Accuracy of neuronal interspike times calculated from a diffusion approximation
The theory of neuronal firing in Stein's model is outlined as well as the corresponding theory for a diffusion approximation which has the same first two infinitesimal moments. The diffusion approximation is derived from the discontinuous model in the limit of large input frequencies and small...
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| Published in | Journal of theoretical biology Vol. 83; no. 3; pp. 377 - 387 |
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| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
England
Elsevier Ltd
07.04.1980
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| Subjects | |
| Online Access | Get full text |
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| Abstract | The theory of neuronal firing in Stein's model is outlined as well as the corresponding theory for a diffusion approximation which has the same first two infinitesimal moments. The diffusion approximation is derived from the discontinuous model in the limit of large input frequencies and small postsynaptic potential amplitudes. A comparison of the calculated mean interspike intervals is made for various values of the threshold for firing and various input frequencies. The diffusion approximation can underestimate the interspike interval by up to 100% or severely overestimate it, depending on the input frequencies and the threshold. A general relation between the predictions of the two models is deduced. |
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| AbstractList | The theory of neuronal firing in Stein's model is outlined as well as the corresponding theory for a diffusion approximation which has the same first two infinitesimal moments. The diffusion approximation is derived from the discontinuous model in the limit of large input frequencies and small postsynaptic potential amplitudes. A comparison of the calculated mean interspike intervals is made for various values of the threshold for firing and various input frequencies. The diffusion approximation can underestimate the interspike interval by up to 100% or severely overestimate it, depending on the input frequencies and the threshold. A general relation between the predictions of the two models is deduced. |
| Author | Cope, Davis K. Tuckwell, Henry C. |
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| Cites_doi | 10.1103/RevModPhys.17.323 10.1007/BF02477011 10.1007/BF00326692 10.1016/S0006-3495(65)86709-1 10.2307/3212877 10.1016/0025-5564(78)90015-9 10.1016/S0006-3495(67)86574-3 10.1016/0022-5193(79)90138-3 10.1016/0022-5193(79)90174-7 10.1103/PhysRev.36.823 10.1007/BF00288750 10.1016/0006-8993(75)90796-9 10.1016/0025-5564(78)90027-5 10.1007/BF02476897 10.1214/aoms/1177728918 |
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| References | Abramowitz, Stegun (BIB1) 1964 Roy, Smith (BIB10) 1969; 31 Johannesma (BIB8) 1968 Tuckwell (BIB17) 1979; 77 Thomas (BIB15) 1975; 12 Wang, Uhlenbeck (BIB19) 1945; 17 Tuckwell (BIB16) 1975; 18 Gluss (BIB6) 1967; 29 Sato (BIB11) 1978; 39 Uhlenbeck, Ornstein (BIB18) 1930; 36 Stratonovich (BIB14) 1963; vol. I. Cope, Tuckwell (BIB4) 1979; 80 Stein (BIB12) 1965; 5 Yang, Chen (BIB20) 1978; 38 Holden (BIB7) 1976 Stein (BIB13) 1967; 7 Calvin (BIB3) 1975; 84 Capocelli, Ricciardi (BIB2) 1971; 8 Darling, Siegert (BIB5) 1953; 24 Keilson, Ross (BIB9) 1975; 3 Keilson (10.1016/0022-5193(80)90045-4_BIB9) 1975; 3 Capocelli (10.1016/0022-5193(80)90045-4_BIB2) 1971; 8 Tuckwell (10.1016/0022-5193(80)90045-4_BIB17) 1979; 77 Abramowitz (10.1016/0022-5193(80)90045-4_BIB1) 1964 Gluss (10.1016/0022-5193(80)90045-4_BIB6) 1967; 29 Cope (10.1016/0022-5193(80)90045-4_BIB4) 1979; 80 Wang (10.1016/0022-5193(80)90045-4_BIB19) 1945; 17 Holden (10.1016/0022-5193(80)90045-4_BIB7) 1976 Roy (10.1016/0022-5193(80)90045-4_BIB10) 1969; 31 Thomas (10.1016/0022-5193(80)90045-4_BIB15) 1975; 12 Stein (10.1016/0022-5193(80)90045-4_BIB12) 1965; 5 Yang (10.1016/0022-5193(80)90045-4_BIB20) 1978; 38 Stein (10.1016/0022-5193(80)90045-4_BIB13) 1967; 7 Uhlenbeck (10.1016/0022-5193(80)90045-4_BIB18) 1930; 36 Calvin (10.1016/0022-5193(80)90045-4_BIB3) 1975; 84 Sato (10.1016/0022-5193(80)90045-4_BIB11) 1978; 39 Tuckwell (10.1016/0022-5193(80)90045-4_BIB16) 1975; 18 Johannesma (10.1016/0022-5193(80)90045-4_BIB8) 1968 Darling (10.1016/0022-5193(80)90045-4_BIB5) 1953; 24 Stratonovich (10.1016/0022-5193(80)90045-4_BIB14) 1963; vol. I. |
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Statist doi: 10.1214/aoms/1177728918 contributor: fullname: Darling |
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| Title | Accuracy of neuronal interspike times calculated from a diffusion approximation |
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