Pattern of frustration formation in the functional brain network

Abstract The brain is a frustrated system that contains conflictual link arrangements named frustration. The frustration as a source of disorder prevents the system from settling into low-energy states and provides flexibility for brain network organization. In this research, we tried to identify the pattern of frustration formation in the brain at the levels of region, connection, canonical network, and hemisphere. We found that frustration formation has no uniform pattern. Some subcortical elements have an active role in frustration formation, despite low contributions from many cortical elements. Frustrating connections are mostly between-network connections, and triadic frustrations are mainly formed between three regions from three distinct canonical networks. We did not find any significant differences between brain hemispheres or any robust differences between the frustration formation patterns of various life-span stages. Our results may be interesting for those who study the organization of brain links and promising for those who want to manipulate brain networks.


Figures:
Figure S1.Between-stage comparison of regional contribution in frustration formation.Violet regions denote ROIs that have between-stage differences with corrected p-value lower than 0.05 and medium effect sizes.

Figure S2
. Comparison of actual regional pattern's entropies with shuffled regional pattern's entropies.The left and right subfigures refer to regions with significantly higher contribution and regions with the significantly lower contribution in frustration formation.Histograms show shuffled pattern's entropies and vertical dashed lines denote to the value of the actual pattern's entropies shown in Figure 3.

Figure S3 .
Figure S3.Comparison of actual connectional pattern's entropies with shuffled connectional pattern's entropies.The left and right subfigures refer to connections with significantly higher contribution and connections with the significantly lower contribution in frustration formation.Histograms show shuffled pattern's entropies and vertical dashed lines denote the value of the actual pattern's entropies shown in Figure 4.

Figure S4 .
Figure S4.Between-stage comparison of connectional contribution in frustration formation.Shen's 268 ROIs are categorized into 10 networks of Fig. 2 by axes coloring.Cells also represent functional connections between every two ROIs.Violet cells denote connections that have between-stage differences with corrected p-value lower than 0.05 and medium effect sizes.Black squares discriminate between network connections.Abbreviation; VIS: visual, SM: somatomotor, DA: dorsal attention, VA: ventral attention, LIM: limbic, FP: frontoparietal, DM: default mode, SCS: subcortical structures, BS: brainstem, CB: cerebellum.

Figure S5 .
Figure S5.Projection of Shen's ROIs into Yeo's canonical networks.Colorbar denotes the Dice coefficient for each pair of ROI and canonical networks.Yeo's atlas is a cortical parcellation so subcortical ROIs can not project into it, corresponding null cells.Abbreviation; VIS: visual, SM: somatomotor, DA: dorsal attention, VA: ventral attention, LIM: limbic, FP: frontoparietal, DM: default mode.

Figure S6 .
Figure S6.Percentages of positive and negative links before and after Global Signal Regression (GSR).

Figure S7 .
Figure S7.The pattern of regional contribution in frustration formation when we added global signal regression to preprocessing.Red-colored and blue-colored areas of the brain maps indicate Shen's regions with significantly greater and significantly lower contributions in frustration formation.Brain maps demonstrate the patterns for various lifespan stages and all stages in three representational planes of sagittal, axial, and coronal.Abbreviation; VIS: visual, SM: somatomotor, DA: dorsal attention, VA: ventral attention, LIM: limbic, FP: frontoparietal, DM: default mode, SCS: subcortical structures, BS: brainstem, CB: cerebellum.

Figure S8 -
Figure S8 -Contribution maps of functional connections in frustration formation when we added global signal regression to preprocessing.The first five maps demonstrate the maps related to lifespan stages and the last one corresponds without considering the stage.Shen's 268 ROIs are categorized into 10 networks of Figure 2 by axes coloring.Cells also represent functional connections between every two ROIs.Red cells display those connections with a significantly greater contribution to frustration formation and blue cells indicate those connections with significantly lower involvement.Black squares discriminate between network connections.Abbreviation; VIS: visual, SM: somatomotor, DA: dorsal attention, VA: ventral attention, LIM: limbic, FP: frontoparietal, DM: default mode, SCS: subcortical structures, BS: brainstem, CB: cerebellum.

Figure S9 .
Figure S9.Projection of DKT atlas ROIs into Yeo's canonical networks.Colorbar denotes the Dice coefficient for each pair of ROI and canonical networks.Yeo's atlas is a cortical parcellation so subcortical ROIs can not project into it, corresponding null cells.Abbreviation; VIS: visual, SM: somatomotor, DA: dorsal attention, VA: ventral attention, LIM: limbic, FP: frontoparietal, DM: default mode.

Figure S10 .
Figure S10.The pattern of regional contribution in frustration formation for DKT parcellation.Red-colored and blue-colored areas of the brain maps indicate DKT atlas's regions with significantly greater and significantly lower contributions in frustration formation.Brain maps demonstrate the patterns for various lifespan stages and all stages in three representational planes of sagittal, axial, and coronal.Abbreviation; VIS: visual, SM: somatomotor, DA: dorsal attention, VA: ventral attention, LIM: limbic, FP: frontoparietal, DM: default mode, SCS: subcortical structures, BS: brainstem, CB: cerebellum.

Figure S11 -
Figure S11 -Contribution maps of functional connections in frustration formation for DKT parcellation.The first five maps demonstrate the maps related to lifespan stages and the last one corresponds without considering the stage.Shen's 268 ROIs are categorized into 10 networks of Figure 2 by axes coloring.Cells also represent functional connections between every two ROIs.Red cells display those connections with a significantly greater contribution to frustration formation and blue cells indicate those connections with significantly lower involvement.Black squares discriminate between network connections.Abbreviation; VIS: visual, SM: somatomotor, DA: dorsal attention, VA: ventral attention, LIM: limbic, FP: frontoparietal, DM: default mode, SCS: subcortical structures, BS: brainstem, CB: cerebellum.

Table S1 . Statistics related to within-network contribution of canonical networks in frustration formation
. Corrected p-values of the Wilcoxon paired signed-rank test are presented in cells and corresponding r effect sizes are parenthesized below them.Highlighted cells denote corrected pvalue lower than 0.05 with a large r effect size.Table S2.Statistics related to between-network (type I) contribution of canonical networks in frustration formation.Corrected p-values of the Wilcoxon paired signed-rank test are presented in cells and corresponding r effect sizes are parenthesized below them.Highlighted cells denote corrected p-value lower than 0.05 with a large r effect size.

Table S3 . Statistics related to between-network (type II) contribution of canonical networks in frustration formation.
Corrected p-values of the Wilcoxon paired signed-rank test are presented in cells and corresponding r effect sizes are parenthesized below them.Highlighted cells denote corrected p-value lower than 0.05 with a large r effect size.

Table S4 . Statistics related to between-network (type III) contribution of canonical networks in frustration formation.
Corrected p-values of the Wilcoxon paired signed-rank test are presented in cells and corresponding r effect sizes are parenthesized below them.Highlighted cells denote corrected p-value lower than 0.05 with a large r effect size.

Table S6 . Subject demographics. Table S5. Statistics related to Hemisphere contribution in frustration formation.
Corrected pvalues of the Wilcoxon paired signed-rank test are presented in cells and corresponding r effect sizes are parenthesized below them.