Multivariate Correlation Measures Reveal Structure and Strength of Brain–Body Physiological Networks at Rest and During Mental Stress

FIGURE 1. Schematic representation of the data acquisition and analysis steps. (A) Graphical representation of the positioning of the 14 EEG electrodes over the scalp. (B) Physiological systems and variables considered in this work: cardiac variable η (R–R interval of the ECG), respiratory variable ρ (respiration amplitude), and cardiovascular variable π (pulse arrival time) for the body subnetwork X; amplitude of the δ, θ, α, and β EEG waves for the scalp subnetwork Y; the two subnetworks form the overall physiological network Z. (C) Venn diagrams depicting the multivariate interaction measures used in this work: on the left, multivariate brain–body interaction, quantifying the variability shared by the two subnetworks X and Y (light green area); in the middle, “direct” interaction between two individual variables (here, the cardiac and respiratory variables η and ρ), when all other variables are considered (orange area); on the right, decomposition of the interaction between one target variable (here, the cardiac variable η) and all other variables (green + blue areas) as the sum of the interactions internal to the target subnetwork (here, the body subnetwork X; green area) and the…

FIGURE 2. Spatial distribution of (A) the median multivariate interaction between brain and body, R(X; Y), and (B) the number of subjects with statistically significant values of the index, in the three analyzed conditions (REST, MENTAL, and GAME). Markers are located at EEG electrode positions and in (A) are colored according to the results of statistical analysis (white: p < 0.05 MENTAL vs. REST or GAME vs. REST).

FIGURE 3. Spatial distribution over the scalp of (A) the median multivariate interaction between a target x_i of the body subnetwork and all remaining variables, R(xi;Xi,Y), and (B) the number of subjects with statistically significant values of the index, in the three analyzed conditions (REST, MENTAL, and GAME); the index is computed with target corresponding to the cardiac process η (upper row panels), to the respiratory process ρ (middle row panels), and to the cardiovascular process π (lower row panels). Markers are located at EEG electrode positions and in (A) are colored according to the results of statistical analysis (white: p < 0.05 MENTAL vs. REST or GAME vs. REST). Asterisk (*) on an electrode indicates p < 0.05 MENTAL vs. GAME.

FIGURE 4. Spatial distribution over the scalp of (A) the median multivariate interaction between a target y_j of the brain subnetwork and all remaining variables, R(yj;Yj,X), and (B) the number of subjects with statistically significant values of the index, in the three analyzed conditions (REST, MENTAL, and GAME); the index is computed with target corresponding to the EEG power band processes δ,θ,α,β (from upper to lower row panels). Markers are located at EEG electrode positions and in (A) are colored according to the results of statistical analysis (white: p < 0.05 MENTAL vs. REST or GAME vs. REST). Asterisk (*) on an electrode indicates p < 0.05 MENTAL vs. GAME. Hash symbols indicate results of Kruskal–Wallis test (#: p < 0.05, non-homogeneity of the spatial distribution).

FIGURE 5. (A) Distributions of the multivariate interaction between a target x_i of the body subnetwork and the two other variables of the same subnetwork, R(xi;Xi), and (B) number of subjects with statistically significant values of the index, in the three analyzed conditions (REST, MENTAL, and GAME); the index is computed with target corresponding to the cardiac, respiratory, and cardiovascular processes η,ρ, and π. In (A), pKW indicates results of Kruskal–Wallis test, while hash symbols indicate a p-value lower than 0.05 obtained using post-hoc test for the analysis between REST and the considered condition (#: p < 0.05 MENTAL vs. REST or GAME vs. REST).

FIGURE 6. Spatial distribution over the scalp of (A) the median multivariate interaction between a target y_j of the brain subnetwork and the three other variables in the same subnetwork, R(yj;Yj), and (B) number of subjects with statistically significant values of the index, in the three analyzed conditions (REST, MENTAL, and GAME); the index is computed with target corresponding to the EEG power band processes δ,θ,α,β (from upper to lower row panels). Markers are located at EEG electrode positions and in (A) are colored according to the results of statistical analysis (white: p < 0.05 MENTAL vs. REST or GAME vs. REST). Asterisk (*) on an electrode indicates p < 0.05 MENTAL vs. GAME. Hash symbols indicate results of Kruskal–Wallis test (#: p < 0.05, non-homogeneity of the spatial distribution).

FIGURE 7. Spatial distribution over the scalp of (A) the median multivariate interaction between a target x_i of the body subnetwork and all variables of the brain subnetwork, conditioned on the two remaining variables of the body subnetwork, R(xi;Y|Xi), and (B) the number of subjects with statistically significant values of the index, in the three analyzed conditions (REST, MENTAL, and GAME); the index is computed with target corresponding to the cardiac process η (upper row panels), to the respiratory process ρ (middle row panels), and to the cardiovascular process π (lower row panels). Markers are located at EEG electrode positions and in (A) are colored according to the results of statistical analysis (white: p < 0.05 MENTAL vs. REST or GAME vs. REST). Asterisk (*) on an electrode indicates p < 0.05 MENTAL vs. GAME. Hash symbols indicate results of Kruskal–Wallis test (#: p < 0.05, non-homogeneity of the spatial distribution).

FIGURE 8. Spatial distribution over the scalp of (A) the median multivariate interaction between a target y_j of the brain subnetwork and all variables of the body subnetwork, conditioned on the three remaining variables of the brain subnetwork, R(yj;X|Yj), and (B) the number of subjects with statistically significant values of the index, in the three analyzed conditions (REST, MENTAL, and GAME); the index is computed with target corresponding to the EEG power band processes δ,θ,α,β (from upper to lower row panels). Markers are located at EEG electrode positions and in (A) are colored according to the results of statistical analysis (white: p < 0.05 MENTAL vs. REST or GAME vs. REST). Asterisk (*) on an electrode indicates p < 0.05 MENTAL vs. GAME. Hash symbols indicate results of Kruskal–Wallis test (#: p < 0.05, non-homogeneity of the spatial distribution).

FIGURE 9. Topological representation of the interaction between pairs of nodes z_i and z_j of the physiological network (zi,zj ∈ Z = {η,ρ,π,δ,θ,α,β}), provided by the statistically significant values of the conditional MI measure R(zi;zj|Z\{zi,zj}), during the three considered states (REST, MENTAL, and GAME). Thickness of the lines is proportional to the number of subjects for which the corresponding link is statistically significant (p < 0.05, Fisher’s F-test). Red, blue, and black lines denote the links relevant to body–body, brain–brain, and brain–body interactions.