AstrocyteAstrocytes (from Ancient Greek ἄστρον, ástron, "star" + κύτος, kútos, "cavity", "cell"), also known collectively as astroglia, are characteristic star-shaped glial cells in the brain and spinal cord. They perform many functions, including biochemical control of endothelial cells that form the blood–brain barrier, provision of nutrients to the nervous tissue, maintenance of extracellular ion balance, regulation of cerebral blood flow, and a role in the repair and scarring process of the brain and spinal cord following infection and traumatic injuries.
NeuronWithin a nervous system, a neuron, neurone, or nerve cell is an electrically excitable cell that fires electric signals called action potentials across a neural network. Neurons communicate with other cells via synapses - specialized connections that commonly use minute amounts of chemical neurotransmitters to pass the electric signal from the presynaptic neuron to the target cell through the synaptic gap. The neuron is the main component of nervous tissue in all animals except sponges and placozoa.
Ordinary differential equationIn mathematics, an ordinary differential equation (ODE) is a differential equation (DE) dependent on only a single independent variable. As with other DE, its unknown(s) consists of one (or more) function(s) and involves the derivatives of those functions. The term "ordinary" is used in contrast with partial differential equations which may be with respect to one independent variable. A linear differential equation is a differential equation that is defined by a linear polynomial in the unknown function and its derivatives, that is an equation of the form where a_0(x), .
Differential equationIn mathematics, a differential equation is an equation that relates one or more unknown functions and their derivatives. In applications, the functions generally represent physical quantities, the derivatives represent their rates of change, and the differential equation defines a relationship between the two. Such relations are common; therefore, differential equations play a prominent role in many disciplines including engineering, physics, economics, and biology.
AstrogliosisAstrogliosis (also known as astrocytosis or referred to as reactive astrogliosis) is an abnormal increase in the number of astrocytes due to the destruction of nearby neurons from central nervous system (CNS) trauma, infection, ischemia, stroke, autoimmune responses or neurodegenerative disease. In healthy neural tissue, astrocytes play critical roles in energy provision, regulation of blood flow, homeostasis of extracellular fluid, homeostasis of ions and transmitters, regulation of synapse function and synaptic remodeling.
Linear differential equationIn mathematics, a linear differential equation is a differential equation that is defined by a linear polynomial in the unknown function and its derivatives, that is an equation of the form where a0(x), ..., an(x) and b(x) are arbitrary differentiable functions that do not need to be linear, and y′, ..., y(n) are the successive derivatives of an unknown function y of the variable x. Such an equation is an ordinary differential equation (ODE).
Rostral migratory streamThe rostral migratory stream (RMS) is a specialized migratory route found in the brain of some animals along which neuronal precursors that originated in the subventricular zone (SVZ) of the brain migrate to reach the main olfactory bulb (OB). The importance of the RMS lies in its ability to refine and even change an animal's sensitivity to smells, which explains its importance and larger size in the rodent brain as compared to the human brain, as our olfactory sense is not as developed.
Neuroimmune systemThe neuroimmune system is a system of structures and processes involving the biochemical and electrophysiological interactions between the nervous system and immune system which protect neurons from pathogens. It serves to protect neurons against disease by maintaining selectively permeable barriers (e.g., the blood–brain barrier and blood–cerebrospinal fluid barrier), mediating neuroinflammation and wound healing in damaged neurons, and mobilizing host defenses against pathogens.
GliosisGliosis is a nonspecific reactive change of glial cells in response to damage to the central nervous system (CNS). In most cases, gliosis involves the proliferation or hypertrophy of several different types of glial cells, including astrocytes, microglia, and oligodendrocytes. In its most extreme form, the proliferation associated with gliosis leads to the formation of a glial scar. The process of gliosis involves a series of cellular and molecular events that occur over several days.
Homogeneous differential equationA differential equation can be homogeneous in either of two respects. A first order differential equation is said to be homogeneous if it may be written where f and g are homogeneous functions of the same degree of x and y. In this case, the change of variable y = ux leads to an equation of the form which is easy to solve by integration of the two members. Otherwise, a differential equation is homogeneous if it is a homogeneous function of the unknown function and its derivatives.
