Forward Problem Of Electrocardiology
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Forward Problem Of Electrocardiology
The forward problem of electrocardiology is a computational and mathematical approach to study the electrical activity of the heart through the body surface. The principal aim of this study is to computationally reproduce an electrocardiogram (ECG), which has important clinical relevance to define cardiac pathologies such as ischemia and infarction, or to test pharmaceutical intervention. Given their important functionalities and the relative small invasiveness, the electrocardiography techniques are used quite often as clinical diagnostic tests. Thus, it is natural to proceed to computationally reproduce an ECG, which means to mathematically model the cardiac behaviour inside the body. The three main parts of a forward model for the ECG are: * a model for the cardiac electrical activity; * a model for the diffusion of the electrical potential inside the torso, which represents the extracardiac region; * some specific heart-torso coupling conditions. Thus, to obtain an ECG, a ...
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CG Heart
CG, Cg or cg may refer to: Arts and entertainment * Chaotic Good, an alignment in the role-playing game ''Dungeons & Dragons'' * Classical guitar, a type of guitar Businesses and organizations Businesses * Central of Georgia Railway, between Macon and Savannah, Georgia in the US *Chappe et Gessalin, a French automobile maker *Chaudhary Group, a multinational company based in Nepal * Cigna, formed in Hartford in 1865 as the Connecticut General Life Insurance Company *Colorado General Hospital, now known as University of Colorado Hospital *PNG Air, an airline from Papua New Guinea (IATA code CG) *The Carlyle Group, a private equity firm (stock symbol CG) Military units *Ceremonial Guard, an ''ad hoc'' military unit in the Canadian Forces *Coast guard, a national organization responsible for various services at sea Political parties *Galician Coalition, a Galician political party with a Galician nationalist and centrist ideology *Galician Convergence, a Galician political part ...
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Finite Difference
A finite difference is a mathematical expression of the form . If a finite difference is divided by , one gets a difference quotient. The approximation of derivatives by finite differences plays a central role in finite difference methods for the numerical solution of differential equations, especially boundary value problems. The difference operator, commonly denoted \Delta is the operator that maps a function to the function \Delta /math> defined by :\Delta x)= f(x+1)-f(x). A difference equation is a functional equation that involves the finite difference operator in the same way as a differential equation involves derivatives. There are many similarities between difference equations and differential equations, specially in the solving methods. Certain recurrence relations can be written as difference equations by replacing iteration notation with finite differences. In numerical analysis, finite differences are widely used for approximating derivatives, and the term " ...
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Lead
Lead is a chemical element with the symbol Pb (from the Latin ) and atomic number 82. It is a heavy metal that is denser than most common materials. Lead is soft and malleable, and also has a relatively low melting point. When freshly cut, lead is a shiny gray with a hint of blue. It tarnishes to a dull gray color when exposed to air. Lead has the highest atomic number of any stable element and three of its isotopes are endpoints of major nuclear decay chains of heavier elements. Lead is toxic, even in small amounts, especially to children. Lead is a relatively unreactive post-transition metal. Its weak metallic character is illustrated by its amphoteric nature; lead and lead oxides react with acids and bases, and it tends to form covalent bonds. Compounds of lead are usually found in the +2 oxidation state rather than the +4 state common with lighter members of the carbon group. Exceptions are mostly limited to organolead compounds. Like the lighter members of the ...
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Augustus Desiré Waller
Augustus Desiré Waller FRS (12 July 1856 – 11 March 1922) was a British physiologist and the son of Augustus Volney Waller. He was born in Paris, France. He studied medicine at Aberdeen University, where he qualified in 1878 and obtained his M.D. in 1881. In 1883, he became a lecturer in physiology at the London School of Medicine for Women. Whilst there he met his wife, Alice Palmer, who was one of his students and daughter of George Palmer, MP for Reading and founder of the biscuit manufacturers Huntley and Palmer. In 1884 he became a lecturer in physiology at St Mary's Hospital. In 1887 he used a capillary electrometer to record the first human electrocardiogram. He created the first practical ECG machine with surface electrodes. He lectured on it in Europe and America, often using his dog Jimmy in his ECG demonstrations. Initially Waller did not think electrocardiograms would be useful in hospitals. However, eventually other physiologists such as  ...
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Willem Einthoven
Willem Einthoven (21 May 1860 – 29 September 1927) was a Dutch doctor and physiologist. He invented the first practical electrocardiograph (ECG or EKG) in 1895 and received the Nobel Prize in Physiology or Medicine in 1924 for it ("for the discovery of the mechanism of the electrocardiogram"). original URL now redirects to https://ethw.org/Willem_Einthoven Background Willem Einthoven was born in Semarang on Java in the Dutch East Indies (now Indonesia), the son of Louise Marie Mathilde Caroline de Vogel and Jacob Einthoven. His father, a doctor, died when Willem was a child. His mother returned to the Netherlands with her children in 1870 and settled in Utrecht. His father was of Jewish and Dutch descent, and his mother's ancestry was Dutch and Swiss. In 1885, Einthoven received a medical degree from the University of Utrecht. He became a professor at the University of Leiden in 1886. He married his first cousin Frédérique Jeanne Louise de Vogel (7 September 1861 31 Januar ...
