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Cable Theory
Classical cable theory uses mathematical models to calculate the electric current (and accompanying voltage) along passive neurites, particularly the dendrites that receive synaptic inputs at different sites and times. Estimates are made by modeling dendrites and axons as cylinders composed of segments with capacitances c_m and resistances r_m combined in parallel (see Fig. 1). The capacitance of a neuronal fiber comes about because electrostatic forces are acting through the very thin lipid bilayer (see Figure 2). The resistance in series along the fiber r_l is due to the axoplasm's significant resistance to movement of electric charge. History Cable theory in computational neuroscience has roots leading back to the 1850s, when Professor William Thomson (later known as Lord Kelvin) began developing mathematical models of signal decay in submarine (underwater) telegraphic cables. The models resembled the partial differential equations used by Fourier to describe heat cond ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cable Theory Neuron RC Circuit V3
Cable may refer to: Mechanical * Nautical cable, an assembly of three or more ropes woven against the weave of the ropes, rendering it virtually waterproof * Wire rope, a type of rope that consists of several strands of metal wire laid into a helix ** Arresting cable, part of a system used to rapidly decelerate an aircraft as it lands ** Bowden cable, a mechanical cable for transmitting forces * Rope generally, especially a thick, heavy ("cable laid") variety Transmission * Electrical cable, an assembly of one or more wires which may be insulated, used for transmission of electrical power or signals ** Coaxial cable, an electrical cable comprising an inner conductor surrounded by a flexible, tubular insulating layer, coated or surrounded by a tubular conducting shield ** Power cable, a cable used to transmit electrical power ** Submarine communications cable, a cable laid on the sea bed to carry telecommunication signals between land-based stations * Fiber-optic cable, a cable con ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Neuronal
A neuron, neurone, or nerve cell is an electrically excitable cell that communicates with other cells via specialized connections called synapses. The neuron is the main component of nervous tissue in all animals except sponges and placozoa. Non-animals like plants and fungi do not have nerve cells. Neurons are typically classified into three types based on their function. Sensory neurons respond to stimuli such as touch, sound, or light that affect the cells of the sensory organs, and they send signals to the spinal cord or brain. Motor neurons receive signals from the brain and spinal cord to control everything from muscle contractions to glandular output. Interneurons connect neurons to other neurons within the same region of the brain or spinal cord. When multiple neurons are connected together, they form what is called a neural circuit. A typical neuron consists of a cell body (soma), dendrites, and a single axon. The soma is a compact structure, and the axon and dendri ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Partial Differential Equation
In mathematics, a partial differential equation (PDE) is an equation which imposes relations between the various partial derivatives of a Multivariable calculus, 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 Numerical methods for partial differential equations, numerically approximate solutions of certain partial differential equations using computers. Partial differential equations also occupy a large sector of pure mathematics, 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 a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ohm's Law
Ohm's law states that the current through a conductor between two points is directly proportional to the voltage across the two points. Introducing the constant of proportionality, the resistance, one arrives at the usual mathematical equation that describes this relationship: :I = \frac, where is the current through the conductor, ''V'' is the voltage measured ''across'' the conductor and ''R'' is the resistance of the conductor. More specifically, Ohm's law states that the ''R'' in this relation is constant, independent of the current. If the resistance is not constant, the previous equation cannot be called ''Ohm's law'', but it can still be used as a definition of static/DC resistance. Ohm's law is an empirical relation which accurately describes the conductivity of the vast majority of electrically conductive materials over many orders of magnitude of current. However some materials do not obey Ohm's law; these are called non-ohmic. The law was named after t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Specific Electrical Resistance
Specific may refer to: * Specificity (other) * Specific, a cure or therapy for a specific illness Law * Specific deterrence, focussed on an individual * Specific finding, intermediate verdict used by a jury in determining the final verdict * Specific jurisdiction over an out-of-state party, specific to cases that have a substantial connection to the party's in-state activity * Order of specific performance, court order to perform a specific act Economics, finance, and accounting * Asset specificity, the extent to which the investments made to support a particular transaction have a higher value to that transaction than they would have if they were redeployed for any other purpose * Specific identification (inventories), summing purchase costs of all inventory items * Specific rate duty, duty paid at a specific amount per unit * Specific risk, risk that affects a very small number of assets Psychology * Domain specificity, theory that many aspects of cognition are ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Farad
The farad (symbol: F) is the unit of electrical capacitance, the ability of a body to store an electrical charge, in the International System of Units (SI). It is named after the English physicist Michael Faraday (1791–1867). In SI base units 1 F = 1 kg−1⋅ m−2⋅ s4⋅ A2. Definition The capacitance of a capacitor is one farad when one coulomb of charge changes the potential between the plates by one volt. Equally, one farad can be described as the capacitance which stores a one-coulomb charge across a potential difference of one volt. The relationship between capacitance, charge, and potential difference is linear. For example, if the potential difference across a capacitor is halved, the quantity of charge stored by that capacitor will also be halved. For most applications, the farad is an impractically large unit of capacitance. Most electrical and electronic applications are covered by the following SI prefixes: *1 mF (millifarad, one thousandth ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Wilfrid Rall
