9 MRI - DTI
9.0.1 Diffusion‑Tensor MR Imaging (DTI) — Core Ideas
1. Why ordinary diffusion‑weighted MRI isn’t enough
Conventional DW‑MRI measures the mean mobility of water in each voxel but ignores the fact that, in ordered tissues such as white‑matter tracts, water diffuses preferentially along the fibre direction. DTI overcomes this by sampling diffusion in many directions and modelling it with a 3 × 3 symmetric “diffusion tensor.” (Radiopaedia, NCBI)
2. The diffusion tensor and its geometry
After fitting the signal from ≥ 6 non‑collinear gradient directions, the tensor is diagonalised into three eigenvalues (λ₁ ≥ λ₂ ≥ λ₃) and corresponding eigenvectors (ɛ₁, ɛ₂, ɛ₃). These can be visualised as an ellipsoid whose axes lengths equal the eigenvalues.
- ● Isotropic tissue: λ₁ ≈ λ₂ ≈ λ₃ → sphere.
- ● Anisotropic tissue: λ₁ ≫ λ₂, λ₃ → cigar‑shaped ellipsoid aligned with the principal fibre. (Questions and Answers in MRI, pages.stat.wisc.edu)
3. Key scalar maps derived from the tensor
| Metric | Formula (eigenvalues) | Intuition | Typical brain values* |
|---|---|---|---|
| Fractional anisotropy (FA) | %5E2%2B(%5Clambda_2-MD)%5E2%2B(%5Clambda_3-MD)%5E2%7D%7B%5Clambda_1%5E2%2B%5Clambda_2%5E2%2B%5Clambda_3%5E2%7D%7D.png) |
Degree of directional preference (0 = isotropic, 1 = fully directional) | WM ≈ 0.6–0.8, GM ≈ 0.15, CSF ≈ 0 |
| Mean diffusivity (MD / ADC) | (λ₁+λ₂+λ₃)/3 | Average overall diffusivity | WM ≈ 0.7 ×10⁻³ mm²/s |
| Axial diffusivity (AD) | λ₁ | Diffusion along the tract | ↓ in axonal injury |
| Radial diffusivity (RD) | (λ₂+λ₃)/2 | Diffusion across the tract | ↑ in demyelination |
*Rough adult brain values at b ≈ 1000 s/mm², 3 T. (carpentries-incubator.github.io, Questions and Answers in MRI)
4. How the data are acquired
- At least six (often ≥ 30) diffusion‐weighted volumes with different gradient directions, plus a b = 0 image.
- Typical b‑values 700–1000 s/mm² (higher for advanced models).
- Parallel imaging or multiband EPI to tame echo‑train length and susceptibility artefacts. (Radiopaedia)
5. From tensors to pictures
- Scalar maps – FA, MD, AD, RD overlaid on anatomical images.
- Colour‑coded FA – direction encoded RGB (red =L↔︎R, green =A↔︎P, blue =S↔︎I).
- Tractography – streamlines follow ɛ₁ voxel‑to‑voxel (deterministic) or a probability cloud (probabilistic) to reconstruct white‑matter pathways. (Nature)
6. Clinical and research applications
| Domain | What DTI adds | Examples |
|---|---|---|
| Neurosurgical planning | Maps eloquent tracts to avoid during tumour resection or DBS lead placement. | Corticospinal, arcuate fasciculus |
| Neuro‑development & aging | Tracks maturation/myelination and age‑related decline. | Preterm infants, dementia |
| Diffuse axonal injury | FA ↓, RD ↑ along affected fibres even when structural MRI is normal. | TBI prognostication |
| Demyelinating disease | RD ↑ precedes visible T2 lesions; helps quantify repair. | Multiple sclerosis |
| Psychiatric & cognitive research | Network‑based biomarker of connectivity. | Schizophrenia, autism |
7. Limitations & pitfalls
- Single‑tensor model fails in voxels with crossing or kissing fibres (≈ 60 % of white matter).
- Susceptibility and motion artefacts (EPI).
- Partial‑volume with CSF lowers FA if voxels too large; isotropic resolution ≤ 2 mm helps.
- Tractography is inference, not a direct depiction of axons—interpret pathways cautiously. (PMC)
9.0.1.1 Connecting back to the video
The YouTube clip you watched animates the ellipsoid representation nicely—what you see as stretching of the ball along one axis is simply λ₁ > λ₂, λ₃, the physical basis for FA mapping. Now you can relate each colour‑coded streamline in the demo to the principal eigenvector (ɛ₁) “threading” through neighbouring voxels.