Abstract
The cortical thickness is a characteristic biomarker for a wide variety of neurological disorders. While the structural organization of the cerebral cortex is tightly regulated and evolutionarily preserved, its thickness varies widely between 1.5 and 4.5 mm across the healthy adult human brain. It remains unclear whether these thickness variations are a cause or consequence of cortical development. Recent studies suggest that cortical thickness variations are primarily a result of genetic effects. Previous studies showed that a simple homogeneous bilayered system with a growing layer on an elastic substrate undergoes a unique symmetry breaking into a spatially heterogeneous system with discrete gyri and sulci. Here, we expand on that work to explore the evolution of cortical thickness variations over time to support our finding that cortical pattern formation and thickness variations can be explained – at least in part – by the physical forces that emerge during cortical folding. Strikingly, as growth progresses, the developing gyri universally thicken and the sulci thin, even in the complete absence of regional information. Using magnetic resonance images, we demonstrate that these naturally emerging thickness variations agree with the cortical folding pattern in n = 9 healthy adult human brains, in n = 564 healthy human brains ages 7–64, and in n = 73 infant brains scanned at birth, and at ages one and two. Additionally, we show that cortical organoids develop similar patterns throughout their growth. Our results suggest that genetic, geometric, and physical events during brain development are closely interrelated. Understanding regional and temporal variations in cortical thickness can provide insight into the evolution and causative factors of neurological disorders, inform the diagnosis of neurological conditions, and assess the efficacy of treatment options.
References
W. His, Unsere Körperform und das physiologische Problem ihrer Entstehung (F.C.W. Vogel, Leipzig, 1874)
W.E. Le Gros Clark, Deformation patterns in the cerebral cortex, in Essays on Growth and Form (Oxford University Press, London, 1945), pp. 1–22
D.P. Richman, R.M. Stewart, J.W. Hutchinson, V.S. Caviness, Science 189, 18 (1975)
R. Toro, Y. Burnod, Cerebral Cortex 15, 1900 (2005)
S. Herculano-Houzel, B. Mota, P. Wong, J.H. Kaas, Proc. Natl. Acad. Sci. 107, 19008 (2010)
P.V. Bayly, R. Okamoto, G. Xu, Y. Shi, L.A. Taber, Phys. Bio. 10, 016005 (2013)
T. Sun, R.F. Hevner, Nat. Rev. Neurosci. 15, 217 (2014)
E. Taverna, M. Götz, W.B. Huttner, Ann. Rev. Cell Develop. Bio. 30, 465 (2014)
B. Mota, S. Herculano-Houzel, Science 349, 74 (2015)
Y. Wang, J. Necus, M. Kaiser, B. Mota, Proc. Natl. Acad. Sci. 113, 12820 (2016)
T. Tallinen, J.Y. Chung, J. Biggins, L. Mahadevan, Proc. Natl. Acad. Sci. 111, 12667 (2014)
