The diagnostic tests in cardiology are methods of identifying heart conditions associated with healthy vs. unhealthy, pathologic heart function.
Electrocardiography is the process of producing an electrocardiogram. It is a graph of voltage versus time of the electrical activity of the heart using electrodes placed on the skin. These electrodes detect the small electrical changes that are a consequence of cardiac muscle depolarization followed by repolarization during each cardiac cycle (heartbeat). Changes in the normal ECG pattern occur in numerous cardiac abnormalities, including cardiac rhythm disturbances, inadequate coronary artery blood flow, and electrolyte disturbances.
In mathematics, particularly in complex analysis, a Riemann surface is a one-dimensional complex manifold. These surfaces were first studied by and are named after Bernhard Riemann. Riemann surfaces can be thought of as deformed versions of the complex plane: locally near every point they look like patches of the complex plane, but the global topology can be quite different. For example, they can look like a sphere or a torus or several sheets glued together.
In physics, Wick rotation, named after Italian physicist Gian Carlo Wick, is a method of finding a solution to a mathematical problem in Minkowski space from a solution to a related problem in Euclidean space by means of a transformation that substitutes an imaginary-number variable for a real-number variable. This transformation is also used to find solutions to problems in quantum mechanics and other areas.
In mathematics, the Hodge star operator or Hodge star is a linear map defined on the exterior algebra of a finite-dimensional oriented vector space endowed with a nondegenerate symmetric bilinear form. Applying the operator to an element of the algebra produces the Hodge dual of the element. This map was introduced by W. V. D. Hodge.
In mathematics, engineering, and manufacturing, a solid of revolution is a solid figure obtained by rotating a plane curve around some straight line that lies on the same plane.
In relativity, proper time along a timelike world line is defined as the time as measured by a clock following that line. It is thus independent of coordinates, and is a Lorentz scalar. The proper time interval between two events on a world line is the change in proper time. This interval is the quantity of interest, since proper time itself is fixed only up to an arbitrary additive constant, namely the setting of the clock at some event along the world line. The proper time interval between two events depends not only on the events but also the world line connecting them, and hence on the motion of the clock between the events. It is expressed as an integral over the world line. An accelerated clock will measure a smaller elapsed time between two events than that measured by a non-accelerated (inertial) clock between the same two events. The twin paradox is an example of this effect.
A cardiac stress test is a cardiological test that measures the heart's ability to respond to external stress in a controlled clinical environment. The stress response is induced by exercise or by intravenous pharmacological stimulation.
In physics, the Hamilton–Jacobi equation, named after William Rowan Hamilton and Carl Gustav Jacob Jacobi, is an alternative formulation of classical mechanics, equivalent to other formulations such as Newton's laws of motion, Lagrangian mechanics and Hamiltonian mechanics. The Hamilton–Jacobi equation is particularly useful in identifying conserved quantities for mechanical systems, which may be possible even when the mechanical problem itself cannot be solved completely.
In mathematics, the Poincaré metric, named after Henri Poincaré, is the metric tensor describing a two-dimensional surface of constant negative curvature. It is the natural metric commonly used in a variety of calculations in hyperbolic geometry or Riemann surfaces.
Self-phase modulation (SPM) is a nonlinear optical effect of light-matter interaction. An ultrashort pulse of light, when travelling in a medium, will induce a varying refractive index of the medium due to the optical Kerr effect. This variation in refractive index will produce a phase shift in the pulse, leading to a change of the pulse's frequency spectrum.
The method of reassignment is a technique for sharpening a time-frequency representation by mapping the data to time-frequency coordinates that are nearer to the true region of support of the analyzed signal. The method has been independently introduced by several parties under various names, including method of reassignment, remapping, time-frequency reassignment, and modified moving-window method. In the case of the spectrogram or the short-time Fourier transform, the method of reassignment sharpens blurry time-frequency data by relocating the data according to local estimates of instantaneous frequency and group delay. This mapping to reassigned time-frequency coordinates is very precise for signals that are separable in time and frequency with respect to the analysis window.
Cardiovascular magnetic resonance imaging is a medical imaging technology for non-invasive assessment of the function and structure of the cardiovascular system. Conventional MRI sequences are adapted for cardiac imaging by using ECG gating and high temporal resolution protocols. The development of CMR is an active field of research and continues to see a rapid expansion of new and emerging techniques.
In mathematics, a line integral is an integral where the function to be integrated is evaluated along a curve. The terms path integral, curve integral, and curvilinear integral are also used; contour integral is used as well, although that is typically reserved for line integrals in the complex plane.
Vectorcardiography (VCG) is a method of recording the magnitude and direction of the electrical forces that are generated by the heart by means of a continuous series of vectors that form curving lines around a central point.
In mathematical physics, the Peres metric is defined by the proper time
Electrocardiography in suspected myocardial infarction has the main purpose of detecting ischemia or acute coronary injury in emergency department populations coming for symptoms of myocardial infarction (MI). Also, it can distinguish clinically different types of myocardial infarction.
SATRO-EKG - a computer program analysing electro-cardiology signals. It is based on the SFHAM model. It facilitates the evaluation of electrical activity of myocardium, and therefore, early detection of ischemic changes in the heart.
Coronary CT angiography (CTA) is the use of computed tomography (CT) angiography to assess the coronary arteries of the heart. The subject receives an intravenous injection of radiocontrast and then the heart is scanned using a high speed CT scanner, allowing physicians to assess the extent of occlusion in the coronary arteries, usually in order to diagnose coronary artery disease.
In the mathematics of dynamical systems, the double-scroll attractor is a strange attractor observed from a physical electronic chaotic circuit with a single nonlinear resistor. The double-scroll system is often described by a system of three nonlinear ordinary differential equations and a 3-segment piecewise-linear equation. This makes the system easily simulated numerically and easily manifested physically due to Chua's circuits' simple design.
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