Statistical Analysis of Functional Images

To capture the modulatory impact of glucose administration on the association between the activity of brain regions and plasma insulin or glucose levels under different metabolic states, we performed two multiple linear regression analyses (MLRA) using SPM12, the first “before” and the second “after” oral glucose treatment. Each MLRA was designed with two covariates (plasma insulin and glucose levels). Briefly, MLRA is used to describe how a “linear combination” of multiple variables, called independent or explanatory variables, to predict a single response variable, referred to as the dependent or target variable. The contribution of each independent variable to the model is assessed by looking at the regression coefficients (Nathans et al., 2012). In this study, we used MLRA to figure out the contribution of plasma insulin (an independent variable) to the prediction of brain activity (the dependent variable) when taking the effect of plasma glucose (another independent variable) into account (Kiebel and Holmes, 2007; Field, 2014), and vice versa. Accordingly, our multiple linear regression model is:

where Y_j is a dependent variable (such as fALFF at a particular voxel) and j = 1,…,J indexes the observation. The regression coefficient μ represents a constant term (the mean of the dependent variable when all predictors are zero), while β₁ represents the regression slope, which quantifies the association of Y with x₁ (such as plasma insulin), adjusting for the effect of x₂ (plasma glucose) on Y and vice versa for β₂ and ∈ is the error associated with the regression (the variance of the dependent variable from its mean when all predictors are zero). The parameters were estimated by using the least squares method. To find significant voxels whose activity was affected by hunger vs. satiety or by glucose or insulin, we used one-sample t-tests for each regression coefficient on the voxel level per MLRA (see section below). The resulting statistics indicate whether the regression coefficient of a particular voxel is significantly different from the error in that estimate (Field, 2014). To correct for multiple comparisons, the topological false discovery rate (FDR) q = 0.05 was employed with a cluster defining threshold of p < 0.001 for the t-tests (Chumbley et al., 2010).

In the 1st MLRA (before glucose administration), we contrasted hunger vs. satiety states while controlling the moderating fluctuation of glucose and insulin. We calculated differences [delta (Δ) = hunger-satiety] of fALFF maps before oral glucose treatment. For glucose and insulin, the area under the concentration-time curve (AUC) of the first four samples (Figures 1A,B) was calculated and the Δ of the AUC was obtained. The AUC has been used as an index to assess the regulation of glucose and insulin (Tzagournis and Skillman, 1970; Owen et al., 2012). It was calculated using the standard trapezoid method, which is computing the AUC with respect to ground (see formula 2 in Pruessner et al., 2003). The group level analysis was performed using Δ AUC of glucose and insulin as covariates (independent variables) and the Δ fALFF maps as the dependent variable in the MLRA. Notably, the Δ AUC of glucose and insulin were not significantly correlated (|r| = 0.3, p = 0.1). To check whether the AUC of plasma glucose and insulin influence our findings, we also recomputed the 1st MLRA by including the Δ plasma glucose and insulin based on the value 20 min before glucose ingestion (Figure 1) as independent variables. The results of this model (see Supplementary Table S1 and Supplementary Figure S2 in the supplementary material) were similar to the results of the model with AUC (see Table 1 and Figure 4A). The AUC provides an overview of plasma glucose and insulin level profiles under diet or standard meal vs. time (Johnson et al., 2006). Also, we believe that the changes in brain activity before glucose ingestion may be related to profile change more than single glucose and insulin values. Therefore, we will report the AUC model results only.

Changes and associations of fractional amplitude of low-frequency fluctuation (fALFF) with food conditions and hormone levels.

Notes: The table shows three local maxima [Montreal Neurological Institute (MNI) coordinates] more than 8.0 mm, the adjusted (adj.) p-values are reported at p < 0.001 (height threshold) and q < 0.05 (FDR extent threshold). T, peak of T values; K, cluster size; Hes, hemisphere; L, left; R, right.

Hunger vs. satiety effects on brain activity. (A) Mean fractional amplitude of low-frequency fluctuation (fALFF) value of all voxels of a significant cluster per condition across participants. (B) Results of the first model (before glucose administration). (C) Mean fALFF value of all voxels of a significant cluster per condition across participants. (D) Results of the second model (after glucose administration). Abbreviations: PCC, posterior cingulate cortex; PCUN, precuneus; IPG, inferior parietal gyrus.

The 2nd MLRA (after glucose administration) had a similar design as first MLRA. Differences (Δ) of amplitude rs-fMRI signals were calculated by subtracting the fALFF maps of hunger condition from satiety condition. The Δ calculated for glucose and insulin was based on the value 20 min after glucose ingestion (Figure 1) only to keep the temporal association of endocrine and functional imaging data as clear as possible. Δ glucose and Δ insulin were used as covariates in the MLRA. Again, glucose and insulin were not significantly correlated (|r| = 0.14, p = 0.5). Additional glucose and insulin samples collected after oral glucose intake were not included in this analysis, because they were taken after the second rs-fMRI recording.

To ensure that the correlation between specific brain regions and glucose or insulin values is not biased (Esterman et al., 2010), we extracted fALFF values by averaging across voxels in each cluster that survived the cluster-significance test. Then, we performed the leave-one-out cross-validation (LOOCV) of Pearson correlation to evaluate the relationship between averaged ΔfALFF values of each brain region with Δ of the plasma glucose and insulin. Finally, we performed full and partial correlation analyses between clusters linked to plasma insulin levels to investigate the association between them and the effects of glucose and insulin values on that association.

Finally, to investigate the acute effect of glucose administration on the interaction between brain activity and physiological changes, we performed two additional MLRA. The 3rd and 4th MLRAs estimate the correlations between changes in fALFF (Δ fALFF = pre-post glucose ingestion) and changes in plasma glucose/insulin (Δ of plasma glucose/insulin were calculated based on the value of 20 min before and after glucose ingestion; Figure 1) under satiety and hunger conditions separately, respectively.

We used the automated anatomical labeling (AAL) atlas (Tzourio-Mazoyer et al., 2002) included in the xjView toolbox¹ to label the anatomical location of significant clusters. Thalamic nuclei were identified by applying the MNI-based Morel Atlas (Jakab et al., 2012).