Cerebral circulationCerebral circulation is the movement of blood through a network of cerebral arteries and veins supplying the brain. The rate of cerebral blood flow in an adult human is typically 750 milliliters per minute, or about 15% of cardiac output. Arteries deliver oxygenated blood, glucose and other nutrients to the brain. Veins carry "used or spent" blood back to the heart, to remove carbon dioxide, lactic acid, and other metabolic products. The neurovascular unit regulates cerebral blood flow so that activated neurons can be supplied with energy in the right amount and at the right time.
GeometryGeometry (; ) is a branch of mathematics concerned with properties of space such as the distance, shape, size, and relative position of figures. Geometry is, along with arithmetic, one of the oldest branches of mathematics. A mathematician who works in the field of geometry is called a geometer. Until the 19th century, geometry was almost exclusively devoted to Euclidean geometry, which includes the notions of point, line, plane, distance, angle, surface, and curve, as fundamental concepts.
Cerebral hemisphereThe vertebrate cerebrum (brain) is formed by two cerebral hemispheres that are separated by a groove, the longitudinal fissure. The brain can thus be described as being divided into left and right cerebral hemispheres. Each of these hemispheres has an outer layer of grey matter, the cerebral cortex, that is supported by an inner layer of white matter. In eutherian (placental) mammals, the hemispheres are linked by the corpus callosum, a very large bundle of nerve fibers.
Cerebral arteriovenous malformationA cerebral arteriovenous malformation (cerebral AVM, CAVM, cAVM, brain AVM, or BAVM) is an abnormal connection between the arteries and veins in the brain—specifically, an arteriovenous malformation in the cerebrum. The most frequently observed problems related to a cerebral arteriovenous malformation (AVM) are headaches and seizures, cranial nerve afflictions including pinched nerve and palsy, backaches, neckaches, and nausea from coagulated blood that has made its way down to be dissolved in the cerebrospinal fluid.
Differential geometryDifferential geometry is a mathematical discipline that studies the geometry of smooth shapes and smooth spaces, otherwise known as smooth manifolds. It uses the techniques of differential calculus, integral calculus, linear algebra and multilinear algebra. The field has its origins in the study of spherical geometry as far back as antiquity. It also relates to astronomy, the geodesy of the Earth, and later the study of hyperbolic geometry by Lobachevsky.
Non-Euclidean geometryIn mathematics, non-Euclidean geometry consists of two geometries based on axioms closely related to those that specify Euclidean geometry. As Euclidean geometry lies at the intersection of metric geometry and affine geometry, non-Euclidean geometry arises by either replacing the parallel postulate with an alternative, or relaxing the metric requirement. In the former case, one obtains hyperbolic geometry and elliptic geometry, the traditional non-Euclidean geometries.
Euclidean geometryEuclidean geometry is a mathematical system attributed to ancient Greek mathematician Euclid, which he described in his textbook on geometry, Elements. Euclid's approach consists in assuming a small set of intuitively appealing axioms (postulates) and deducing many other propositions (theorems) from these. Although many of Euclid's results had been stated earlier, Euclid was the first to organize these propositions into a logical system in which each result is proved from axioms and previously proved theorems.
Elliptic geometryElliptic geometry is an example of a geometry in which Euclid's parallel postulate does not hold. Instead, as in spherical geometry, there are no parallel lines since any two lines must intersect. However, unlike in spherical geometry, two lines are usually assumed to intersect at a single point (rather than two). Because of this, the elliptic geometry described in this article is sometimes referred to as single elliptic geometry whereas spherical geometry is sometimes referred to as double elliptic geometry.
Human brainThe human brain is the central organ of the human nervous system, and with the spinal cord makes up the central nervous system. The brain consists of the cerebrum, the brainstem and the cerebellum. It controls most of the activities of the body, processing, integrating, and coordinating the information it receives from the sense organs, and making decisions as to the instructions sent to the rest of the body. The brain is contained in, and protected by, the skull bones of the head.
Hyperbolic geometryIn mathematics, hyperbolic geometry (also called Lobachevskian geometry or Bolyai–Lobachevskian geometry) is a non-Euclidean geometry. The parallel postulate of Euclidean geometry is replaced with: For any given line R and point P not on R, in the plane containing both line R and point P there are at least two distinct lines through P that do not intersect R. (Compare the above with Playfair's axiom, the modern version of Euclid's parallel postulate.) The hyperbolic plane is a plane where every point is a saddle point.
