Figure 1.
Examples of how conventional approaches that separately summarize each condition of a pair could misrepresent patterns of changes in connectivity.
A) When a binary graph is used, changes in correlation near the threshold value (threshold ) can lead to an over/under-estimation of connectivity changes. In this example, one edge increases its correlation by 0.02 in between conditions 1 and 2, which leads an increase in degree for condition 2. However, this increase in correlation and degree is likely not meaningful. B) When a weighted graph is used, increases and decreases in connectivity between conditions could cancel each other out. In this example, half of a node's edges increase their correlation while half of its edges decrease their correlation in condition 2 compared to condition 1. When all edges are averaged together, no change between the conditions is detected, despite that a change is clearly present.
Figure 2.
Flow chart describing coupled-ICD.
For data consisting of paired conditions, coupled-ICD jointly analyzes both conditions and then creates a summary of the difference in connectivity between conditions for each voxel. First, a “seed” connectivity map is created for a voxel (shown as the blue square through the flow chart) in each condition. The resulting “seed” maps are then subtracted and a histogram of the differences is computed. The survival function of the distribution of the difference (labeled as coupled-ICD curve) is calculated and modeled with a stretched exponential. This process is repeated for each voxel in the gray matter. The final output is an image where each voxel represents a summary of the difference between two “seed” maps using that voxel as the seed region.
Figure 3.
Comparison of coupled-ICD and conventional approaches for detecting connectivity changes due to anesthesia.
Regions of large A) increased connectivity and B) decreased connectivity under anesthesia detected by coupled-ICD and thresholded using the Top Percent method. For some regions, coupled-ICD was able to detect regions with both increased and decreased connectivity. One of these areas (the right parietal lobe; black circle) was used for further analysis. Regions of significant change in connectivity detected by conventional voxel-based approaches are shown in C) ICD and D) wGBC. While a general correspondence was observed between all methods, the coupled-ICD results suggest a decrease in connectivity for the left frontal lobe (black circle) while the conventional approaches suggest an increase in connectivity. This region was selected for further analysis. While the conventional voxel-based approaches, C) ICD and D) wGBC, suggested more focal changes in connectivity, E) matrix connectivity and coupled-ICD suggest more widespread changes due to anesthesia. Only edges that were significantly difference at p<0.05 with FDR correction are shown. The size of the node is proportional to the number of significantly different edges touching that node such that a larger node has more significantly different edges.
Figure 4.
Seed-based connectivity results using seeds detected by coupled-ICD.
A) Several regions of the brain displayed evidence for both increased and decreased connectivity during the anesthesia state as detected by coupled-ICD. A follow-up seed-based analysis on independent data for one of these regions (the right parietal lobe; green region) revealed both significant (p<0.05 corrected) increases and decreases in connectivity to this region, echoing the coupled-ICD results. B) For some regions of the brain, coupled-ICD and conventional approaches showed seemingly conflicting results, with coupled-ICD suggesting decreased connectivity while conventional approaches suggest increased connectivity due to anesthesia. Seed connectivity for one of these regions (the left frontal lobe; green region) revealed both significant (p<0.05 corrected) increased and decreased connectivity, demonstrating that the different approaches may be sensitive to different aspects of changes in connectivity.
Figure 5.
Comparison of coupled-ICD and conventional approaches for detecting group-by-condition interaction for cocaine-dependent subjects (CD) and healthy controls (HC).
As the comparison between CD and HC subjects involves contrasting a metric (coupled-ICD) that already measures the difference between two conditions, this result can be interpreted in a similar manner to the interaction term of a classic 2×2 two-way ANOVA. A) Coupled-ICD detected more widespread significant interactions than the two conventional approaches, B) ICD and C) wGBC. D) ROI-based matrix connectivity method also detects widespread interaction between group and condition provide support that the coupled-ICD results are not simply artifacts. Only edges that were significantly difference at p<0.05 with FDR correction are shown. The size of the node is proportional to the number of significantly different edges touching that node. A larger node has more significantly different edges.
Figure 6.
Follow-up seed-based connectivity results using a seed detected by coupled-ICD.
A follow-up, seed-based connectivity analysis was performed using a region in the left putamen detected by coupled-ICD but not by conventional ICD and degree analysis. This region shows significant group interaction (p<0.05, corrected) in the caudate and nucleus accumbens. The subjects analyzed in the seed analysis were not used in the voxel-based analysis, providing additional evidence of coupled-ICD robustness and utility. The green region shows the location of the seed ROI.