Table 1 The equations of the used functional connectivity measures. For each functional connectivity measure, it is indicated whether they observe associations between signals based on amplitude (A), phase (P) or both (A/P)
From: Reproducibility of EEG functional connectivity in Alzheimer’s disease
Measure | Equation | |
|---|---|---|
1. Coherency | A/P | \( c=\frac{\left\langle {A}_1{A}_2{e}^{i\Delta \varphi}\right\rangle }{\sqrt{\left\langle {A}_1^2\right\rangle \left\langle {A}_2^2\right\rangle }} \) |
2. Phase locking value/phase coherence | P | \( R=\left|\left\langle {e}^{i\Delta {\varphi}_{ij}(t)}\right\rangle \right|=\left|\frac{1}{N}\sum \limits_{k=0}^{N-1}{e}^{i\Delta \varphi \left({t}_k\right)}\right| \) |
3. Amplitude envelope | A | \( A(t)=\sqrt{{\left[x(t)\right]}^2+{\left[\overset{\sim }{x}(t)\right]}^2} \) |
4. Imaginary coherence | A/P | \( \mathit{\operatorname{Im}}\left\{c\right\}=\frac{\left\langle {A}_1{A}_2s\mathrm{in}\Delta \varphi \right\rangle }{\sqrt{\left\langle {A}_1^2\right\rangle \left\langle {A}_2^2\right\rangle }} \) |
5. Phase lag index | P | PLI = |〈sign[sin(∆φ(tk))]〉| |
6. Weighted phase lag index | P | \( \mathrm{wPLI}\equiv \frac{\mid E\left\{\mathfrak{I}(Z)\right\}\mid }{\mathrm{E}\left\{\mathfrak{I}\left(\mathrm{Z}\right)\right\}}=\frac{\mid E\left\{\left|\mathfrak{I}(Z)\right|\mathit{\operatorname{sign}}\left(\mathfrak{I}(Z)\right)\right\}\mid }{E\left\{\left|\mathfrak{I}(Z)\right|\right\}} \) |