ELEC5622 Chap.4 Diffusion MRI, Tensor Imaging and Tractography
Diffusion MRI, Tensor Imaging and Tractography
This chapter covers imaging of water motion. Diffusion weighting makes moving water lose signal, and two images at different b-values give the apparent diffusion coefficient in every voxel. Because diffusion in white matter is directional, measurements along many directions are fitted to a tensor whose eigenvalues give FA and MD and whose main eigenvector guides tractography.
The chapter also explains why bright and dark swap between a DWI and its ADC map. It also lists the software the lecture names for diffusion processing, including FSL, TrackVis, FreeSurfer, MRtrix and Camino. The worked examples compute an ADC from two signals and FA and MD from three eigenvalues, the two calculations most likely to appear with numbers.
What this chapter covers
- 01
Brownian motion, isotropic and anisotropic diffusion
- 02
The b-value and diffusion weighting
- 03
DWI brightness and the ADC map
- 04
The diffusion tensor and its ellipsoid
- 05
Fractional anisotropy and mean diffusivity
- 06
Colour-coded orientation maps
- 07
Deterministic and probabilistic tractography
Worked example · free
FA and MD from three eigenvalues
- 1MD = (1.5 + 0.5 + 0.4) / 3 = 0.8 × 10⁻³ mm²/s.
- 1Deviations from MD are 0.7, −0.3 and −0.4; their squares sum to 0.74, and the eigenvalue squares sum to 2.66.
- 1FA = √1.5 × √(0.74 / 2.66) = √0.417 ≈ 0.65.
- 1An FA of about 0.65 shows strongly directional diffusion, typical of an organised fibre bundle.
Key terms
- Apparent diffusion coefficient
- The apparent diffusion coefficient is the voxel-wise diffusion rate solved from images acquired at two b-values.
- Fractional anisotropy
- Fractional anisotropy is a 0 to 1 index of how strongly diffusion in a voxel depends on direction.
- Tractography
- Tractography reconstructs likely white-matter pathways by following estimated diffusion orientations between voxels.
- Diffusion-weighted imaging
- Diffusion-weighted imaging is MRI whose contrast depends on how freely water molecules move in tissue.
- Eigenvector
- An eigenvector of the diffusion tensor is one principal axis direction; the first points along maximum diffusivity.
Diffusion MRI, Tensor Imaging and Tractography FAQ
Why are three gradient directions not enough for fibre orientation?
A fibre can run at any angle, not just along x, y or z. Measuring along many directions and fitting a symmetric 3 × 3 tensor, which has six unknowns, lets the main eigenvector point along the true fibre axis.
Does a high FA tell you which way a fibre runs?
No. FA measures how directional diffusion is, but two voxels with fibres pointing different ways can share one FA. Orientation comes from the main eigenvector, shown in colour maps as red, green or blue by axis.
What does probabilistic tractography output?
It launches many pathways from a seed, each sampling from a distribution of directions, and reports the proportion reaching each voxel. That proportion expresses connection likelihood; even a high value does not prove the tract exists.
Why do two b-values let you measure diffusion?
One image mixes proton density, T1, T2 and diffusion effects in a single intensity. Two images that differ only in b share every other term, so their ratio depends on diffusion alone and its logarithm gives the coefficient.
What stops a deterministic streamline?
Tracking parameters end it, for example when fractional anisotropy drops below 0.15 or when the direction turns by more than 50 degrees between steps. Streamlines can also halt in regions where the tensor is nearly isotropic.
What is the difference between isotropic and anisotropic diffusion?
Isotropic diffusion has no preferred direction, like water in a glass, so measurements along any axis agree. Anisotropic diffusion is faster along some directions because fibres and membranes restrict motion across them, which is what makes white matter visible to diffusion imaging.
Exam move
Practise the ADC formula with your own signal pairs and check that every answer is positive. Then compute FA and MD for a sphere, a disc and a needle-shaped tensor to see the range. Finish by listing one strength and one limitation of each tractography family in a sentence each. Explain aloud why the same tissue is bright on a DWI and dark on its ADC map, and why colour-coded FA shows orientation but not direction.
Keep a short list of what limits deterministic tracking, such as crossing fibres, and match each limit to the way probabilistic tracking responds.
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