Framewise Displacement

Calculate Framewise Displacement (FD)

FD(
  X,
  trans_units = c("mm", "cm", "in"),
  rot_units = c("deg", "rad", "mm", "cm", "in"),
  brain_radius = NULL,
  detrend = FALSE,
  cutoff = 0.3
)

Arguments

X	An \(N\) by \(6\) matrix in which the first three columns represent the translational RPs (trans_units), and the second three columns represent the rotational RPs (rot_units). If rot_units measures an angle, it will be converted to trans_units by measuring displacement on a sphere of radius brain_radius trans_units. Alternatively, this can be the file path to an \(N\) by \(6\) matrix which can be read with read.table (fields separated by white-space; no header).
trans_units	"mm" for millimeters (default), "cm" for centimeters, or "in" for inches.
rot_units	"deg" for degrees (default), "rad" for radians, or one of the trans_units options.
brain_radius	If rot_units measures an angle, the rotational RPs are transformed to a spatial measurement representing the displacement on a sphere of radius brain_radius trans_units. If brain_radius is NULL (default), its value will be set to (the equivalent of) 50 mm.
detrend	Detrend each RP with the DCT before computing FD? Default: FALSE. Can be a number of DCT bases to use, or TRUE to use 4.
cutoff	FD values higher than this will be flagged. Default: .3.

Value

A list with components

measure

A length \(N\) vector of FD values in trans_units.

measure_info

"FD"

outlier_cutoff

cutoff

outlier_flag

A length-N logical vector, where TRUE indicates suspected outlier presence.

Details

The FD formula is taken from Power et. al. (2012):

$$FD_i = | \Delta x_i | + | \Delta y_i | + | \Delta z_i | + | \Delta \alpha_i | + | \Delta \beta_i | + | \Delta \gamma_i |$$

where \(i\) is the timepoint; \(x\), \(y\) and \(z\) are the translational realignment parameters (RPs); \(\alpha\), \(\beta\) and \(\gamma\) are the rotational RPs; and \(\Delta x_i = x_{i-1} - x_i\) (and similarly for the other RPs).

References

• Power, J. D., Barnes, K. A., Snyder, A. Z., Schlaggar, B. L. & Petersen, S. E. Spurious but systematic correlations in functional connectivity MRI networks arise from subject motion. Neuroimage 59, 2142-2154 (2012).