Mechanisms of Brain Morphogenesis - Computer Models in Biomechanics - page 329

and Lumsden, 2005 ). Before they disappear, rhombomere boundaries facilitate spa-
tially dependent patterns of axonal migration, cell differentiation, and gene expres-
sion. In a recent study in zebrafish, rhombomere boundaries abnormally persisted in
hyper-contracted mutants (Gutzman and Sive, 2010 ), suggesting that rhombomere
formation and subsequent dissolution may be a consequence of regulated patterns
of cytoskeletal contraction.
24.4 Cortical Folding
24.4.1 Cerebral Cortex Development and Theories for Folding
Following vesicle formation, the brain rapidly expands due to an increasing lumen
pressure. This expansion is primarily a growth response, rather than a simple infla-
tion (Desmond and Jacobson, 1977 ; Pacheco et al., 1986 ). During these stages of
rapid growth, the forebrain subdivides into the diencephalon and the more anterior
telencephalon, which gives rise to the neocortex. Neurons generated in the devel-
oping neocortex differentiate and migrate along radially aligned glial fibers to form
the characteristic layers of the mature brain in an inside-out manner (Bystron et al.,
2008 ). In large mammals, folding of the cortex begins after these stages of neuronal
migration and proliferation. The primary folding patterns are generally conserved
across species, but secondary folds can differ considerably.
Several hypotheses have been proposed for cortical folding mechanisms, and
many are based on the idea that folds are produced by differential or constrained
growth. A straightforward idea is that the brain grows faster than the skull, which
therefore exerts compressive forces on the brain that cause it to buckle. To study
this hypothesis, Raghavan et al. ( 1997 ), modeled the cerebral cortex as a thin curved
beam that grows within a semicircular boundary representing the skull. With some
ad hoc assumptions, these authors obtained realistic folding patterns. Experimental
evidence, however, indicates that the brain can fold without external constraints
(Barron, 1950 ).
The cerebral cortex is more accurately modeled as a thin shell. Such a model was
proposed by Richman et al. ( 1975 ), who assumed that the outer layers of the cor-
tex grow faster than the inner layers, causing compressive stresses that buckle the
cortex (Fig. 24.5 A). Their analysis yielded wavelengths consistent with those mea-
sured in the normal brain, as well as in brains with a microgyric (short wavelength)
or lissencephalic (long wavelength) cortex. However, these investigators neglected
nonlinear effects, which become increasingly important as folds grow large.
Several other computational models for growth-driven cortical folding have been
proposed. Toro and Burnod ( 2005 ) modeled the cortex as a ring of 2D truss elements
with growth constrained by radially aligned elastoplastic fibers. Extending a similar
model to 3D, Nie et al. ( 2009 ) examined the effects of constraint of skull constraint,
growth rate, regional variations in growth, and initial geometry of folding patterns.
In addition, Geng et al. ( 2009 ) examined folding of small 3D regions of the cortex