Spectral Analysis II: Advanced Applications in Neuroscience

1. Spectral analysis II: Applications Bijan Pesaran Center for Neural Science New York University

2. Outline • Example I: LFP spectrograms • Example II: Spike rates, spectra and coherence • Example III: Spike-LFP coherence • Example IV: Decoding and single trial analysis • Example V: Combining SVD and spectra

3. Spiking and LFP activity • Extracellular potential Spikes LFP • Current summation determines the amplitude of LFP • Spatial and temporal

4. How do we analyze spike trains and field potentials together? • Use spectral methods for a hybrid point-continuous process Continuous process LFP Voltage Point process Spike times

5. Spectrum power Spike times 1/T + power = T Coherency frequency High Low Spikes Field Spectral intuition = LFP Voltage

6. Example I: LFP spectrograms • LFP recording from Macaque area LIP Cue Memory Saccade Memory Saccade Task Pesaran et al (2002)

7. Cue Saccade Cue Saccade Example I: LFP spectrograms • Example recording

8. Example I: LFP spectrograms • Estimation issues • Bias • Narrow band • Broad band • Variance

9. Example I: LFP spectrograms • Confidence intervals • Chi2 • Assume Gaussian process • Jackknife • Does not assume Gaussian process

10. Multitaper estimate - Single Trial, [5,9] Periodogram – Single Trial Example I: LFP spectrograms

11. Example I: LFP spectrograms Periodogram – Single Trial Multitaper estimate - Single Trial

12. Multitaper estimate - Nine Trials [5,9] Example I: LFP spectrograms Multitaper estimate - Single Trial [5,9]

13. Example I: LFP spectrograms Multitaper estimate - Single Trial Multitaper estimate - Nine Trials

14. Multitaper estimate - 95% Jackknife Leave-one-out Example I: LFP spectrograms Multitaper estimate - 95% Chi2

15. Multitaper estimate - T = 0.2s, W = 25Hz Example I: LFP spectrograms Multitaper estimate - T = 0.5s, W = 10Hz

16. Example II: Spike rates, spectra and coherence • Simultaneous two-cell recording from Macaque area LIP Cue Delay Reach and Saccade Reach and Saccade Task Pesaran et al (Unpublished)

17. Locfit estimate nn = 0.1 Example II: Spike rates, spectra and coherence Binning estimate T = 50ms

18. Example II: Spike rates, spectra and coherence Multitaper spectrum [8,15] Auto-correlation fn

19. Example II: Spike rates, spectra and coherence • Inter-spike intervals

20. Example II: Spike rates, spectra and coherence • Inter-spike intervals • Spike spectrum properties • High frequency limit • Low freq suppression • Spectral peaks

21. Example II: Spike rates, spectra and coherence Multitaper coherence 9 trials, [8,15] Cross-correlation fn

22. Example II: Spike rates, spectra and coherence Multitaper coherence 9 trials, [8,15] Multitaper coherence 9 trials, [12,23]

23. Example III: Spike-field coherence • Experimental paradigm Womelsdorf et al (2006)

24. Example III: Spike-field coherence • Hypothesis testing Womelsdorf et al (2006)

25. Example III: Spike-field coherence • Single trial analysis Womelsdorf et al (2006)

26. Example IV: Decoding and single trial analysis • Decoding LFP spectra Pesaran et al (2002)

27. Example V: SVD and spectra • SVD • Time-channel decomposition • Reduced dimensionality data set • Estimate spectra of modes

28. Example V: SVD and spectra Fall et al (Unpublished)

29. Summary • Presented examples of neuronal time series • Compared methods for their analysis • Demonstrated advantages of spectral analysis