Step 12: Fiber Orientation Distributions (MSMT-CSD)

Overview

This step turns the diffusion signal into a fiber orientation distribution (FOD) at every voxel: a function on the sphere whose peaks point along the fiber bundles passing through that voxel. Tractography follows those peaks, so the FOD image is the direct input to every tracking algorithm downstream.

It is the last modeling step before tractography.

Conceptual Background

The Tensor Is Not Enough

The diffusion tensor from Step 9 describes each voxel with a single ellipsoid, which means a single dominant direction. That is a reasonable summary in the middle of a large coherent tract, but it fails wherever bundles cross, fan, or kiss, which is most of the white matter. Estimates commonly put crossing-fiber voxels at 60–90% of white matter.

An FOD has no such limit. It can represent two, three, or more distinct orientations in one voxel, which is what makes it possible to track through crossings instead of stopping or turning at them.

Deconvolution

Step 11 established the response function: the signal a single coherent fiber bundle produces. The measured signal in a voxel is that response convolved with however the fibers are actually arranged.

Constrained spherical deconvolution (CSD) inverts that operation. Knowing the response and the measured signal, it solves for the orientation distribution that must have produced them. The constraint is that the resulting distribution is non-negative; fiber density cannot be negative, and imposing that suppresses the spurious ringing that unconstrained deconvolution produces.

Multi-Shell Multi-Tissue

Single-tissue CSD assumes every voxel is pure white matter. At tissue boundaries that assumption breaks: partial-volume CSF or gray matter gets deconvolved as if it were fiber signal, producing spurious peaks and, downstream, streamlines that leak into ventricles and cortex.

MSMT-CSD uses the different b-value behavior of the three tissues (established in Step 11) to split each voxel's signal into white matter, gray matter, and CSF compartments, and deconvolves only the white matter part. The result is much cleaner FODs at boundaries, which matters for small subcortical targets sitting near CSF.

Normalization Is Not Optional

mtnormalise corrects the overall intensity scaling of the FODs so that tissue compartments sum sensibly and so that amplitudes are comparable across participants.

Without it, a participant scanned with slightly different coil loading or receive gain has globally larger or smaller FOD amplitudes than everyone else. Since tractography stops when FOD amplitude falls below a cutoff, that participant is effectively tracked at a different threshold, producing systematically more or fewer streamlines for a reason that has nothing to do with their brain.

The normalized white-matter FOD, wm_fod_norm.mif, is the file tractography should use. The un-normalized wm_fod.mif is an intermediate, and mixing the two across participants reintroduces the scaling problem normalization exists to remove.

Prerequisites

Requirement	Source
`dwi.mif` with embedded gradient table	Step 11
`mask.mif` brain mask	Step 11
Group response functions (WM, GM, CSF)	Step 11
MRtrix3 installed	Tool setup

Every participant must be deconvolved against the same group response files. That is the reason Step 11 averages them.

Commands

Estimate the FODs

dwi2fod msmt_csd \
  "$subj_dir/dwi.mif" \
  "$project_dir/group_wm_response.txt"  "$subj_dir/wm_fod.mif" \
  "$project_dir/group_gm_response.txt"  "$subj_dir/gm_fod.mif" \
  "$project_dir/group_csf_response.txt" "$subj_dir/csf_fod.mif" \
  -mask "$subj_dir/mask.mif"

Argument	Description
`msmt_csd`	The multi-shell multi-tissue algorithm. Requires 2+ non-zero shells.
response / output pairs	Each tissue is given as a pair: its response file, then the FOD image to write. Order is WM, GM, CSF.
`-mask`	Restricts fitting to inside the brain. Substantially reduces runtime.

The response/output arguments are positional pairs. Swapping the WM and CSF responses runs without error and produces nonsense; the command has no way to know which file is which.

Normalize

mtnormalise \
  "$subj_dir/wm_fod.mif"  "$subj_dir/wm_fod_norm.mif" \
  "$subj_dir/gm_fod.mif"  "$subj_dir/gm_fod_norm.mif" \
  "$subj_dir/csf_fod.mif" "$subj_dir/csf_fod_norm.mif" \
  -mask "$subj_dir/mask.mif"

All three tissues are passed together because normalization is a joint operation: it solves for a spatially smooth scaling that makes the three compartments sum coherently. Normalizing white matter alone is not equivalent and is not supported.

