# Connectivity measures

## Other connectivity 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 (Zang et al. 2007)

with BOLD(x,t) = original BOLD timeseries before band- or low- pass filtering

h(t) = low- or band-pass filter; note: * represents a linear convolution operation

N = number of timepoints

**ALFF(x) = Amplitude of Low-Frequency Fluctuations **at voxel x

*Implementation notes: BOLD(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/sessions*

*note: 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 (Zang et al. 2007)

with BOLD(x,t) = original BOLD timeseries before band- or low- pass filtering

h(t) = low- or band-pass filter; note: * represents a linear convolution operation

** fALFF(x) = Fractional Amplitude of Low-Frequency Fluctuations **at voxel x