Revisiting Amplitude of Low-Frequency Fluctuations (ALFF) in Resting-state fMRI: Clarifications and Improvements

The amplitude of low-frequency fluctuations (ALFF) and its related measure, fractional ALFF (fALFF), are widely used resting-state fMRI techniques for quantifying spontaneous neural activity within specific frequency bands. However, inconsistencies in the definition and implementation of ALFF have led to confusion in the field. In this study, we provide a mathematical clarification of ALFF and fALFF by introducing two variants: the arithmetic mean-defined ALFF/fALFF (amALFF/amfALFF) and the quadratic mean-defined ALFF/fALFF (qmALFF/qmfALFF). We examine the relationships between mean BOLD intensity (MBI), amALFF, and qmALFF across both subjects and voxels using two independent datasets mapped onto different brain templates. Additionally, we investigate the impact of z-scoring the original BOLD signal on ALFF and fALFF metrics. Our key findings include: (1) MBI is positively correlated with both amALFF and qmALFF, highlighting the need for normalization to subject-level means; (2) normalized qmALFF and qmfALFF are highly correlated with normalized amALFF and amfALFF, respectively, at both the subject and voxel levels; (3) z-scoring the BOLD signal does not affect amfALFF or qmfALFF, but it substantially alters amALFF and qmALFF. Based on these findings, we present a comprehensive flowchart of the (f)ALFF algorithm implemented in the temporal domain. The full procedure is implemented in R, and the corresponding script is available at: https://github.com/lejianhuang/ALFF.