Normalization is only as good as the brain mask. A mask that includes non-brain tissue, or that clips the temporal poles, biases the fit without failing; the command completes normally and the output looks plausible. The symptom surfaces much later, as one participant whose tractography behaves differently from everyone else's at the same settings. If a participant looks like an outlier downstream, re-check their mask from Step 6 before adjusting tracking parameters.

Single-Shell Data

MSMT-CSD needs at least two non-zero shells. With single-shell data, use single-tissue CSD instead: a white-matter-only response, the csd algorithm, and intensity normalization of the DWI before fitting rather than mtnormalise after.

# Response: tournier picks single-fiber WM voxels from the data alone
dwi2response tournier "$subj_dir/dwi.mif" "$subj_dir/wm_response.txt" \
  -mask "$subj_dir/mask.mif"

# Group-average as in Step 11
responsemean "$project_dir"/*/wm_response.txt "$project_dir/group_wm_response.txt"

# Normalize DWI intensity in a white-matter mask (FA > 0.4 from Step 9 works)
dwinormalise individual "$subj_dir/dwi.mif" "$subj_dir/wm_mask.mif" \
  "$subj_dir/dwi_norm.mif"

# Single-tissue CSD
dwi2fod csd "$subj_dir/dwi_norm.mif" \
  "$project_dir/group_wm_response.txt" "$subj_dir/wm_fod_norm.mif" \
  -mask "$subj_dir/mask.mif"

The output is named wm_fod_norm.mif so the required outputs are unchanged; the normalization happened on the DWI instead of the FOD.

Single-tissue CSD models every voxel as white matter. Gray matter and CSF partial volume are not separated out, so FODs at tissue boundaries carry spurious peaks that the three-tissue model would have removed. For deep or small targets near CSF this is a limitation of the acquisition, not something a different setting recovers. Do not mix single-shell and multi-shell participants in one group response.

Batch Processing Script

FOD estimation is memory-hungry. Total load is roughly max_jobs × nthreads, so size both against your machine rather than maximizing either alone.

#!/bin/bash
# fod_estimation.sh — MSMT-CSD and intensity normalization for all subjects

base_dir="/path/to/project"
dwi_dir="$base_dir/dwi"
nthreads=4
max_jobs=4

subjects=$(ls -d "$dwi_dir"/sub-* 2>/dev/null | xargs -n1 basename)

# Group responses must already exist (Step 11, phase 2)
for tissue in wm gm csf; do
    if [ ! -f "$dwi_dir/group_${tissue}_response.txt" ]; then
        echo "ERROR: missing group_${tissue}_response.txt — run Step 11 first"
        exit 1
    fi
done

for subj in $subjects; do
    (
        d="$dwi_dir/$subj"

        if [ ! -f "$d/dwi.mif" ]; then
            echo "  WARNING: $subj missing dwi.mif — skipping"
            exit 0
        fi

        if [ -f "$d/wm_fod_norm.mif" ]; then
            echo "  $subj: FODs already exist — skipping"
            exit 0
        fi

        echo "  $subj: estimating FODs"
        dwi2fod msmt_csd "$d/dwi.mif" \
            "$dwi_dir/group_wm_response.txt"  "$d/wm_fod.mif" \
            "$dwi_dir/group_gm_response.txt"  "$d/gm_fod.mif" \
            "$dwi_dir/group_csf_response.txt" "$d/csf_fod.mif" \
            -mask "$d/mask.mif" -nthreads "$nthreads" -force -quiet

        # Write to a temporary name so an interrupted run cannot leave a
        # truncated wm_fod_norm.mif that later steps would silently trust.
        echo "  $subj: normalizing"
        if mtnormalise \
            "$d/wm_fod.mif"  "$d/wm_fod_norm.partial.mif" \
            "$d/gm_fod.mif"  "$d/gm_fod_norm.mif" \
            "$d/csf_fod.mif" "$d/csf_fod_norm.mif" \
            -mask "$d/mask.mif" -force -quiet; then
            mv -f "$d/wm_fod_norm.partial.mif" "$d/wm_fod_norm.mif"
        else
            rm -f "$d/wm_fod_norm.partial.mif"
            echo "  ERROR: $subj normalization failed"
        fi
    ) &

    while [ "$(jobs -r | wc -l)" -ge "$max_jobs" ]; do sleep 2; done
done
wait

echo "FOD estimation complete."

