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How to Measure Cortical Folding from MR Images: a Step-by-Step Tutorial to Compute Local Gyrification Index

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Gaussian curvature

In differential geometry, the Gaussian curvature or Gauss curvature Κ of a smooth surface in three-dimensional space at a point is the product of the principal curvatures, κ1 and κ2, at the given point: The Gaussian radius of curvature is the reciprocal of Κ. For example, a sphere of radius r has Gaussian curvature 1/r2 everywhere, and a flat plane and a cylinder have Gaussian curvature zero everywhere. The Gaussian curvature can also be negative, as in the case of a hyperboloid or the inside of a torus.

Scalar curvature

In the mathematical field of Riemannian geometry, the scalar curvature (or the Ricci scalar) is a measure of the curvature of a Riemannian manifold. To each point on a Riemannian manifold, it assigns a single real number determined by the geometry of the metric near that point. It is defined by a complicated explicit formula in terms of partial derivatives of the metric components, although it is also characterized by the volume of infinitesimally small geodesic balls.

Neocortex

The neocortex, also called the neopallium, isocortex, or the six-layered cortex, is a set of layers of the mammalian cerebral cortex involved in higher-order brain functions such as sensory perception, cognition, generation of motor commands, spatial reasoning and language. The neocortex is further subdivided into the true isocortex and the proisocortex. In the human brain, the cerebral cortex consists of the larger neocortex and the smaller allocortex. The neocortex is made up of six layers, labelled from the outermost inwards, I to VI.

Gyrus

In neuroanatomy, a gyrus (: gyri) is a ridge on the cerebral cortex. It is generally surrounded by one or more sulci (depressions or furrows; : sulcus). Gyri and sulci create the folded appearance of the brain in humans and other mammals. The gyri are part of a system of folds and ridges that create a larger surface area for the human brain and other mammalian brains. Because the brain is confined to the skull, brain size is limited.

Neuroscience and intelligence

Neuroscience and intelligence refers to the various neurological factors that are partly responsible for the variation of intelligence within species or between different species. A large amount of research in this area has been focused on the neural basis of human intelligence. Historic approaches to studying the neuroscience of intelligence consisted of correlating external head parameters, for example head circumference, to intelligence. Post-mortem measures of brain weight and brain volume have also been used.

Brain

A brain is an organ that serves as the center of the nervous system in all vertebrate and most invertebrate animals. It is located in the head, usually close to the sensory organs for senses such as vision. It is the most complex organ in a vertebrate's body. In a human, the cerebral cortex contains approximately 14–16 billion neurons, and the estimated number of neurons in the cerebellum is 55–70 billion. Each neuron is connected by synapses to several thousand other neurons.

Central sulcus

In neuroanatomy, the central sulcus (also central fissure, fissure of Rolando, or Rolandic fissure, after Luigi Rolando) is a sulcus, or groove, in the cerebral cortex in the brains of vertebrates. It is sometimes confused with the longitudinal fissure. The central sulcus is a prominent landmark of the brain, separating the parietal lobe from the frontal lobe and the primary motor cortex from the primary somatosensory cortex.

Visual cortex

The visual cortex of the brain is the area of the cerebral cortex that processes visual information. It is located in the occipital lobe. Sensory input originating from the eyes travels through the lateral geniculate nucleus in the thalamus and then reaches the visual cortex. The area of the visual cortex that receives the sensory input from the lateral geniculate nucleus is the primary visual cortex, also known as visual area 1 (V1), Brodmann area 17, or the striate cortex.

Principal curvature

In differential geometry, the two principal curvatures at a given point of a surface are the maximum and minimum values of the curvature as expressed by the eigenvalues of the shape operator at that point. They measure how the surface bends by different amounts in different directions at that point. At each point p of a differentiable surface in 3-dimensional Euclidean space one may choose a unit normal vector. A normal plane at p is one that contains the normal vector, and will therefore also contain a unique direction tangent to the surface and cut the surface in a plane curve, called normal section.

Topographic map (neuroanatomy)

A topographic map is the ordered projection of a sensory surface, like the retina or the skin, or an effector system, like the musculature, to one or more structures of the central nervous system. Topographic maps can be found in all sensory systems and in many motor systems. Retinotopy The visual system refers to the part of the central nervous system that allows an organism to see. It interprets information from visible light to build a representation of the world.