# Connectivity measures

## Other connectivity measures

This section describes two additional measures characterizing some aspects of the BOLD timeseries which are often disregarded by most functional connectivity (FC) metrics. All correlation-based metrics are scale invariant, so the actual overall size of the BOLD fluctuations driving many observed FC measures remains unknown. The measures described in this section estimate the variability of the BOLD signal within the standard frequency window of interest (e.g. 0.008Hz to 0.09Hz). While strictly speaking these are not measures of functional connectivity, they are nevertheless useful metrics as they offer often complementary information to many other FC measures.

### Amplitude of Low-Frequency Fluctuations (ALFF)

ALFF maps represent a measure of BOLD signal power within the frequency band of interest (e.g. 0.01 - 0.10 Hz). ALFF is defined as the root mean square of BOLD signal at each individual voxel after low- or band- pass filtering (Yang et al. 2007)

where S is original BOLD timeseries before band- or low- pass filtering, h is a low- or band-pass filter, N is the number of timepoints, and ALFF is the Amplitude of Low-Frequency Fluctuations map

Implementation notes: S(x,t) timeseries are the signals after preprocessing and the initial denoising linear regression step (e.g. session-specific regression of aCompCor, motion, outlier scans, mean, and trend factors) but before the last denoising band-pass filtering step. Filtering is implemented using a Discrete Cosine Transform (DCT) rectangular window for each session-specific BOLD signal timeseries, and the resulting timeseries are then concatenated across multiple runs/sessionsnote: an alternative/equivalent formulation in terms of the mean and variance of the denoised and filtered timeseries is the following
where mu & sigma are the mean and variance, respectively, of the denoised and filtered BOLD signal

### Fractional Amplitude of Low-Frequency Fluctuations (fALFF)

fALFF maps represent a relative measure of BOLD signal power within the frequency band of interest (e.g. 0.01 - 0.10 Hz) compared to that over the entire frequency spectrum. fALFF is defined as the ratio of root mean square of BOLD signal at each individual voxel after vs. before low- or band- pass filtering (Zou et al. 2008)

where S is original BOLD timeseries before band- or low- pass filtering, h is a low- or band-pass filter, and fALFF is the Fractional Amplitude of Low-Frequency Fluctuations map

Yang, H., Long, X. Y., Yang, Y., Yan, H., Zhu, C. Z., Zhou, X. P., ... & Gong, Q. Y. (2007). Amplitude of low frequency fluctuation within visual areas revealed by resting-state functional MRI. Neuroimage, 36(1), 144-152.

Zou, Q. H., Zhu, C. Z., Yang, Y., Zuo, X. N., Long, X. Y., Cao, Q. J., ... & Zang, Y. F. (2008). An improved approach to detection of amplitude of low-frequency fluctuation (ALFF) for resting-state fMRI: fractional ALFF. Journal of neuroscience methods, 172(1), 137-141.