A. Goriely, M.G.D. Geers, G.A. Holzapfel, J. Jayamohan, A. Jérusalem, S. Sivaloganathan, W. Squier, J.A.W. van Dommelen, S. Waters, E. Kuhl, Biomech. Model Mechanobio. 14, 931 (2015)
T. Tallinen, J.Y. Chung, F. Rousseau, N. Girard, J. Lefevre, L. Mahadevan, Nat. Phys. 12, 588 (2016)
E. Kuhl, Nat. Phys. 12, 533 (2016)
A. Goriely, The Mathematics and Mechanics of Biological Growth (Springer-Verlag, New York, 2017)
E. Karzbrun, A. Kshirsagar, S.R. Cohen, J.H. Hanna, O. Reiner, Nat. Phys. 14, 515 (2018)
L. Ronan, N. Voets, C. Rua, A. Alexander-Bloch, M. Hough, C. Mackay, T.J. Crow, A. James, J.N. Giedd, P.C. Fletcher, Cerebral Cortex 24, 2219 (2014)
S. Budday, C. Raybaud, E. Kuhl, Sci. Rep. 4, 5644 (2014)
M.A. Holland, B. Li, X.Q. Feng, E. Kuhl, J. Mech. Phys. Solids 98, 350 (2017)
M.A. Holland, S. Budday, A. Goriely, E. Kuhl, Phys. Rev. Lett. 121, 228002 (2018)
H. Alawiye, E. Kuhl, A. Goriely, Philos. Trans. R. Soc. A 377, 20180076 (2019)
C. de Juan Romero, C. Bruder, U. Tomasello, J.M. Sanz-Anguela, V. Borrell, EMBO J. 34, 1859 (2015)
N.D. Amin, S.P. Pasca, Neuron 100, 389 (2018)
V. Fernandez, C. Llinares-Benadero, V. Borrell, EMBO J. 35, 1021 (2016)
X. Wang, C. Studholme, P.L. Grigsby, A.E. Frias, V.C. Cuzon Carlson, C.D. Kroenke, J. Neurosci. 37, 1971 (2017)
B.I. Shraiman, Proc. Natl. Acad. Sci. USA 102, 3318 (2005)
E. Ben-Jacob, I. Cohen, H. Levine, Adv. Phys. 49, 395 (2000)
L.M. Carreira, A. Ferreira, F. Liste Burilo, Anatom. Rec. 294, 1920 (2011)
S. Budday, P. Steinmann, A. Goriely, E. Kuhl, Extr. Mech. Lett. 4, 193 (2015)
A.Y. Hardan, R.J. Jou, M.S. Keshavan, R. Varma, N.J. Minshew, Psychiatry Res. Neuroimaging 131, 263 (2004)
R.J. Jou, A.Y. Hardan, M.S. Keshavan, Schizophrenia Res. 75, 309 (2005)
A. Harvey, S. Mandelstam, W. Maixner, R. Leventer, M. Semmelroch, D. MacGregor, R. Kalnins, Y. Perchyonok, G. Fitt, S. Barton, M. Kean, G. Fabinyi, G. Jackson, Neurology 84, 2021 (2015)
B. Fischl, A.M. Dale, Proc. Natl. Acad. Sci. 97, 11044 (2000)
W. Welker, Why does cerebral cortex fissure and fold? A review of determinants of gyri and sulci, in Cerebral Cortex, edited by E.G. Jones, A. Peters (Springer Science+Business Media, New York, 1990), Vol. 8B
Y. He, Z.J. Chen, A.C. Evans, Cerebral Cortex 17, 2407 (2007)
K. Brodmann, Vergleichende Lokalisationslehre der Großhirnrinde (Johann Ambrosius Barth Verlag, Leipzig, 1909)
M.A. Biot, Proc. R. Soc. London A 242, 444 (1957)
A. Goriely, M. Ben Amar, Phys. Rev. Lett. 94, 198103 (2005)
K. Garikipati, Appl. Mech. Rev. 62, 030801 (2009)
M. Ben Amar, A. Bordner, J. Elasticity 1, 213 (2017)
A. Auguste, L. Jin, Z. Suo, R.C. Hayward, Extr. Mech. Lett. 11, 30 (2017)
J.W. Hutchinson, Philos. Trans. R. Soc. A 371, 20120422 (2014)
D. Ambrosi, M. BenAmar, C.J. Cyron, A. DeSimone, A. Goriely, J.D. Humphrey, E. Kuhl, J.R. Soc, Interface 16, 20190233 (2019)
S. Budday, P. Steinmann, E. Kuhl, J. Mech. Phys. Solids 72, 75 (2014)