Delay differential equationIn mathematics, delay differential equations (DDEs) are a type of differential equation in which the derivative of the unknown function at a certain time is given in terms of the values of the function at previous times. DDEs are also called time-delay systems, systems with aftereffect or dead-time, hereditary systems, equations with deviating argument, or differential-difference equations. They belong to the class of systems with the functional state, i.e.
Haemodynamic responseIn haemodynamics, the body must respond to physical activities, external temperature, and other factors by homeostatically adjusting its blood flow to deliver nutrients such as oxygen and glucose to stressed tissues and allow them to function. Haemodynamic response (HR) allows the rapid delivery of blood to active neuronal tissues. The brain consumes large amounts of energy but does not have a reservoir of stored energy substrates.
Partial differential equationIn mathematics, a partial differential equation (PDE) is an equation which computes a function between various partial derivatives of a multivariable function. The function is often thought of as an "unknown" to be solved for, similar to how x is thought of as an unknown number to be solved for in an algebraic equation like x2 − 3x + 2 = 0. However, it is usually impossible to write down explicit formulas for solutions of partial differential equations.
Glial fibrillary acidic proteinGlial fibrillary acidic protein (GFAP) is a protein that is encoded by the GFAP gene in humans. It is a type III intermediate filament (IF) protein that is expressed by numerous cell types of the central nervous system (CNS), including astrocytes and ependymal cells during development. GFAP has also been found to be expressed in glomeruli and peritubular fibroblasts taken from rat kidneys, Leydig cells of the testis in both hamsters and humans, human keratinocytes, human osteocytes and chondrocytes and stellate cells of the pancreas and liver in rats.
Stochastic differential equationA stochastic differential equation (SDE) is a differential equation in which one or more of the terms is a stochastic process, resulting in a solution which is also a stochastic process. SDEs have many applications throughout pure mathematics and are used to model various behaviours of stochastic models such as stock prices, random growth models or physical systems that are subjected to thermal fluctuations. SDEs have a random differential that is in the most basic case random white noise calculated as the derivative of a Brownian motion or more generally a semimartingale.
Subventricular zoneThe subventricular zone (SVZ) is a region situated on the outside wall of each lateral ventricle of the vertebrate brain. It is present in both the embryonic and adult brain. In embryonic life, the SVZ refers to a secondary proliferative zone containing neural progenitor cells, which divide to produce neurons in the process of neurogenesis. The primary neural stem cells of the brain and spinal cord, termed radial glial cells, instead reside in the ventricular zone (VZ) (so-called because the VZ lines the inside of the developing ventricles).
BiophysicsBiophysics is an interdisciplinary science that applies approaches and methods traditionally used in physics to study biological phenomena. Biophysics covers all scales of biological organization, from molecular to organismic and populations. Biophysical research shares significant overlap with biochemistry, molecular biology, physical chemistry, physiology, nanotechnology, bioengineering, computational biology, biomechanics, developmental biology and systems biology. The term biophysics was originally introduced by Karl Pearson in 1892.
Mathematical modelA mathematical model is an abstract description of a concrete system using mathematical concepts and language. The process of developing a mathematical model is termed mathematical modeling. Mathematical models are used in applied mathematics and in the natural sciences (such as physics, biology, earth science, chemistry) and engineering disciplines (such as computer science, electrical engineering), as well as in non-physical systems such as the social sciences (such as economics, psychology, sociology, political science).
Brain ischemiaBrain ischemia is a condition in which there is insufficient bloodflow to the brain to meet metabolic demand. This leads to poor oxygen supply or cerebral hypoxia and thus leads to the death of brain tissue or cerebral infarction/ischemic stroke. It is a sub-type of stroke along with subarachnoid hemorrhage and intracerebral hemorrhage. Ischemia leads to alterations in brain metabolism, reduction in metabolic rates, and energy crisis.
Mathematical psychologyMathematical psychology is an approach to psychological research that is based on mathematical modeling of perceptual, thought, cognitive and motor processes, and on the establishment of law-like rules that relate quantifiable stimulus characteristics with quantifiable behavior (in practice often constituted by task performance). The mathematical approach is used with the goal of deriving hypotheses that are more exact and thus yield stricter empirical validations.
