A Distinct Second Spectral Peak in White Matter BOLD Signals: Mathematical Modeling, Spatial Distribution and Age-Related Evolution.

White matter blood-oxygenation-level-dependent (BOLD) signals in resting-state functional magnetic resonance imaging (rs-fMRI) are increasingly recognized for their physiological significance, yet their intrinsic spectral architecture remains largely uncharted. In this work, using high quality data from the Human Connectome Project (HCP), we mathematically model and quantitatively characterize a robustly detectable "second peak" superimposed on the canonical exponentially decaying white matter BOLD spectrum. The spectral signature, with a peak frequency around ~ 0.06 Hz, emerges as a stable individual-level phenotype with broad spatial penetrance across white matter. Cross-tissue analyses reveal that while BOLD signals in cerebrospinal fluid (CSF) exhibit similar low frequency dynamics, white matter provides the most prominent and organized manifestation of this spectral feature. Spatially, the peak follows distinct gradients that mirror macroscopic white matter anatomy. Exploratory analyses in the HCP-Aging cohort further suggest that this band-specific spectral signature undergoes systematic evolution with age. Synthesizing the frequency profile, spatial distribution, and aging trajectory, we propose that the white matter second peak may serve as an organized, tissue-modulated readout of ubiquitous low-frequency physiological dynamics, potentially linked to glymphatic or perivascular clearance mechanisms in the brain. Together, these findings point to a robust spectral phenotype that may open a new noninvasive dimension for investigating white matter functional integrity, brain aging, and relevant physiological mechanisms.