The brain is a complex high-order system. Body movements or mental activities are both dependent on the transmission of information among billions of neurons. However, potential patterns are hardly discoverable due to the high dimensionality in neural signals. Previous studies have identified rotary trajectories in rhythm and nonrhythm movements when projecting the neural electrical signals into a two-dimensional space. However, it is unclear how well this analogy holds at the resting state. Given the low-frequency fluctuations noted during spontaneous neural activities using functional magnetic resonance imaging (fMRI), it is natural to hypothesize that the neural response at resting state also shows a periodic trajectory. In this study, we explored the potential patterns in resting state fMRI data at four frequency bands (slow 2–slow 5) on two cohorts, one of which consisted of young and elderly adults and the other of patients with Alzheimer’s disease and normal controls (NC). The jPCA algorithm was applied to reduce the high-dimensional BOLD signal into a two-dimensional space for visualization of the trajectory. The results indicated that the “resting state” is a basic state showing an inherent dynamic pattern with a low frequency and long period during normal aging, with changes appearing in the rotary period at the slow 4 frequency band (0.027–0.073 Hz) during the pathological process of Alzheimer’s disease (AD). These findings expand the original understanding that neural signals can rotate themselves and that motor executive signals consist of neural signals. Meanwhile, the rotary period at band slow 4 may be a physiological marker for AD, and studies of this frequency band may be useful for understanding the potential pathophysiology of AD and ultimately facilitate characterization and auxiliary diagnosis of AD.
Nonlinear manifold learning in functional magnetic resonance imaging uncovers a low‐dimensional space of brain dynamics
