神经元模型对比分析

徐泠风; 李传东; 陈玲

doi:10.7498/aps.65.240701

摘要

近年来，生物神经元模型的建立与应用已经获得了越来越多的关注，逐渐成为神经科学的一个重要分支.神经元模型不仅在仿生学、存储器设计、逻辑运算、信号处理等方面有重大应用，对分析研究神经系统的动力学特性也具有重要意义.本文总结了自1907年第一个神经元模型建立以来的发展历程，归纳出17种最具代表性的数学模型，分为电导依赖模型和非电导依赖模型进行比较分析，重点展示包括最新神经芯片TrueNorth上的神经元在内的5种经典模型，分析其仿真特性，以及电路实现的需求，方便研究者根据具体需求选择和改进神经元模型.

关键词:

作者及机构信息

1.
西南大学电子信息工程学院, 重庆 400715;

2.
中国科学技术大学信息科学技术学院, 合肥 230027

通信作者: 李传东, licdswu@163.com

基金项目: 国家自然科学基金（批准号：61374078，61503307）、重庆市基础与前沿技术研究项目（批准号：cstc2015jcyjBX0052，cstc2016jcyjA0261）、中央高校基本科研业务费专项资金（批准号：XDJK2015C079）和博士后科学基金（批准号：2016M590854）资助的课题.

