Symmetry Breaking in Wrinkling Patterns: Gyri Are Universally Thicker than Sulci

Holland M, Goriely A, Budday S, Kuhl E (2018)

Publication Type: Journal article, Original article

Publication year: 2018


Book Volume: 121

Article Number: 228002

DOI: 10.1103/PhysRevLett.121.228002


Wrinkling instabilities appear in soft materials when a flat elastic layer on an elastic substrate is sufficiently stressed that it buckles with a wavy pattern to minimize the energy of the system. This instability is known to play an important role in engineering, but it also appears in many biological systems. In these systems, the stresses responsible for the wrinkling instability are often created through differential growth of the two layers. Beyond the instability, the upper and lower sides of the elastic layer are subject to different forces. This difference in forces leads to an interesting symmetry breaking whereby the thickness becomes larger at ridges than at valleys. Here we carry out an extensive analysis of this phenomenon by combining analytical, computational, and simple polymer experiments to show that symmetry breaking is a generic property of such systems. We apply our idea to the cortical folding of the brain for which it has been known for over a century that there is a thickness difference between gyri and sulci. An extensive analysis of hundreds of human brains reveals a systematic region-dependent thickness variation. Our results suggest that the evolving thickness patterns during brain development, similar to our polymer experiments, follow simple physics-based laws: Gyri are universally thicker than sulci.

Authors with CRIS profile

Involved external institutions

How to cite


Holland, M., Goriely, A., Budday, S., & Kuhl, E. (2018). Symmetry Breaking in Wrinkling Patterns: Gyri Are Universally Thicker than Sulci. Physical Review Letters, 121.


Holland, Maria, et al. "Symmetry Breaking in Wrinkling Patterns: Gyri Are Universally Thicker than Sulci." Physical Review Letters 121 (2018).

BibTeX: Download