1. Brain Lab Imaging Didactics
An Introduction to
Diffusion Tensor Imaging (DTI)

2. Obligatory Warning NOTE: this talk focuses on concepts, not details
As such, it glosses over various things; it is (hopefully) not inaccurate, but it is incomplete!

3. The 10,000 Foot View
Would like to image details of neuroanatomic structure
Would especially like a method responsive to changes (injury/infarction)
As it happens, an MRI “problem” can provide some help

4. The Diffusion “Problem”
We get signal from the spins of hydrogen atoms (≈ water molecules)
We assume sequential pulses always affect the same molecules…
… though in fact diffusion (microscopic movement) occurs, reducing signal

5. Diffusion Gradients
Recall that dephasing-rephasing pulses will cancel… if all is stable

6. Spin Echo Recap
“Hahn Echo” (Hahn, 1950) - Wikipedia

7. Diffusion Gradients
When incoherent motion (diffusion) occurs, individual molecules lose signal

8. The Diffusion “Problem”
So...
In general, we lose signal when diffusion occurs
Using a diffusion “encoding” or “sensitizing” gradient, the signal lost is proportional to diffusion in one direction
… Let's use that to measure diffusion!

9. Diffusion Weighted Imaging
Diffusion turns out to be helpful clinically
The diffusion signal is directional, so DWI needs to average over 3 orthogonal directions (minimum)
DWI FLAIR
Prion disease
bestpractice.bmj.com
Dr M. Geschwind

10. RGB Coded Diffusion Map
R = Left/Right G = Front/Back B = Up/Down
Helpful, but coarse
We can extend this idea further…
Figure 16c.  Extraction of scalar values from diffusion tensor imaging. (a) Image shows mean diffusion, which is the trace of the diffusion tensor. An image of ADC averaged over three orthogonal directions would have a similar appearance. (b) Image shows the fractional anisotropy, which is computed from the eigenvalues of the diffusion tensor. (c) Color-coded image shows the orientation of the principal direction of diffusion, with red, blue, and green representing diffusion along x-, y-, and z-axes, respectively. The color intensity is proportional to the fractional anisotropy.
Hagmann P et al. Radiographics 2006;26:S205-S223
©2006 by Radiological Society of North America

11. A Brownian Digression Known since the 19th century
Apparently random movement of very small particles (e.g. pollen)
The “drunkard's walk”

12. Einstein’s Contribution
The Einstein Relation (1905):
Brownian motion can be explained mathematically as diffusion
Expresses observed distance traveled in relation to a diffusion coefficient, D
In free water, D is the same in all directions
In the brain, “anisotropy” exists
Need multiple D values to model that

13. So, How Does This Help?
DWI shows the average apparent diffusivity (ADC: apparent diffusion coefficient)
“ADC”, not “D”, because we're not in free water
D will be different in different directions
We need a mathematical construct that stores multiple D values at each point...

14. The Tensor A tensor is a way of structuring data
Instead of scalar values (i.e. numbers), we can use tensors with multiple parameters per point
For instance, diffusion can be represented by a tensor D at each point composed of D values

15. The Diffusion Tensor The diffusion tensor has the form
The on-diagonal elements represent diffusion along the three main axes
The remaining elements tell how correlated random diffusion is between them

16. The Diffusion Tensor The diffusion tensor has the form
Free water, or similar
The on-diagonal elements represent diffusion along the three main axes
The remaining elements tell how correlated random diffusion is between them

17. Eigen Representation
A diffusion tensor D might correspond to unrealistic states (e.g. Dxy  Dyx)
Let's assume D is well formed (technically, “positive semi-definite” and symmetric)
Then, it has 6 independent values
These can be decomposed into three perpendicular eigen-components…

18. Eigen What Now?
Eigenvalues and eigenvectors are basic concepts from linear algebra
Eigen-analysis can be done with principal components analysis (PCA), for example
Eigenvector = principal component
Eigenvalue () = loading
Ultimately, we get 3 orthogonal directions and lambdas (diffusions) along them

19. ODFs “ODF”: Orientation Distribution Function
Interprets diffusion measurements in a model
Probabilistic – tries to explain the data we see
The eigen-representation is one ODF
Note that it reduces from 6 independent D values to 3 lambdas… information is lost
More sophisticated ODFs are possible, but simplicity has its advantages

20. Ellipsoid Representation
The eigen representation of a tensor can be shown graphically as an ellipsoid
We can order the axes based on their eigenvalues: 1 largest, 3 smallest
In free water, 1 = 2 = 3

21. Anisotropy in Axons
Diffusion is not free in most of the brain (only pure CSF)
We can think about restrictions in terms of axons
The 1 direction aligns with axonal bundles

22. Lots of Little Ellipsoids
Each voxel has one tensor/ellipsoid
Two analysis paths:
Tensor derived scalars
Tractography

23. Diffusion Tensor Imaging
Using the three lambdas, we can arrive at various scalar values of interest:
MD (mean diffusivity): equivalent to ADC
FA (fractional anisotropy): orientedness
DA (axial diffusivity): first lambda
DR (radial diffusivity): mean of 2 & 3
Then we have one value per voxel, and can plot/compare images

24. Tractography Pros Cons Looks cool! Better reflects structure
Can be time consuming to find
More difficult to compare across subjects

25. General DTI Issues
“Crossing fibers” (or in general, complex architecture)
The “axonal assumption”

26. Crossing Fibers
Source: Brain Imaging Lab, DTITK tool
Would like to assume each voxel's tensor represents “that tissue”
Latest estimate: % of brain voxels (2.4mm) contain crossing fibers [1]
[1] Jeurissen, B., Leemans, A., Tournier, J.-D., Jones, D. K. & Sijbers, J. (2012) Investigating the prevalence of complex fiber configurations in white matter tissue with diffusion magnetic resonance imaging. Hum. Brain Mapp. 34(11): 2747–66.

27. Crossing Fibers
When fibers cross, the tensor is an average of both/all
Bad for following tracts
Also bad for (some) tensor-based scalar values

28. Axonal Assumption
Axonal fibers are pretty consistent with our tensor model (absent crossing fibers)
Unfortunately, there are more things in the brain than axons!

29. Wrapup
DTI is a useful tool, but as with all imaging it helps to know its limitations and assumptions
Analysis methods have been evolving
Tensor based normalization
Tract-based group analysis
Can also extend how data are collected…

30. Q-Space Analogous to “k- space” of regular MRIs
In addition to changing gradient directions, we can change their strength (b-value)
HARDI, HYDI, QBI, …
Hagmann P et al. Radiographics 2006;26:S205-S223
©2006 by Radiological Society of North America

31. Bonus Material Actual pulse sequence: Standard spin-echo
Additional “diffusion gradient” (applied twice, with effect reversed by 180° pulse)
Hagmann P et al. Radiographics 2006;26:S205-S223
©2006 by Radiological Society of North America