参考文献

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[2]	Cassidy A S, Merolla P, Arthur J V, Esser S K, Jackson B, Alvarez-Icaza R, Datta P, Sawada Jun, Wong T M, Feldman V, Amir A, Rubin D B, Akopyan F, McQuinn E, Risk W P, Modha D S 2013 The 2013 International Joint Conference on Neural Networks (IJCNN) Dallas, USA, August 4-9, 2013 p1
[3]	Smith G D, Cox C L, Sherman S M, Rinzel J 2000 J. Neurophysiol. 83 588
[4]	Fourcaud-Trocmé D, Hansel D, van Vreeswijk C, Brunel N 2003 J. Neurosci. 23 11628
[5]	Lapicque L 1907 J. Physiol. Pathol. Gen. 9 620
[6]	Abbott L F 1999 Brain Res. Bull. 50 303
[7]	Brunel N, van Rossum M C W 2007 Biol. Cybern. 97 337
[8]	McCulloch W S, Pitts W 1943 Bull. Math. Biol. 5 115
[9]	Bernstein J 1902 Pflgers Arch. 92 521
[10]	Hodgkin A L 1939 J. Physiol. 94 560
[11]	Hodgkin A L, Katz B 1949 J. Physiol. 108 37
[12]	Bonhoeffer K F 1948 J. Gen. Physiol. 32 69
[13]	Hodgkin A L 1948 J. Physiol. 107 165
[14]	Hebb D O 1949 The Organization of Behavior:A Neuropsychological Theory (1st Ed.) (London:Chapman & Hall) pp17-78
[15]	Hodgkin A L, Huxley A F, Katz B 1952 J. Physiol. 116 424
[16]	Eccles J C, Eccles R M, Lundberg A 1957 J. Physiol. 137 22
[17]	Rosenblatt F 1958 Psychol. Rev. 65 386
[18]	Fitzhugh R 1960 J. Gen. Physiol. 43 867
[19]	Nagumo J, Arimoto S, Yoshizawa S 1962 Proc. IRE 50 2061
[20]	Fuortes M G F, Mantegazzini F 1962 J. Gen. Physiol. 45 1163
[21]	Stein R B 1965 Biophys. J. 5 173
[22]	Geisler C D, Goldberg J M 1966 Biophys. J. 6 53
[23]	Rall W 1967 J. Neurophysiol. 30 1138
[24]	Stein R B 1967 Proc. R. Soc. Lond. B:Biol. Sci. 167 64
[25]	Knight B W 1972 J. Gen. Physiol. 59 734
[26]	Kernell D, Sj·holm H 1973 Acta Physiol. Scand. 87 40
[27]	Hodgkin A L, Huxley A F 1952 J. Physiol. 117 500
[28]	Shapiro B I, Lenherr F K 1972 Biophys. J. 12 1145
[29]	Krinskii V I, Iu M K 1973 Biofizika 18 506
[30]	Krinskii V I, Iu M K 1973 Biofizika 18 878
[31]	Plant R E, Kim M 1976 Biophys. J. 16 227
[32]	Plant R E 1976 Computer Programs Biomed. 6 85
[33]	Rinzel J 1978 Studies in Mathematical Biology (1st Ed.) (Washington:Mathematical association of America) pp1-66
[34]	Fitzhugh R 1961 Biophys. J. 1 445
[35]	Connor J A, Stevens C F 1971 J. Physiol. 213 31
[36]	Connor J A, Walter D, Mckown R 1977 Biophys. J. 18 81
[37]	Morris C, Lecar H 1981 Biophys. J. 35 193
[38]	Rinzel J, Troy W C 1982 J. Chem. Phys. 76 1775
[39]	Chay T R 1985 Physica D 16 233
[40]	Chay T R, Keizer J 1983 Biophys. J. 42 181
[41]	Ermentrout G B, Kopell N 1986 SIAM J. Appl. Math. 46 233
[42]	Hindmarsh J L, Rose R M 1982 Nature 296 162
[43]	Hindmarsh J L, Rose R M 1984 Proc. R. Soc. Lond. B:Biol. Sci. 221 87
[44]	Rose R M, Hindmarsh J L 1985 Proc. R. Soc. Lond. B:Biol. Sci. 225 161
[45]	Rose R M, Hindmarsh J L 1989 Proc. R. Soc. Lond. B:Biol. Sci. 237 267
[46]	Rose R M, Hindmarsh J L 1989 Proc. R. Soc. Lond. B:Biol. Sci. 237 289
[47]	Rose R M, Hindmarsh J L 1989 Proc. R. Soc. Lond. B:Biol. Sci. 237 313
[48]	Chay T R, Rinzel J 1985 Biophys. J. 47 357
[49]	Connor J A, Stevens C F 1971 J. Physiol. 213 1
[50]	Connor J A, Stevens C F 1971 J. Physiol. 213 21
[51]	Connor J 1975 J. Neurophysiol. 38 922
[52]	Jack J J B, Noble D, Tsien R W 1975 Electric Current Flow in Excitable Cells (1st Ed.) (Oxford:Clarendon Press) pp132-224
[53]	Connors B W, Gutnick M J, Prince D A 1982 J. Neurophysiol. 48 1302
[54]	Plant R E 1978 Biophys. J. 21 217
[55]	Rinzel J 1985 Ordinary and Partial Differential Equations (1st Ed.) (Berlin:Springer-Verlag) pp304-316
[56]	Rinzel J 1985 Fed. Proc. 44 2944
