[1][2] Lorente de No Rall [3][4][5][6] 2 3 E m I m I m φ ( 1) ( ) SUA, MUA, LFP, ECoG, EEG 1 1) 1 ( ) φ(lfp,ecog) 2) 1 φ ECoG decoding 2 φ 2.1 φ 1)

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1 ) ( ) (LFP,ECoG) 2) ECoG decoding 1 ( 1) * 1 SUA MUA LFP ECoG EEG multiunit field cortico- local electro- activity potential gram singleunit activity electroencephalogram (AHP ) > 300Hz < 300Hz > 200KΩ 40k 120kΩ 200k 800kΩ < 2kΩ < 1kΩ tip 2 4mm 4 10mm ( ) < 50µm µm 0.5 3mm 5mm > 10mm 1 Hodgkin-Huxley pooneil68@gmail.com *1 1

2 [1][2] Lorente de No Rall [3][4][5][6] *2 *3 E m I m I m φ ( 1) ( ) SUA, MUA, LFP, ECoG, EEG 1 1) 1 ( ) φ(lfp,ecog) 2) 1 φ ECoG decoding 2 φ 2.1 φ 1) 2 a) φ I m r φ = 1 I m 4πσ r (1) σ conductance (1) φ ( ) current I m 2 b) (sink) *4 active passive *2 Lorente de No 1000 (J. Comp. Neurol. 300:1-4 (1990)) part 2 ch.16 p *3 Nunez Electric fields of the brain 2 [7] 3 4 sculp EEG *4 2

3 a) b) Axon terminal Sink Source Pyramidal neuron Pyramidal neuron 2 a) dendrite I m φ b) φ active (sink) passive (source) (source) φ active, passive I m *5 φ = 1 4πσ n i=1 I m (i) r(i) (2) *6 n I m (i) = 0 (3) i=1 3 sink ( 2 ) E m V m *7 λ 2 2 V m z 2 + τ V m t + V m = E m (4) source sink *5 I m active sink passive source sink source 0 J J = I m source sink return current charge sink source J = 0 passive source sink return current ( passive current ) *6 dipole *7 (4) V m E m z t E m z = 0 non-zero 3

4 3 Passive (4) E m V m λ length constant V m ( ) ( ) τ time constant V m ( ) V m I m I m = g m V m + c m V m t (5) sink(= E m ) V m I m (2) I m φ 4 Passive volume conduction 4 (SUA, MUA, LFP, ECoG, EEG) (EEG σ ) 2.2 1: V m φ Single-unit activity φ V m 5 Rat CA1 4

5 ([8] ) 5 V m φ [8] V m 1KHz (5) I m = g m V m + c m V m t c m V m t V m t (6) single-unit activity (< 50µm) sink r φ sink I m (1) (6)(7) φ = 1 I m 4πσ r I m (7) φ I m V m t (8) φ V m 2.3 2: φ φ 6 [9] 5

6 6 [9] Buzsaki Koch rat CA1 (Buzsaki) φ dendrite φ (Koch) φ 2.4 3: φ low-pass 7 Human ECoG hand movement rest low-frequency band (8-32Hz) High frequency band (76-100Hz) 7 Human ECoG low-frequency band high-frequency band [10] 1) low-frequency band High frequency band 2) (volume conduction ) RC low-pass 1) 2) Logothetis awake monkey V1 intracortical electrode 4*4 array (spacing mm) LFP [11] coherence coherence population coherence 6

7 LFP frequency band 2-8Hz 2.9mm Hz 1.3mm Logothetis LFP ( 4) Volume conduction low-pass (2) σ Logothetis Neuron 2007[12] low-pass * % low-pass volume conduction low-pass 4 (4) λ 1 f (9) space constant(λ) f [13] space constant passsive V m f I m φ f [7] ( 8) * 9 low-pass Passive volume conduction 8 ECoG,LFP *8 conductance σ 10Hz (conductance ) 26Ω/cm 1KHz 23Ω/cm 6µF/cm 100Hz *9 CA1 LFP Schaffer collateral Pyramidal layer sink (population spike) source stratum radiatum (Schaffer collateral apical dendrite ) sink source passive source 7

