Skip to main content

Step 9: Tensor Fitting (DTIFIT)

Overview​

This step fits the diffusion tensor model to the corrected DWI data, producing voxelwise maps of the core DTI metrics: Fractional Anisotropy (FA), Mean Diffusivity (MD), Axial Diffusivity (AD), and Radial Diffusivity (RD). These scalar maps are the primary output of most DTI studies and form the basis for group-level statistical analyses, tract-based spatial statistics (TBSS), and tractography-based analyses.

Further reading: TBSS #5: Fitting the Tensors — Andy's Brain Book explanation of eigenvalue decomposition and how FA, MD, AD, RD are derived from the tensor

Conceptual Background​

The Diffusion Tensor​

At each voxel, the diffusion tensor is a 3x3 symmetric positive-definite matrix that describes the magnitude and preferred orientation of water diffusion. Because the matrix is symmetric, it has six unique elements, which means at least six diffusion-weighted measurements (plus one b=0 image) are required to estimate it.

Tensor Estimation​

FSL's dtifit uses weighted least squares (WLS) regression to fit the tensor to the log-transformed DWI signal at each voxel. The relationship between the DWI signal and the tensor is described by the Stejskal-Tanner equation:

S(g) = S0 * exp(-b * g^T * D * g)

where S(g) is the signal for gradient direction g, S0 is the non-diffusion-weighted signal, b is the b-value, and D is the diffusion tensor.

Only the b=1000 Shell Is Used​

The single-tensor model assumes Gaussian diffusion, which holds best at moderate b-values (typically b=1000 s/mm^2). At higher b-values, the DWI signal reveals non-Gaussian effects such as diffusion kurtosis and signal contributions from crossing fibers, which violate the assumptions of the single-tensor model. Including higher b-value shells in the tensor fit biases the resulting scalar maps, so extract only the b=0 and b=1000 volumes before running dtifit (Shell Extraction).

From Eigenvalues to DTI Metrics​

The tensor is decomposed into three eigenvalues (L1 >= L2 >= L3) and their corresponding eigenvectors (V1, V2, V3). The eigenvalues represent the magnitude of diffusion along each principal axis. The DTI scalar metrics are derived directly from these eigenvalues:

  • Fractional Anisotropy (FA) quantifies how directionally constrained the diffusion is, ranging from 0 (perfectly isotropic) to 1 (perfectly anisotropic):

    FA = sqrt(3/2) * sqrt(((L1 - MD)^2 + (L2 - MD)^2 + (L3 - MD)^2) / (L1^2 + L2^2 + L3^2))

  • Mean Diffusivity (MD) is the average diffusion across all three axes:

    MD = (L1 + L2 + L3) / 3

  • Axial Diffusivity (AD) is diffusion along the principal axis (the direction of the primary eigenvector):

    AD = L1

  • Radial Diffusivity (RD) is the average diffusion perpendicular to the principal axis:

    RD = (L2 + L3) / 2

Prerequisites​

Before running this step, you should have completed:

RequirementSource
Eddy-corrected DWI dataStep 8 (Eddy Correction)
b=0 and b=1000 volumesShell Extraction (optional)
Brain maskStep 5 or Step 8
Rotated bvecs from eddyStep 8 (Eddy Correction)

Use the rotated bvecs output by eddy, not the original bvecs. Eddy correction involves volume-by-volume rotations, and the gradient directions must be rotated accordingly. Using the original bvecs will produce incorrect tensor estimates and corrupted FA/MD maps.

Tool & Command Reference​

Running DTIFIT​

Tool: FSL dtifit

dtifit \
  --data="$input_dir/${subj}_data_1000.nii.gz" \
  --out="$output_dir/${subj}_DTI" \
  --mask="$mask_dir/${subj}_brain_mask.nii.gz" \
  --bvecs="$input_dir/${subj}_data_1000.bvec" \
  --bvals="$input_dir/${subj}_data_1000.bval"

Flag explanations:

FlagDescription
--dataThe input 4D DWI file. Tensor fitting conventionally uses only the b=0 and b=1000 volumes, which Shell Extraction produces.
--outThe output basename. DTIFIT appends suffixes like _FA, _MD, _L1, etc. to this prefix.
--maskA binary brain mask. Tensor fitting is performed only within this mask, which speeds up computation and prevents noisy fits outside the brain.
--bvecsThe b-vector file corresponding to the extracted shell. These must be the rotated bvecs from eddy correction.
--bvalsThe b-value file corresponding to the extracted shell.