[57]	Mircea S, Jones E G, Llinás R R 1990 Thalamic Oscillations and Signaling (1st Ed.) (New York:John Wiley) pp1-43
[58]	Rinzel J 1987 Mathematical Topics in Population Biology, Morphogenesis and Neurosciences (1st Ed.) (Berlin:Springer) pp267-281
[59]	Connors B W, Gutnick M J 1990 Trends Neurosci. 13 99
[60]	Rall W 1989 Methods in Neuronal Modeling:from Ions to Networks (2nd Ed.) (Cambridge:MIT Press) pp9-62
[61]	Ermentrout B 1996 Neural Comput. 8 979
[62]	Hoppensteadt F C, Izhikevich E M 1997 Weakly Connected Neural Networks (1st Ed.) (New York:Springer-Verlag) pp25-101
[63]	Rinzel J, Ermentrout G B 1989 Methods in Neuronal Modeling (1st Ed.) (Cambridge:MIT Press) pp135-169
[64]	Roth A, Häusser M 2001 J. Physiol. 535 445
[65]	Chay T R 1991 Biopolymers 31 1483
[66]	Stevens C F, Zador A M 1998 Proceedings of 5th Joint Symposium on Neural Computation San Diego, USA, May 16, 1998 p172
[67]	Wilson H R 1999 J. Theor. Biol. 200 375
[68]	Izhikevich E M 1999 IEEE Trans. Neural Netw. 10 499
[69]	Izhikevich E M 2001 SIAM Rev. 43 315
[70]	Izhikevich E M, Hoppensteadt F 2004 Int. J. Bifurcat. Chaos 14 3847
[71]	Abbott L F, van Vreeswijk C 1993 Phys. Rev. E 48 1483
[72]	Destexhe A, Rudolph M, Pare D 2003 Nat. Rev. Neurosci. 4 739
[73]	Avoli M, Hwa G G, Lacaille J C, Olivier A, Villemure J G 1994 Exp. Brain Res. 98 135
[74]	Hutcheon B, Miura R M, Puil E 1996 J. Neurophysiol. 76 683
[75]	Mainen Z F, Sejnowski T J 1996 Nature 382 363
[76]	Bower J M, Beeman D 1998 The Book of Genesis (1st Ed.) (New York:Springer) pp51-130
[77]	Destexhe A, Mainen Z F, Sejnowski T J 1994 J. Comput. Neurosci. 1 195
[78]	Hutcheon B, Yarom Y 2000 Trends Neurosci. 23 216
[79]	Latham P E, Richmond B J, Nelson P G, Nirenberg S 2000 J. Neurophysiol. 83 808
[80]	Pike F G, Goddard R S, Suckling J M, Ganter P, Kasthuri N, Paulsen O 2000 J. Physiol. 529 205
[81]	Hansel D, Mato G 2001 Phys. Rev. Lett. 86 4175
[82]	Izhikevich E M 2004 IEEE Trans. Neural Netw. 15 1063
[83]	Segev I, Fleshman J W, Burke R E 1989 Methods in Neuronal Modeling (1st Ed.) (Cambridge:MIT Press) pp63-96
[84]	Pinsky P F, Rinzel J 1994 J. Comput. Neurosci. 1 39
[85]	Wang X J, Buzsáki G 1996 J. Neurosci. 16 6402
[86]	Hutcheon B, Miura R M, Puil E 1996 J. Neurophysiol. 76 698
[87]	Manor Y, Rinzel J, Segev I, Yarom Y 1997 J. Neurophysiol. 77 2736
[88]	Koch C, Segev I 1998 Methods in Neuronal Modeling:From Ions to Networks (2nd Ed.) (Cambridge:MIT Press) pp93-136
[89]	Feng J, Brown D 2000 Bull. Math. Biol. 62 467
[90]	Feng J 2001 Neural Netw. 14 955
[91]	Kistler W M, Gerstner W, van Hemmen J L 1997 Neural Comput. 9 1015
[92]	Izhikevich E M 2000 Int. J. Bifurcat. Chaos 10 1171
[93]	Izhikevich E M 2001 Neural Netw. 14 883
[94]	Gerstner W, Kistler W M 2002 Spiking Neuron Models:Single Neurons, Populations, Plasticity (1st Ed.) (Cambridge:Cambridge University Press) pp31-146
[95]	Izhikevich E M 2003 IEEE Trans. Neural Netw. 14 1569
[96]	Jolivet R, Lewis T J, Gerstner W 2004 J. Neurophysiol. 92 959
[97]	Brette R, Gerstner W 2005 J. Neurophysiol. 94 3637
[98]	Mihalas S, Niebur E 2009 Neural Comput. 21 704
[99]	McCormick D A, Wang Z, Huguenard J 1993 Cereb. Cortex 3 387
[100]	Lumer E D 1998 Cereb. Cortex 8 553
[101]	Yang Z Q 2010 Acta Phys. Sin. 59 5319 (in Chinese)[杨卓琴2010物理学报 59 5319]
[102]	Liang X B, Liu X S, Liu A Z, Wang B L 2009 Acta Phys. Sin. 58 5065 (in Chinese)[梁晓冰, 刘希顺, 刘安芝, 王博亮2009物理学报 58 5065]
[103]	Wang H Q, Yu L C, Chen Y 2009 Acta Phys. Sin. 58 5070 (in Chinese)[王慧巧, 俞连春, 陈勇2009物理学报 58 5070]

