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.
