1. MR-DTI: Non-invasive imaging of neuroanatomy of white matter Guido Gerig

2. Acknowledgments Contributors: Martin Styner Susumu Mori Andy Alexander
Gordon Kindlmann
Randy Gollub
National Alliance for Medical Image Computing (NIH U54EB005149)

3. Use of these slides
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4. T1w
T2w

6. 5D
6Mo
14Mo

7. Networking and Brain Connectivity
Major Fiber Tracts extracted from DT MRI
UNC Computer Science: Network wire cabinets

8. Diffusion Tensor Imaging (DT MRI) reveals White Matter Structure
Gray matter
White matter
Courtesy of Susumu Mori, JHU

9. White Matter Structure
Goal: Measure properties associated with the direction of white matter Fibers
White Matter
Fibers
White matter

10. Example: Corticospinal Tract
Source: Duke NeuroAnatomy Web Resources (Christine Hulette)
B: Superior longitudinal fasciculus
C: Superior occipitofrontal fasciculus
D: Cingulum
E: Inferior longitudinal fasciculus
F: Inferior occipitofrontal fasciculus
Tractography: Coronal view

11. Diffusion Random ‘Walk’ of Water Molecules t1 t2 t3
DT-MRI A. Alexander

12. Diffusion Diffusion: Brownian motion of one material through another
Anisotropy: diffusion rate depends on direction
Kleenex
newspaper
Gordon Kindlimann

13. Biological Restricted Diffusion
Sextra >> Sintra
Diffusion influenced by mean free path
Tortuosity
DT-MRI A. Alexander

14. Biological Restricted Diffusion
Cellular degeneration (necrosis) - Diffusion increases
DT-MRI A. Alexander

15. Aniostropic Restricted Diffusion
Diffusion has angular dependence
DT-MRI A. Alexander

16. How can we measure diffusion without perturbing the system?

18. Diffusion and white matter
Diffusion MRI measures diffusion of mainly water molecules
Isotropic medium → molecules move with Brownian motion.
In biological tissues diffusion is often anisotropic
In white matter: “Local structure”
Insulating myelin sheet, low probability to cross into axon
Dense axon bundles exhibits strongly directional local structure
Diffusion along fiber bundle is main diffusion direction
Myelin sheet
Nodes of Ranvier
Main diffusion direction

19. (An)isotropic diffusion
Free diffusion
Isotropic diffusion
Probability Distribution
Restricted diffusion
Anisotropic diffusion
Probability Distribution
Courtesy of Susumu Mori, John Hopkins University Medical School

20. DWI (indirectly) senses the structure of the tissue by measuring water molecule displacement along a chosen direction. r'
End
diffusion
coefficient
in the
y direction
(= Dy) y r
Start

21. If the path of the water molecule is affected by restrictions such as cellular material, the measured diffusion coefficient is reduced
intracellular
space r r'
extracellular
space

22. If the tissue structures are oriented, the path of the water molecule (and the measured diffusion coefficients) will reflect this. r'
diffusion
coefficient
in the
y direction
(= Dy) y r
diffusion coefficient
in the x direction(= Dx) x
Dx > Dy

23. Magnetic Resonance Imaging (MRI)
Larmor Frequency
Magnetic Field Gradient, G

24. Diffusion Weighted (DW) MRI
Accumulated Phase

25. DW-MRI II
Attenuation!

26. The pixel signal intensity, S, is related to the
b-value and the diffusion coefficient, D, through:
This equation (Steyskal Tanner Equation) has two unknowns, the signal intensity for b = 0 (S0) and D. Therefore, at least 2 measurements must be made, each at a different b-value to calculate D.

27. Equation for the diffusion attenuation G  S    ln    2 G 2  2   D
= - bD S  3 
Signal Intensity D
b-value

28. Measuring D for a Given Direction: Simplified model of two b values
(b=0 and b=nnnn)
intercept = S0
b-value
1000
slope = D
ln(S)

29. DWI and ADC
1 G/cm G/cm 10 G/cm G/cm
Signal Intensity
b-value

30. The b-value is the contrast “knob” in a diffusion experiment and is varied in magnitude and in a specified number of directions.
Increasing the b-value increases the contrast between slow and fast diffusing water molecules.
Images courtesy: Susumu Mori (JHU)
Increasing b-value

31. Apparent Diffusion Coefficient (ADC) Map with Different Measurement Direction
Gradient direction X Y Z
Only the diffusion along a gradient direction can be
measured
Courtesy of Susumu Mori, John Hopkins University Medical School

32. Diffusion Weighted Images
T2W Reference
So (b ~ 0 sec/mm2)
12 DW encoding directions
Si (b=912 sec/mm2)
ASNR 2003 –Washington,DC
DT-MRI Alexander
Courtesy JE Lee

33. Measurement along Multiple Directions
Diffusion MRI measures along single gradient directions
Diffusion Weighted Images (DWI)
In principle: Arbitrary gradient directions
6 different directions → Tensor
12/24 directions → stability
Diffusion Tensor Imaging (DTI)
High angular acquisition
Sampling of orientation diffusion
Higher order representations (fiber crossings)
Qball (D. Tuch, MGH), >256 dirs
Others: Van Wedeen (MIT), Frank (UCSD)
Modified from DavidTuch, MGH

34. DWI: Three Coordinate Systems
fast=I
medium=J
slow=K
Image:
“IJK”
Gradients:
g1 = (1,0,1)
g2 = (1,-1,0) …
 Dxx, Dxy … x y z
right
anterior
superior
World:
e.g. “RAS”
“Image
Orientation”
“Measurement
Frame”

35. Measured Apparent Diffusivities
12 encoding directions
ASNR 2003 –Washington,DC
DT-MRI Alexander
Courtesy JE Lee

36. What is “Diffusion – Weighted” Imaging?
In “Conventional” MRI, image contrast reflects
the local relaxation (T1, T2) environment
of the water molecules.
In “Diffusion-Weighted” Imaging (DWI), image
contrast reflects the physical structure of the
Tissue (via the local diffusion distribution).

37. Simplification and assumption
Orientational Diffusion Fct
Diffusion ellipsoid
Courtesy of Susumu Mori, John Hopkins University Medical School

38. The Diffusion Tensor Courtesy JE Lee ASNR 2003 –Washington,DC
DT-MRI Alexander
Courtesy JE Lee

39. DWI summary: MRI newspaper Kleenex
Diffusion: Brownian motion of one material through another
Anisotropy: diffusion rate depends on direction
Magnetic gradients create spatial planar waves of proton phase
Destructive interference measures diffusion along gradient direction only
Kleenex
newspaper

40. DWI crash course: Model
Single Tensor Model (Basser 1994) Ai
Tensor
estimation
Dxx
Dxy
Dxz D A0
Dyy
Dyz
Dzz gi

41. Anisotropy & Color-coded Orientation
Isotropic GM
Anisotropic WM
Courtesy of Susumu Mori, John Hopkins University Medical School

42. DTI Tensor Visualization
Color: FA value
ITK: DTIFiberTubeSpatialObject & SpatialObjectViewers (Julien Jomier)

43. Here comes Ross Whitaker