Spinal stenosisSpinal stenosis is an abnormal narrowing of the spinal canal or neural foramen that results in pressure on the spinal cord or nerve roots. Symptoms may include pain, numbness, or weakness in the arms or legs. Symptoms are typically gradual in onset and improve with leaning forward. Severe symptoms may include loss of bladder control, loss of bowel control, or sexual dysfunction. Causes may include osteoarthritis, rheumatoid arthritis, spinal tumors, trauma, Paget's disease of the bone, scoliosis, spondylolisthesis, and the genetic condition achondroplasia.
Complex normal distributionIn probability theory, the family of complex normal distributions, denoted or , characterizes complex random variables whose real and imaginary parts are jointly normal. The complex normal family has three parameters: location parameter μ, covariance matrix , and the relation matrix . The standard complex normal is the univariate distribution with , , and . An important subclass of complex normal family is called the circularly-symmetric (central) complex normal and corresponds to the case of zero relation matrix and zero mean: and .
Log-normal distributionIn probability theory, a log-normal (or lognormal) distribution is a continuous probability distribution of a random variable whose logarithm is normally distributed. Thus, if the random variable X is log-normally distributed, then Y = ln(X) has a normal distribution. Equivalently, if Y has a normal distribution, then the exponential function of Y, X = exp(Y), has a log-normal distribution. A random variable which is log-normally distributed takes only positive real values.
StenosisA stenosis (from Ancient Greek στενός, "narrow") is an abnormal narrowing in a blood vessel or other tubular organ or structure such as foramina and canals. It is also sometimes called a stricture (as in urethral stricture). Stricture as a term is usually used when narrowing is caused by contraction of smooth muscle (e.g. achalasia, prinzmetal angina); stenosis is usually used when narrowing is caused by lesion that reduces the space of lumen (e.g. atherosclerosis).
Lumbar spinal stenosisLumbar spinal stenosis (LSS) is a medical condition in which the spinal canal narrows and compresses the nerves and blood vessels at the level of the lumbar vertebrae. Spinal stenosis may also affect the cervical or thoracic region, in which case it is known as cervical spinal stenosis or thoracic spinal stenosis. Lumbar spinal stenosis can cause pain in the low back or buttocks, abnormal sensations, and the absence of sensation (numbness) in the legs, thighs, feet, or buttocks, or loss of bladder and bowel control.
Fluid dynamicsIn physics, physical chemistry and engineering, fluid dynamics is a subdiscipline of fluid mechanics that describes the flow of fluids—liquids and gases. It has several subdisciplines, including aerodynamics (the study of air and other gases in motion) and hydrodynamics (the study of liquids in motion). Fluid dynamics has a wide range of applications, including calculating forces and moments on aircraft, determining the mass flow rate of petroleum through pipelines, predicting weather patterns, understanding nebulae in interstellar space and modelling fission weapon detonation.
Pressure measurementPressure measurement is the measurement of an applied force by a fluid (liquid or gas) on a surface. Pressure is typically measured in units of force per unit of surface area. Many techniques have been developed for the measurement of pressure and vacuum. Instruments used to measure and display pressure mechanically are called pressure gauges, vacuum gauges or compound gauges (vacuum & pressure). The widely used Bourdon gauge is a mechanical device, which both measures and indicates and is probably the best known type of gauge.
PressurePressure (symbol: p or P) is the force applied perpendicular to the surface of an object per unit area over which that force is distributed. Gauge pressure (also spelled gage pressure) is the pressure relative to the ambient pressure. Various units are used to express pressure. Some of these derive from a unit of force divided by a unit of area; the SI unit of pressure, the pascal (Pa), for example, is one newton per square metre (N/m2); similarly, the pound-force per square inch (psi, symbol lbf/in2) is the traditional unit of pressure in the imperial and US customary systems.
Blood pressure measurementArterial blood pressure is most commonly measured via a sphygmomanometer, which historically used the height of a column of mercury to reflect the circulating pressure. Blood pressure values are generally reported in millimetres of mercury (mmHg), though aneroid and electronic devices do not contain mercury. For each heartbeat, blood pressure varies between systolic and diastolic pressures. Systolic pressure is peak pressure in the arteries, which occurs near the end of the cardiac cycle when the ventricles are contracting.
TurbulenceIn fluid dynamics, turbulence or turbulent flow is fluid motion characterized by chaotic changes in pressure and flow velocity. It is in contrast to a laminar flow, which occurs when a fluid flows in parallel layers, with no disruption between those layers. Turbulence is commonly observed in everyday phenomena such as surf, fast flowing rivers, billowing storm clouds, or smoke from a chimney, and most fluid flows occurring in nature or created in engineering applications are turbulent.
Incompressible flowIn fluid mechanics or more generally continuum mechanics, incompressible flow (isochoric flow) refers to a flow in which the material density is constant within a fluid parcel—an infinitesimal volume that moves with the flow velocity. An equivalent statement that implies incompressibility is that the divergence of the flow velocity is zero (see the derivation below, which illustrates why these conditions are equivalent). Incompressible flow does not imply that the fluid itself is incompressible.