施引文献

[1]	Durstewitz D, Seamans J K, Sejnowski T J 2000 Nat. Neurosci. 3 1184
[2]	Cassidy A S, Merolla P, Arthur J V, Esser S K, Jackson B, Alvarez-Icaza R, Datta P, Sawada Jun, Wong T M, Feldman V, Amir A, Rubin D B, Akopyan F, McQuinn E, Risk W P, Modha D S 2013 The 2013 International Joint Conference on Neural Networks (IJCNN) Dallas, USA, August 4-9, 2013 p1
[3]	Smith G D, Cox C L, Sherman S M, Rinzel J 2000 J. Neurophysiol. 83 588
[4]	Fourcaud-Trocmé D, Hansel D, van Vreeswijk C, Brunel N 2003 J. Neurosci. 23 11628
[5]	Lapicque L 1907 J. Physiol. Pathol. Gen. 9 620
[6]	Abbott L F 1999 Brain Res. Bull. 50 303
[7]	Brunel N, van Rossum M C W 2007 Biol. Cybern. 97 337
[8]	McCulloch W S, Pitts W 1943 Bull. Math. Biol. 5 115
[9]	Bernstein J 1902 Pflgers Arch. 92 521
[10]	Hodgkin A L 1939 J. Physiol. 94 560
[11]	Hodgkin A L, Katz B 1949 J. Physiol. 108 37
[12]	Bonhoeffer K F 1948 J. Gen. Physiol. 32 69
[13]	Hodgkin A L 1948 J. Physiol. 107 165
[14]	Hebb D O 1949 The Organization of Behavior:A Neuropsychological Theory (1st Ed.) (London:Chapman & Hall) pp17-78
[15]	Hodgkin A L, Huxley A F, Katz B 1952 J. Physiol. 116 424
[16]	Eccles J C, Eccles R M, Lundberg A 1957 J. Physiol. 137 22
[17]	Rosenblatt F 1958 Psychol. Rev. 65 386
[18]	Fitzhugh R 1960 J. Gen. Physiol. 43 867
[19]	Nagumo J, Arimoto S, Yoshizawa S 1962 Proc. IRE 50 2061
[20]	Fuortes M G F, Mantegazzini F 1962 J. Gen. Physiol. 45 1163
[21]	Stein R B 1965 Biophys. J. 5 173
[22]	Geisler C D, Goldberg J M 1966 Biophys. J. 6 53
[23]	Rall W 1967 J. Neurophysiol. 30 1138
[24]	Stein R B 1967 Proc. R. Soc. Lond. B:Biol. Sci. 167 64
[25]	Knight B W 1972 J. Gen. Physiol. 59 734
[26]	Kernell D, Sj·holm H 1973 Acta Physiol. Scand. 87 40
[27]	Hodgkin A L, Huxley A F 1952 J. Physiol. 117 500
[28]	Shapiro B I, Lenherr F K 1972 Biophys. J. 12 1145
[29]	Krinskii V I, Iu M K 1973 Biofizika 18 506
[30]	Krinskii V I, Iu M K 1973 Biofizika 18 878
[31]	Plant R E, Kim M 1976 Biophys. J. 16 227
[32]	Plant R E 1976 Computer Programs Biomed. 6 85
[33]	Rinzel J 1978 Studies in Mathematical Biology (1st Ed.) (Washington:Mathematical association of America) pp1-66
[34]	Fitzhugh R 1961 Biophys. J. 1 445
[35]	Connor J A, Stevens C F 1971 J. Physiol. 213 31
[36]	Connor J A, Walter D, Mckown R 1977 Biophys. J. 18 81
[37]	Morris C, Lecar H 1981 Biophys. J. 35 193
[38]	Rinzel J, Troy W C 1982 J. Chem. Phys. 76 1775
[39]	Chay T R 1985 Physica D 16 233
[40]	Chay T R, Keizer J 1983 Biophys. J. 42 181
[41]	Ermentrout G B, Kopell N 1986 SIAM J. Appl. Math. 46 233
[42]	Hindmarsh J L, Rose R M 1982 Nature 296 162
[43]	Hindmarsh J L, Rose R M 1984 Proc. R. Soc. Lond. B:Biol. Sci. 221 87
[44]	Rose R M, Hindmarsh J L 1985 Proc. R. Soc. Lond. B:Biol. Sci. 225 161
[45]	Rose R M, Hindmarsh J L 1989 Proc. R. Soc. Lond. B:Biol. Sci. 237 267
[46]	Rose R M, Hindmarsh J L 1989 Proc. R. Soc. Lond. B:Biol. Sci. 237 289
[47]	Rose R M, Hindmarsh J L 1989 Proc. R. Soc. Lond. B:Biol. Sci. 237 313
[48]	Chay T R, Rinzel J 1985 Biophys. J. 47 357
[49]	Connor J A, Stevens C F 1971 J. Physiol. 213 1
[50]	Connor J A, Stevens C F 1971 J. Physiol. 213 21
[51]	Connor J 1975 J. Neurophysiol. 38 922
[52]	Jack J J B, Noble D, Tsien R W 1975 Electric Current Flow in Excitable Cells (1st Ed.) (Oxford:Clarendon Press) pp132-224
[53]	Connors B W, Gutnick M J, Prince D A 1982 J. Neurophysiol. 48 1302
[54]	Plant R E 1978 Biophys. J. 21 217
[55]	Rinzel J 1985 Ordinary and Partial Differential Equations (1st Ed.) (Berlin:Springer-Verlag) pp304-316