Computing Radial Diffusivity​

DTIFIT does not output an RD map directly. RD is computed as the average of the second and third eigenvalues:

fslmaths "$output_dir/${subj}_DTI_L2" \
  -add "$output_dir/${subj}_DTI_L3" \
  -div 2 \
  "$output_dir/${subj}_DTI_RD"

This takes the L2 eigenvalue map, adds the L3 eigenvalue map, and divides by 2 to produce the mean radial diffusivity at each voxel.

Expected Output​

After running dtifit and computing RD, your output directory should contain the following files:

FileDescription
${subj}_DTI_FA.nii.gzFractional Anisotropy map (range 0-1)
${subj}_DTI_MD.nii.gzMean Diffusivity map
${subj}_DTI_L1.nii.gzFirst eigenvalue (equivalent to Axial Diffusivity)
${subj}_DTI_L2.nii.gzSecond eigenvalue
${subj}_DTI_L3.nii.gzThird eigenvalue
${subj}_DTI_RD.nii.gzRadial Diffusivity map (computed via fslmaths)
${subj}_DTI_V1.nii.gzPrimary eigenvector (direction of maximum diffusion)
${subj}_DTI_V2.nii.gzSecond eigenvector
${subj}_DTI_V3.nii.gzThird eigenvector
${subj}_DTI_MO.nii.gzMode of anisotropy (describes tensor shape: planar vs. linear)
${subj}_DTI_S0.nii.gzEstimated baseline signal (S0) with no diffusion weighting

Quality Check​

Visual Inspection of the FA Map​

Open the FA map in FSLeyes:

fsleyes "$output_dir/${subj}_DTI_FA.nii.gz" -cm hot

What to look for:

  • White matter should appear bright (high FA, typically 0.3-0.8), reflecting the highly directional diffusion along myelinated axon bundles.
  • Gray matter should appear moderate to dark (lower FA, typically 0.1-0.3).
  • CSF should appear very dark (FA near 0), reflecting free isotropic diffusion.
  • The corpus callosum, internal capsule, and corona radiata should be clearly visible as high-FA structures.

Checking Value Ranges​

Verify that FA and MD values fall within physiologically reasonable ranges:

MetricExpected RangeTissue
FA0.0 - 1.0Full brain
FA0.3 - 0.8White matter
MD~0.7 - 1.0 x 10^-3 mm^2/sWhite matter
MD~1.5 - 3.0 x 10^-3 mm^2/sCSF

You can check the range with:

fslstats "$output_dir/${subj}_DTI_FA.nii.gz" -R
fslstats "$output_dir/${subj}_DTI_MD.nii.gz" -R

Inspect the V1 (Eigenvector) Map​

In FSLeyes, load the V1 map as a directionally encoded color (DEC) map to verify anatomical plausibility:

  • Red = left-right (e.g., corpus callosum)
  • Green = anterior-posterior (e.g., cingulum, IFOF)
  • Blue = superior-inferior (e.g., corticospinal tract)

Common Issues​

IssueLikely CauseSolution
FA values greater than 1Masking problem — tensor fitted to voxels outside the brain or in noisy regionsRe-generate or tighten the brain mask; ensure the mask matches the DWI data geometry
Negative eigenvaluesNon-positive-definite tensor estimates, often in low-SNR voxelsThis is expected in a small number of voxels. If widespread, check data quality and mask
FA map looks noisy or blurredUsing wrong bvecs (not the rotated ones from eddy)Confirm you are using the bvecs rotated by eddy, not the original acquisition bvecs
Unexpected bright spots in CSFPoor brain extraction or susceptibility artifactsCheck the mask overlay on the DWI data; re-run BET if needed
MD values unreasonably high or lowIncorrect b-value file or data scaling issuesVerify that the bval file matches the extracted shell data

References​

Next Step​

Proceed to Step 10: Registration (FLIRT) to register your DTI maps to a standard space template for group-level analyses.