VeinVeins are blood vessels in the circulatory system of humans and most other animals that carry blood toward the heart. Most veins carry deoxygenated blood from the tissues back to the heart; exceptions are those of the pulmonary and fetal circulations which carry oxygenated blood to the heart. In the systemic circulation arteries carry oxygenated blood away from the heart, and veins return deoxygenated blood to the heart, in the deep veins. There are three sizes of veins, large, medium, and small.
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.
Venous thrombosisVenous thrombosis is blockage of a vein caused by a thrombus (blood clot). A common form of venous thrombosis is deep vein thrombosis (DVT), when a blood clot forms in the deep veins. If a thrombus breaks off (embolizes) and flows to the lungs to lodge there, it becomes a pulmonary embolism (PE), a blood clot in the lungs. The conditions of DVT only, DVT with PE, and PE only, are all captured by the term venous thromboembolism (VTE).
Potential flowIn fluid dynamics, potential flow (or ideal flow) describes the velocity field as the gradient of a scalar function: the velocity potential. As a result, a potential flow is characterized by an irrotational velocity field, which is a valid approximation for several applications. The irrotationality of a potential flow is due to the curl of the gradient of a scalar always being equal to zero. In the case of an incompressible flow the velocity potential satisfies Laplace's equation, and potential theory is applicable.
Boundary conditions in fluid dynamicsBoundary conditions in fluid dynamics are the set of constraints to boundary value problems in computational fluid dynamics. These boundary conditions include inlet boundary conditions, outlet boundary conditions, wall boundary conditions, constant pressure boundary conditions, axisymmetric boundary conditions, symmetric boundary conditions, and periodic or cyclic boundary conditions. Transient problems require one more thing i.e., initial conditions where initial values of flow variables are specified at nodes in the flow domain.
DataIn common usage and statistics, data (USˈdætə; UKˈdeɪtə) is a collection of discrete or continuous values that convey information, describing the quantity, quality, fact, statistics, other basic units of meaning, or simply sequences of symbols that may be further interpreted formally. A datum is an individual value in a collection of data. Data is usually organized into structures such as tables that provide additional context and meaning, and which may themselves be used as data in larger structures.
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.
Central venous catheterA central venous catheter (CVC), also known as a central line (c-line), central venous line, or central venous access catheter, is a catheter placed into a large vein. It is a form of venous access. Placement of larger catheters in more centrally located veins is often needed in critically ill patients, or in those requiring prolonged intravenous therapies, for more reliable vascular access.
Venous ulcerVenous ulcer is defined by the American Venous Forum as "a full-thickness defect of skin, most frequently in the ankle region, that fails to heal spontaneously and is sustained by chronic venous disease, based on venous duplex ultrasound testing." Venous ulcers are wounds that are thought to occur due to improper functioning of venous valves, usually of the legs (hence leg ulcers). They are an important cause of chronic wounds, affecting 1% of the population.
Numerical analysisNumerical analysis is the study of algorithms that use numerical approximation (as opposed to symbolic manipulations) for the problems of mathematical analysis (as distinguished from discrete mathematics). It is the study of numerical methods that attempt at finding approximate solutions of problems rather than the exact ones. Numerical analysis finds application in all fields of engineering and the physical sciences, and in the 21st century also the life and social sciences, medicine, business and even the arts.
Robin boundary conditionIn mathematics, the Robin boundary condition (ˈrɒbɪn; properly ʁɔbɛ̃), or third type boundary condition, is a type of boundary condition, named after Victor Gustave Robin (1855–1897). When imposed on an ordinary or a partial differential equation, it is a specification of a linear combination of the values of a function and the values of its derivative on the boundary of the domain. Other equivalent names in use are Fourier-type condition and radiation condition.
Dirichlet boundary conditionIn the mathematical study of differential equations, the Dirichlet (or first-type) boundary condition is a type of boundary condition, named after Peter Gustav Lejeune Dirichlet (1805–1859). When imposed on an ordinary or a partial differential equation, it specifies the values that a solution needs to take along the boundary of the domain. In finite element method (FEM) analysis, essential or Dirichlet boundary condition is defined by weighted-integral form of a differential equation.
Chronic venous insufficiencyChronic venous insufficiency (CVI) is a medical condition in which blood pools in the veins, straining the walls of the vein. The most common cause of CVI is superficial venous reflux which is a treatable condition. As functional venous valves are required to provide for efficient blood return from the lower extremities, this condition typically affects the legs. If the impaired vein function causes significant symptoms, such as swelling and ulcer formation, it is referred to as chronic venous disease.
Boundary value problemIn the study of differential equations, a boundary-value problem is a differential equation subjected to constraints called boundary conditions. A solution to a boundary value problem is a solution to the differential equation which also satisfies the boundary conditions. Boundary value problems arise in several branches of physics as any physical differential equation will have them. Problems involving the wave equation, such as the determination of normal modes, are often stated as boundary value problems.
Cerebral venous sinus thrombosisCerebral venous sinus thrombosis (CVST), cerebral venous and sinus thrombosis or cerebral venous thrombosis (CVT), is the presence of a blood clot in the dural venous sinuses (which drain blood from the brain), the cerebral veins, or both. Symptoms may include severe headache, visual symptoms, any of the symptoms of stroke such as weakness of the face and limbs on one side of the body, and seizures, which occur in around 40% of patients.
Neumann boundary conditionIn mathematics, the Neumann (or second-type) boundary condition is a type of boundary condition, named after Carl Neumann. When imposed on an ordinary or a partial differential equation, the condition specifies the values of the derivative applied at the boundary of the domain. It is possible to describe the problem using other boundary conditions: a Dirichlet boundary condition specifies the values of the solution itself (as opposed to its derivative) on the boundary, whereas the Cauchy boundary condition, mixed boundary condition and Robin boundary condition are all different types of combinations of the Neumann and Dirichlet boundary conditions.
Numerical integrationIn analysis, numerical integration comprises a broad family of algorithms for calculating the numerical value of a definite integral, and by extension, the term is also sometimes used to describe the numerical solution of differential equations. This article focuses on calculation of definite integrals. The term numerical quadrature (often abbreviated to quadrature) is more or less a synonym for numerical integration, especially as applied to one-dimensional integrals.
Cauchy boundary conditionIn mathematics, a Cauchy (koʃi) boundary condition augments an ordinary differential equation or a partial differential equation with conditions that the solution must satisfy on the boundary; ideally so as to ensure that a unique solution exists. A Cauchy boundary condition specifies both the function value and normal derivative on the boundary of the domain. This corresponds to imposing both a Dirichlet and a Neumann boundary condition. It is named after the prolific 19th-century French mathematical analyst Augustin-Louis Cauchy.
Open-channel flowIn fluid mechanics and hydraulics, open-channel flow is a type of liquid flow within a conduit with a free surface, known as a channel. The other type of flow within a conduit is pipe flow. These two types of flow are similar in many ways but differ in one important respect: open-channel flow has a free surface, whereas pipe flow does not. Open-channel flow can be classified and described in various ways based on the change in flow depth with respect to time and space.
Arteriovenous fistulaAn arteriovenous fistula is an abnormal connection or passageway between an artery and a vein. It may be congenital, surgically created for hemodialysis treatments, or acquired due to pathologic process, such as trauma or erosion of an arterial aneurysm. Hereditary hemorrhagic telangiectasia is a condition where there is direct connection between arterioles and venules without intervening capillary beds, at the mucocutaneous region and internal bodily organs. Those who are affected by this conditions usually do not experience any symptoms.