Expected Output

dwi/sub-001/
├── wm_fod.mif            # white matter FOD (intermediate)
├── gm_fod.mif            # gray matter compartment
├── csf_fod.mif           # CSF compartment
├── wm_fod_norm.mif       # normalized WM FOD: the tractography input
├── gm_fod_norm.mif
└── csf_fod_norm.mif

wm_fod_norm.mif is the file that matters downstream. The others are kept for QC and because normalization needs all three.

Quality Check

Build a Tissue-Composition Image

A standard MRtrix QC check is to combine the three compartments into one RGB-style volume, where white matter, gray matter, and CSF each drive a channel:

# Take the l=0 term of the WM FOD, then stack CSF / GM / WM into one image
mrconvert -coord 3 0 "$subj_dir/wm_fod_norm.mif" - | \
  mrcat "$subj_dir/csf_fod_norm.mif" "$subj_dir/gm_fod_norm.mif" - \
        "$subj_dir/vf_norm.mif"

mrview "$subj_dir/vf_norm.mif"

The result should look like a clean tissue segmentation: white matter bright in one channel, cortical ribbon in another, ventricles in the third. If the compartments are visibly mixed, with CSF signal spread through white matter for instance, the response functions or the mask are suspect.

Inspect the FODs Directly

mrview "$subj_dir/vf_norm.mif" -odf.load_sh "$subj_dir/wm_fod_norm.mif"

Zoom into a region with known crossings, the centrum semiovale being the usual choice, and confirm you can see multiple distinct lobes per voxel. In the corpus callosum the FODs should be single, sharp, and left-right oriented. Outside the brain there should be essentially nothing.

Confirm Every Participant Finished

for d in "$dwi_dir"/sub-*; do
    if [ -f "$d/wm_fod_norm.mif" ]; then s="ok"; else s="MISSING"; fi
    echo "$(basename "$d")  $s"
done

Common Issues

Symptom	Likely cause	Fix
`dwi2fod` reports "not enough shells"	Data is single-shell	Use single-tissue CSD, above
FODs look noisy everywhere	Wrong response order, or unrotated bvecs	Confirm WM/GM/CSF ordering; re-check Step 8 rotated bvecs
Tissue image shows CSF inside white matter	Poor response estimation	Re-inspect Step 11 responses in `shview`
`mtnormalise` fails or produces flat output	Mask includes non-brain, or a compartment is empty	Tighten the mask; confirm all three FODs were written
Out-of-memory during batch run	`max_jobs × nthreads` too high	Lower both; FODs are large in memory

References

Jeurissen, B., Tournier, J.-D., Dhollander, T., Connelly, A., & Sijbers, J. (2014). Multi-tissue constrained spherical deconvolution for improved analysis of multi-shell diffusion MRI data. NeuroImage, 103, 411–426.
Tournier, J.-D., Calamante, F., & Connelly, A. (2007). Robust determination of the fibre orientation distribution in diffusion MRI: non-negativity constrained super-resolved spherical deconvolution. NeuroImage, 35(4), 1459–1472.
Raffelt, D., et al. (2017). Bias field correction and intensity normalisation for quantitative analysis of apparent fibre density. ISMRM, 25, 3541.
MRtrix3 dwi2fod documentation

Next Step

The modeling is finished. Proceed to the Outputs for Tractography to verify that your outputs match what a tractography workflow expects before you start tracking.

Overview​

Conceptual Background​

The Tensor Is Not Enough​

Deconvolution​

Multi-Shell Multi-Tissue​

Normalization Is Not Optional​

Prerequisites​

Commands​

Estimate the FODs​

Normalize​

Single-Shell Data​

Batch Processing Script​

Expected Output​

Quality Check​

Build a Tissue-Composition Image​

Inspect the FODs Directly​

Confirm Every Participant Finished​

Common Issues​

References​

Next Step​