[FieldTrip] Partial Directed Coherence computation

[Schoffelen, J.M. (Jan Mathijs)]

Hi Giovanna,

w.r.t. 1: yes, the convention is that i goes to j.

w.r.t. 2: it seems that you performed the spectral factorisation on the 17 multivariate time series simultaneously. If there is a strong linear/instantaneous dependence between the individual time series (i.e. the EEG channels between themselves), it could be that the factorisation does not converge to a desired result, or it could be that the computation of the PDC breaks down (it requires a matrix inversion of the NxN transfer matrices, which are expected to be numerically well-conditioned). However, in either case I would expect some warnings thrown by matlab, but I am not entirely sure about that.

I would assume that you are primarily interested in the interaction between the EEG on the one hand, and the thalamus LFP signal on the other hand. Interpretation of the between EEG electrodes connectivity does not make much sense to begin with. To get a better idea of what’s going on, I would suggest 1): to use Granger causality as connectivity metric, and/because 2) it can be computed in a pairwise fashion (i.e. using a pairwise factorisation). The latter can be achieved by specifying cfg.granger.sfmethod = ‘bivariate’, and with an additional cfg.channelcmb you can define the pairs of channels between which you wish to compute the connectivity.

Good luck,
Jan-Mathijs




On 18 Apr 2023, at 11:37, Aiello Giovanna via fieldtrip <fieldtrip at science.ru.nl<mailto:fieldtrip at science.ru.nl>> wrote:

Good morning,
I am interested in understanding the directed connectivity between the thalamus, where I am recording a Local Field Potential (in 1 channel) and the cortex, where I am recording EEGs (in 16 channels).

My signal is epoched in 4-seconds windows, and I am not interested in understanding the evolution of the directed connectivity in time but rather just which structure is leading which.


I have computed Partial Directed Connectivity (pdc) with the fieldtrip function ft_connectivityanalysis, feeding into the code the transformed, Fourier spectrum (complex double) of my signal (rpttap x channels x frequencies, where rpttap is repetitions (i.e., number of epochs) x tapers).

My final matrix of pdc is 17 x 17 x frequencies (where frequencies are my frequencies of interest). The first 16 channels represent the EEG channels, the 17th channel is the LFP channel in the thalamus. Let’s call this matrix A.
I have two questions:

1) Did I understand correctly that the element A( i, j, f ) for a given frequency f indicates the directed connectivity from element i to element j? (And not the other way around)

2) In my case, A( 1:16 , j  , f ) is a column vector containing the same number!
It looks like, independently on what EEG channel I am considering (unless I am considering the channel in the thalamus), the contribution of directed connectivity to a certain channel j is always the same. This also stays for the thalamus, so if I take A( 1:16, 17, f ), it seems like all the eeg channels have the same directed connectivity to the thalamus. Is that possible? I think it does not really make sense. Please notice that the numbers are not exactly the same, but differ in the 4th decimal digit.



Thank you in advance for your help
Giovanna


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