Functional connectivity: AEC

using NeuroAnalyzer
using Plots
eeg = load("files/eeg.hdf")
e10 = epoch(eeg, ep_len = 10)

Amplitude Envelope Correlation (AEC) measures the correlation between the envelopes of two signals (e.g., Hilbert-transformed signals).

Formula:

\[ \text{AEC} = \text{corr}(A_1(t), A_2(t)) \]

where \(A_1(t)\) and \(A_2(t)\) are the amplitude envelopes of the two signals.

Interpretation:

• AEC = 1: Perfect correlation between amplitude envelopes.
• AEC = 0: No correlation.

Use Case: Studying co-activation of brain regions in specific frequency bands.

Limitations:

• Not phase-specific: Does not capture timing relationships.
• Sensitive to volume conduction.

ep = 1
aec = aecor(e10,
            e10,
            ch1 = "Fp1",
            ch2 = "Fp2",
            ep1 = ep,
            ep2 = ep)
println("AEC: $(aec[1])")

AEC: 0.1485864621741476

Tip: aecor() uses the Hilbert transform to calculate instantaneous amplitudes, therefore the signal should be narrowband prior the analysis.

Another approach is to use env_cor(), which provides the p-value for the correlation test.

Calculating upper envelopes for channels “Fp1”, epoch 1 and “Fp2”, epoch 2:

ep = 1
ch1_data = e10.data[get_channel(e10, ch = "Fp1")[1], :, ep]
ch2_data = e10.data[get_channel(e10, ch = "Fp2")[1], :, ep]
env1 = env_up(ch1_data, e10.epoch_time)
env2 = env_up(ch2_data, e10.epoch_time)

Calculating Envelope Correlation:

ec_data = env_cor(reshape(env1, 1, :, 1),
                  reshape(env2, 1, :, 1))
println("EC: $(ec_data.ec[1]), p: $(ec_data.p[1])")

EC: 0.038233081217970685, p: 0.053086047967827864

Tip: envelopes must be provided as arrays of shape (channels, samples, epochs).

Envelope-to-Signal Correlation

Envelope-to-Signal Correlation (ESC) is similar to AEC, but the the amplitude of the first signal is signed; and thus the phase information is preserved.

\[ \text{ESC} = \text{corr}(S_1(t), A_2(t)) \]

where \(S_1(t)\) is the first signal and \(A_2(t)\) is the amplitude envelope of the second signal.

ESC uses the Hilbert transform to calculate instantaneous amplitudes, hence the signal should be narrowband.

ep = 1
esc = escor(e10,
            e10,
            ch1 = "Fp1",
            ch2 = "Fp2",
            ep1 = ep,
            ep2 = ep);
println("ESC: $(esc[1])")

ESC: 0.04131366983715709