Geodesic
A~sequence of reductions in mathematical models of primary visual cortex
Matematičeskaâ biologiâ i bioinformatika, Tome 5 (2010), pp. 150-161.

Voir la notice de l'article provenant de la source Math-Net.Ru

A hierarchical sequence of primary visual cortex models is constructed, each model processing the information about visual stimulus orientation. The most detailed model is based on the Conductance-Based Refractory Density (CBRD) approach for a population of realistic, Hodgkin–Huxley-like neurons. Populations in a continuum distributed along the cortical surface interact by means of synaptic connections. A certain set of parameters of connections and stimulation according to the pinwheel structure provides the effect of orientation tuning for different levels of stimulus contrast. The model realistically reproduces the stationary and transient regimes of cortical activity. The reduction of the model includes: 1) adaptive two-compartmental excitatory neurons and non-adaptive one-compartmental interneurons are substituted by the leaked integrate-and-fire (LIF) neurons; 2) pinwheel-like architecture of orientational hypercolumns is approximated by a ring of visual stimulus intensity gradient orientations; 3) the second order synaptic kinetics is reduced to transient kinetics; 4) the consideration of excitatory and inhibitory populations is reduced to only one explicit population; 5) the CBRD approach for LIF-neurons is substituted by the Fokker–Planck (FP) equation for neuronal density in the membrane potential space; 6) the FP equation is approximated by the stationary rate-current-conductance (f-I-G) dependence, and 7) f-I-G-function is reduced to threshold-linear f-I-function. Finally, the reduction leads to the canonical firing-rate ring-model. The comparison reveals the distinct roles of assumptions made during the reduction procedure. 
@article{MBB_2010_5_a7,
     author = {A. V. Chizhov},
     title = {A~sequence of reductions in mathematical models of primary visual cortex},
     journal = {Matemati\v{c}eska\^a biologi\^a i bioinformatika},
     pages = {150--161},
     publisher = {mathdoc},
     volume = {5},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MBB_2010_5_a7/}
}
TY  - JOUR
AU  - A. V. Chizhov
TI  - A~sequence of reductions in mathematical models of primary visual cortex
JO  - Matematičeskaâ biologiâ i bioinformatika
PY  - 2010
SP  - 150
EP  - 161
VL  - 5
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MBB_2010_5_a7/
LA  - ru
ID  - MBB_2010_5_a7
ER  - 
%0 Journal Article
%A A. V. Chizhov
%T A~sequence of reductions in mathematical models of primary visual cortex
%J Matematičeskaâ biologiâ i bioinformatika
%D 2010
%P 150-161
%V 5
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MBB_2010_5_a7/
%G ru
%F MBB_2010_5_a7
A. V. Chizhov. A~sequence of reductions in mathematical models of primary visual cortex. Matematičeskaâ biologiâ i bioinformatika, Tome 5 (2010), pp. 150-161. http://geodesic.mathdoc.fr/item/MBB_2010_5_a7/

[1] Hubel D. H., Wiesel T. N., “Reception fields, binocular interaction and functional architecture in the cats visual cortex”, J. Physiol. Lond., 160 (1962), 106–154

[2] Hansel D., Sompolinsky H., “Modeling feature selectivity in local cortical circuits”, Methods in neuronal modeling: From synapses to networks, 2nd ed., eds. Koch C., Segev I., MIT Press, Cambridge, MA, 1998, 499–567

[3] Chizhov A. V., Graham L. J., “Efficient evaluation of neuron populations receiving colorednoise current based on a refractory density method”, Phys. Rev. E, 77 (2008), 011910 <ext-link ext-link-type='doi' href='https://doi.org/10.1103/PhysRevE.77.011910'>10.1103/PhysRevE.77.011910</ext-link>

[4] Chizhov A. V., Graham L. J., “Population model of hippocampal pyramidal neurons, linking a refractory density approach to conductance-based neurons”, Phys. Rev. E, 75 (2007), 011924 <ext-link ext-link-type='doi' href='https://doi.org/10.1103/PhysRevE.75.011924'>10.1103/PhysRevE.75.011924</ext-link><ext-link ext-link-type='mr-item-id' href='http://mathscinet.ams.org/mathscinet-getitem?mr=2324651'>2324651</ext-link>

