Fractal dimensionIn mathematics, a fractal dimension is a term invoked in the science of geometry to provide a rational statistical index of complexity detail in a pattern. A fractal pattern changes with the scale at which it is measured. It is also a measure of the space-filling capacity of a pattern, and it tells how a fractal scales differently, in a fractal (non-integer) dimension. The main idea of "fractured" dimensions has a long history in mathematics, but the term itself was brought to the fore by Benoit Mandelbrot based on his 1967 paper on self-similarity in which he discussed fractional dimensions.
FractalIn mathematics, a fractal is a geometric shape containing detailed structure at arbitrarily small scales, usually having a fractal dimension strictly exceeding the topological dimension. Many fractals appear similar at various scales, as illustrated in successive magnifications of the Mandelbrot set. This exhibition of similar patterns at increasingly smaller scales is called self-similarity, also known as expanding symmetry or unfolding symmetry; if this replication is exactly the same at every scale, as in the Menger sponge, the shape is called affine self-similar.
GliaGlia, also called glial cells (gliocytes) or neuroglia, are non-neuronal cells in the central nervous system (brain and spinal cord) and the peripheral nervous system that do not produce electrical impulses. The neuroglia make up more than one half the volume of neural tissue in our body. They maintain homeostasis, form myelin in the peripheral nervous system, and provide support and protection for neurons. In the central nervous system, glial cells include oligodendrocytes, astrocytes, ependymal cells and microglia, and in the peripheral nervous system they include Schwann cells and satellite cells.
Fractal analysisFractal analysis is assessing fractal characteristics of data. It consists of several methods to assign a fractal dimension and other fractal characteristics to a dataset which may be a theoretical dataset, or a pattern or signal extracted from phenomena including topography, natural geometric objects, ecology and aquatic sciences, sound, market fluctuations, heart rates, frequency domain in electroencephalography signals, digital images, molecular motion, and data science. Fractal analysis is now widely used in all areas of science.
MicrogliaMicroglia are a type of neuroglia (glial cell) located throughout the brain and spinal cord. Microglia account for about 10-15% of cells found within the brain. As the resident macrophage cells, they act as the first and main form of active immune defense in the central nervous system (CNS). Microglia (and other neuroglia including astrocytes) are distributed in large non-overlapping regions throughout the CNS. Microglia are key cells in overall brain maintenance—they are constantly scavenging the CNS for plaques, damaged or unnecessary neurons and synapses, and infectious agents.
Fractal curveA fractal curve is, loosely, a mathematical curve whose shape retains the same general pattern of irregularity, regardless of how high it is magnified, that is, its graph takes the form of a fractal. In general, fractal curves are nowhere rectifiable curves — that is, they do not have finite length — and every subarc longer than a single point has infinite length. A famous example is the boundary of the Mandelbrot set. Fractal curves and fractal patterns are widespread, in nature, found in such places as broccoli, snowflakes, feet of geckos, frost crystals, and lightning bolts.
Magnetic resonance imagingMagnetic resonance imaging (MRI) is a medical imaging technique used in radiology to form pictures of the anatomy and the physiological processes of the body. MRI scanners use strong magnetic fields, magnetic field gradients, and radio waves to generate images of the organs in the body. MRI does not involve X-rays or the use of ionizing radiation, which distinguishes it from computed tomography (CT) and positron emission tomography (PET) scans.
Nervous systemIn biology, the nervous system is the highly complex part of an animal that coordinates its actions and sensory information by transmitting signals to and from different parts of its body. The nervous system detects environmental changes that impact the body, then works in tandem with the endocrine system to respond to such events. Nervous tissue first arose in wormlike organisms about 550 to 600 million years ago. In vertebrates it consists of two main parts, the central nervous system (CNS) and the peripheral nervous system (PNS).
Schwann cellSchwann cells or neurolemmocytes (named after German physiologist Theodor Schwann) are the principal glia of the peripheral nervous system (PNS). Glial cells function to support neurons and in the PNS, also include satellite cells, olfactory ensheathing cells, enteric glia and glia that reside at sensory nerve endings, such as the Pacinian corpuscle. The two types of Schwann cells are myelinating and nonmyelinating. Myelinating Schwann cells wrap around axons of motor and sensory neurons to form the myelin sheath.
Fractal expressionismFractal expressionism is used to distinguish fractal art generated directly by artists from fractal art generated using mathematics and/or computers. Fractals are patterns that repeat at increasingly fine scales and are prevalent in natural scenery (examples include clouds, rivers, and mountains). Fractal expressionism implies a direct expression of nature's patterns in an art work. The initial studies of fractal expressionism focused on the poured paintings by Jackson Pollock (1912-1956), whose work has traditionally been associated with the abstract expressionist movement.
