Low-density lipoproteinLow-density lipoprotein (LDL) is one of the five major groups of lipoprotein that transport all fat molecules around the body in extracellular water. These groups, from least dense to most dense, are chylomicrons (aka ULDL by the overall density naming convention), very low-density lipoprotein (VLDL), intermediate-density lipoprotein (IDL), low-density lipoprotein (LDL) and high-density lipoprotein (HDL). LDL delivers fat molecules to cells. LDL is involved in atherosclerosis, a process in which it is oxidized within the walls of arteries.
High-density lipoproteinHigh-density lipoprotein (HDL) is one of the five major groups of lipoproteins. Lipoproteins are complex particles composed of multiple proteins which transport all fat molecules (lipids) around the body within the water outside cells. They are typically composed of 80–100 proteins per particle (organized by one, two or three ApoA). HDL particles enlarge while circulating in the blood, aggregating more fat molecules and transporting up to hundreds of fat molecules per particle.
CholesterolCholesterol is the principal sterol of all higher animals, distributed in body tissues, especially the brain and spinal cord, and in animal fats and oils. Cholesterol is biosynthesized by all animal cells and is an essential structural component of animal cell membranes. In vertebrates, hepatic cells typically produce the greatest amounts. It is absent among prokaryotes (bacteria and archaea), although there are some exceptions, such as Mycoplasma, which require cholesterol for growth.
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.
LipoproteinA lipoprotein is a biochemical assembly whose primary function is to transport hydrophobic lipid (also known as fat) molecules in water, as in blood plasma or other extracellular fluids. They consist of a triglyceride and cholesterol center, surrounded by a phospholipid outer shell, with the hydrophilic portions oriented outward toward the surrounding water and lipophilic portions oriented inward toward the lipid center. A special kind of protein, called apolipoprotein, is embedded in the outer shell, both stabilising the complex and giving it a functional identity that determines its role.
HypercholesterolemiaHypercholesterolemia, also called high cholesterol, is the presence of high levels of cholesterol in the blood. It is a form of hyperlipidemia (high levels of lipids in the blood), hyperlipoproteinemia (high levels of lipoproteins in the blood), and dyslipidemia (any abnormalities of lipid and lipoprotein levels in the blood). Elevated levels of non-HDL cholesterol and LDL in the blood may be a consequence of diet, obesity, inherited (genetic) diseases (such as LDL receptor mutations in familial hypercholesterolemia), or the presence of other diseases such as type 2 diabetes and an underactive thyroid.
Apolipoprotein BApolipoprotein B (ApoB) is a protein that in humans is encoded by the gene. It is commonly used to detect risk of atherosclerotic cardiovascular disease. Apolipoprotein B is the primary apolipoprotein of chylomicrons, VLDL, Lp(a), IDL, and LDL particles (LDL—commonly known as "bad cholesterol" when in reference to both heart disease and vascular disease in general), which is responsible for carrying fat molecules (lipids), including cholesterol, around the body to all cells within all tissues.
HyperlipidemiaHyperlipidemia is abnormally elevated levels of any or all lipids (fats, cholesterol, or triglycerides) or lipoproteins in the blood. The term hyperlipidemia refers to the laboratory finding itself and is also used as an umbrella term covering any of various acquired or genetic disorders that result in that finding. Hyperlipidemia represents a subset of dyslipidemia and a superset of hypercholesterolemia. Hyperlipidemia is usually chronic and requires ongoing medication to control blood lipid levels.
Lipid profileA lipid profile or lipid panel is a panel of blood tests used to find abnormalities in lipids, such as cholesterol and triglycerides. The results of this test can identify certain genetic diseases and can determine approximate risks for cardiovascular disease, certain forms of pancreatitis, and other diseases. Lipid panels are usually ordered as part of a physical exam, along with other panels such as the complete blood count (CBC) and basic metabolic panel (BMP).
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).
Hyperbolic partial differential equationIn mathematics, a hyperbolic partial differential equation of order is a partial differential equation (PDE) that, roughly speaking, has a well-posed initial value problem for the first derivatives. More precisely, the Cauchy problem can be locally solved for arbitrary initial data along any non-characteristic hypersurface. Many of the equations of mechanics are hyperbolic, and so the study of hyperbolic equations is of substantial contemporary interest. The model hyperbolic equation is the wave equation.
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.
Aortic stenosisAortic stenosis (AS or AoS) is the narrowing of the exit of the left ventricle of the heart (where the aorta begins), such that problems result. It may occur at the aortic valve as well as above and below this level. It typically gets worse over time. Symptoms often come on gradually with a decreased ability to exercise often occurring first. If heart failure, loss of consciousness, or heart related chest pain occur due to AS the outcomes are worse. Loss of consciousness typically occurs with standing or exercising.
Stochastic partial differential equationStochastic partial differential equations (SPDEs) generalize partial differential equations via random force terms and coefficients, in the same way ordinary stochastic differential equations generalize ordinary differential equations. They have relevance to quantum field theory, statistical mechanics, and spatial modeling. One of the most studied SPDEs is the stochastic heat equation, which may formally be written as where is the Laplacian and denotes space-time white noise.
Elliptic partial differential equationSecond-order linear partial differential equations (PDEs) are classified as either elliptic, hyperbolic, or parabolic. Any second-order linear PDE in two variables can be written in the form where A, B, C, D, E, F, and G are functions of x and y and where , and similarly for . A PDE written in this form is elliptic if with this naming convention inspired by the equation for a planar ellipse.
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.
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), .
Mathematical logicMathematical logic is the study of formal logic within mathematics. Major subareas include model theory, proof theory, set theory, and recursion theory (also known as computability theory). Research in mathematical logic commonly addresses the mathematical properties of formal systems of logic such as their expressive or deductive power. However, it can also include uses of logic to characterize correct mathematical reasoning or to establish foundations of mathematics.
ParameterA parameter (), generally, is any characteristic that can help in defining or classifying a particular system (meaning an event, project, object, situation, etc.). That is, a parameter is an element of a system that is useful, or critical, when identifying the system, or when evaluating its performance, status, condition, etc. Parameter has more specific meanings within various disciplines, including mathematics, computer programming, engineering, statistics, logic, linguistics, and electronic musical composition.
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.
