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A simple algorithm to generate firing times for leaky integrate-and-fire neuronal model
Diffusion approximation of neuronal models revisited
1. | Institute of Physiology, Academy of Sciences of the Czech Republic, Videnska 1083, 142 20 Prague 4, Czech Republic |
References:
[1] |
J. M. Bower and D. Beeman, "The Book of GENESIS: Exploring Realistic Neural Models with the GEneral NEural Simulation System," Springer-Verlag, New York, 1998. |
[2] |
S. Ditlevsen and P. Lansky, Estimation of the input parameters in the Feller neuronal model, Phys. Rev. E (3), 73 (2006), 061910, 9 pp.
doi: 10.1103/PhysRevE.73.061910. |
[3] |
L. C. Giancarlo, M. Giugliano, W. Senn and S. Fusi, The response of cortical neurons to in vivo-like input current: Theory and experiment, Biol. Cybern., 99 (2008), 279-301. |
[4] |
F. B. Hanson and H. C. Tuckwell, Diffusion approximations for neuronal activity including synaptic reversal potentials, J. Theor. Neurobiol., 2 (1983), 127-153. |
[5] |
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 (1952), 500-544. |
[6] |
C. Koch and I. Segev, "Methods in Neuronal Modeling: From Synapses to Networks," Mass. MIT Press, Cambridge, 1989. |
[7] |
L. Kostal, Approximate information capacity of the perfect integrate-and-fire neuron using the temporal code, Brain Res., 1434 (2012), 136-141.
doi: 10.1016/j.brainres.2011.07.007. |
[8] |
V. Lanska and P. Lansky and C. E. Smith, Synaptic transmission in a diffusion model for neural activity, J. Theor. Biol., 166 (1994), 393-406. |
[9] |
P. Lansky, On approximations of Stein's neuronal model, J. Theor. Biol., 107 (1984), 631-647. |
[10] |
P. Lánský and V. Lánská, Diffusion approximation of the neuronal model with synaptic reversal potentials, Biol. Cybern., 56 (1987), 19-26.
doi: 10.1007/BF00333064. |
[11] |
P. Lánský, L. Sacerdote and F. Tomassetti, On the comparison of Feller and Ornstein-Uhlenbeck models for neural activity, Biol. Cybern., 73 (1995), 457-465. |
[12] |
M. Musila and P. Lánský, Generalized Stein's model for anatomically complex neurons, Biosystems, 25 (1991), 179-191.
doi: 10.1016/0303-2647(91)90004-5. |
[13] |
M. Musila and P. Lánský, On the interspike intervals calculated from diffusion approximations of Stein's neuronal model with reversal potentials, J. Theor. Biol., 171 (1994), 225-232.
doi: 10.1006/jtbi.1994.1226. |
[14] |
L. M. Ricciardi, "Diffusion Processes and Related Topics in Biology," Notes taken by Charles E. Smith, Lecture Notes in Biomathematics, Vol. 14, Springer-Verlag, Berlin-New York, 1977. |
[15] |
L. M. Ricciardi and L. Sacerdote, Ornstein-Uhlenbeck process as a model for neuronal activity, Biol. Cybern., 35 (1979), 1-9.
doi: 10.1007/BF01845839. |
[16] |
M. J. E. Richardson, Firing-rate response of linear and nonlinear integrate-and-fire neurons to modulated current-based and conductance-based synaptic drive, Phys. Rev. E, 76 (2007), 021919.
doi: 10.1103/PhysRevE.76.021919. |
[17] |
H. Risken, "The Fokker-Planck Equation: Methods of Solution and Applications," Springer Series in Synergetics, 18, Springer-Verlag, Berlin, 1989.
doi: 10.1007/978-3-642-61544-3. |
[18] |
M. Rudolph and A. Destexhe, An extended analytic expression for the membrane potential distribution of conductance-based synaptic noise, Neural Comput., 17 (2005), 2301-2315.
doi: 10.1162/0899766054796932. |
[19] |
R. F. Schmidt, "Fundamentals of Neurophysiology," Springer-Verlag, Berlin, 1978. |
[20] |
C. E. Smith and M. W. Smith, Moments of voltage trajectories for Stein's model with synaptic reversal potentials, J. Theor. Neurobiol., 3 (1984), 67-77. |
[21] |
R. B. Stein, A theoretical analysis of neuronal variability, Biophys. J., 5 (1965), 173-194.
doi: 10.1016/S0006-3495(65)86709-1. |
[22] |
H. C. Tuckwell, Synaptic transmission in a model for stochastic neural activity, J. Theor. Biol., 77 (1979), 65-81.
doi: 10.1016/0022-5193(79)90138-3. |
[23] |
H. C. Tuckwell and D. K. Cope, Accuracy of neuronal interspike times calculated from a diffusion approximation, J. Theor. Biol., 83 (1980), 377-387.
doi: 10.1016/0022-5193(80)90045-4. |
[24] |
H. C. Tuckwell and P. Lánský, On the simulation of biological diffusion processes, Comput. Biol. Med., 27 (1997), 1-7.
doi: 10.1016/S0010-4825(96)00033-9. |
[25] |
W. J. Wilbur and J. Rinzel, A theoretical basis for large coefficient of variation and bimodality in neuronal interspike interval distributions, J. Theor. Biol., 105 (1983), 345-368.