8 3 φ 3.1 φ φ ( 9) volume conduction 9 I m φ volume conduction φ = 1 4πσ n i=1 I m (i) r(i) φ I σ 2 φ = I 3.2 LFP CSD 10 a) φ(i) I m (j) φ(i) I m (j) 8

9 a) b) 10 a) b) ( ) ( 10 b)) ( ) I(i) φ(i) (10) * 10 σ 2 φ = I (10) mesoscopic : 1) Quasi-static (< 5KHz ) 2) Conductance(σ) EEG LFP ECoG intracortial (z) x, y z ( appendix A ) σ 2 φ = I (11) z2 φ 2 I CSD 2 2 CSD LFP *10 I E σ E = I E φ quasi-static E = φ σ 2 φ = I LFP local field potential (field) (potential) 9

10 MED EEG source localization 3.3 CSD CSD 1950 Walter Pitts John C. Eccles [14] Mitzdorf [14] CSD LFP Source L3 L3 L4 Sink L4 L5 L5 11 CSD [14] cat optic radiation 17 50µm LFP ( 11 ) 2 CSD( 11 ) ( ( 2 3ms) layer 4 sink( ) layer 3 source( ) ( 5 10ms) layer 4 source-sink-source layer 4 sink layer 3 source layer 4 LGN ( 11 ) layer 5 sink source layer 5 pyramidal neuron apical dendrite *11 (< 10ms) CSD sink-source ( 12) *11 sink source 10

11 Source Sink Sink Source 12 CSD CSD recurrent 2 CSD LFP SGS SGI [15] SGS SGI reciprocal CSD I I m ( 13) CSD Mesoscopic CSD LFP Microscopic 13 / 1 1 dendrite 1( ) CSD1 2( modulation) CSD2 classifier Henry Markram blue brain project 1 1 gamma frequency simulation LFP CSD simulation [16] 11

12 3.4 ECoG dipole a) b) 14 a)ecog b)ecog current dipole localization ECoG ECoG φ ( 14 a)) CSD ECoG *12 sink sink I source I current dipole ( 14 b)) sink source I I m 0 (3) Dipole Id dipole moment I dipole d Pyramidal neuron( 15 a) apical dendrite sink source (open field) dipole moment Id basket cell( 15 b) dendrite sink source (closed field) dipole moment Id LFP ECoG pyramidal neuron Dipole φ volume conduction (2) (sink source ) dipole φ h d *13 *12 ECoG current source ECoG EEG localization φ 7 localization spacing *13 h d EEG (h > 10mm) ECoG ECoG dipole localization EEG ECoG 12

13 a) b) 15 Open field closed field φ Id 4πσh 2 (12) ( appendix B ) φ dipole moment Id dipole φ ECoG x h φ ( h x )3 φ (13) ( appendix C ) 2mm h = 1mm ECoG spacing 10mm x = 10mm φ 1/1000 *14 ECoG φ dipole moment Id ECoG spacing spacing source localization ( 5mm 2mm ) Dipole ECoG sink- source ECoG ( (12) ) source- sink ECoG ECoG movement-related potential potential [17] ECoG potential CSD current dipole *14 h = 1mm x = 10mm (2) d < φ φ 13

14 4 ( 16) Passive volume conduction SUA Layer CSD CSD LFP Dipole ECoG Dipole moment 16 ECoG LFP LFP-ECoG LFP-SUA Logothetis LFP SUA LFP (90Hz ) SUA [18] SUA SUA source localization ECoG decode CSD 2 source localization decode φ decode 14

