Participation in magnetic resonance imaging (MRI) scanning is associated with increased anxiety, thus possibly impacting baseline recording for functional MRI studies. The goal of the paper is to elucidate the significant hemispheric asymmetry between blood-oxygenation-level-dependent (BOLD) signals from precentral gyrus (PCG) and insula in 23 healthy individuals without any former MRI experience recently published in a PLOSONE paper. In addition to BOLD signals state anxiety and heart rate variability (HRV) were analyzed in two resting state sessions (R1, R2). Phase-locking and time delays from BOLD signals were computed in the frequency band 0.07-0.13 Hz. Positive (pTD) and negative time delays (nTD) were found. The pTD characterize descending neural BOLD oscillations spreading from PCG to insula and nTD characterize ascending vascular BOLD oscillations related to blood flow in the middle cerebral artery. HRV power in two low frequency bands 0.06-0.1 Hz and 0.1-0.14 Hz was computed. Based on the anxiety change from R1 to R2, two groups were separated: one with a strong anxiety decline (large change group) and one with a moderate decline or even anxiety increase (small change group). A significant correlation was found only between the left-hemispheric time delay (pTD, nTD) and anxiety change, with a dominance of nTD in the large change group. The analysis of within-scanner HRV revealed a pronounced increase of low frequency power between both resting states, dominant in the band 0.06-0.1 Hz in the large change group and in the band 0.1-0.14 Hz in the small change group. These results suggest different mechanisms related to anxiety processing in healthy individuals. One mechanism (large anxiety change) could embrace an increase of blood circulation in the territory of the left middle cerebral artery (vascular BOLD) and another (small anxiety change) translates to rhythmic central commands (neural BOLD) in the frequency band 0.1-0.14 Hz.