Brain entropy mapping using fMRI

Abstract

Entropy is an important trait for life as well as the human brain. Characterizing brain entropy (BEN) may provide an informative tool to assess brain states and brain functions. Yet little is known about the distribution and regional organization of BEN in normal brain. The purpose of this study was to examine the whole brain entropy patterns using a large cohort of normal subjects. A series of experiments were first performed to validate an approximate entropy measure regarding its sensitivity, specificity, and reliability using synthetic data and fMRI data. Resting state fMRI data from a large cohort of normal subjects (n = 1049) from multi-sites were then used to derive a 3-dimensional BEN map, showing a sharp low-high entropy contrast between the neocortex and the rest of brain. The spatial heterogeneity of resting BEN was further studied using a data-driven clustering method, and the entire brain was found to be organized into 7 hierarchical regional BEN networks that are consistent with known structural and functional brain parcellations. These findings suggest BEN mapping as a physiologically and functionally meaningful measure for studying brain functions.

Figure 1. Evaluations of entropy mapping using fMRI.

A) image of a cylinder water phantom; B) entropy map of the phantom. The color bar indicates the display color window for the entropy map; C) visual and sensorimotor functional activation induced brain entropy decrease as compared to the resting state. Red and green represent the test (session 1) and retest (session 2) experiment, respectively. The color bars indicate the color window used to display the statistical comparison results (t maps of the paired student t-testing). The statistical threshold for identifying the entropy decreasing clusters is p<0.001 and cluster size>30 (uncorrected for multiple comparisons); D) the correlation coefficient (CC) map of 50 subjects' resting BEN maps. The color bar was used to map the CC value from 0.5 to 1.

Figure 2. The BEN maps with and without background.

A) BEN map of a representative subject. B) average BEN map of 1049 subjects. The background voxels were removed for a better visualization.The gray scale and color scale indicate BEN values for Figure 2a and 2b, respectively.

Figure 3. Spatial distribution and regional organization of BEN.

A) The statistically defined higher-than-average BEN network (hot color) and lower-than-average BEN network (cool color). The significance level used for thresholding the distribution map (the statistical parametric map of the student t-test) is p<0.01 (corrected for multiple comparison); B) The 8 BEN clusters identified by clustering: a) OFC, b) TPLS, c) WM, d) VIS, e) DMN, f) MC, g) PFC, h) peripheral artifact. The text above each axial slice in B, C, and D indicates the slice location (z and x mean the x and z coordinate in mm, respectively) in the MNI space. The left side of image corresponds to the left side of brain.

Figure 4. The hierachy and ranking of the BEN-derived brain subdivisions.

A) the across-subject BEN similarity matrix, B) the hierarchical structure of the 7 BEN clusters. C) Mean and standard errors of the mean rBEN in the 7 clusters. The color map in A represents the correlations of BEN within and between BEN clusters. The inset in C lists the probability of the rBEN comparisons between a pair of BEN clusters.