15 5 ( LFP MUA ) [1] Lemon R. Methods for neuronal recording in conscious animals. New York:. W iley, 1984 [2] Llinas R, Nicholson C (1974) Analysis of field potentials in the central nervous system. In: Handbook of EEG and clinical neurophysiology (Stevens CF, ed.), pp Amsterdam: Elsevier [3] Lorente de No, R. (1947a) A study of nerve physiology. Part 1 In: Studies from the Rockefeller Institute of Medical Research, 131: [4] Lorente de No, R. (1947b) A study of nerve physiology. Part 2 In: Studies from the Rockefeller Institute of Medical Research, 132: [5] Rall W. (1962) Electrophysiology of a dendritic neuron model. Biophys J. 2(2 Pt 2): [6] Rall W, Shepherd GM. (1968) Theoretical reconstruction of field potentials and dendrodendritic synaptic interactions in olfactory bulb. J Neurophysiol. 31(6): [7] Nunez, P.L., and Srinivasan, R. (2006). Electric fields of the brain : The neurophysics of EEG (2nd. ed.). New York : Oxford University Press. [8] Henze, D. et.al., (2000) Intracellular features predicted by extracellular recordings in the hippocampus in vivo. J Neurophysiol. 84, [9] Gold C et.al., (2006) On the origin of the extracellular action potential waveform: A modeling study. J Neurophysiol. 95(5): [10] Miller KJ et.al. (2007) Spectral changes in cortical surface potentials during motor movement. J Neurosci. 27(9): [11] Goense JB, Logothetis NK. (2008) Neurophysiology of the BOLD fmri signal in awake monkeys. Curr Biol. 6;18(9): [12] Logothetis NK, Kayser C, Oeltermann A. (2007) In vivo measurement of cortical impedance spectrum in monkeys: implications for signal propagation. Neuron 6;55(5): [13] Pettersen KH, Einevoll GT. (2008) Amplitude variability and extracellular low-pass filtering of neuronal spikes. Biophys J. 94(3): [14] Mitzdorf U. (1985) Current source-density method and application in cat cerebral cortex: investigation of evoked potentials and EEG phenomena. Physiol Rev. 65(1): [15] Phongphanphanee P, Kaneda K, Isa T. (2008) Spatiotemporal profiles of field potentials in mouse superior colliculus analyzed by multichannel recording. J Neurosci. 28(37): [16] Markram H. (2006) The blue brain project. Nat Rev Neurosci. 7(2): [17] Mehring C et.al. (2004) Comparing information about arm movement direction in single channels of local and epicortical field potentials from monkey and human motor cortex. J Physiol Paris. 98(4-6): [18] Rasch MJ et.al. (2008) Inferring spike trains from local field potentials. J Neurophysiol. 99(3): Appendix A CSD x, y, z σ 2 φ = I σ ( 2 φ x φ y φ z 2 ) = I x, y 2 φ x 2 = 2 φ y 2 = 0 15

16 x, y activation σ 2 φ z 2 = I Appendix B Dipole moment φ +I, r h d I, r h 1 2 d (2) φ = I 4πσ ( 1 h d 1 h 1 2 d ) φ = Id 4πσ ( 1 h 2 ( d 2 )2 ) h d h 2 ( d 2 )2 h 2 φ Id 4πσh 2 Appendix C Dipole moment φ Dipole Dipole θ h d r cos θ = h φ φ Id cos θ 4πσr 2 Idh 4πσr 3 Dipole φ r = h φ Id 4πσh 2 φ r = x 2 + h 2 φ Idh 4πσ( x 2 + h 2 ) 3 x h x 2 + h 2 x φ = ( h ( x 2 + h 2 ) )3 φ φ φ = ( h x )3 16

passive passive active 1 ( ) LTP 1 1) 2) 1 1

11 8 25 passive passive active 1 ( ) LTP 1 1) 2) 1 1 1997 CA1 12 13 1990 2 K A K 1997 transient 3 transient 4-aminopyridine 4- AP A K A A [ 1 conductivity recording transient 4 ] 2 ( K ) i) A K CA1 A K