1. MR Diffusion Tensor Imaging, Tractography
Richard Watts, D.Phil.
Citigroup Biomedical Imaging Center
Weill Medical College of Cornell University
Box 234, 1300 York Avenue, New York, NY 10021
Telephone

2. Acknowledgements Weill Medical College of Cornell University
Department of Radiology
Aziz Ulug, Linda Heier.
Citigroup Biomedical Imaging Center
Doug Ballon, Jon Dyke, Katherine Kolbert.
Sackler Institute
BJ Casey, Matt Davidson, Katie Thomas.

4. Outline Background Methods Examples Diffusion
Restricted Diffusion and Anisotropy
Methods
Data Acquisition
Display of Diffusion Tensor Data
Fiber Tracking
Problems and Limitations
Examples

5. Diffusion

6. Diffusion Equation r = Displacement (mm) D = Diffusion constant
(mm2/s)
t = Time (mm)

7. Distance Scales
Question: What distance do protons travel during an EPI readout time?
Assume: Diffusion constant ~ 10-3 mm2/s
Time ~ 100 ms = 0.1s
The root mean square (RMS) distance is ~0.02mm = 20μm
Such an experiment is sensitive to changes in diffusion caused by structures on this scale or smaller

8. Diffusion Imaging of Leukemia

9. Diffusion Imaging of Leukemia

10. Spin Echo

11. Spin Echo

12. Spin Echo

13. Data Acquisition – Spin Echo
time
90º
180º RF
Echo TE
where   g
Diffusion Gradients Gx

14. Restricted Diffusion

15. Diffusion Ellipsoid in White Matter

16. Anisotropy Isotropic: Anisotropic:
Having the same properties in all directions
Anisotropic:
Not isotropic; having different properties in different directions
Webster’s Dictionary

17. Data Acquisition – Spin Echo
time
90º
180º RF
Echo TE Gx Gy Gz
Linear combination of gradients - measure component of diffusion in any direction

18. Diffusion Tensor Imaging
Tensor is a mathematical model of the directional anisotropy of diffusion
Represented by a 3x3 symmetric matrix  6 degrees of freedom
Fit experimental data to the tensor model
From the tensor, we can calculate
Direction of greatest diffusion
Degree of anisotropy
Diffusion constant in any direction

19. Calculated Quantities…
* Various definitions
T2-Weighted Image
“Average” Diffusion*
Degree of Anisotropy*
Diffusion along X
Diffusion along Y
Diffusion along Z

20. 1. (Approximately) Isotropic Diffusion
How a blob of ink would spread out

21. 2. Anisotropic Diffusion
How a blob of ink would spread out

22. Vector Plot
In-plane
Through-plane

23. Direction of Greatest Diffusion+ + +
X-component
Y-component
Z-component
Anisotropy
Color (Hue) = Direction of highest diffusion
Brightness = Degree of anisotropy =

24. Diffusion Tensor – Colour Map
Left-Right
Anterior-Posterior
Superior-Inferior

25. DTI – Color Map

26. Diffusion Tensor – 3D Colour Map
Left-Right
Anterior-Posterior
Superior-Inferior

27. How Many Measurements?

28. Which Directions?
Isotropic resolution diffusion tensor imaging with whole brain acquisition in a clinically acceptable time
D.K. Jones, S.C.R. Williams, D. Gasston, M.A. Horsfield, A. Simmons, R. Howard
Human Brain Mapping 15, (2002)

29. Fiber Tracking – Discrete Case
Direction of
Greatest diffusion

30. Fiber Tracking – Discrete Case
Direction of
Greatest diffusion

31. Fiber Tracking – Continuous Case
Direction of
Greatest diffusion
Mori et al, 1999

32. Fiber Tracking – Where to Start
Everywhere: Seed points distributed evenly throughout volume

33. DTI Tractography

34. Fiber Tracking – Where to Start
Within a plane: All fibers within or crossing a selected plane are tracked

35. Fiber Tracking – Corpus Callosum

36. Fiber Tracking – Corpus Callosum

37. Fiber Tracking – Where to Start
Within a small volume

38. Fiber Tracking - CST

39. “Human Neuroanatomy” Carpenter & Sutin 1981
Upper Extremity
Trunk
Lower Extremity
Posterior limb of internal capsule from a standard neuroanatomy textbook
Corticospinal fibers in the anterior part of the PLIC
Fibers arranged from
anterior = upper extremity
through trunk
posterior = lower extremity
2 years later…

40. “Human Neuroanatomy” Carpenter & Sutin 1983
Same textbook, new edition
New data from electrical stimulation and pathological studies
Corticospinal fibers now in the posterior part of the PLIC
anterior = upper extremity
middle = trunk
posterior = lower extremity
“Evidence that fibers of the corticospinal tract are somatotopically arranged in ...a compact region in the posterior half of the PLIC… seems relatively crude”
Upper Extremity
Trunk
Lower Extremity

41. Fiber Tracking - CST

42. Fiber Tracking - CST

43. Combining DTI and fMRI

44. fMRI – Feet Movement
Medial activations when volunteer asked to move their feet
Time course of MR signal clearly shows five periods of rest and activation

45. fMRI – Finger Tapping
Activations more lateral for finger tapping

46. fMRI – Tongue Movement
Tongue movement – volunteer asked to move tongue from side to side
Activations still more lateral

47. Results – fMRI – Feet, Fingers, Tongue
Overlaying 3 sets of functional data together
Red = Feet, Green = Fingers, Blue = Tongue
Arranged medial (feet) to lateral (tongue) on a coronal slice
Is this what we would expect?