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Macroscopic
The macroscopic scale is the length scale on which objects or phenomena are large enough to be visible with the naked eye, without magnifying optical instruments. It is the opposite of microscopic. Overview When applied to physical phenomena and bodies, the macroscopic scale describes things as a person can directly perceive them, without the aid of magnifying devices. This is in contrast to observations (microscopy) or theories ( microphysics, statistical physics) of objects of geometric lengths smaller than perhaps some hundreds of micrometers. A macroscopic view of a ball is just that: a ball. A microscopic view could reveal a thick round skin seemingly composed entirely of puckered cracks and fissures (as viewed through a microscope) or, further down in scale, a collection of molecules in a roughly spherical shape (as viewed through an electron microscope). An example of a physical theory that takes a deliberately macroscopic viewpoint is thermodynamics. An example of a topi ...
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Fibers
Fiber or fibre (from la, fibra, links=no) is a natural or artificial substance that is significantly longer than it is wide. Fibers are often used in the manufacture of other materials. The strongest engineering materials often incorporate fibers, for example carbon fiber and ultra-high-molecular-weight polyethylene. Synthetic fibers can often be produced very cheaply and in large amounts compared to natural fibers, but for clothing natural fibers can give some benefits, such as comfort, over their synthetic counterparts. Natural fibers Natural fibers develop or occur in the fiber shape, and include those produced by plants, animals, and geological processes. They can be classified according to their origin: *Vegetable fibers are generally based on arrangements of cellulose, often with lignin: examples include cotton, hemp, jute, flax, abaca, piña, ramie, sisal, bagasse, and banana. Plant fibers are employed in the manufacture of paper and textile (cloth), and diet ...
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Microscopic
The microscopic scale () is the scale of objects and events smaller than those that can easily be seen by the naked eye, requiring a lens (optics), lens or microscope to see them clearly. In physics, the microscopic scale is sometimes regarded as the scale between the macroscopic scale and the quantum realm, quantum scale. Microscopic units and measurements are used to classify and describe very small objects. One common microscopic length scale unit is the micrometre (also called a ''micron'') (symbol: μm), which is one millionth of a metre. History Whilst compound microscopes were first developed in the 1590s, the significance of the microscopic scale was only truly established in the 1600s when Marcello Malpighi, Marcello Malphigi and Antonie van Leeuwenhoek microscopically observed frog lungs and microorganisms. As microbiology was established, the significance of making scientific observations at a microscopic level increased. Published in 1665, Robert Hooke’s book Mi ...
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Circulatory System
The blood circulatory system is a system of organs that includes the heart, blood vessels, and blood which is circulated throughout the entire body of a human or other vertebrate. It includes the cardiovascular system, or vascular system, that consists of the heart and blood vessels (from Greek ''kardia'' meaning ''heart'', and from Latin ''vascula'' meaning ''vessels''). The circulatory system has two divisions, a systemic circulation or circuit, and a pulmonary circulation or circuit. Some sources use the terms ''cardiovascular system'' and ''vascular system'' interchangeably with the ''circulatory system''. The network of blood vessels are the great vessels of the heart including large elastic arteries, and large veins; other arteries, smaller arterioles, capillaries that join with venules (small veins), and other veins. The Closed circulatory system, circulatory system is closed in vertebrates, which means that the blood never leaves the network of blood vessels. Some in ...
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Blood
Blood 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. Plasma, which constitutes 55% of blood fluid, is mostly water (92% by volume), and contains proteins, glucose, mineral ions, hormones, carbon dioxide (plasma being the main medium for excretory product transportation), and blood cells themselves. Albumin is the main protein in plasma, and it functions to regulate the colloidal osmotic pressure of blood. The blood cells are mainly red blood cells (also called RBCs or erythrocytes), white blood cells (also called WBCs or leukocytes) and platelets (also called thrombocytes). The most abundant cells in vertebrate blo ...
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Heart Muscle
Cardiac muscle (also called heart muscle, myocardium, cardiomyocytes and cardiac myocytes) is one of three types of vertebrate muscle tissues, with the other two being skeletal muscle and smooth muscle. It is an involuntary, striated muscle that constitutes the main tissue of the wall of the heart. The cardiac muscle (myocardium) forms a thick middle layer between the outer layer of the heart wall (the pericardium) and the inner layer (the endocardium), with blood supplied via the coronary circulation. It is composed of individual cardiac muscle cells joined by intercalated discs, and encased by collagen fibers and other substances that form the extracellular matrix. Cardiac muscle contracts in a similar manner to skeletal muscle, although with some important differences. Electrical stimulation in the form of a cardiac action potential triggers the release of calcium from the cell's internal calcium store, the sarcoplasmic reticulum. The rise in calcium causes the cell's ...
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Cell Membrane
The cell membrane (also known as the plasma membrane (PM) or cytoplasmic membrane, and historically referred to as the plasmalemma) is a biological membrane that separates and protects the interior of all cells from the outside environment (the extracellular space). The cell membrane consists of a lipid bilayer, made up of two layers of phospholipids with cholesterols (a lipid component) interspersed between them, maintaining appropriate membrane fluidity at various temperatures. The membrane also contains membrane proteins, including integral proteins that span the membrane and serve as membrane transporters, and peripheral proteins that loosely attach to the outer (peripheral) side of the cell membrane, acting as enzymes to facilitate interaction with the cell's environment. Glycolipids embedded in the outer lipid layer serve a similar purpose. The cell membrane controls the movement of substances in and out of cells and organelles, being selectively permeable to ions a ...
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