S. Budday, G. Sommer, C. Birkl, C. Langkammer, J. Hayback, J. Kohnert, M. Bauer, F. Paulsen, P. Steinmann, E. Kuhl, G.A. Holzapfel, Acta Biomater. 48, 319 (2017)
S. Budday, S. Andres, B. Walter, P. Steinmann, E. Kuhl, Philos. Trans. R. Soc. A 375, 2016.0163 (2017)
G. Li, J. Nie, L. Wang, F. Shi, W. Lin, J.H. Gilmore, D. Shen, Cerebral Cortex 23, 2724 (2013)
L. Wang, F. Shi, P.T. Yap, W. Lin, J.H. Gilmore, D. Shen, Hum. Brain Mapp. 34, 956 (2013)
G. Li, W. Lin, J.H. Gilmore, D. Shen, J. Neurosci. 35, 9150 (2015)
G. Li, J. Nie, L. Wang, F. Shi, J.H. Gilmore, W. Lin, D. Shen, Neuroimage 90, 226 (2014)
R.S. Desikan, F. Ségonne, B. Fischl, B.T. Quinn, B.C. Dickerson, D. Blacker, R.L. Buckner, A.M. Dale, R.P. Maguire, B.T. Hyman, M.S. Albert, R.J. Killiany, Neuroimage 31, 968 (2006)
M. Saggar, E.M. Quintin, E. Kineitz, N.T. Bott, Z. Sun, W.C. Hong, Y.H. Chien, N. Liu, R.F. Dougherty, A. Rohalty, G. Hawthrone, A.L. Reiss, Sci. Rep. 5, 10894 (2015)
A.M. Dale, B. Fischl, M.I. Sereno, Neuroimage 9, 179 (1999)
C. Destrieux, B. Fischl, A. Dale, E. Halgren, Neuroimage 15, 1 (2010)
R. Toro, M. Perron, B. Pike, L. Richter, S. Veillette, Z. Pausova, T. Paus, Cerebral Cortex 18, 2352 (2008)
C. Craddock, Y. Benhajali, C. Chu, F. Chouinard, A. Evans, A. Jakab, B.S. Khundrakpam, J.D. Lewis, Q. Li, M. Milham, C. Yan, P. Bellec, The Neuro Bureau Preprocessing Initiative: open sharing of preprocessed neuroimaging data and derivatives, in Neuroinformatics (Stockholm, Sweden, 2013)
H.G. Allen, Analysis and Design of Structural Sandwich Panels (PergamonPress, Oxford, 1969)
S. Budday, E. Kuhl, J.W. Hutchinson, Philos. Mag. 95, 3208 (2015)
K. Brodmann, Zentralbl. Nervenheilkunde Psychiatrie 31, 781 (1908)
T. Tallinen, J.S. Biggins, L. Mahadevan, Phys. Rev. Lett. 110, 024302 (2013)
L. Jin, A. Auguste, R.C. Hayward, Z. Suo, J. Appl. Mech. 82, 061008 (2015)
P.V. Bayly, L.A. Taber, C.D. Kroenke, J. Mech. Behav. Bio. Mat. 29, 568 (2014)
T. Tallinen, J.S. Biggins, Phys. Rev. E 92, 022720 (2015)
S. Budday, T.C. Ovaert, G.A. Holzapfel, P. Steinmann, E. Kuhl, Arch. Comput. Meth. Eng. 27, 1187 (2020)
M.A. Green, L.E. Bilston, R. Sinkurs, NMR Biomed. 21, 755 (2008)
A.F. Christ, K. Franze, H. Gautier, P. Moshayedi, J. Fawcett, R.J.M. Franklin, R.T. Karadottir, J. Guck, J. Biomech. 43, 2986 (2010)
M.T. Prange, S.S. Margulies, J. Biomech. Eng. 124, 244 (2002)
S. Budday, R. Nay, R. de Rooij, P. Steinmann, T. Wyrobek, T.C. Ovaert, E. Kuhl, J. Mech. Behav. Biomed. Mat. 46, 318 (2015)
T. Kaster, I. Sack, A. Samani, J. Biomech. 44, 1158 (2011)
J. Weickenmeier, R. de Rooij, S. Budday, T.C. Ovaert, E. Kuhl, J. Mech. Behav. Bio. Mat. 76, 119 (2017)
J. Weickenmeier, M. Kurt, E. Ozkaya, R. de Rooij, T.C. Ovaert, R.L. Ehman, K. Butts Pauly, E. Kuhl, J. Mech. Beh. Biomed. Mat. 84, 88 (2018)
M.A. Biot, Mechanics of Incremental Deformations (Wiley, New York, 1965)
