Gyrification

(CC) Photo: University of Wisconsin and Michigan State Comparative Mammalian Brain Collections and National Museum of Health and Medicine (see http://www.brainmuseum.org/)
Comparative anatomy of brains from various vertebrate species, highlighting the gradual differences in gyrification.

In the brain sciences, gyrification (or cortical folding, cortical convolution, fissuration or fissurization) refers to both the process and the extent of folding of the cerebral cortex in mammals as a consequence of brain growth during embryonic and early postnatal development.

In the process (also known as gyrogenesis), gyri (ridges) and sulci (fissures) form on the external surface of the brain (i.e. at the boundary between the cerebrospinal fluid and the gray matter). A low extent of gyrification in a given brain is commonly referred to as lissencephaly (which may range from agyria, the total absence of folding, to pachygyria), while gyrencephaly describes a high degree of folding.

The term gyrification is also sometimes used instead of the more common term foliation to describe the folding patterns of the cerebellum, which is highly convoluted in other taxa, too, e.g. in birds.

Phylogeny

See also brain evolution.

As illustrated in the figure, gyrification occurs across mammals: It generally increases slowly with overall brain size, following a power law , though exceptions exist: While several groups of small-brained placental species are indeed lissencephalic, so is the monotreme platypus but the monotreme echidna is gyrencephalic. Conversely, large-brained mammals are usually highly gyrencephalic, with sirenians being a notable exception. A range of theoretical models exist as to the degree to which gyrification hints at the evolution of cognitive abilities in a given range of species.

Ontogeny

See also brain development.

The folding process usually starts during fetal development -- in humans around mid-gestation -- or shortly after birth, as in ferrets. It proceeds synchronously in both hemispheres by an expansion of gyral tissue, while the sulcal roots remain in a relatively stable position throughout gyrogenesis. In the human brain, variations due to gender and ethnicity have been demonstrated, and such interindividual differences appear to be highest in regions with strong gyrification.

Mechanism

While the extent of cortical folding has been found to be partly determined by genetic factors, the underlying biomechanical mechanisms are not yet well understood. The overall folding pattern, however, can be mechanistically explained in terms of the cerebral cortex behaving as a gel that buckles under the influence of non-isotropic forces. Possible causes of the non-isotropy include thermal noise, differential growth of the cortical layers due to variations in the number and timing of cell divisions, cell migration, myelinization, cortical connectivity, synaptic pruning, brain size and metabolism (phospholipids in particular), all of which may interact. The folding, in turn, imposes constraints on the shape of cells, particulary in the outer cortical layers (V and VI).

Function

The primary effect of a folding process is always an increase of surface area relative to volume. Due to the laminar arrangement of the cerebral cortex, an increased cerebral surface area correlates with an increased number of neurons, which is presumed to enhance the computational capacities of the cortex within some metabolic and connectivity limits. In some areas of the human brain, gyrification appears indeed to reflect functional development and thus to correlate with measures of intelligence, even though variations of these effects due to gender and age have been described .

Medical relevance

A number of disorders exist of which abnormal gyrification is a dominant feature, e.g. polymicrogyria or lissencephalic disorders like agyria to pachygyria. They usually occur bilaterally but cases of, e.g., unilateral lissencephaly, have been described. Beyond these gross modifications of gyrification, more subtle variations occur in a number of neuropsychiatric disorders whose variety reflects the multitude of processes underlying gyrification. Due to methodological advances in neuroimaging and computational morphometry since the late 1990s, folding patterns and abnormalities thereof can now be determined non-invasively. This is becoming increasingly important for clinical diagnostics, particular in relation to neuropsychiatric diseases like schizophrenia, autism, epilepsy, dyslexia, velocardiofacial syndrome or Williams syndrome. The direction of disease-associated changes depends on the cortical region and the disease subtype. In schizophrenics, for instance, gyrification has been found to increase in the dorsolateral prefrontal cortex and, in different populations, to decrease in frontal and parietal regions of the left hemisphereor even throughout both hemispheres.

Quantification

Folding of a brain can be described in both local and global terms, once a suitable representation of a brain surface has been obtained from neuroimaging data by some surface extraction technique. The latter usually delivers a triangulated surface representing either the boundary between the cerebrospinal fluid and the gray matter or between the latter and the white matter but in principle, any surface in between would do as well (e.g. the central layer which is also sometimes used). Leaving the multiple issues of resolution and artifacts in these surface representations aside, the brain surface mesh, like any mesh of a closed three-dimensional manifold, can then be analyzed in terms of local curvature measures, from which global measures can be derived. Over the last decades, several such measures have been proposed. Following the developments in imaging techniques, they were initially focused on quantification in two-dimensional spaces, later in three-dimensional ones. Some examples that are commonly used include:

• $L^{2}norms$:
  • $LN_{G}={\tfrac {1}{4\pi }}\textstyle {\sqrt {\sum _{A}K^{2}}}$, with $K=k_{1}k_{2}$ being the Gaussian curvature, computed from the two principal curvatures $k_{1}$ and $k_{2}$
  • $LN_{M}={\tfrac {1}{4\pi }}\textstyle \sum _{A}H^{2}$, with $H={\tfrac {1}{2}}(k_{1}+k_{2})$ being the Mean curvature and $A$ the area of the surface in question
• Folding index
  • $FI={\tfrac {1}{4\pi }}\textstyle \sum _{A}k^{\ddagger }$, with $k^{\ddagger }=|k_{1}|(|k_{1}|-|k_{2}|)$
• Intrinsic curvature index
  • $ICI={\tfrac {1}{4\pi }}\textstyle \sum _{A}K^{+}$, with $K^{+}$ being the positive Gaussian curvature

• Gyrification index
  • $GI(n)={\tfrac {A(n)_{pial}}{A(n)_{gc}}}$, with $n$ indicating the number of the slice, and $A(n)_{pial}$ and $A(n)_{gc}$ being the pial surface area in that slice and the surface area of the boundary between gray matter and cerebrospinal fluid, respectively
• Gyrification-White index
  • $GWI={\tfrac {A_{gw}}{A_{gc}}}$, with $A_{gw}$ being the surface area of the boundary between gray matter and white matter
• White matter folding
  • $WMF={\tfrac {A_{gw}}{{V_{w}}^{2/3}}}$, with $V_{w}$ being the volume of the white matter
• Cortical complexity
• Fractal dimension
• Global gyrification index
• Local gyrification index
• Shape index
• Curvedness
• Roundness
  • $Rn={\tfrac {A}{^{3}{\sqrt {36\pi V^{2}}}}}$