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J Mizrahi - One of the best experts on this subject based on the ideXlab platform.
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generalized cable equation model for Myelinated Nerve Fiber
IEEE Transactions on Biomedical Engineering, 2005Co-Authors: P D Einziger, L M Livshitz, J MizrahiAbstract:Herein, the well-known cable equation for nonMyelinated axon model is extended analytically for Myelinated axon formulation. The Myelinated membrane conductivity is represented via the Fourier series expansion. The classical cable equation is thereby modified into a linear second order ordinary differential equation with periodic coefficients, known as Hill's equation. The general internal source response, expressed via repeated convolutions, uniformly converges provided that the entire periodic membrane is passive. The solution can be interpreted as an extended source response in an equivalent nonMyelinated axon (i.e., the response is governed by the classical cable equation). The extended source consists of the original source and a novel activation function, replacing the periodic membrane in the Myelinated axon model. Hill's equation is explicitly integrated for the specific choice of piecewise constant membrane conductivity profile, thereby resulting in an explicit closed form expression for the transmembrane potential in terms of trigonometric functions. The Floquet's modes are recognized as the Nerve Fiber activation modes, which are conventionally associated with the nonlinear Hodgkin-Huxley formulation. They can also be incorporated in our linear model, provided that the periodic membrane point-wise passivity constraint is properly modified. Indeed, the modified condition, enforcing the periodic membrane passivity constraint on the average conductivity only leads, for the first time, to the inclusion of the Nerve Fiber activation modes in our novel model. The validity of the generalized transmission-line and cable equation models for a Myelinated Nerve Fiber, is verified herein through a rigorous Green's function formulation and numerical simulations for transmembrane potential induced in three-dimensional Myelinated cylindrical cell. It is shown that the dominant pole contribution of the exact modal expansion is the transmembrane potential solution of our generalized model.
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transmission line model for Myelinated Nerve Fiber
International Conference of the IEEE Engineering in Medicine and Biology Society, 2005Co-Authors: P D Einziger, L M Livshitz, J MizrahiAbstract:Herein, the well-known cable equation for non-Myelinated axon model is extended analytically for Myelinated axon formulation. The classical cable equation is thereby modified into a linear second order ordinary differential equation with periodic coefficient, known as Hill's equation. Hill's equation exhibits periodic solutions, known as Floquet's modes. The Floquet's modes are recognized as the Nerve Fiber activation modes, which are conventionally associated with the nonlinear Hodgkin-Huxley formulation. They can also be incorporated in our linear model
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generalized transmission line model for Myelinated Nerve Fiber
IEEE Antennas and Propagation Society International Symposium, 2004Co-Authors: L M Livshitz, P D Einziger, M Dolgin, J MizrahiAbstract:The validity of the generalized transmission-line and cable equation models for Myelinated Nerve Fiber, is verified herein through rigorous Green's function formulation for transmembrane potential induced in a 3D Myelinated cylindrical cell. It is shown that the dominant pole contribution of the exact modal expansion is the transmembrane potential solution of our generalized model.
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novel cable equation model for Myelinated Nerve Fiber
International IEEE EMBS Conference on Neural Engineering, 2003Co-Authors: P D Einziger, L M Livshitz, A Dolgin, J MizrahiAbstract:The cable equation is capable of handling analytically linear and non-linear non-Myelinated axon models. Unfortunately, it hasn't been extended yet analytically for Myelinated axon model, which is crucially important for applications involving vertebrates. Herein, the well known non-Myelinated axon model is extended analytically by incorporating periodic membrane conductivity. The classical cable equation is thereby modified into a linear second order ordinary differential with periodic coefficient, known as Hill's equation. The general internal source response, expressed via repeated convolutions, uniformly converges provided that the periodic membrane is passive. The solution can be interpreted as an extended source response in an equivalent non-Myelinated axon (i.e., the response is governed by the classical cable equation). The extended source consists of the original source and a novel activation function, replacing the periodic membrane in the Myelinated axon model. Furthermore, the conductivity of the equivalent axon is the precise average of the periodic Myelinated axon conductivity. Hill's formulation is further reduced into Mathieu's equation for the specific choice of sinusoidal conductivity, thereby resulting in explicit closed form expression for the transmembrane potential.
P D Einziger - One of the best experts on this subject based on the ideXlab platform.
