# Debiased spike field coherence?

Hi Mike,
Congratulations on the new website/ discussion forum platform! It’s a really great resource.

I have a question about computing the spike - LFP coherence:
In principle this is straight forward operation but simply taking the instantaneous phase at which a point process occurs has the caveat that a non-uniform distribution of phase values at a particular frequency may bias our estimation of phase locking strength to that frequency.
I was wondering if to overcome this issue, one could use a similar approach to this one, where you use a linear subtraction to correct for any biases in the phase distribution. In this case the term to be subtracted will be the resultant vector from the entire phase time series, as :

ITPC = abs(mean(exp(1i * spike_phases ) - mean(exp(1i * all_phases ))

where spike_phases are the phases at which a spike occurred and all_phases is the entire phase time series.

An alternative to this approach would be to bin the phases, compute the phase occupancy for each bin and then resample the phases taken to compute our resultant vector such that they are uniformly distributed.

Maybe I’m missing something and there are already existing methods to deal with this issue?
Thank you in advance for any inputs!

-Noam

Hi Noam. Nice to hear from you

Interesting thought about adding that debias term from the LFP phases. It makes sense intuitively, and sticks pretty close to what we proposed in that paper.

However, before interpreting real data using that method, I think it would be good to run a simulation to validate that it does what it should. I think a simulation should be pretty straightforward – use the code we provided with the paper and generate spikes at (1) random or (2) nonrandom phases, while having the simulated LFP data be (1) sinusoidal or periodic-non-sinusoidal. Hopefully, you’ll find that the results are consistent with your simulations.

As for existing methods to deal with this… I’m not sure. Vinck has a method for low spike-counts, but I don’t know if that’s robust to non-uniform phase distributions (that wasn’t built in to the design of the method). I proposed a multivariate spike-field coherence method (Cohen, Elife, 2017), which is completely robust to waveform shape, but that’s only for multichannel data and might be more complicated than what you need.

Hi Mike,

Thanks for the quick reply and suggestion!
I followed your suggestion and simulated Poisson spikes at random or locked to the peak of a sinusoidal and non-sinusoidal signals (1000 spikes of which 500 are locked to 0 in the locked condition). Similar to your paper, a non-uniform distribution of phases generates an spurious clustering even when spikes are completely random and pulls down the spike phase clustering to the opposite direction when spikes are clustered around the peak.
For non-locked random spikes, linear subtraction of the phase time series completely removes the spurious locking. However, for locked spikes, it brings the coherence values to what is expected by subtracting the phase clustering of the non-corrected locked spikes from 1 (perfect locking). My interpretation is that, as the phase distribution of our time series becomes more uniform, the contribution of random spikes grows so the phase locking approaches the true value (around 0.5) - would this interpretation be correct?

thanks,

Noam

Wow, that looks amazing! And it seems like the method extends very well to spikes.

Just a minor suggestion: I think the x-axis might be more interpretable as the LFP phase bias – the magnitude of the average phases.