Fig 1.
Workflow from DTI to the model of functional connectivity and comparison with empirical EEG data.
Each processing step in the reference procedure can be replaced by several alternative methods. From left to right: Probabilistic tracts derived from DTI are preprocessed to give the structural connectivity matrix. From there we simulate functional connectivity and optimize free model parameters to maximize the global correlation with the empirical functional connectivity. The empirical functional connectivity is calculated between all pairs of ROIs after projecting EEG scalp recordings to source space using spatial filters. Alternatively, the comparison between simulated and empirical connectomes can be done in sensor space by projecting the simulated functional connectivity into sensor space using the leadfields.
Fig 2.
Comparison of empirical and simulated FC in the reference procedure.
A: Structural connectivity among 66 cortical regions after normalization for ROI size and excluding self-connections (see chapter Reference Procedure, section Reconstructing the structural connectome). B: The correlation of the simulated network based on structural connectivity using the SAR model with optimal global scaling parameter k = 0.65 and homotopic connection strength h = 0.1. C: Upper: The respective simulated (k = 0.65, h = 0.1) and empirical connection strengths are z-transformed and plotted for each connection. Correlation is used as a global performance measure. The local model error per connection is evaluated as the distance (red arrow) to the total-least-squares fit (green line). Lower: Color indicates the correlation strength at a range of different global connection strength scaling parameters k, and fraction of added homotopic connections (h). The black cross indicates the parameters with the maximum correlation. D: The empirical functional connectivity as the coherence between source reconstructed time series at the cortical regions. All connectivity matrices (A, B, D) were normalized to have strengths between 0 (no connection) and 1 (strong connection).
Fig 3.
Dependence of residual and model error (absolute value of residual) on edge and node characteristics.
A: linear fit of the log of the model error per connection showing a negative correlation with fiber distance. B: linear fit of the average model error per ROI showing a negative correlation with the size of the ROI. C: linear fit of the average model error per ROI showing a negative correlation with the betweenness centrality of the ROI. The angle brackets <> denote the average over all edges of the corresponding ROI. Residuals in A-C are calculated from the total least squares fit, negative values (blue dots) indicate that the average modeled functional connectivity per node was higher than the empirical functional connectivity, positive values (yellow dots) indicate that the the modeled functional connectivity per node was smaller than the empirical functional connectivity.
Fig 4.
Structural connectivity preprocessing.
The correlation between modeled and empirical functional connectivity for different preprocessing steps of structural connectivity. In the reference procedure, the number of tracked fibers between two regions was normalized by the product of the region sizes. The model based on the original structural connectivity is shown in blue and the baseline model which is based on shuffled structural connectivity in yellow. The gray box marks the reference procedure.
Fig 5.
Model of functional connectivity.
A: Performance comparison between the SAR model (reference model), the Kuramoto model and directly between the empirical and structural connectivity. The model based on the original structural connectivity is shown in blue and the baseline model which is based on shuffled structural connectivity in yellow. The gray box marks the reference procedure based on the SAR model. B: Performance of the Kuramoto model for different parameters k and h close to the optimal point with fixed velocity = 1.7 m/s and delay = 1.25 ms. C: Same as B but with varying velocity v and delay d with fixed k = 700 and h = 0.12. In panels B and C the X marks the parameter that was selected for the corresponding other panel.
Fig 6.
Comparisons of forward projection and source reconstruction.
A: Global correlation between simulated and empirical functional connectivity in sensor space by applying the forward projection to the SAR model, or in source space by applying the LCMV beamformer to the EEG time series. Blue bars show simulations based on original structural connectivity and yellow bars simulations for randomly shuffled structural connectivity. The gray box marks the reference procedure. B: EEG functional connectivity measured by coherence (left) and the forward projected modeled functional connectivity (right), both in sensor space.
Fig 7.
The correlation between modeled and empirical functional connectivity for different source reconstruction algorithms. The model based on the original structural connectivity is shown in blue and the baseline model which is based on shuffled structural connectivity in yellow. The gray box marks the reference procedure.
Table 1.
Functional Connectivity Metrics.
Fig 8.
Functional connectivity metrics.
The bars show the correlation between the empirical functional connectivity and the simulated functional connectivity obtained using the SAR model. The model based on the original structural connectivity is shown in blue and the baseline model which is based on shuffled structural connectivity in yellow. The gray box marks the reference procedure.