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Monodomain Model
The monodomain model is a reduction of the bidomain model of the electrical propagation in myocardial tissue. The reduction comes from assuming that the intra- and extracellular domains have equal anisotropy ratios. Although not as physiologically accurate as the bidomain model, it is still adequate in some cases, and has reduced complexity. Formulation Being \mathbb T the domain boundary of the model, the monodomain model can be formulated as follows \frac \nabla \cdot \left(\mathbf\Sigma_i \nabla v \right) = \chi \left( C_m \frac + I_\text \right) \quad \quad \text\mathbb T , where \mathbf\Sigma_i is the intracellular conductivity tensor, v is the transmembrane potential, I_\text is the transmembrane ionic current per unit area, C_m is the membrane capacitance per unit area, \lambda is the intra- to extracellular conductivity ratio, and \chi is the membrane surface area per unit volume (of tissue). Derivation The monodomain model can be easily derived from the bidomain mo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bidomain Model
The bidomain model is a mathematical model to define the electrical activity of the heart. It consists in a continuum (volume-average) approach in which the cardiac mictrostructure is defined in terms of muscle fibers grouped in sheets, creating a complex three-dimensional structure with anisotropical properties. Then, to define the electrical activity, two interpenetrating domains are considered, which are the intracellular and extracellular domains, representing respectively the space inside the cells and the region between them. The bidomain model was first proposed by Schmitt in 1969 before being formulated mathematically in the late 1970s. Since it is a continuum model, rather than describing each cell individually, it represents the average properties and behaviour of group of cells organized in complex structure. Thus, the model results to be a complex one and can be seen as a generalization of the cable theory to higher dimensions and, going to define the so-called bidomai ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bidomain
The bidomain model is a mathematical model to define the electrical activity of the heart. It consists in a continuum (volume-average) approach in which the cardiac mictrostructure is defined in terms of muscle fibers grouped in sheets, creating a complex three-dimensional structure with anisotropical properties. Then, to define the electrical activity, two interpenetrating domains are considered, which are the intracellular and extracellular domains, representing respectively the space inside the cells and the region between them. The bidomain model was first proposed by Schmitt in 1969 before being formulated mathematically in the late 1970s. Since it is a continuum model, rather than describing each cell individually, it represents the average properties and behaviour of group of cells organized in complex structure. Thus, the model results to be a complex one and can be seen as a generalization of the cable theory to higher dimensions and, going to define the so-called bidomai ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bidomain Model
The bidomain model is a mathematical model to define the electrical activity of the heart. It consists in a continuum (volume-average) approach in which the cardiac mictrostructure is defined in terms of muscle fibers grouped in sheets, creating a complex three-dimensional structure with anisotropical properties. Then, to define the electrical activity, two interpenetrating domains are considered, which are the intracellular and extracellular domains, representing respectively the space inside the cells and the region between them. The bidomain model was first proposed by Schmitt in 1969 before being formulated mathematically in the late 1970s. Since it is a continuum model, rather than describing each cell individually, it represents the average properties and behaviour of group of cells organized in complex structure. Thus, the model results to be a complex one and can be seen as a generalization of the cable theory to higher dimensions and, going to define the so-called bidomai ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cardiac Electrophysiology
Cardiac electrophysiology is a branch of cardiology and basic science focusing on the electrical activities of the heart. The term is usually used in clinical context, to describe studies of such phenomena by invasive (intracardiac) catheter recording of spontaneous activity as well as of cardiac responses to programmed electrical stimulation - clinical cardiac electrophysiology. However, cardiac electrophysiology also encompasses basic research and translational research components. Specialists studying cardiac electrophysiology, either clinically or solely through research, are known as cardiac electrophysiologists. Description Electrophysiological (EP) studies are performed to assess complex arrhythmias, elucidate symptoms, evaluate abnormal electrocardiograms, assess risk of developing arrhythmias in the future, and design treatment. These procedures include therapeutic methods (typically radiofrequency ablation, or cryoablation) in addition to diagnostic and prognostic proced ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Differential Equations
In 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. Mainly the study of differential equations consists of the study of their solutions (the set of functions that satisfy each equation), and of the properties of their solutions. Only the simplest differential equations are solvable by explicit formulas; however, many properties of solutions of a given differential equation may be determined without computing them exactly. Often when a closed-form expression for the solutions is not available, solutions may be approximated numerically using computers. The theory of d ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Electrophysiology
Electrophysiology (from Greek , ''ēlektron'', "amber" etymology of "electron"">Electron#Etymology">etymology of "electron" , ''physis'', "nature, origin"; and , '' -logia'') is the branch of physiology that studies the electrical properties of biological cells and tissues. It involves measurements of voltage changes or electric current or manipulations on a wide variety of scales from single ion channel proteins to whole organs like the heart. In neuroscience, it includes measurements of the electrical activity of neurons, and, in particular, action potential activity. Recordings of large-scale electric signals from the nervous system, such as electroencephalography, may also be referred to as electrophysiological recordings. They are useful for electrodiagnosis and monitoring. Definition and scope Classical electrophysiological techniques Principle and mechanisms Electrophysiology is the branch of physiology that pertains broadly to the flow of ions (ion current) in biologi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Partial Differential Equations
In mathematics, a partial differential equation (PDE) is an equation which imposes relations between the various partial derivatives of a multivariable function. The function is often thought of as an "unknown" to be solved for, similarly to how is thought of as an unknown number to be solved for in an algebraic equation like . However, it is usually impossible to write down explicit formulas for solutions of partial differential equations. There is, correspondingly, a vast amount of modern mathematical and scientific research on methods to numerically approximate solutions of certain partial differential equations using computers. Partial differential equations also occupy a large sector of pure mathematical research, in which the usual questions are, broadly speaking, on the identification of general qualitative features of solutions of various partial differential equations, such as existence, uniqueness, regularity, and stability. Among the many open questions are the e ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
