Average Fractional Anisotropy
Compute voxel FA from nonnegative tensor eigenvalues and an ROI-weighted average, rather than averaging tensor eigenvalues before deriving FA.
Description
Fractional anisotropy summarizes differences among a tensor’s three eigenvalues.
Fractional anisotropy summarizes differences among a tensor’s three eigenvalues. Averaging voxel FA within a region differs from computing FA of an averaged tensor.
The tool returns voxelFa (voxel fa); weightedMeanFa (weighted mean fa). Input measurements and model parameters are supplied by the caller; the tool computes the stated summary rather than acquiring those measurements.
When to use Average Fractional Anisotropy
Use Average Fractional Anisotropy when you already have eigenvalues, voxelWeights and want voxelFa, weightedMeanFa. This is useful for checking a supplied calculation, documenting a measurement convention, or comparing observations prepared on the same basis.
How to use Average Fractional Anisotropy and understand its results
- Enter eigenvalues, voxelWeights using the field table below. Match the units, ordering and data boundaries described in the calculation.
- Run the tool after checking the stated bounds and matching paired observations or categories. A malformed request gives a tool error rather than a usable measurement.
- Read voxelFa, weightedMeanFa. Use the calculation and interpretation below to distinguish amounts, ratios, signs and decision flags where applicable.
- Review the supplied parameters and assumptions before using the result in a report or comparing it with another observation.
| Input field | Meaning | Value type and bounds | Requirement |
|---|---|---|---|
| eigenvalues | Eigenvalues | list of list of number | Required |
| voxelWeights | Voxel weights | list of number | Required |
Require three nonnegative eigenvalues per voxel with nonzero squared sum, nonnegative aligned weights and positive total weight.
FA = sqrt(1.5 × Σ(λ−meanλ)²/Σλ²); ROI FA = Σweight×FA/Σweight The symbols refer to the supplied quantities or generated values described above; unit conversions and comparison boundaries follow the stated implementation.
{
"input": {
"eigenvalues": [
[
1,
1,
1
],
[
2,
0,
0
]
],
"voxelWeights": [
1,
3
]
},
"output": {
"voxelFa": [
0,
1
],
"weightedMeanFa": 0.75
}
}Limitations and assumptions
The tool does not estimate tensors or model crossing fibers. Every voxel, even zero-weight ones, must have valid eigenvalues.
Numerical inputs must be finite. The tool checks its declared input shape and calculation constraints; those checks do not verify the quality, calibration or representativeness of the supplied observations.
Alternative or Complementary methods
Average Mean Diffusivity: Derive mean diffusivity from each diffusion tensor eigenvalue triplet and aggregate supplied ROI weights; eigenvalues share one caller-selected diffusivity unit. Color Coded Fractional Anisotropy: Compute FA-weighted absolute principal-direction RGB and rounded 8-bit channels; coordinate-axis orientation must match the caller’s image convention.
Methodological background: DTIFIT: diffusion tensor output measures.1
References
-
DTIFIT: diffusion tensor output measures — FMRIB Software Library developers
Similar or alternative tools
- Average Mean Diffusivity
Derive mean diffusivity from each diffusion tensor eigenvalue triplet and aggregate supplied ROI weights; eigenvalues share one caller-selected diffusivity unit.
- Color Coded Fractional Anisotropy
Compute FA-weighted absolute principal-direction RGB and rounded 8-bit channels; coordinate-axis orientation must match the caller’s image convention.