Hello,
I had a question regarding the appropriate time window for computing phase amplitude coupling.
In the toutorial it is written :
" In order to have a reliable result from this method it is required to use a signal which length is at least ten cycles of the slowest oscillation in your low oscillation band.
Considering this point is more important in analysis of real databases, where the noise level (and/or background brain activity) can be higher than synthesized data, and the coupling intensity can be low. Thus, if you want to examine the coupling for slow oscillations in [2, 14] Hz, it would be better to use a signal with minimum length of 10 cycles of the slowest oscillation, which would be 10 x 0.5 = 5 S."
Does anyone has the refrence for this?
Also, does brainstorm extimates PAC using MVL or MI ?
This is more a rule of thumb. In theory you would need to have at least one cycle of the slow frequency (phase), so there is a full "circle" in the complex place A_fa(t)·e^i(phi_p). However, this is very little data so the mean vector length will be sensitive to low SNR. The proposed more than 10 cycles aim to improve the SNR. Take into account that the more than 10 cycles can be addressed either with longer windows, or with more trials. If the duration of each trial is 2 cycles, by computing PAC across 100 trials, is equivalent to compute PAC on a signal of 200 cycles. You can check Chapter 30 (Cross-Frequency Coupling) in Analyzing Neural Time Series Data: Theory and Practice by Mike X Cohen for a more detailed discussion in this subject
In Brainstorm PAC is estimated as the mean vector length (MVL) scaled by the power.
The term modulation index (MI) can be a bit confusing, as in Canolty 2006, it corresponds to MVL (described in its Supplementary material). However in Tort 2010, they introduce their own definition of MI which is different.
Yes I have also read the Cohen's argument. Which basically I interpreted as even 1 cycle is enough; for example 1 cycle of 100 trials is better than 2 cycles of 40 trials, no?
And to be comepletly sure, in brainstorm its Canolty's not Tort's. Right?
That's right, if you want only one PAC value from all the data, and ergodicity is assumed (PAC value is the same for one cycle, regardless if it is the next cycle or the cycle in the next trial)
Yes, it is Canolty's, but scaled by sqrt(n) / sqrt(power_fa)
where DirectPAC before the scaling is the complex sum of all the vectors in the complex plane A_fa(t)·e^i(phi_p) so its size is [nSignals, nFreqP, nFreqA]