Simulated data and relation between HRF-conv. GC and neural GC.

<p>A: Flowchart illustrating the process from neural to HRF-convolved neural to fMRI data. B: An example of the process in A where the neural time series (blue) was generated using AR(1) model and was convolved with a canonical HRF to yield the HRF-convolved neural time series (red), which, after down-sampling to TR = 2 s and addition of 20% white noise (SNR = 5), became the fMRI time series (Green). C: GC for HRF-convolved neural time series as a monotonically increasing function of neural GC where the slope of fitted linear trend is close to 1. D: HRF-conv. GC in the opposite direction is zero (unidirectional coupling).</p

Relation between fMRI GC and neural GC (unidirectional coupling).

<p>A: A typical experiment where fMRI GC is a monotonically increasing function of neural GC. B: fMRI GC and neural GC along opposite directions are uncorrelated. C: Distributions of correlation coefficients between neural GC and fMRI GC along the same direction (red) and along opposite directions (blue). D: TPR, FPR and TDR as functions of correlation significance threshold.</p

Effects of TR and noise.

<p>A: TDR, TPR and FPR as functions of fMRI TR. B: TDR, TPR and FPR as functions of the noise level.</p

Relation between fMRI GC and neural GC (bidirectional coupling).

<p>A: A typical experiment where fMRI GC is a monotonically increasing function of neural GC. B: fMRI GC and neural GC along opposite directions are uncorrelated. C: Distributions of correlation coefficients between neural GC and fMRI GC along the same direction (red) and along the opposite directions (blue). D: TPR, FPR and TDR as functions of correlation significance threshold.</p

The log and penalty terms versus candidate order k and the bound BD versus the temporal data size.

<p>A) The variation of the negative log-likelihood with k at different noise levels. B) The penalty terms of AIC, KIC and MDL versus k. C) The variation of the negative log-likelihood with candidate order k at different temporal data size with SD = 1. D) The variation of the bound <i>BD</i> versus the temporal data size.</p

The variation of means of the 50 estimations with the temporal data size(A–C) and FWHM of Gaussian filter(D–F) at three different white noise levels.

<p>A) SD = 1. B) SD = 2. C) SD = 3. D) SD = 1. E) SD = 2. F) SD = 3.</p

Seven simulated sources.

<p>A) The actived spatial regions. B) The corresponding time courses.</p

Results of the real resting fMRI data.

<p>A) Estimations of fMRI data with different added Gaussian noise levels. B) Estimations of fMRI data with different added AR(1) coefficient levels (SD = 2). C) Estimations of fMRI data with different added SD of AR(1) noise (q = 0.5). D) Estimations of data with different temporal data size. E) Estimations of data spatially smoothed by Gaussian filter with different FWHM.</p

The variation of <i>D_k</i> versus candidate order k.

<p>A) Different AR(1) coefficient levels. B) Different SD of AR(1) noise. C) Different temporal data size. D) Different FWHM.</p

Results of the simulated data with varied Gaussian white noise levels.

<p>A) Means of the 50 estimations versus SD of Gaussian noises. B) Accuracy rate versus SD of Gaussian noises. The curves in the figures represent the estimation of different criteria as is specified in the legend.</p