Resting-state functional connectivity based on total correlations. Functional connectivity between brain regions was measured using resting-state fMRI at baseline (chow) and after 3.5 and 6 months of treatment with HFD, HFD + exercise, and HFD + BCAA + exercise. Total correlation matrixes show the connectivity between the dorsal hippocampus (DH), ventral hippocampus (VH), auditory cortex (AC), motor cortex (MC), somatosensory cortex (SSC), and visual cortex (VC) for the left (L) and right (R) hemisphere, respectively, at each neuroimaging time point, respectively. High-fat diet (HFD), branched-chain amino acids (BCAA).