Q41. What are the FIM+ sub-bricks?
The Compute FIM+ menu item (on the FIM menu in a graph window) calculates a "functional bucket" dataset that contains up to seven sub-bricks. In each voxel, these values are computed from the data time series x(t) as follows (cf. Q35):

• Fit Coef
  This is the least squares estimate to the fit coefficient a in the time series model
  x(t) = a r(t) + b + c (t-tmid) + orts + noise ,
  where r(t) is the reference (or ideal) waveform, and tmid is the time in the middle of the scan. Note that magnitude of a will depend on the magnitude of r(t), since doubling r(t) will perforce require halving a.
• Best Index
  When more than one time series r(t) is in the *.1D file chosen as the ideal, then this is the index of which one gave the best fit (in the least squares sense) to the time series model. The index starts at 1. If the different r(t)'s are just time shifted versions of each other, then the Best Index can be used as a crude estimator for hemodynamic delay.
• % Change
  If r(t) is normalized to vary between 0 and 1, then this is equal to 100 a/baseline. Since the user may input an r(t) that is not normalized to lie between 0 and 1, the program allows for this in the calculation. The baseline used is equal to a min[r]+b, plus the sum of the averages of the orts (including the constant and linear trend).

  Please note that the % Change computed in the interactive AFNI is not the same as that computed in the program 3dfim. This is because the two programs were written by two different people. The difference is that 3dfim uses the time series mean as the baseline, rather than the calculation described above. The difference is usually small. When will this difference be reconciled? [begin music] The answer, my friend, is blowing in the wind. [end music]

• Baseline
  This is just the baseline estimate described above. It is not computed by default, but can be enabled from the Compute FIM+ menu.
• Correlation
  This is the correlation coefficient of x(t) with r(t), after detrending the baseline and the orts:
  xd(t) = x(t) - b - c (t-tmid) - orts .
  Then the correlation coefficient estimate is
  rho = sum[ xd(t) r(t) ] / { sum[ xd(t)**2 ] sum[ r(t)**2 ] }**0.5 .
  In terms of the Fit Coef a, this can be written as
  rho = a sum[r(t)**2]**0.5 / { a**2 sum[r(t)**2] + sum[noise**2] }**0.5 .
  This shows that as a gets large and positive, the correlation tends to 1.

  If r(t) is a square wave ("boxcar" function), then thresholding on rho is mathematically equivalent to thresholding a t-statistic between the "on" and "off" intervals. This elementary fact has appeared several times in the FMRI literature, but still does not seem to be widely known.

  One disadvantage of using rho as a measure of activation magnitude is that its definition not only contains the BOLD response a r(t), but also contains the noise level. That is, two otherwise identical voxels with different amounts of noise will have the same a (and the same % Change), but will have different values of the correlation coefficient. For this reason, I usually recommend using either the Fit Coef or the % Change as a measure of the BOLD response.

• % From Ave
  This is the same as % Change, but the denominator is each voxel's average rather than baseline. For positive signals, this will result in a smaller value than the % Change, since the baseline will be larger. For negative signals, the opposite will occur.
  [Requested by Andrzej Jesmanowicz of MCW, 08 Sep 1999.]
• Average
  This is the average value of each voxel's time series, as computed by the linear regression underlying the FIM calculations.
• % From Top
  This is the percent signal change again, but the denominator is each voxel's peak value rather than the base or average value.
• Topline
  This is the estimate of each voxel's peak value, as fit by the linear regression.
• Sigma Resid
  This is the estimate of each voxel's residual standard deviation, after the linear regressors (ideals and orts) have been subtracted.

By default, the FIM+ computations calculate the following values:

    Fit Coef   Best Index   % Change   Correlation

[Answer last changed 04 Jan 2000]