[56]	Rinzel J 1985 Fed. Proc. 44 2944
[57]	Mircea S, Jones E G, Llinás R R 1990 Thalamic Oscillations and Signaling (1st Ed.) (New York:John Wiley) pp1-43
[58]	Rinzel J 1987 Mathematical Topics in Population Biology, Morphogenesis and Neurosciences (1st Ed.) (Berlin:Springer) pp267-281
[59]	Connors B W, Gutnick M J 1990 Trends Neurosci. 13 99
[60]	Rall W 1989 Methods in Neuronal Modeling:from Ions to Networks (2nd Ed.) (Cambridge:MIT Press) pp9-62
[61]	Ermentrout B 1996 Neural Comput. 8 979
[62]	Hoppensteadt F C, Izhikevich E M 1997 Weakly Connected Neural Networks (1st Ed.) (New York:Springer-Verlag) pp25-101
[63]	Rinzel J, Ermentrout G B 1989 Methods in Neuronal Modeling (1st Ed.) (Cambridge:MIT Press) pp135-169
[64]	Roth A, Häusser M 2001 J. Physiol. 535 445
[65]	Chay T R 1991 Biopolymers 31 1483
[66]	Stevens C F, Zador A M 1998 Proceedings of 5th Joint Symposium on Neural Computation San Diego, USA, May 16, 1998 p172
[67]	Wilson H R 1999 J. Theor. Biol. 200 375
[68]	Izhikevich E M 1999 IEEE Trans. Neural Netw. 10 499
[69]	Izhikevich E M 2001 SIAM Rev. 43 315
[70]	Izhikevich E M, Hoppensteadt F 2004 Int. J. Bifurcat. Chaos 14 3847
[71]	Abbott L F, van Vreeswijk C 1993 Phys. Rev. E 48 1483
[72]	Destexhe A, Rudolph M, Pare D 2003 Nat. Rev. Neurosci. 4 739
[73]	Avoli M, Hwa G G, Lacaille J C, Olivier A, Villemure J G 1994 Exp. Brain Res. 98 135
[74]	Hutcheon B, Miura R M, Puil E 1996 J. Neurophysiol. 76 683
[75]	Mainen Z F, Sejnowski T J 1996 Nature 382 363
[76]	Bower J M, Beeman D 1998 The Book of Genesis (1st Ed.) (New York:Springer) pp51-130
[77]	Destexhe A, Mainen Z F, Sejnowski T J 1994 J. Comput. Neurosci. 1 195
[78]	Hutcheon B, Yarom Y 2000 Trends Neurosci. 23 216
[79]	Latham P E, Richmond B J, Nelson P G, Nirenberg S 2000 J. Neurophysiol. 83 808
[80]	Pike F G, Goddard R S, Suckling J M, Ganter P, Kasthuri N, Paulsen O 2000 J. Physiol. 529 205
[81]	Hansel D, Mato G 2001 Phys. Rev. Lett. 86 4175
[82]	Izhikevich E M 2004 IEEE Trans. Neural Netw. 15 1063
[83]	Segev I, Fleshman J W, Burke R E 1989 Methods in Neuronal Modeling (1st Ed.) (Cambridge:MIT Press) pp63-96
[84]	Pinsky P F, Rinzel J 1994 J. Comput. Neurosci. 1 39
[85]	Wang X J, Buzsáki G 1996 J. Neurosci. 16 6402
[86]	Hutcheon B, Miura R M, Puil E 1996 J. Neurophysiol. 76 698
[87]	Manor Y, Rinzel J, Segev I, Yarom Y 1997 J. Neurophysiol. 77 2736
[88]	Koch C, Segev I 1998 Methods in Neuronal Modeling:From Ions to Networks (2nd Ed.) (Cambridge:MIT Press) pp93-136
[89]	Feng J, Brown D 2000 Bull. Math. Biol. 62 467
[90]	Feng J 2001 Neural Netw. 14 955
[91]	Kistler W M, Gerstner W, van Hemmen J L 1997 Neural Comput. 9 1015
[92]	Izhikevich E M 2000 Int. J. Bifurcat. Chaos 10 1171
[93]	Izhikevich E M 2001 Neural Netw. 14 883
[94]	Gerstner W, Kistler W M 2002 Spiking Neuron Models:Single Neurons, Populations, Plasticity (1st Ed.) (Cambridge:Cambridge University Press) pp31-146
[95]	Izhikevich E M 2003 IEEE Trans. Neural Netw. 14 1569
[96]	Jolivet R, Lewis T J, Gerstner W 2004 J. Neurophysiol. 92 959
[97]	Brette R, Gerstner W 2005 J. Neurophysiol. 94 3637
[98]	Mihalas S, Niebur E 2009 Neural Comput. 21 704
[99]	McCormick D A, Wang Z, Huguenard J 1993 Cereb. Cortex 3 387
[100]	Lumer E D 1998 Cereb. Cortex 8 553
[101]	Yang Z Q 2010 Acta Phys. Sin. 59 5319 (in Chinese)[杨卓琴2010物理学报 59 5319]
[102]	Liang X B, Liu X S, Liu A Z, Wang B L 2009 Acta Phys. Sin. 58 5065 (in Chinese)[梁晓冰, 刘希顺, 刘安芝, 王博亮2009物理学报 58 5065]
[103]	Wang H Q, Yu L C, Chen Y 2009 Acta Phys. Sin. 58 5070 (in Chinese)[王慧巧, 俞连春, 陈勇2009物理学报 58 5070]