Wilfrid Rall (August 29, 1922 - April 1, 2018) was a neuroscientist who spent most of his career at the National Institutes of Health. He is considered one of the founders of computational neuroscience, and was a pioneer in establishing the integrative functions of neuronal dendrites. Rall developed the use of cable theory in neuroscience, as well as passive and active compartmental modeling of the neuron. Rall studied physics at Yale University, from which he graduated with highest honors in 1943, and where he was Chairman of the Yale Political Union's Labor Party.''The History of Neuroscience in Autobiography''. Ed. Squire, Larry R. Volume 5. Academic Press, 1996. 553. He was involved with the Manhattan Project at the University of Chicago during the war, and subsequently worked with K.S. Cole at Woods Hole. He then moved to the University of Otago in Dunedin to work with John Carew Eccles for his PhD, and remained there after Eccles' departure for Australia. In 1954, he sp ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Biological Neuron Model
Biological neuron models, also known as a spiking neuron models, are mathematical descriptions of the properties of certain cells in the nervous system that generate sharp electrical potentials across their cell membrane, roughly one millisecond in duration, called action potentials or spikes (Fig. 2). Since spikes are transmitted along the axon and synapses from the sending neuron to many other neurons, spiking neurons are considered to be a major information processing unit of the nervous system. Spiking neuron models can be divided into different categories: the most detailed mathematical models are biophysical neuron models (also called Hodgkin-Huxley models) that describe the membrane voltage as a function of the input current and the activation of ion channels. Mathematically simpler are integrate-and-fire models that describe the membrane voltage as a function of the input current and predict the spike times without a description of the biophysical processes that shape ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
John Eccles (neurophysiologist)
Sir John Carew Eccles (27 January 1903 – 2 May 1997) was an Australian neurophysiologist and philosopher who won the 1963 Nobel Prize in Physiology or Medicine for his work on the synapse. He shared the prize with Andrew Huxley and Alan Lloyd Hodgkin. Life and work Early life Eccles was born in Melbourne, Australia. He grew up there with his two sisters and his parents: William and Mary Carew Eccles (both teachers, who home schooled him until he was 12). He initially attended Warrnambool High School originally published in ''Historical Records of Australian Science'', vol.13, no.4, 2001. (now Warrnambool College) (where a science wing is named in his honour), then completed his final year of schooling at Melbourne High School (Victoria), Melbourne High School. Aged 17, he was awarded a senior scholarship to study medicine at the University of Melbourne. As a medical undergraduate, he was never able to find a satisfactory explanation for the interaction of mind and body; he s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dendrites
Dendrites (from Greek δένδρον ''déndron'', "tree"), also dendrons, are branched protoplasmic extensions of a nerve cell that propagate the electrochemical stimulation received from other neural cells to the cell body, or soma, of the neuron from which the dendrites project. Electrical stimulation is transmitted onto dendrites by upstream neurons (usually via their axons) via synapses which are located at various points throughout the dendritic tree. Dendrites play a critical role in integrating these synaptic inputs and in determining the extent to which action potentials are produced by the neuron. Dendritic arborization, also known as dendritic branching, is a multi-step biological process by which neurons form new dendritic trees and branches to create new synapses. The morphology of dendrites such as branch density and grouping patterns are highly correlated to the function of the neuron. Malformation of dendrites is also tightly correlated to impaired nervous syste ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Neurons
A neuron, neurone, or nerve cell is an electrically excitable cell that communicates with other cells via specialized connections called synapses. The neuron is the main component of nervous tissue in all animals except sponges and placozoa. Non-animals like plants and fungi do not have nerve cells. Neurons are typically classified into three types based on their function. Sensory neurons respond to stimuli such as touch, sound, or light that affect the cells of the sensory organs, and they send signals to the spinal cord or brain. Motor neurons receive signals from the brain and spinal cord to control everything from muscle contractions to glandular output. Interneurons connect neurons to other neurons within the same region of the brain or spinal cord. When multiple neurons are connected together, they form what is called a neural circuit. A typical neuron consists of a cell body (soma), dendrites, and a single axon. The soma is a compact structure, and the axon and dend ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rafael Lorente De Nó
Rafael Lorente de Nó (April 8, 1902 – April 2, 1990) was a Spanish neuroscientist who advanced the scientific understanding of the nervous system with his seminal research. He was a member of the National Academy of Sciences. The National Academies Press called him "one of the premier neurophysiologists in the United States". Life and career Lorente de Nó was born in Zaragoza, Spain. He received his medical degree from the University of Madrid in 1923. He immigrated to the United States in 1931 when he accepted a position at the Central Institute for the Deaf in St. Louis. In 1936, he joined The Rockefeller University, then known as The Rockefeller Institute for Medical Research, as an associate. He was made an associate member in 1938 and a full member in 1941. Lorente de Nó was an active member of several academic societies, among them the American Physiological Society and the American Association of Anatomists. Awards and distinctions Lorente de Nó was elected ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