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generalized cable equation model for Myelinated Nerve Fiber
IEEE Transactions on Biomedical Engineering, 2005Co-Authors: P D Einziger, L M Livshitz, J MizrahiAbstract:Herein, the well-known cable equation for nonMyelinated axon model is extended analytically for Myelinated axon formulation. The Myelinated membrane conductivity is represented via the Fourier series expansion. The classical cable equation is thereby modified into a linear second order ordinary differential equation with periodic coefficients, known as Hill's equation. The general internal source response, expressed via repeated convolutions, uniformly converges provided that the entire periodic membrane is passive. The solution can be interpreted as an extended source response in an equivalent nonMyelinated axon (i.e., the response is governed by the classical cable equation). The extended source consists of the original source and a novel activation function, replacing the periodic membrane in the Myelinated axon model. Hill's equation is explicitly integrated for the specific choice of piecewise constant membrane conductivity profile, thereby resulting in an explicit closed form expression for the transmembrane potential in terms of trigonometric functions. The Floquet's modes are recognized as the Nerve Fiber activation modes, which are conventionally associated with the nonlinear Hodgkin-Huxley formulation. They can also be incorporated in our linear model, provided that the periodic membrane point-wise passivity constraint is properly modified. Indeed, the modified condition, enforcing the periodic membrane passivity constraint on the average conductivity only leads, for the first time, to the inclusion of the Nerve Fiber activation modes in our novel model. The validity of the generalized transmission-line and cable equation models for a Myelinated Nerve Fiber, is verified herein through a rigorous Green's function formulation and numerical simulations for transmembrane potential induced in three-dimensional Myelinated cylindrical cell. It is shown that the dominant pole contribution of the exact modal expansion is the transmembrane potential solution of our generalized model.
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transmission line model for Myelinated Nerve Fiber
International Conference of the IEEE Engineering in Medicine and Biology Society, 2005Co-Authors: P D Einziger, L M Livshitz, J MizrahiAbstract:Herein, the well-known cable equation for non-Myelinated axon model is extended analytically for Myelinated axon formulation. The classical cable equation is thereby modified into a linear second order ordinary differential equation with periodic coefficient, known as Hill's equation. Hill's equation exhibits periodic solutions, known as Floquet's modes. The Floquet's modes are recognized as the Nerve Fiber activation modes, which are conventionally associated with the nonlinear Hodgkin-Huxley formulation. They can also be incorporated in our linear model
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generalized transmission line model for Myelinated Nerve Fiber
IEEE Antennas and Propagation Society International Symposium, 2004Co-Authors: L M Livshitz, P D Einziger, M Dolgin, J MizrahiAbstract:The validity of the generalized transmission-line and cable equation models for Myelinated Nerve Fiber, is verified herein through rigorous Green's function formulation for transmembrane potential induced in a 3D Myelinated cylindrical cell. It is shown that the dominant pole contribution of the exact modal expansion is the transmembrane potential solution of our generalized model.
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novel cable equation model for Myelinated Nerve Fiber
International IEEE EMBS Conference on Neural Engineering, 2003Co-Authors: P D Einziger, L M Livshitz, A Dolgin, J MizrahiAbstract:The cable equation is capable of handling analytically linear and non-linear non-Myelinated axon models. Unfortunately, it hasn't been extended yet analytically for Myelinated axon model, which is crucially important for applications involving vertebrates. Herein, the well known non-Myelinated axon model is extended analytically by incorporating periodic membrane conductivity. The classical cable equation is thereby modified into a linear second order ordinary differential with periodic coefficient, known as Hill's equation. The general internal source response, expressed via repeated convolutions, uniformly converges provided that the periodic membrane is passive. The solution can be interpreted as an extended source response in an equivalent non-Myelinated axon (i.e., the response is governed by the classical cable equation). The extended source consists of the original source and a novel activation function, replacing the periodic membrane in the Myelinated axon model. Furthermore, the conductivity of the equivalent axon is the precise average of the periodic Myelinated axon conductivity. Hill's formulation is further reduced into Mathieu's equation for the specific choice of sinusoidal conductivity, thereby resulting in explicit closed form expression for the transmembrane potential.
Morton B Brown - One of the best experts on this subject based on the ideXlab platform.
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effect of aldose reductase inhibition on Nerve conduction and morphometry in diabetic neuropathy
Neurology, 1999Co-Authors: Joseph C Arezzo, Morton B BrownAbstract:Objective: To determine whether the aldose reductase inhibitor (ARI) zenarestat improves Nerve conduction velocity (NCV) and Nerve morphology in diabetic peripheral polyneuropathy (DPN). Methods: A 52-week, randomized, placebo-controlled, double-blinded, multiple-dose, clinical trial with the ARI zenarestat was conducted in patients with mild to moderate DPN. NCV was measured at baseline and study end. Contralateral sural Nerve biopsies were obtained at 6 weeks and at the study’s end for Nerve sorbitol measurement and computer-assisted light morphometry to determine Myelinated Nerve Fiber density (number of Fibers/mm 2 cross-sectional area) in serial bilateral sural Nerve biopsies. Results: Dose-dependent increments in sural Nerve zenarestat level and sorbitol suppression were accompanied by significant improvement in NCV. In a secondary analysis, zenarestat doses producing >80% sorbitol suppression were associated with a significant increase in the density of small-diameter ( Conclusions: Aldose reductase pathway inhibition improves NCV slowing and small Myelinated Nerve Fiber loss in DPN in humans, but >80% suppression of Nerve sorbitol content is required. Thus, even low residual levels of aldose reductase activity may be neurotoxic in diabetes, and potent ARIs such as zenarestat may be required to stop or reverse progression of DPN.