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神经元模型对比分析

摘要

作者及机构信息

1.
西南大学电子信息工程学院, 重庆 400715;

2.
中国科学技术大学信息科学技术学院, 合肥 230027

通信作者: 李传东, licdswu@163.com

参考文献

施引文献

目录

计量

神经元模型对比分析

通信作者: 李传东, licdswu@163.com

English Abstract

Contrastive analysis of neuron model

1.
College of Electronic and Information Engineering, Southwest University, Chongqing 400715, China;

2.
School of Information Science and Technology, University of Science and Technology of China, Hefei 230027, China

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神经元模型对比分析

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作者及机构信息

1. 西南大学电子信息工程学院, 重庆 400715; 2. 中国科学技术大学信息科学技术学院, 合肥 230027

通信作者: 李传东, licdswu@163.com

参考文献

施引文献

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出版历程

神经元模型对比分析

通信作者: 李传东, licdswu@163.com

English Abstract

Contrastive analysis of neuron model

1. College of Electronic and Information Engineering, Southwest University, Chongqing 400715, China; 2. School of Information Science and Technology, University of Science and Technology of China, Hefei 230027, China

全文HTML

目录

作者中心

审稿中心

关于期刊

关于我们

1.
西南大学电子信息工程学院, 重庆 400715;

2.
中国科学技术大学信息科学技术学院, 合肥 230027

1.
College of Electronic and Information Engineering, Southwest University, Chongqing 400715, China;

2.
School of Information Science and Technology, University of Science and Technology of China, Hefei 230027, China