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On the growth and form of cortical convolutions

Nature Physics volume 12, pages 588–593 (2016)Cite this article

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Abstract

The rapid growth of the human cortex during development is accompanied by the folding of the brain into a highly convoluted structure1,2,3. Recent studies have focused on the genetic and cellular regulation of cortical growth4,5,6,7,8, but understanding the formation of the gyral and sulcal convolutions also requires consideration of the geometry and physical shaping of the growing brain9,10,11,12,13,14,15. To study this, we use magnetic resonance images to build a 3D-printed layered gel mimic of the developing smooth fetal brain; when immersed in a solvent, the outer layer swells relative to the core, mimicking cortical growth. This relative growth puts the outer layer into mechanical compression and leads to sulci and gyri similar to those in fetal brains. Starting with the same initial geometry, we also build numerical simulations of the brain modelled as a soft tissue with a growing cortex, and show that this also produces the characteristic patterns of convolutions over a realistic developmental course. All together, our results show that although many molecular determinants control the tangential expansion of the cortex, the size, shape, placement and orientation of the folds arise through iterations and variations of an elementary mechanical instability modulated by early fetal brain geometry.

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Figure 1: Physical mimic and numerical simulation of tangential cortical expansion.
Figure 2: Sectional views of model brains during convolutional development.
Figure 3: Mechanical stress orients convolutions.
Figure 4: Comparison of real and simulated folding patterns.

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Acknowledgements

We thank CSC—IT Center for Science, Finland, for computational resources and J. C. Weaver for help with 3D printing. This work was supported by the Academy of Finland (T.T.), Agence Nationale de la Recherche (ANR-12-JS03-001-01, “Modegy”) (N.G. and J.L.), the Wyss Institute for Biologically Inspired Engineering (J.Y.C. and L.M.), and fellowships from the MacArthur Foundation and the Radcliffe Institute (L.M.).

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Author notes

  1. Tuomas Tallinen and Jun Young Chung: These authors contributed equally to this work.

Authors and Affiliations

  1. Department of Physics and Nanoscience Center, University of Jyvaskyla, FI-40014 Jyväskylä, Finland

    Tuomas Tallinen

  2. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts 02138, USA

    Jun Young Chung & L. Mahadevan

  3. Wyss Institute for Biologically Inspired Engineering, Harvard University, Cambridge, Massachusetts 02138, USA

    Jun Young Chung & L. Mahadevan

  4. Institut Mines-Telecom, Telecom Bretagne, INSERM U1101 LaTIM, 29609 Brest, France

    François Rousseau

  5. Aix-Marseille Université, CRMBM UMR 7339, 13385 Marseille, France

    Nadine Girard

  6. Service de Neuroradiologie, Hópital de la Timone, 13005 Marseille, France

    Nadine Girard

  7. Aix-Marseille Université, CNRS, ENSAM, Université de Toulon, LSIS UMR 7296, 13397 Marseille, France

    Julien Lefèvre

  8. Institut de Neurosciences de la Timone UMR 7289, Aix Marseille Université, CNRS, 13385 Marseille, France

    Julien Lefèvre

  9. Departments of Organismic and Evolutionary Biology, and Physics, Harvard University, Cambridge, Massachusetts 02138, USA

    L. Mahadevan

  10. Kavli Institute for Nanobio Science and Technology, Harvard University, Cambridge, Massachusetts 02138, USA

    L. Mahadevan

Authors
  1. Tuomas Tallinen
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  2. Jun Young Chung
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  3. François Rousseau
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  4. Nadine Girard
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  5. Julien Lefèvre
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  6. L. Mahadevan
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Contributions

T.T., J.Y.C. and L.M. conceived the model and wrote the paper. T.T. developed and performed the numerical simulations. J.Y.C. developed and performed the physical experiments. J.L. developed and performed the morphometric analyses. F.R., N.G. and J.L. provided MRI images and provided feedback on the manuscript. T.T. and L.M. coordinated the project.

Corresponding authors

Correspondence to Tuomas Tallinen or L. Mahadevan.

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The authors declare no competing financial interests.

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Tallinen, T., Chung, J., Rousseau, F. et al. On the growth and form of cortical convolutions. Nature Phys 12, 588–593 (2016). https://doi.org/10.1038/nphys3632

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