Cerebral cortexThe cerebral cortex, also known as the cerebral mantle, is the outer layer of neural tissue of the cerebrum of the brain in humans and other mammals. The cerebral cortex mostly consists of the six-layered neocortex, with just 10% consisting of allocortex. It is separated into two cortices, by the longitudinal fissure that divides the cerebrum into the left and right cerebral hemispheres. The two hemispheres are joined beneath the cortex by the corpus callosum. The cerebral cortex is the largest site of neural integration in the central nervous system.
Projective geometryIn mathematics, projective geometry is the study of geometric properties that are invariant with respect to projective transformations. This means that, compared to elementary Euclidean geometry, projective geometry has a different setting, projective space, and a selective set of basic geometric concepts. The basic intuitions are that projective space has more points than Euclidean space, for a given dimension, and that geometric transformations are permitted that transform the extra points (called "points at infinity") to Euclidean points, and vice-versa.
Synthetic geometrySynthetic geometry (sometimes referred to as axiomatic geometry or even pure geometry) is geometry without the use of coordinates. It relies on the axiomatic method for proving all results from a few basic properties initially called postulate, and at present called axioms. The term "synthetic geometry" has been coined only after the 17th century, and the introduction by René Descartes of the coordinate method, which was called analytic geometry.
Internal carotid arteryThe internal carotid artery (Latin: arteria carotis interna) is an artery in the neck which supplies the anterior circulation of the brain. In human anatomy, the internal and external carotids arise from the common carotid arteries, where these bifurcate at cervical vertebrae C3 or C4. The internal carotid artery supplies the brain, including the eyes, while the external carotid nourishes other portions of the head, such as the face, scalp, skull, and meninges.
AgeingAgeing (or aging in American English) is the process of becoming older. The term refers mainly to humans, many other animals, and fungi, whereas for example, bacteria, perennial plants and some simple animals are potentially biologically immortal. In a broader sense, ageing can refer to single cells within an organism which have ceased dividing, or to the population of a species. In humans, ageing represents the accumulation of changes in a human being over time and can encompass physical, psychological, and social changes.
Algebraic geometryAlgebraic geometry is a branch of mathematics which classically studies zeros of multivariate polynomials. Modern algebraic geometry is based on the use of abstract algebraic techniques, mainly from commutative algebra, for solving geometrical problems about these sets of zeros. The fundamental objects of study in algebraic geometry are algebraic varieties, which are geometric manifestations of solutions of systems of polynomial equations.
Cerebral edemaCerebral edema is excess accumulation of fluid (edema) in the intracellular or extracellular spaces of the brain. This typically causes impaired nerve function, increased pressure within the skull, and can eventually lead to direct compression of brain tissue and blood vessels. Symptoms vary based on the location and extent of edema and generally include headaches, nausea, vomiting, seizures, drowsiness, visual disturbances, dizziness, and in severe cases, coma and death.
GoalA goal or objective is an idea of the future or desired result that a person or a group of people envision, plan and commit to achieve. People endeavour to reach goals within a finite time by setting deadlines. A goal is roughly similar to a purpose or aim, the anticipated result which guides reaction, or an end, which is an object, either a physical object or an abstract object, that has intrinsic value. Goal setting Goal-setting theory was formulated based on empirical research and has been called one of the most important theories in organizational psychology.
Aging brainAging of the brain is a process of transformation of the brain in older age, including changes all individuals experience and those of illness (including unrecognised illness). Usually this refers to humans. Since life extension is only pertinent if accompanied by health span extension, and, more importantly, by preserving brain health and cognition, finding rejuvenating approaches that act simultaneously in peripheral tissues and in brain function is a key strategy for development of rejuvenating technology.
Extracellular matrixIn biology, the extracellular matrix (ECM), also called intercellular matrix, is a network consisting of extracellular macromolecules and minerals, such as collagen, enzymes, glycoproteins and hydroxyapatite that provide structural and biochemical support to surrounding cells. Because multicellularity evolved independently in different multicellular lineages, the composition of ECM varies between multicellular structures; however, cell adhesion, cell-to-cell communication and differentiation are common functions of the ECM.
