Compliance (physiology)Compliance is the ability of a hollow organ (vessel) to distend and increase volume with increasing transmural pressure or the tendency of a hollow organ to resist recoil toward its original dimensions on application of a distending or compressing force. It is the reciprocal of "elastance", hence elastance is a measure of the tendency of a hollow organ to recoil toward its original dimensions upon removal of a distending or compressing force. The terms elastance and compliance are of particular significance in cardiovascular physiology and respiratory physiology.
Preload (cardiology)In cardiac physiology, preload is the amount of sarcomere stretch experienced by cardiac muscle cells, called cardiomyocytes, at the end of ventricular filling during diastole. Preload is directly related to ventricular filling. As the relaxed ventricle fills during diastole, the walls are stretched and the length of sarcomeres increases. Sarcomere length can be approximated by the volume of the ventricle because each shape has a conserved surface-area-to-volume ratio.
Error functionIn mathematics, the error function (also called the Gauss error function), often denoted by erf, is a complex function of a complex variable defined as: Some authors define without the factor of . This nonelementary integral is a sigmoid function that occurs often in probability, statistics, and partial differential equations. In many of these applications, the function argument is a real number. If the function argument is real, then the function value is also real.
BloodBlood is a body fluid in the circulatory system of humans and other vertebrates that delivers necessary substances such as nutrients and oxygen to the cells, and transports metabolic waste products away from those same cells. Blood in the circulatory system is also known as peripheral blood, and the blood cells it carries, peripheral blood cells. Blood is composed of blood cells suspended in blood plasma.
Decompression (diving)The decompression of a diver is the reduction in ambient pressure experienced during ascent from depth. It is also the process of elimination of dissolved inert gases from the diver's body which accumulate during ascent, largely during pauses in the ascent known as decompression stops, and after surfacing, until the gas concentrations reach equilibrium. Divers breathing gas at ambient pressure need to ascend at a rate determined by their exposure to pressure and the breathing gas in use.
Numerical methods for partial differential equationsNumerical methods for partial differential equations is the branch of numerical analysis that studies the numerical solution of partial differential equations (PDEs). In principle, specialized methods for hyperbolic, parabolic or elliptic partial differential equations exist. Finite difference method In this method, functions are represented by their values at certain grid points and derivatives are approximated through differences in these values.
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).
Seven-dimensional cross productIn mathematics, the seven-dimensional cross product is a bilinear operation on vectors in seven-dimensional Euclidean space. It assigns to any two vectors a, b in \mathbb{R}^7 a vector a × b also in \mathbb{R}^7. Like the cross product in three dimensions, the seven-dimensional product is anticommutative and a × b is orthogonal both to a and to b. Unlike in three dimensions, it does not satisfy the Jacobi identity, and while the three-dimensional cross product is unique up to a sign, there are many seven-dimensional cross products.
Gamma functionIn mathematics, the gamma function (represented by Γ, the capital letter gamma from the Greek alphabet) is one commonly used extension of the factorial function to complex numbers. The gamma function is defined for all complex numbers except the non-positive integers. For every positive integer n, Derived by Daniel Bernoulli, for complex numbers with a positive real part, the gamma function is defined via a convergent improper integral: The gamma function then is defined as the analytic continuation of this integral function to a meromorphic function that is holomorphic in the whole complex plane except zero and the negative integers, where the function has simple poles.
Safety valveA safety valve is a valve that acts as a fail-safe. An example of safety valve is a pressure relief valve (PRV), which automatically releases a substance from a boiler, pressure vessel, or other system, when the pressure or temperature exceeds preset limits. Pilot-operated relief valves are a specialized type of pressure safety valve. A leak tight, lower cost, single emergency use option would be a rupture disk. Safety valves were first developed for use on steam boilers during the Industrial Revolution.
