nature physics LETTERS PUBLISHED ONLINE:1 FEBRUARY 20161DO1: 10.1038/NPHYS3632 On the growth and form of cortical convolutions Tuomas Tallinenl * , Jun Young Chung2'3 ' , Francois Rousseau'', Nadine Girard5.6, Julien Lefevres and L. Mahadevan23.9.'" The rapid growth of the human cortex during development is accompanied by the folding of the brain into a highly convoluted structure' 3. Recent studies have focused on the genetic and cellular regulation of cortical growth", but understanding the formation of the gyral and sulcal convolutions also requires consideration of the geometry and physical shaping of the growing brain'-'. 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. The convoluted shape of the human cerebral cortex is the result of gyrification that begins after mid-gestation" (Fig. la); before the sixth month of fetal life, the cerebral surface is smooth. The first sulci appear as short isolated lines or triple junctions during the sixth month. These primary sulci soon elongate and branch, and secondary and tertiary sulci form, resulting in a complex pattern of gyri and sulci a