### Abstract

We model the elasticity of the cerebral cortex as a layered material with bending energy along the layers and elastic energy between them in both planar and polar geometries. The cortex is also subjected to axons pulling from the underlying white matter. Above a critical threshold force, a 'flat' cortex configuration becomes unstable and periodic undulations emerge, i.e. a buckling instability occurs. These undulations may indeed initiate folds in the cortex. We identify analytically the critical force and the critical wavelength of the undulations. Both quantities are physiologically relevant values. Our model is a revised version of the axonal tension model for cortex folding, with our version taking into account the layered structure of the cortex. Moreover, our model draws a connection with another competing model for cortex folding, namely the differential growth-induced buckling model. For the polar geometry, we study the relationship between brain size and the critical force and wavelength to understand why small mice brains exhibit no folds, while larger human brains do, for example. Finally, an estimate of the bending rigidity constant for the cortex can be made based on the critical wavelength.

Original language | English (US) |
---|---|

Article number | 123058 |

Journal | New Journal of Physics |

Volume | 16 |

DOIs | |

State | Published - Dec 22 2014 |

### Fingerprint

### Keywords

- cerebral cortex
- liquid crystal
- mechanics

### ASJC Scopus subject areas

- Physics and Astronomy(all)

### Cite this

*New Journal of Physics*,

*16*, [123058]. https://doi.org/10.1088/1367-2630/16/12/123058

**Elastic instabilities in a layered cerebral cortex : A revised axonal tension model for cortex folding.** / Manyuhina, O. V.; Mayett, David; Schwarz, Jennifer M.

Research output: Contribution to journal › Article

*New Journal of Physics*, vol. 16, 123058. https://doi.org/10.1088/1367-2630/16/12/123058

}

TY - JOUR

T1 - Elastic instabilities in a layered cerebral cortex

T2 - A revised axonal tension model for cortex folding

AU - Manyuhina, O. V.

AU - Mayett, David

AU - Schwarz, Jennifer M

PY - 2014/12/22

Y1 - 2014/12/22

N2 - We model the elasticity of the cerebral cortex as a layered material with bending energy along the layers and elastic energy between them in both planar and polar geometries. The cortex is also subjected to axons pulling from the underlying white matter. Above a critical threshold force, a 'flat' cortex configuration becomes unstable and periodic undulations emerge, i.e. a buckling instability occurs. These undulations may indeed initiate folds in the cortex. We identify analytically the critical force and the critical wavelength of the undulations. Both quantities are physiologically relevant values. Our model is a revised version of the axonal tension model for cortex folding, with our version taking into account the layered structure of the cortex. Moreover, our model draws a connection with another competing model for cortex folding, namely the differential growth-induced buckling model. For the polar geometry, we study the relationship between brain size and the critical force and wavelength to understand why small mice brains exhibit no folds, while larger human brains do, for example. Finally, an estimate of the bending rigidity constant for the cortex can be made based on the critical wavelength.

AB - We model the elasticity of the cerebral cortex as a layered material with bending energy along the layers and elastic energy between them in both planar and polar geometries. The cortex is also subjected to axons pulling from the underlying white matter. Above a critical threshold force, a 'flat' cortex configuration becomes unstable and periodic undulations emerge, i.e. a buckling instability occurs. These undulations may indeed initiate folds in the cortex. We identify analytically the critical force and the critical wavelength of the undulations. Both quantities are physiologically relevant values. Our model is a revised version of the axonal tension model for cortex folding, with our version taking into account the layered structure of the cortex. Moreover, our model draws a connection with another competing model for cortex folding, namely the differential growth-induced buckling model. For the polar geometry, we study the relationship between brain size and the critical force and wavelength to understand why small mice brains exhibit no folds, while larger human brains do, for example. Finally, an estimate of the bending rigidity constant for the cortex can be made based on the critical wavelength.

KW - cerebral cortex

KW - liquid crystal

KW - mechanics

UR - http://www.scopus.com/inward/record.url?scp=84920264875&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84920264875&partnerID=8YFLogxK

U2 - 10.1088/1367-2630/16/12/123058

DO - 10.1088/1367-2630/16/12/123058

M3 - Article

AN - SCOPUS:84920264875

VL - 16

JO - New Journal of Physics

JF - New Journal of Physics

SN - 1367-2630

M1 - 123058

ER -