J A Halter - One of the best experts on this subject based on the ideXlab platform.
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an electrodiffusion model of the mammalian Myelinated Nerve Fiber
International Conference of the IEEE Engineering in Medicine and Biology Society, 1995Co-Authors: J A Halter, B ZupanAbstract:A new model of the mammalian Myelinated Nerve Fiber is presented which includes the representation of longitudinal electrodiffusion of component ions within the intra-axonal and periaxonal volumes. The model utilizes a non-uniform compartmental approximation to the detailed anatomy of the nodal and paranodal regions. The axonal membrane includes ionic pumps and multiple types of ionic channels whose spatial distribution and dynamics are derived from contemporary experimental studies. The model takes the form of a system of coupled non-linear parabolic partial differential equations with time-varying coefficients. A finite-difference approximation to this system is formed and solved utilizing an implicit numerical integration method. This model also includes a graphical user interface as well as a simulation management and optimization environment. The model reproduces conduction behavior seen in previous experimental and modeling efforts. Importantly, this model represents activity-dependent changes in ion concentration within the Myelinated Nerve Fiber. In particular, significant changes can be seen in the concentration of potassium ions in the restricted periaxonal volume contained between the inner layer of the myelin sheath and the axon.
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a distributed parameter model of the Myelinated Nerve Fiber
Journal of Theoretical Biology, 1991Co-Authors: J A Halter, J W ClarkAbstract:This paper presents a new model for the characterization of electrical activity in the nodal, paranodal and internodal regions of isolated amphibian and mammalian Myelinated Nerve Fibers. It differs from previous models in the following ways: (1) in its ability to incorporate detailed anatomical and electrophysiological data; (2) in its approach to the Myelinated Nerve Fiber as a multi-axial cable; and (3) in the numerical algorithm used to obtain distributed model equation solutions for potential and current. The morphometric properties are taken from detailed electron microscopic anatomical studies ( Berthold & Rydmark, 1983a, Experientia 39, 964–976). The internodal axolemma is characterized as an excitable membrane and model-generated nodal and internodal membrane action potentials are presented. A system of describing equations for the equivalent network model is derived, based on the application of Kirchoff's Current Law, which take the form of multiple cross-coupled parabolic partial differential equations. An implicit numerical integration method is developed and the numerical solution implemented on a parallel processor. Non-uniform spatial step sizes are used, enabling detailed representation of the nodal region while minimizing the number of total segments necessary to represent the overall Fiber. Conduction velocities of 20·2 m sec−1 at 20°C for a 15 μm diameter amphibian Fiber and 57·6 m sec−1 at 37°C for a 17·5 μm diameter mammalian Fiber are achieved, which agrees qualitatively with published experimental data at similar temperatures ( Huxley & Stampfli, 1949 , J. Physiol., Lond. 108, 315–339; Rasminsky, 1973 , Arch, Neurol. 28, 287–292). The simulation results demonstrate the ability of this model to produce detailed representations of the transaxonal, transmyelin and transFiber potentials and currents, as well as the longitudinal extra-axonal, periaxonal and intra-axonal currents. Also indicated is the potential contribution of the paranodal axolemma to nodal activity as well as the presence of significant longitudinal currents in the periaxonal space adjacent to the node of Ranvier.
Rudolf Reiter - One of the best experts on this subject based on the ideXlab platform.
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Nerve growth factor ngf and diabetic neuropathy in the rat morphological investigations of the sural Nerve dorsal root ganglion and spinal cord
Experimental Neurology, 1998Co-Authors: Jurgen W Unger, T Klitzsch, S Pera, Rudolf ReiterAbstract:Abstract A number of functions for Nerve growth factor (NGF) have been described over the past years, including its role for neuronal function and regeneration during toxic or metabolic neuropathies. In order to further assess the effects of NGF on the somatosensory system in diabetic neuropathy, the sural Nerve, dorsal root ganglia (DRG), and dorsal horn of the spinal cord were investigated by morphological and quantitative methods in rats after 12 weeks of uncontrolled streptozotocin-induced diabetes mellitus. The results from our study suggest a twofold effect of NGF: (1) In sural Nerve treatment with NGF (0.1 or 0.5 mg/kg) for 12 weeks was able to reverse distinct diabetes-related alterations in Myelinated Nerve Fiber morphology, such as myelin thickness. These changes occured in the entire Myelinated population of sensory Nerves and were not restricted to nociceptive Nerve Fibers. (2) The NGF effect on neurotransmitters of the sensory, nociceptive system was reflected by increased CGRP and substance P content in the DRG and in the dorsal horn of the spinal cord. No change of trkA receptor immunostaining was seen in DRGs of diabetic rats; however, a reduction of trkA immunoreactivity of DRG neurons was noted after long-term NGF treatment of healthy controls. The data demonstrate that NGF regulates a number of neuronal parameters along peripheral and central parts of the somatosensory pathway in the adult. This neurotrophic support may be essential for inducing functionally significant regenerative mechanisms in diabetic neuropathy.