Radial glial cellRadial glial cells, or radial glial progenitor cells (RGPs), are bipolar-shaped progenitor cells that are responsible for producing all of the neurons in the cerebral cortex. RGPs also produce certain lineages of glia, including astrocytes and oligodendrocytes. Their cell bodies (somata) reside in the embryonic ventricular zone, which lies next to the developing ventricular system. During development, newborn neurons use radial glia as scaffolds, traveling along the radial glial fibers in order to reach their final destinations.
Central nervous systemThe central nervous system (CNS) is the part of the nervous system consisting primarily of the brain and spinal cord. The CNS is so named because the brain integrates the received information and coordinates and influences the activity of all parts of the bodies of bilaterally symmetric and triploblastic animals—that is, all multicellular animals except sponges and diploblasts. It is a structure composed of nervous tissue positioned along the rostral (nose end) to caudal (tail end) axis of the body and may have an enlarged section at the rostral end which is a brain.
Glial scarA glial scar formation (gliosis) is a reactive cellular process involving astrogliosis that occurs after injury to the central nervous system. As with scarring in other organs and tissues, the glial scar is the body's mechanism to protect and begin the healing process in the nervous system. In the context of neurodegeneration, formation of the glial scar has been shown to have both beneficial and detrimental effects.
MyelinIn most vertebrates (including humans), myelin is a lipid-rich material that surrounds nerve cell axons (the nervous system's "wires") to insulate them and increase the rate at which electrical impulses (called action potentials) are passed along the axon. The myelinated axon can be likened to an electrical wire (the axon) with insulating material (myelin) around it. However, unlike the plastic covering on an electrical wire, myelin does not form a single long sheath over the entire length of the axon.
Nuclear magnetic resonanceNuclear magnetic resonance (NMR) is a physical phenomenon in which nuclei in a strong constant magnetic field are perturbed by a weak oscillating magnetic field (in the near field) and respond by producing an electromagnetic signal with a frequency characteristic of the magnetic field at the nucleus. This process occurs near resonance, when the oscillation frequency matches the intrinsic frequency of the nuclei, which depends on the strength of the static magnetic field, the chemical environment, and the magnetic properties of the isotope involved; in practical applications with static magnetic fields up to ca.
Chronic inflammatory demyelinating polyneuropathyChronic inflammatory demyelinating polyneuropathy (CIDP) is an acquired autoimmune disease of the peripheral nervous system characterized by progressive weakness and impaired sensory function in the legs and arms. The disorder is sometimes called chronic relapsing polyneuropathy (CRP) or chronic inflammatory demyelinating polyradiculoneuropathy (because it involves the nerve roots). CIDP is closely related to Guillain–Barré syndrome and it is considered the chronic counterpart of that acute disease.
Hausdorff dimensionIn mathematics, Hausdorff dimension is a measure of roughness, or more specifically, fractal dimension, that was introduced in 1918 by mathematician Felix Hausdorff. For instance, the Hausdorff dimension of a single point is zero, of a line segment is 1, of a square is 2, and of a cube is 3. That is, for sets of points that define a smooth shape or a shape that has a small number of corners—the shapes of traditional geometry and science—the Hausdorff dimension is an integer agreeing with the usual sense of dimension, also known as the topological dimension.
Minkowski–Bouligand dimensionIn fractal geometry, the Minkowski–Bouligand dimension, also known as Minkowski dimension or box-counting dimension, is a way of determining the fractal dimension of a set in a Euclidean space , or more generally in a metric space . It is named after the Polish mathematician Hermann Minkowski and the French mathematician Georges Bouligand. To calculate this dimension for a fractal , imagine this fractal lying on an evenly spaced grid and count how many boxes are required to cover the set.
Medical imagingMedical imaging is the technique and process of imaging the interior of a body for clinical analysis and medical intervention, as well as visual representation of the function of some organs or tissues (physiology). Medical imaging seeks to reveal internal structures hidden by the skin and bones, as well as to diagnose and treat disease. Medical imaging also establishes a database of normal anatomy and physiology to make it possible to identify abnormalities.
Pathophysiology of multiple sclerosisMultiple sclerosis is an inflammatory demyelinating disease of the CNS in which activated immune cells invade the central nervous system and cause inflammation, neurodegeneration, and tissue damage. The underlying cause is currently unknown. Current research in neuropathology, neuroimmunology, neurobiology, and neuroimaging, together with clinical neurology, provide support for the notion that MS is not a single disease but rather a spectrum.
