Mathematical Biosciences and Engineering (MBE)

A leaky integrate-and-fire model with adaptation for the generation of a spike train
Pages: 483 - 493, Issue 3, June 2016

doi:10.3934/mbe.2016002      Abstract        References        Full text (600.6K)           Related Articles

Aniello Buonocore - Dipartimento di Matematica e Applicazioni “R. Caccioppoli”, Università di Napoli Federico II, Via Cintia, 80126 Napoli, Italy (email)
Luigia Caputo - Dipartimento di Matematica e Applicazioni, Università di Napoli Federico II, Via Cintia, Napoli, Italy (email)
Enrica Pirozzi - Dipartimento di Matematica e Applicazioni, Università di Napoli Federico II, Via Cintia, Napoli, Italy (email)
Maria Francesca Carfora - Istituto per le Appplicazioni del Calcolo "Mauro Picone", Consiglio Nazionale delle Ricerche, Via Pietro Castellino, Napoli, Italy (email)

1 J. Benda and A. W. M. Herz, A universal model for spike-frequency adaptation, Neural Computation, 15 (2003), 2523-2564.
2 R. Brette and W. Gerstner, Adaptive exponential integrate-and-fire model as an effective description of neuronal activity, Journal of Neurophysiology, 94 (2005), 3637-3642.
3 D. A. Brown and P. R. Adams, Muscarinic supression of a novel voltage-sensitive K+ current in a vertebrate neuron, Nature, 183 (1980), 673-676.
4 A. Buonocore, L. Caputo, E. Pirozzi and M. F. Carfora, A simple algorithm to generate firing times for leaky integrate-and-fire neuronal model, Mathematical Biosciences and Engineering, 11 (2014), 1-10.       
5 A. Buonocore, L. Caputo, E. Pirozzi and L. M. Ricciardi, On a generalized leaky integrate-and-fire model for single neuron activity, in Computer Aided Systems Theory - EUROCAST 2005, Lecture Notes in Computer Science, 5717, Springer, Berlin-Heidelberg, 2009, 152-158.
6 A. Buonocore, L. Caputo, E. Pirozzi and L. M. Ricciardi, On a stochastic leaky integrate-and-fire neuronal model, Neural Computation, 22 (2010), 2558-2585.       
7 A. Buonocore , A. G. Nobile and L. M. Ricciardi, A new integral equation for the evaluation of first-passage-time probability densities, Advances in Applied Probability, 19 (1987), 784-800.       
8 A. N. Burkitt, A review of the integrate-and-fire neuron model: I. Homogeneous synaptic input, Biological Cybernetics, 95 (2006), 1-19.       
9 M. J. Chacron, K. Pakdaman and A. Longtin, Interspike interval correlations, memory, adaptation, and refractoriness in a leaky integrate-and-fire model with threshold fatigue, Neural Computation, 15 (2003), 253-278.
10 S. M. Crook, G. B. Ermentrout and J. M. Bower, Spike frequency adaptation affects the synchronization properties of networks of cortical oscillators, Neural Computation, 10 (1998), 837-854.
11 Y. Dong, F. Mihalas and E. Niebur, Improved integral equation solution for the first passage time of leaky integrate-andfire neurons, Neural Computation, 23 (2011), 421-434.       
12 B. Ermentrout, M. Pascal and B. Gutkin, The effects of spike frequency adaptation and negative feedback on the synchronization of neural oscillators, Neural Computation, 13 (2001), 1285-1310.
13 I. A. Fleidervish, A. Friedman and M. J. Gutnick, Slow inactivation of Na+ current and slow cumulative spike adaptation in mouse and guinea-pig neocortical neurones in slices, The Journal of Physiology, 493 (1996), 83-97.
14 G. Fuhrmann, H. Markram and M. Tsodyks, Spike frequency adaptation and neocortical rhythms, Journal of Neurophysiology, 88 (2002), 761-770.
15 R. Granit, D. Kernell and G. K. Shortess, Quantitative aspects of repetitive firing of mammalian motoneurones, caused by injected currents, The Journal of Physiology, 168 (1963), 911-931.
16 B. Hille, Ion Channels of Excitable Membranes, Sinauer Associates, Sunderland, MA, 2001.
17 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.
18 A. V. Holden, Models of the Stochastic Activity of Neurones, Springer-Verlag, New York, 1976.       
19 R. Jolivet, R. Kobayashi, A. Rauch, R. Naud, S. Shinomoto and W. Gerstner, A benchmark test for a quantitative assessment of simple neuron models, Journal of Neuroscience Methods, 169 (2008), 417-424.
20 R. Kobayashi, Y. Tsubo and S. Shinomoto, Made-to-order spiking neuron model equipped with a multi-timescale adaptive threshold, Frontiers in Computational Neuroscience, 3 (2009), p9.
21 G. La Camera, A. Rauch, H. R. Luescher, W. Senn and S. Fusi, Minimal models of adapted neuronal response to in vivo-like input currents, Neural Computation, 16 (2004), 2101-2124.
22 Y. H. Liu and X. J. Wang, Spike-frequency adaptation of a generalized leaky integrate-and-fire model neuron, Journal of Computational Neuroscience, 10 (2001), 24-45.
23 D. V. Madison and R. A. Nicoll, Control of the repetitive discharge of rat CA1 pyramidal neurones in vitro, The Journal of Physiology, 354 (1984), 319-331.
24 A. G. Nobile, L. M. Ricciardi and L. Sacerdote, Exponential trends of Ornstein-Uhlenbeck first-passage-time densities, Journal of Applied Probability, 22 (1985), 360-369.       
25 R. K. Powers, A. Sawczuk, J. R. Musick and M. D. Binder, Multiple mechanisms of spike-frequency adaptation in motoneurones, Journal of Physiology, 93 (1999), 101-114.
26 A. Rauch, G. La Camera, H. R. Luescher, W. Senn and S. Fusi, Neocortical cells respond as integrate-and-fire neurons to in vivo-like input currents, Journal of Neurophysiology, 90 (2003), 1598-1612.
27 L. Sacerdote and M. Giraudo, Stochastic integrate and fire models: A review on mathematical methods and their applications, in Stochastic Biomathematical Models with Applications to Neuronal Modeling (eds. Bachar, Batzel and Ditlevsen), Lecture Notes in Mathematics 2058, Springer, Berlin-Heidelberg (2013), 99-148.       
28 P. Sah, Ca2+-activated K+ currents in neurones: Types, physiological roles and modulation, Trends in Neurosciences, 19 (1996), 150-154.
29 S. Shinomoto, Y. Sakai and S. Funahashi, The Ornstein-Uhlenbeck process does not reproduce spiking statistics of neurons in prefrontal cortex, Neural Computation, 11 (1999), 935-951.
30 W. R. Softky and C. Koch, The highly irregular firing of cortical cells is inconsistent with temporal integration of random EPSPs, Journal of Neurosciences, 13 (1993), 334-350.
31 H. C. Tuckwell, Introduction to Theoretical Neurobiology, Vol. 2, Cambridge University Press, Cambridge, England, 1988.       

Go to top