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How the statistical validation of functional connectivity patterns can prevent erroneous definition of small-world properties of a brain connectivity network.

Toppi J, De Vico Fallani F, Vecchiato G, Maglione AG, Cincotti F, Mattia D, Salinari S, Babiloni F, Astolfi L - Comput Math Methods Med (2012)

Bottom Line: The application of Graph Theory to the brain connectivity patterns obtained from the analysis of neuroelectrical signals has provided an important step to the interpretation and statistical analysis of such functional networks.However, no common procedure is currently applied for extracting the adjacency matrix from a connectivity pattern.The comparison was performed on the basis of simulated data and of signals acquired on a polystyrene head used as a phantom.

View Article: PubMed Central - PubMed

Affiliation: Department of Computer, Control, and Management Engineering, Sapienza University of Rome, 00185 Rome, Italy.

ABSTRACT
The application of Graph Theory to the brain connectivity patterns obtained from the analysis of neuroelectrical signals has provided an important step to the interpretation and statistical analysis of such functional networks. The properties of a network are derived from the adjacency matrix describing a connectivity pattern obtained by one of the available functional connectivity methods. However, no common procedure is currently applied for extracting the adjacency matrix from a connectivity pattern. To understand how the topographical properties of a network inferred by means of graph indices can be affected by this procedure, we compared one of the methods extensively used in Neuroscience applications (i.e. fixing the edge density) with an approach based on the statistical validation of achieved connectivity patterns. The comparison was performed on the basis of simulated data and of signals acquired on a polystyrene head used as a phantom. The results showed (i) the importance of the assessing process in discarding the occurrence of spurious links and in the definition of the real topographical properties of the network, and (ii) a dependence of the small world properties obtained for the phantom networks from the spatial correlation of the neighboring electrodes.

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Scatterplot of small-worldness clustering coefficient ((a) and (c)) and small- worldness versus path length ((b) and (d)) for each iteration of the adjacency matrix extraction process computed by means of shuffling procedures (first row) and fixed edge density method (second row) for edge densities correspondent to those achieved in Case 2 (edge density as in Figure 5(b)). The line represents the linear fitting computed on the data. The associated values of correlation (r) and r-square (r2) were reported in the boxes.
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fig7: Scatterplot of small-worldness clustering coefficient ((a) and (c)) and small- worldness versus path length ((b) and (d)) for each iteration of the adjacency matrix extraction process computed by means of shuffling procedures (first row) and fixed edge density method (second row) for edge densities correspondent to those achieved in Case 2 (edge density as in Figure 5(b)). The line represents the linear fitting computed on the data. The associated values of correlation (r) and r-square (r2) were reported in the boxes.

Mentions: In order to understand which indices, between the clustering coefficient and the characteristic path length, mainly contributed to the small worldness of the networks achieved by means of shuffling procedure and fixed edge density method, correlations between the small-worldness index and these two indices were computed for the two edge density cases. The results achieved in the case of edge density correspondent to Case 2 (edge density as Figure 2(b)) were showed in Figure 7. The diagram showed the scatterplot of small-woldness versus clustering coefficient (Figures 7(a) and 7(c)) and small-worldness versus path length (Figures 7(b) and 7(d)) for each iteration of the adjacency matrix extraction process computed by means of shuffling procedure (first row) and fixed edge density method (second row) in the case of edge density correspondent to those achieved in Case 2 (edge density as Figure 5(b)). The solid lines in the figure represent the linear fitting computed on the data. In the box, the associated values of correlation (r) and r-square (r2) were reported. The small-worldness of networks achieved by means of shuffling procedure in Case 2 can be due, at the same time, to the clustering coefficient, with a correlation of 0.92 and a r-square of 0.85 and to the path length with a correlation coefficient of −0.69 and a r-square of 0.48. Same consideration could be done for fixed edge density method (small-worldness versus clustering r = 0.83, r2 = 0.70; small-worldness versus path length r = −0.79, r2 = 0.63). The same effect could be described for Case 1 (shuffling procedure: small-worldness versus clustering r = 0.92, r2 = 0.83; small-worldness versus Path Length r = −0.79, r2 = 0.63; fixed edge density: small-worldness versus clustering r = 0.91, r2 = 0.83; smal-worldness versus path length r = −0.87, r2 = 0.76).


