1. Neural Connectivity from
Multiple Spike Trains
충북대학교 물리학과
신경동력학 연구실
한승기, 임태규, 류선영

2. Neural Encoding & Decoding
Network
stimulus
spike
pattern
Encoding
Decoding
Multi-
electrodes
Visual
cortex

3. Spike Trains from Multi-electrodes
- Simultaneous measurements
- Spike sorting
- Neural coding-population coding
- Neural connectivity

4. Functional Connectivity : Cross-Correlogram
C12()=<S1(t)S2(t+)>
Excitatory
offset peak
Inhibitory
offset trough
Common ex.
central peak
Common in.
central trough 1 2 s + 1 2 s - 1 2 + 1 2 -

5. Phase Analysis for Spike Trains
mean phase velocity
phase plot 1 2
2(2)
1(1,2)
1mod2
2mod2 2 
spike interval = 2  2 T1 T2 T3 T4 T5
time trajectory : 1 & 2  t 2 6 4
10 8

6. Phase Sensitivity & Directionality of Coupling
Phase Velocity
Directionality
Phase Sensitivity

7. Morris-Lecar Model K+
Ca2+

8. Spike Trains
Interspike-Interval
Histogram
Phase Plot

9. 2 1 Excitatory-Excitatory Coupling Cross-Correlogram
Phase Sensitivity 1 2
g21 = 0.5
g12
g1=0.5
g2=0.1
g1=0.5
g2=0.5
g1=0.5
g2=0.9

10. 2 1 Inhibitory-Inhibitory Coupling Cross-Correlogram
Phase Sensitivity 1 2
g21 = 0.5
g12
g1=0.5
g2=0.1
g1=0.5
g2=0.5
g1=0.5
g2=0.9

11. Effective Coupling : Phase Model Analysis
Excitatory coupling
Vsyn = 20mV
Inhibitory coupling
Vsyn = -80mV

12. Effective Coupling
Dependence on Vsyn
Dependence on g2

13. Network Analysis - neural network with 12 neurons
- all-to-all connections

14. Excitatory-Excitatory Coupling1 12
0.395
0.195 2 1
0.409
0.215 6 1
0.143
0.188

15. Inhibitory-Inhibitory Coupling11 5
-0.484
-0.251 8 5
-0.219
-0.004 11 8
-0.161
-0.228

16. Inhibitory-excitatory Coupling5 1
0.474
-0.310 11 1
0.433 8 2
0.207
-0.225

17. Estimation of neural connectivity
Amplitude of the effective coupling vs coupling strength

18. Excitatory-Excitatory Coupling
Phase Analysis
Cross-Correlogram

19. Coupled CR Oscillator Systems: Electric Circuit Experiments
g21=0.015
Vo2
- Coherent resonance oscillator
Noise excitable system
Optimal noise intensity
Synchronization
PRL 83, 1771(1999)
PRE 59, R3791(1999) V1 V2 t

20. Estimation of Connectivity
Cross-Correlogram
Cross-Correlogram : peak height
Phase Sensitivity : amplitude

21. Time locked ERP components

22. Dynamic dependencies between components
t > RT
0 < t < RT

23. Summary
Multiple spike train analysis
- phase model analysis, effective coupling
Network connectivity
- neural network with 12 neurons
- electronic circuit: coupled CR oscillators
- cortical maps: independent ERP components