On the growth and form of cortical convolutions

The rapid growth of the human cortex during development is accompaniedby the foldingof thebrain intoahighly convoluted structure1–3. Recent studies have focused on the genetic and cellular regulation of cortical growth4–8, but understanding the formation of the gyral and sulcal convolutions also requires consideration of the geometry and physical shaping of the growing brain9–15. 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. The convoluted shape of the human cerebral cortex is the result of gyrification that begins after mid-gestation1,2 (Fig. 1a); 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 at birth. Some new sulci develop after birth, further complicating the pattern. Although the course and patterns of gyrification vary across individuals, the primary gyri and sulci have characteristic locations and orientations16. Gyrification is, however, not unique to humans, and also exists in a range of primates and other species17,18. It has evolved as an efficient way of packing a large cortex into a relatively small skull with natural advantages for information processing17,19. Thus, although the functional rationale for gyrification is clear, the physiological mechanism behind gyrification has been unclear. Hypotheses include gyrogenetic theories4,20 proposing that biochemical prepatterning of the cortex controls the rise of gyri, and the axonal tension hypothesis21 proposing that axons in white matter beneath the cortex draw together densely interconnected cortical regions to form gyri. There is, however, no evidence of prepatterning that matches gyral patterns, nor is there evidence of axonal tension driving gyrification10. At present, the most likely hypothesis is also the simplest one: tangential expansion of the cortical layer relative to sublayers generates compressive stress, leading to the mechanical folding of the cortex9–15,22–25. This mechanical folding model produces realistic sizes and shapes of gyral and sulcal patterns15 that are presumably modulated by brain geometry26, but the hypothesis has not been tested before with real three-dimensional (3D) fetal brain geometries in a developmental setting. Here we substantiate and quantify this notion using both physical and numerical models of the brain, guided by the use of 3D magnetic resonance images (MRI) of a smooth fetal brain as a starting point. We construct a physical simulacrum of brain folding by taking advantage of the observation that soft physical gels swell superficially when immersed in solvents. This swelling relative to the interior puts the outer layers of the gel into compression, yielding surface folding patterns qualitatively similar to sulci and gyri15. An MRI image of a smooth fetal brain at gestational week (GW) 22 (Fig. 1b; see Supplementary Methods) serves as a template for a 3D-printed cast of the brain. A mould of this form allows us to create a gel-brain (mimicking the white matter) that is then coated with a thin layer of elastomer gel (mimicking the cortical grey matter layer). When this composite gel is immersed in a solvent (see Supplementary Methods) it swells starting at the surface; this leads to superficial compression and the progressive formation of cusped sulci and smooth gyri in the cortex similar in both morphology and relative timing to those seen in real brains (Fig. 1c and SupplementaryMovie 1).We note that although themechanical creasing or sulcification instability is due to the swelling-induced compression, the effect is convoluted by the complex curvature of the initial shape. To obtain amore quantitative assessment of this process, we carry out a numerical simulation of the developing brain constructed using the same 3D fetal brain MRI (Fig. 1d) as an initial condition for the growth of a soft elastic tissue model of the brain. The model assumes that a cortical layer of thickness h is perfectly adhered to a white matter core and grows with a prescribed tangential expansion ratio g , with both tissues assumed to be soft neo-Hookean elastic solids with similar elastic moduli (see Supplementary Methods). Combining these facts with the known overall isometric growth of the brain3 yields a differential-strain-based elastic model of brain growth that we solve numerically using custom finite-element methods15. For problem parameters, we note that from GW 22 to adulthood (Supplementary Fig. 1) there is an approximately