How the statistical validation of functional connectivity patterns can prevent erroneous definition of small-world properties of a brain connectivity network.

Toppi J, De Vico Fallani F, Vecchiato G, Maglione AG, Cincotti F, Mattia D, Salinari S, Babiloni F, Astolfi L - Comput Math Methods Med (2012)

Scatterplot of small-worldness clustering coefficient ((a) and (c)) and small- worldness versus path length ((b) and (d)) for each iteration of the adjacency matrix extraction process computed by means of shuffling procedures (first row) and fixed edge density method (second row) for edge densities correspondent to those achieved in Case 2 (edge density as in Figure 5(b)). The line represents the linear fitting computed on the data. The associated values of correlation (r) and r-square (r2) were reported in the boxes.
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC3420234&req=5

fig7: Scatterplot of small-worldness clustering coefficient ((a) and (c)) and small- worldness versus path length ((b) and (d)) for each iteration of the adjacency matrix extraction process computed by means of shuffling procedures (first row) and fixed edge density method (second row) for edge densities correspondent to those achieved in Case 2 (edge density as in Figure 5(b)). The line represents the linear fitting computed on the data. The associated values of correlation (r) and r-square (r2) were reported in the boxes.
Mentions: In order to understand which indices, between the clustering coefficient and the characteristic path length, mainly contributed to the small worldness of the networks achieved by means of shuffling procedure and fixed edge density method, correlations between the small-worldness index and these two indices were computed for the two edge density cases. The results achieved in the case of edge density correspondent to Case 2 (edge density as Figure 2(b)) were showed in Figure 7. The diagram showed the scatterplot of small-woldness versus clustering coefficient (Figures 7(a) and 7(c)) and small-worldness versus path length (Figures 7(b) and 7(d)) for each iteration of the adjacency matrix extraction process computed by means of shuffling procedure (first row) and fixed edge density method (second row) in the case of edge density correspondent to those achieved in Case 2 (edge density as Figure 5(b)). The solid lines in the figure represent the linear fitting computed on the data. In the box, the associated values of correlation (r) and r-square (r2) were reported. The small-worldness of networks achieved by means of shuffling procedure in Case 2 can be due, at the same time, to the clustering coefficient, with a correlation of 0.92 and a r-square of 0.85 and to the path length with a correlation coefficient of −0.69 and a r-square of 0.48. Same consideration could be done for fixed edge density method (small-worldness versus clustering r = 0.83, r2 = 0.70; small-worldness versus path length r = −0.79, r2 = 0.63). The same effect could be described for Case 1 (shuffling procedure: small-worldness versus clustering r = 0.92, r2 = 0.83; small-worldness versus Path Length r = −0.79, r2 = 0.63; fixed edge density: small-worldness versus clustering r = 0.91, r2 = 0.83; smal-worldness versus path length r = −0.87, r2 = 0.76).

Bottom Line: The application of Graph Theory to the brain connectivity patterns obtained from the analysis of neuroelectrical signals has provided an important step to the interpretation and statistical analysis of such functional networks.However, no common procedure is currently applied for extracting the adjacency matrix from a connectivity pattern.The comparison was performed on the basis of simulated data and of signals acquired on a polystyrene head used as a phantom.

View Article: PubMed Central - PubMed

Affiliation: Department of Computer, Control, and Management Engineering, Sapienza University of Rome, 00185 Rome, Italy.

ABSTRACT
The application of Graph Theory to the brain connectivity patterns obtained from the analysis of neuroelectrical signals has provided an important step to the interpretation and statistical analysis of such functional networks. The properties of a network are derived from the adjacency matrix describing a connectivity pattern obtained by one of the available functional connectivity methods. However, no common procedure is currently applied for extracting the adjacency matrix from a connectivity pattern. To understand how the topographical properties of a network inferred by means of graph indices can be affected by this procedure, we compared one of the methods extensively used in Neuroscience applications (i.e. fixing the edge density) with an approach based on the statistical validation of achieved connectivity patterns. The comparison was performed on the basis of simulated data and of signals acquired on a polystyrene head used as a phantom. The results showed (i) the importance of the assessing process in discarding the occurrence of spurious links and in the definition of the real topographical properties of the network, and (ii) a dependence of the small world properties obtained for the phantom networks from the spatial correlation of the neighboring electrodes.

Show MeSH
Related in: MedlinePlus