48. “Images of Mind”, Posner and Raichie, 1999
Yes!
Classical view of motor cortex
Medial to lateral we have feet-fingers-tongue
“Images of Mind”, Posner and Raichie, 1999

49. Fiber Tracking - CST
Subject 1
Subject 2
Subject 3
Subject 4

50. Crossing Fibers Feet movement Tongue movement Longitudinal Fasciculus
Corticospinal Tract
Longitudinal Fasciculus
Cingulum
Corpus
Callosum
Tongue movement
Feet movement

51. DTI – Tracking below SLF
Feet
Tongue
Axial section, coloring the points according to the seed volume used previously
Green = Feet, Blue = Fingers, Red = Tongue
Compared to Carpenter & Sutin (1983, right), we also find corticospinal fibers to be concentrated in the posterior half of the PLIC
However, we find then to be arranged more left-right instead of anterior-posterior
Preliminary finding: more work to check reproducibility, need an accurate algorithm to follow tracks through the SLF (rather than just visually)
Fingers
Upper
Trunk
Lower

52. DTI Tractography – Clinical Example

53. DTI Tractography – Clinical Example

54. Limitations of DTI/Fiber Tracking
Partial volume
A single voxel may contain fibers running in multiple directions – average anisotropy measured
Tensor may not be a good representation
Need to distinguish “kissing” and “crossing”
Crossing Fibers
Kissing Fibers

55. More Pretty Pictures…
Isotropic resolution diffusion tensor imaging with whole brain acquisition in a clinically acceptable time
D.K. Jones, S.C.R. Williams, D. Gasston, M.A. Horsfield, A. Simmons, R. Howard
Human Brain Mapping 15, (2002)

56. Conclusions, the Future
DTI provides the only non-invasive method to study organization white matter fibers. Previous studies have been limited to animal models and stroke patients
Current limitations on DTI and Fiber Tracking:
Partial volume effects
SNR
Acquisition time/physiological noise
Advances
High field, faster gradients, more efficient coils, motion detection/correction, new pulse sequences (eg. 3D, spiral…)
Higher SNR can be traded for smaller voxels, reducing partial volume effects
Beyond the tensor model… HARD imaging, q-space imaging
New tracking algorithms

57. DTI – Tracking below SLF

58. DTI – Tracking below SLF

59. References
High-resolution isotropic 3D diffusion tensor imaging of the human brain.
X. Golay, H. Jiang, P.C.M. van Zijl, S. Mori
Magn. Res. Med. 47, (2002)
White matter mapping using diffusion tensor MRI
C.R. Tench, P.S. Morgan, M. Wilson, L.D. Blumhardt
Magn. Res. Med. 47, (2002)
Three-dimensional tracking of axonal projections in the brain by magnetic resonance imaging
S. Mori, B.J. Creain, V.P. Chacko, P.C.M. van Zijl
Ann. Neurol. 45, (1999)
Diffusion tensor imaging: Concepts and applications
D. Le Bihan et al
J. Magn. Res. Imaging 13, (2001)
In vivo three dimensional reconstruction of rat brain axonal projections by diffusion tensor imaging
R. Xue, P.C.M. van Zijl, B.J. Cain, M. Solaiyappan, S.Mori
Magn. Res. Med (1999)
A direct demonstration of both structure and function in the visual system: combining diffusion tensor imaging with functional magnetic resonance imaging
D.J. Werring, C.A. Clark, G.J.M. Parker, D.H. Miller, A.J. Thompson, G.J. Barker
NeuroImage 9, (1999)
Orientation-independent diffusion imaging without tensor diagonalization: anisotropy definitions based on the physical attributes of the diffusion ellipsoid
A.M. Ulug, P.C.M. van Zijl
J. Magn. Res. Imaging 9, (1999)

60. References
Imaging cortical association tracts in the human brain using diffusion-tensor based axonal tracking
S. Mori et al
Magn. Res. Med. 47, (2002)
Isotropic resolution diffusion tensor imaging with whole brain acquisition in a clinically acceptable time
D.K. Jones, S.C.R. Williams, D. Gasston, M.A. Horsfield, A. Simmons, R. Howard
Human Brain Mapping 15, (2002)
Diffusion tensor imaging and axonal tracking in the human brainstem
B. Stietjes et al
NeuroImage (2001)
Tracking neuronal fiber pathways in the living human brain
T.E. Conturo et al
Proc. Natl. Acad. Sci (1999)
The future for diffusion tensor imaging in neuropsychiatry
K.H. Taber et al
J. Neuropsychiatry Clin. Neurosci (2002)
Tensorlines: Advection-diffusion based propogation through diffusion tensor fields
D. Weinstein, G. Kindlmann, E. Lundberg

61. The Diffusion Tensor   g Gx
where
where
Identical if

62. How Many Measurements? 7 degrees of freedom:
S0, Dxx, Dyy, Dzz, Dxy, Dxz, Dyz
Need at least 7 directions – but more is better!
30 slices x 32 directions = 960 images…

63. Corresponding Tensor
mm2/s

64. Eigenvalues and Eigenvectors of the Diffusion Tensor

65. Corresponding Tensor
mm2/s

66. Eigenvalues and Eigenvectors of the Diffusion Tensor