding in autism: a preliminary MRI study", Psychiatry Research: Neuroimaging 131 (3): 263–268, DOI:10.1016/j.pscychresns.2004.06.001
  46. ↑ Ronan, L.; K. Murphy & N. Delanty et al. (2007), "Cerebral Cortical Gyrification: A Preliminary Investigation in Temporal Lobe Epilepsy", Epilepsia 48 (2): 211–219, DOI:10.1111/j.1528-1167.2006.00928.x
  47. ↑ Casanova, Manuel F.; Julio Araque & Jay Giedd et al. (2004), "Reduced Brain Size and Gyrification in the Brains of Dyslexic Patients", Journal of Child Neurology 19 (4): 275, DOI:10.1177/088307380401900407 [e]
  48. ↑ Bearden, Carrie E.; Theo G.M. Van Erp & Rebecca A. Dutton et al. (2009), "Alterations in Midline Cortical Thickness and Gyrification Patterns Mapped in Children with 22q11.2 Deletions", Cerebral Cortex 19 (1): 115, DOI:10.1093/cercor/bhn064
  49. ↑ Schmitt, J.E.; Watts, K.; Eliez, S.; Bellugi, U.; Galaburda, A.M.; Reiss, A.L. (2002). "Increased gyrification in Williams syndrome: evidence using 3D MRI methods". Developmental Medicine & Child Neurology 44 (5): 292-295. DOI:10.1111/j.1469-8749.2002.tb00813.x. Research Blogging.
  50. ↑ Vogeley, K.; T. Schneider-Axmann & U. Pfeiffer et al. (2000), "Disturbed Gyrification of the Prefrontal Region in Male Schizophrenic Patients: A Morphometric Postmortem Study", American Journal of Psychiatry 157 (1): 34-39
  51. ↑ Kulynych, J.J.; L.F. Luevano & D.W. Jones et al. (1997), "Cortical abnormality in schizophrenia: an in vivo application of the gyrification index", Biological Psychiatry 41 (10): 995–999, DOI:10.1016/S0006-3223(96)00292-2
  52. ↑ Sallet, Paulo C.; Helio Elkis & Tania M. Alves et al. (2003), "Reduced Cortical Folding in Schizophrenia: an MRI Morphometric Study", American Journal of Psychiatry 160 (9): 1606-1613, DOI:10.1176/appi.ajp.160.9.1606 [e]
  53. ↑ Rodriguez-Carranza, C.E.; P. Mukherjee & D. Vigneron et al. (2008), "A framework for in vivo quantification of regional brain folding in premature neonates", Neuroimage 41: 462, DOI:10.1016/j.neuroimage.2008.01.008
  54. ↑ Pienaar, R.; B. Fischl & V. Caviness et al. (2008), "A methodology for analyzing curvature in the developing brain from preterm to adult", International Journal of Imaging Systems and Technology 18 (1): 42–68, DOI:10.1002/ima.20138
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