doi: 10.1016/S0022-5193(83)80013-7. |
show all references
References:
[1] |
J. M. Bower and D. Beeman, "The Book of GENESIS: Exploring Realistic Neural Models with the GEneral NEural Simulation System," Springer-Verlag, New York, 1998. |
[2] |
S. Ditlevsen and P. Lansky, Estimation of the input parameters in the Feller neuronal model, Phys. Rev. E (3), 73 (2006), 061910, 9 pp.
doi: 10.1103/PhysRevE.73.061910. |
[3] |
L. C. Giancarlo, M. Giugliano, W. Senn and S. Fusi, The response of cortical neurons to in vivo-like input current: Theory and experiment, Biol. Cybern., 99 (2008), 279-301. |
[4] |
F. B. Hanson and H. C. Tuckwell, Diffusion approximations for neuronal activity including synaptic reversal potentials, J. Theor. Neurobiol., 2 (1983), 127-153. |
[5] |
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 (1952), 500-544. |
[6] |
C. Koch and I. Segev, "Methods in Neuronal Modeling: From Synapses to Networks," Mass. MIT Press, Cambridge, 1989. |
[7] |
L. Kostal, Approximate information capacity of the perfect integrate-and-fire neuron using the temporal code, Brain Res., 1434 (2012), 136-141.
doi: 10.1016/j.brainres.2011.07.007. |
[8] |
V. Lanska and P. Lansky and C. E. Smith, Synaptic transmission in a diffusion model for neural activity, J. Theor. Biol., 166 (1994), 393-406. |
[9] |
P. Lansky, On approximations of Stein's neuronal model, J. Theor. Biol., 107 (1984), 631-647. |
[10] |
P. Lánský and V. Lánská, Diffusion approximation of the neuronal model with synaptic reversal potentials, Biol. Cybern., 56 (1987), 19-26.
doi: 10.1007/BF00333064. |
[11] |
P. Lánský, L. Sacerdote and F. Tomassetti, On the comparison of Feller and Ornstein-Uhlenbeck models for neural activity, Biol. Cybern., 73 (1995), 457-465. |
[12] |
M. Musila and P. Lánský, Generalized Stein's model for anatomically complex neurons, Biosystems, 25 (1991), 179-191.
doi: 10.1016/0303-2647(91)90004-5. |
[13] |
M. Musila and P. Lánský, On the interspike intervals calculated from diffusion approximations of Stein's neuronal model with reversal potentials, J. Theor. Biol., 171 (1994), 225-232.
doi: 10.1006/jtbi.1994.1226. |
[14] |
L. M. Ricciardi, "Diffusion Processes and Related Topics in Biology," Notes taken by Charles E. Smith, Lecture Notes in Biomathematics, Vol. 14, Springer-Verlag, Berlin-New York, 1977. |
[15] |
L. M. Ricciardi and L. Sacerdote, Ornstein-Uhlenbeck process as a model for neuronal activity, Biol. Cybern., 35 (1979), 1-9.
doi: 10.1007/BF01845839. |
[16] |
M. J. E. Richardson, Firing-rate response of linear and nonlinear integrate-and-fire neurons to modulated current-based and conductance-based synaptic drive, Phys. Rev. E, 76 (2007), 021919.
doi: 10.1103/PhysRevE.76.021919. |
[17] |
H. Risken, "The Fokker-Planck Equation: Methods of Solution and Applications," Springer Series in Synergetics, 18, Springer-Verlag, Berlin, 1989.
doi: 10.1007/978-3-642-61544-3. |
[18] |
M. Rudolph and A. Destexhe, An extended analytic expression for the membrane potential distribution of conductance-based synaptic noise, Neural Comput., 17 (2005), 2301-2315.
doi: 10.1162/0899766054796932. |
[19] |
R. F. Schmidt, "Fundamentals of Neurophysiology," Springer-Verlag, Berlin, 1978. |
[20] |
C. E. Smith and M. W. Smith, Moments of voltage trajectories for Stein's model with synaptic reversal potentials, J. Theor. Neurobiol., 3 (1984), 67-77. |
[21] |
R. B. Stein, A theoretical analysis of neuronal variability, Biophys. J., 5 (1965), 173-194.
doi: 10.1016/S0006-3495(65)86709-1. |
[22] |
H. C. Tuckwell, Synaptic transmission in a model for stochastic neural activity, J. Theor. Biol., 77 (1979), 65-81.
doi: 10.1016/0022-5193(79)90138-3. |
[23] |
H. C. Tuckwell and D. K. Cope, Accuracy of neuronal interspike times calculated from a diffusion approximation, J. Theor. Biol., 83 (1980), 377-387.
doi: 10.1016/0022-5193(80)90045-4. |
[24] |
H. C. Tuckwell and P. Lánský, On the simulation of biological diffusion processes, Comput. Biol. Med., 27 (1997), 1-7.
doi: 10.1016/S0010-4825(96)00033-9. |
[25] |
W. J. Wilbur and J. Rinzel, A theoretical basis for large coefficient of variation and bimodality in neuronal interspike interval distributions, J. Theor. Biol., 105 (1983), 345-368.
doi: 10.1016/S0022-5193(83)80013-7. |
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