[5] Chizhov A. V., “Model populyatsii neironov kak element krupnomasshtabnoi neiroseti”, Neirokompyutery: razrabotka, primenenie, 2004, no. 2–3, 60–68

[6] Omurtag A., Knight B. W., Sirovich L., “On the Simulation of Large Populations of Neurons”, Journal of Computational Neuroscience, 8 (2000), 51–63 <ext-link ext-link-type='doi' href='https://doi.org/10.1023/A:1008964915724'>10.1023/A:1008964915724</ext-link><ext-link ext-link-type='zbl-item-id' href='https://zbmath.org/?q=an:1036.92010'>1036.92010</ext-link>

[7] Tuckwell H. C., Stochastic Processes in the Neurosciences, SIAM, Philadelphia, 1989 <ext-link ext-link-type='mr-item-id' href='http://mathscinet.ams.org/mathscinet-getitem?mr=1002192'>1002192</ext-link>

[8] Bakharev B. V., Zhadin M. N., Agladze N. N., “Ritmicheskie protsessy v bioelektricheskoi aktivatsii kory golovnogo mozga pri reaktsii aktivatsii: kachestvennyi nelineinyi analiz s uchetom refrakternosti”, Biofizika, 46:4 (2001), 715–723

[9] Rowe D. L., Robinson P. A., Rennie C. J., “Estimation of neurophysiological parameters from the waking EEG using a biophysical model of brain dynamics”, J. Theor. Biology, 231:3 (2004), 413–433 <ext-link ext-link-type='doi' href='https://doi.org/10.1016/j.jtbi.2004.07.004'>10.1016/j.jtbi.2004.07.004</ext-link><ext-link ext-link-type='mr-item-id' href='http://mathscinet.ams.org/mathscinet-getitem?mr=2106496'>2106496</ext-link>

[10] Dudkin A. O., Sbitnev V. I., “Coupled map lattice simulation of epileptogenesis in hippocampal slices”, Biological Cybernetics, 78:6 (1998), 479–486 <ext-link ext-link-type='doi' href='https://doi.org/10.1007/s004220050451'>10.1007/s004220050451</ext-link><ext-link ext-link-type='mr-item-id' href='http://mathscinet.ams.org/mathscinet-getitem?mr=1706451'>1706451</ext-link><ext-link ext-link-type='zbl-item-id' href='https://zbmath.org/?q=an:0905.92011'>0905.92011</ext-link>

[11] Nycamp D. Q., Tranchina D., “A Population Density Approach That Facilitates Large-Scale Modeling of Neural Networks: Analysis and an Application to Orientation Tuning”, Journal of Computational Neuroscience, 8 (2000), 19–50 <ext-link ext-link-type='doi' href='https://doi.org/10.1023/A:1008912914816'>10.1023/A:1008912914816</ext-link>

[12] Brunel N. and Hakim V., “Fast global oscillations in networks of integrate-and-fire neurons with low firing rates”, Neural Comput., 11 (1999), 1621–1671 <ext-link ext-link-type='doi' href='https://doi.org/10.1162/089976699300016179'>10.1162/089976699300016179</ext-link>

[13] Borg-Graham L., “Interpretations of data and mechanisms for hippocampal pyramidal cell models”, Cerebral Cortex, 13 (1999), 19–138

[14] Kopell N., Ermentrout G. B., Whittington M. A., Traub R. D., “Gamma rhythms and beta rhythms have different synchronization properties”, Neurobiology, 97:4 (2000), 1867–1872

[15] Kang K., Shelley M. and Sompolinsky H., “Mexican hats and pinwheels in visual cortex”, PNAS, 100:5 (2003), 2848–2853 <ext-link ext-link-type='doi' href='https://doi.org/10.1073/pnas.0138051100'>10.1073/pnas.0138051100</ext-link>

[16] Chizhov A. V., “Svyaz postsinapticheskikh potentsialov i tokov, izmeryaemykh poluvnutrikletochno (metodom patch-clamp)”, Biofizika, 49:5 (2004), 877–880 <ext-link ext-link-type='mr-item-id' href='http://mathscinet.ams.org/mathscinet-getitem?mr=2466468'>2466468</ext-link>