E. Lejeune, A. Javili, J. Weickenmeier, E. Kuhl, C. Linder, Soft Matter 12, 5613 (2016)
A. Fjell, H. Grydeland, S.K. Krogsrud, I. Amlien, D.A. Rohani, L. Ferschmann, A.B. Storsve, C.K. Tamnes, R. Sala-Llonch, P. Due-Tonnessen, A. Bjornerud, A.E. Solsens, A. Haberg, J. Skranes, H. Bartsch, C.H. Chen, W.K. Thompson, M.S. Panizzon, W.S. Kremen, A.M. Dale, K.B. Walhovd, Proc. Natl. Acad. Sci. 112, 15462 (2015)
L. Hufnagel, A.A. Teleman, H. Rouault, S.M. Cohen, B.I. Shraiman, Proc. Natl. Acad. Sci. USA 104, 3835 (2007)
D.A. Kessler, J. Koplik, H. Levine, Adv. Phys. 37, 255 (1988)
G. Lorenzo, M.A. Scott, K. Tew, T.J.R. Hughes, Y.J. Zhang, L. Liu, G. Vilanova, H. Gomez, Proc. Natl. Acad. Sci. USA 113, E7663 (2013)
D.H. Salat, R.L. Buckner, A.Z. Snyder, D.N. Greve, R.S. Desikan, E. Busa, J.C. Morris, A.D. Dale, B. Fischl, Cerebral Cortex V14N7, 721 (2004)
I. Bluemcke, H. Vinters, D. Armstrong, E. Aronica, M. Thom, R. Spreafico, Epileptic Disorders 11, 181 (2009)
C. von Economo, G.N. Koskinas, Die Zytoarchitektonik der Hirnrinde des erwachsenen Menschen (Springer-Verlang, Wien, 1925)
S.T. Bok, Neurol. Psychiat. 121, 682 (1929)
M.J. Razavi, T. Zhang, T. Liu, X. Wang, Sci. Rep. 5, 14477 (2015)
M.J. Razavi, T. Zhang, X. Li, T. Liu, X. Wang, Phys. Rev. E. 92, 032701 (2015)
G. Tau, B. Peterson, Neuropsychopharmacology 35, 147 (2010)
R. Toro, Evol. Biol. 39, 600 (2012)
J. Hill, T. Inder, D. Dieker, J. Harwell, D. Van Essen, Proc. Natl. Acad. Sci. USA 107, 13135 (2010)
F. Brau, H. Vandeparre, A. Sabbah, C. Poulard, A. Boudaoud, P. Damman, Nat. Phys. 7, 56 (2011)
M.W. Moon, S. Lee, J.Y. Sun, K.H. Oh, A. Vaziri, J.W. Hutchinson, Proc. Natl. Acad. Sci. USA 104, 113 (2007)
P. Kim, M. Abkarian, H.A. Stone, Nat. Mater. 10, 952 (2011)
B.J. Kim, P. Kim, N.C. Pegard, S.J. Oh, C.R. Kagan, J.W. Fleischer, H.A. Stone, Y.L. Loo, Nat. Mater. 10, 952 (2012)
J. Wang, B. Li, Y.P. Cao, X.Q. Feng, H. Gao, Appl. Phys. Lett. 108, 021903 (2016)
B. Li, Y.P. Cao, X.Q. Feng, H. Gao, Soft Matter 8, 5728 (2012)
E. Lejeune, B. Dortdivanlioglu, E. Kuhl, C. Linder, Soft Matter 15, 2204 (2019)
M.A. Holland, T. Kosmata, A. Goriely, E. Kuhl, Math. Mech. Solids 18, 561 (2013)
R. Chirat, D.E. Moulton, A. Goriely, Proc. Natl. Acad. Sci. USA 110, 6015 (2013)
M. Trejo, C. Douarch, V. Bailleux, C. Poulard, S. Mariot, C. Regeard, E. Raspaud, Proc. Natl. Acad. Sci. USA 110, 2011 (2013)
M. Ben Amar, F. Jia, Proc. Natl. Acad. Sci. USA 110, 10525 (2013)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Open Access This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
About this article
Cite this article
Holland, M.A., Budday, S., Li, G. et al. Folding drives cortical thickness variations. Eur. Phys. J. Spec. Top. 229, 2757–2778 (2020). https://doi.org/10.1140/epjst/e2020-000001-6
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1140/epjst/e2020-000001-6