Derivation of the Cable Equation and the Ac Length Constant

2001 ◽  
pp. 412-416
Author(s):  
Richard D. Veenstra
Author(s):  
Avinash K. Mittal ◽  
Lokendra K. Balyan ◽  
Manoj K. Panda ◽  
Parnika Shrivastava ◽  
Harvindra Singh

2015 ◽  
Vol 460 (1) ◽  
pp. 8-11 ◽  
Author(s):  
V. S. Kuzmin ◽  
Yu. V. Egorov ◽  
V. M. Karimova ◽  
L. V. Rosenshtraukh

2003 ◽  
Vol 91 (1) ◽  
Author(s):  
H. D. Hansen ◽  
U. I. Uggerhøj ◽  
C. Biino ◽  
S. Ballestrero ◽  
A. Mangiarotti ◽  
...  

1981 ◽  
Vol 4 (2) ◽  
pp. 157-161 ◽  
Author(s):  
T. Magchielse ◽  
J. Hooisma ◽  
H. Muijser

1979 ◽  
Vol 78 (1) ◽  
pp. 1-27
Author(s):  
MAURIZIO MIROLLI

1. The input properties and the response to stretch of a coxal receptor, the S fibre of the crab Scylla serrata, were studied using two and three intracellular microelectrodes. 2. In the relaxed receptor the transmembrane potential ranged from about −60 to −70 mV, and the input resistance, RT, from 1 to 3 MΩ. The input IV relationship, studied by injecting slow-rising current ramps, was not linear either in the hyperpolarizing or in the depolarizing quadrants. 3. Low values of RT and a linear IV relationship were associated with a large leakage of the microelectrodes. 4. The response to step stretches was complex, consisting of an initial depolarizing transient, Vα, and a steady-state depolarizing plateau, V8. Both Vα and V8 propagated with decrement in the fibre which was about 9 mm long. The spatial decrement of Vα and V8 was equal to that of the response to distally injected current pulses of comparable duration and amplitude. 5. On the basis of the spatial decrement of both Vα and V8 the dendrite can be considered equivalent, for current flowing from its distal to its proximal end, to a semi-infinite cable having a length constant of between 4 and 6 cm. 6. The voltage transients recorded in response to long current pulses reached 84% of their final value in a time (t84%) ranging from 150 to 180 ms in fibres in which RT was 2 Mω or larger. t84% was smaller in fibres having a lower RT. 7. The time course of the transients recorded in response to injected current pulses deviated from the semi-infinite cable model in a manner suggesting the presence of a partial short circuit. For this reason the membrane time constant of the fibre is considered larger (by an undetermined amount) than t84%. 8. The fibre presented less resistance to current flowing from its proximal to its distal end than to current flowing in the opposite direction. For this reason, and also because of the time course of the voltage transient, it is concluded that the distal sensory endings of the fibre have the properties of a leaky end termination, even in the non-stimulated receptors.


1999 ◽  
Vol 87 (2) ◽  
pp. 119-136 ◽  
Author(s):  
T.I. Tóth ◽  
V. Crunelli
Keyword(s):  

2013 ◽  
Vol 57 (1) ◽  
pp. 1-9 ◽  
Author(s):  
Carmen Ionescu ◽  
Emilian Panaitescu ◽  
Mihai Stoicescu

Abstract In most of the applications involving neural networks, the main problem consists in finding an optimal procedure to reduce the real neuron to simpler models which still express the biological complexity but allow highlighting the main characteristics of the system. We effectively investigate a simple reduction procedure which leads from complex models of Hodgkin-Huxley type to very convenient binary models of Hopfield type. The reduction will allow to describe the neuron interconnections in a quite large network and to obtain information concerning its symmetry and stability. Both cases, on homogeneous voltage across the membrane and inhomogeneous voltage along the axon will be tackled out. Few numerical simulations of the neural flow based on the cable-equation will be also presented.


2014 ◽  
Vol 15 (S1) ◽  
Author(s):  
Alain Destexhe ◽  
Francesca Barbieri ◽  
Claude Bedard

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