Hodgkin, A., and AF, H. A quantitative description of membrane current and its application to conduction and excitation in nerve. J Physiol 117, 4 (1952), 500--544.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....If the volume conductor is assumed infinite, the line source model is simplified considerably while retaining a reasonable accuracy compared with volume con101 duction theory for most types of muscle fibers. With the development of the first mathematical descriptions of the membrane potential [47] [20] realistic simulations were simplified. An efficient implementation of the line source model was presented in [62] where the convolution of the transmembrane current and the electrode weighting function are calculated in the frequency domain using the FFT algorithm. Aliasing may arise, ....

A. L. Hodgkin and A. F. Huxley, "A quantitative description of membrane current and its application to conduction and excitation in nerve," J. Physiol. (Lond.), vol. 117, pp. 500--544, 1952.

....our stimulus is long enough to sample the stimulus features reliably, citeStrong etal 98 Reliability and accuracy of spike timing in stochastic neuron models 4. 1 Introduction Following the formulation of the Hodgkin Huxley (HH) equations for modelling spike initiation in the squid giant axon [72] (see 2.2.1) research into the electrical activity of single neurons followed two main paths: the attempt to discover further macroscopic equations governing di#erent membrane currents (e.g. 199] and the attempt to investigate, and mathematically describe, the behavior of the ion channels ....

A.L. Hodgkin and A.F. Huxley. A quantitative description of membrane current and its application to conduction and excitation in nerve. J. Physiol., 117:500--544, 1952.

.... of these changes correspond to the time course and magnitude of the action potential [69, 68, 70] They then concluded their study and series of papers by introducing a model of excitability in a single cell, which accounts qualitatively for conduction and excitability of the squid giant axon [71]. Hodgkin and Huxley suggested a physical interpretation of the changes in ionic conductances using gating particles which can be either in an open or closed states, and are basically a ball and chain model of ion channels. However, their experimental work did not deal with single channels, ....

....of channels open at any given time is approximately equal to the probability that any one channel is in an open state. Hence, most neuron models use deterministic descriptions of the conductances arising from many channels of a given type. Following Hodgkin and Huxley s physical interpretation [68, 71], and Fitzhugh s work [50] a stochastic version of the HH model, which is based on simulating ion channel noise has been studied in detail as a more biophysically accurate description of the spiking mechanism [163, 42, 31, 170] and is presented in chapter 6. 2.4 The Computational Sketch of a ....

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A.L. Hodgkin and A.F. Huxley. A quantitative description of membrane current and its application to conduction and excitation in nerve. J. Physiol., 117:500--544, 1952.

....1. Introduction The aim of this chapter is to give an overview over mathematical modelling in neuroscience in general, with special emphasis on the early visual system. Mathematical models have been used in visual science for more than a century. Following the success of Hodgkin and Huxley [1] 50 years ago in describing axonal signal transport in nerve cells, arguably the greatest success story of mathematical biology, there seems to be a general consensus that mathematical modelling can be useful in neuroscience, including visual neuroscience. In the first part of the chapter I will ....

....the visual system, the full spatiotemporal response function must be considered [17] For an introduction to this, see Ch. 2 of Dayan and Abbott [9] An important use of descriptive models is to describe input in mechanistic models at a higher level of description. For example, Hodgkin and Huxley [1] used descriptive models of the voltage dependence of ion channels in their mechanistic mathematical modelling which addressed action potential generation in electrically excitable cells (cf. next section) Likewise, in Sec. 6 we use the descriptive DOG model to represent the retinal input in ....

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A.L. Hodgkin and A.F. Huxley, A quantitative description of membrane current and its application to conduction and excitation in nerve, Journal of Physiology 117 (1952) 500-544.

....time the di#usion and the reaction phenomena described by the models above. Hence, 2) becomes: u = div (D#(u) f(u) z) 3) On a physiological point of view, these equations are understood either as a mathematical approximation of the dynamical system introduced by Hodgkin and Huxley [11], as in [8] or as the result of some equilibrium equations that govern the conducting continuum, like in the so called bidomain model [24] The anisotropy of the ventricles is taken into account through the di#usion tensor D: D = d 0 .diag(1, #, #) in a local orthonormal basis (i, j, k) where i ....

A.L. Hodgkin and A.F. Huxley. A quantitative description of membrane current and its application to conduction and excitation in nerve. J. Physiol, 177:500--544, 1952.

....and the reaction phenomena described by the models above. Hence, 1) becomes: t u = div (Dr(u) f(u) z t z = ku z) 2) On a physiological point of view, these equations are understood either as a mathematical approximation of the dynamical system introduced by Hodgkin and Huxley [11], as in [10] or as the result of some equilibrium equations that govern the conducting continuum, like in the so called bidomain model [12] The anisotropy of the ventricles is taken into account through the diffusion tensor D: D = d 0 :diag(1; in a local orthonormal basis (i; j; k) where ....

A.L. Hodgkin and A.F. Huxley, "A quantitative description of membrane current and its application to conduction and excitation in nerve," J. Physiol, vol. 177, pp. 500--544, 1952.

....paradigm involved, yet adapting internal parameters. Effects of collective excitation of the modeled neurons produce signal processing capabilities. Its mathematical abstraction has similarities to Cellular Automata and Coupled Map Lattices [4] Originating from a system of differential equations [5], and being derived from a model used to describe the neural activity in visual cortex of the cat [6] the PCNN represents a discrete simplification of such a regular neural structure. Having emerged in the visual domain, it has primarily found applications in the field of image processing [7] ....

A. L. Hodgkin and A. F. Huxley, "A quantitative description of membrane current and its application to conduction and excitation in nerve," Journal of Physiology, vol. 117, pp. 500--544, 1952.

....di usion and the reaction phenomena described by the models above. Hence, 2) becomes: u = div (Dr(u) f(u) z z = u z) 3) On a physiological point of view, these equations are understood either as a mathematical approximation of the dynamical system introduced by Hodgkin and Huxley [10], as in [7] or as the result of some equilibrium equations that govern the conducting continuum, like in the so called bidomain model [11] The anisotropy of the ventricles is taken into account through the di usion tensor D: D = d 0 :diag(1; in a local orthonormal basis (i; j; k) where i ....

A.L. Hodgkin and A.F. Huxley, A quantitative description of membrane current and its application to conduction and excitation in nerve, J. Physiol, vol. 177, pp. 500544, 1952.

....work has been done by Hodgkin and Huxley. With an extensive series of experiments on the giant axon of the squid, they managed to describe the electrical dynamics of this neuron with a set of differential equations. This description is called the HH Model, and one can find the original work in [7]. As we know from the comprehensive book of Gerstner [5] this model, that describes the biophysical mechanisms of the cells can be simplified by assumptions, and has given birth to various formal spiking neuron models. Probably, the best known one is the leaky Integrate and Fire model (IF model) ....

M. Hodgkin and A.F. Huxley. A quantitative description of membrane current and its application to conduction and excitation in nerve. J. Physiol. (London), 117:500--544, 1952.

....and computational vision. One research goal in this field is to find out what are the biophysical mechanisms underlying information processing and how are these mechanisms used to perform specific tasks ( 78] p. 640) Although the first detailed models of a neuron were proposed in the fifties [58], compu tational biophysics is still at an early stage of development. The study of neuronal function is now approached at different levels, from that of the biophysics and biochemistry of mem branes to the level of ensembles of neurons. In particular, functional understanding is sought through ....

A. L. Hodgkin emd A. F. Huxley. A quantitative description of membrane current and its application to conduction and excitation in nerve. J. Physiol. ;Lond., 116:500-544, 1952.

....from nonlinear dynamics Recognition of the importance of nonlinear phenomena in physiological systems has a long history its beginnings are perhaps represented by the work of van der Pol and van der Mark [76] in the early part of the century. In Nobel Prize winning work, Hodgkin and Huxley [35] related the dynamics of excitable cell membranes to a system of coupled nonlinear differential equations. The recent realization that nonlinear dynamical systems can display deterministic chaos has had a strong impact on research in time series analysis in physiology and medicine [23] Whereas a ....

Hodgkin, AL. Huxley, AF. 1952 "A quantitative description of membrane current and its application ot conduction and excitation in nerve". J. Physiol. (Lond.) 117, 500-544.

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A.L. Hodgkin and A.F. Huxley. A quantitative description of membrane current and its application to conduction and excitation in nerve. Journal of Physiology, vol. 117, pp. 500-544, London 1952.

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Hodgkin A.L., Huxley, A.F., A quantitative description of membrane current and its application to conduction and excitation in nerve, Journal of Physiology, vol 117 pp 500--544, 1952.

....mathematics in describing living systems prevails in the biological and medicial research communities. Neuroscience is maybe the biological subdicipline where the use of mathematical techniques is most established and recognized. An important reason for this is the success of Hodgkin and Huxley [1] 50 years ago of describing signal transport in a single neuron (nerve cell) as a modified electrical circuit where the charge carriers are Na , K , Ca , Cl and other ions flowing through the neuron cell membrane. This mathematical formulation, denoted Hodgkin Huxley theory, could not only ....

A.L. Hodgkin and A.F. Huxley, A quantitative description of membrane current and its application to conduction and excitation in nerve, Journal of Physiology 117 (1952) 500--544.

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Hodgkin, A., and AF, H. A quantitative description of membrane current and its application to conduction and excitation in nerve. J Physiol 117, 4 (1952), 500--544.

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HODGKIN, A.L. & HUXLEY, A.F. (1952). A quantitative description of membrane current and its application to conduction and excitation in nerve. Journal of Physiology 117, 500-544.

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Hodgkin, A. L., & Huxley, A. F. (1952). A quantitative description of membrane current and its application to conduction and excitation in nerve. Journal of Physiology (London) , 117 , 500--544.

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Hodgkin F. and Huxley F. (1952) A quantitative description of membrane current and its application to conduction and excitation in nerve. J. Physiol. Lond., 117: 500-544.

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A. L. Hodgkin and A. F. Huxley, "A quantitative description of membrane current and application to conduction and excitation in nerve",Journal of Physiology, vol. 117, pp. 500-544, 1954.

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Hodgkin, A. L. and Huxley, A. F. (1952) "A Quantitative Description of Membrane Current and its Application to Conduction and Excitation in Nerve" Journal of Physiology 117: 500-544)

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A.L. Hodgkin and A.F. Huxley, "A quantitative description of membrane current and its application to conduction and excitation in nerve", J. Physiol. 117, 500--544, 1952.

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Hodgkin A.L. and Huxley A.F. A quantitative description of membrane current and its application to conduction and excitation in nerve. J. Physiol. (London), 117:500--544, 1952.

No context found.

A.L. Hodgkin and A.F. Huxley. A Quantitative Description of Membrane Current and its Application to Conduction and Excitation in Nerve. Journal of Physiology, 117:500--544, 1952.

No context found.

A. L. Hodgkin and A. F. Huxley. A quantitative description of membrane current and its application to conduction and excitation in nerve. Journal of Physiology (London), 117:500--544, 1952.

No context found.

A. Hodgkin and A. Huxley, "A quantitative description of membrane current and its application to conduction and excitation in nerve," J. Physiol. (Lond.), vol. 117, pp. 500-44, 1952.

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