MR Diffusion Tensor Imaging, Tractography Richard Watts, D.Phil. Citigroup Biomedical Imaging Center Weill Medical College of Cornell University Box 234,

MR Diffusion Tensor Imaging, Tractography

Richard Watts, D.Phil.Citigroup Biomedical Imaging Center

Weill Medical College of Cornell UniversityBox 234, 1300 York Avenue, New York, NY 10021

Email [email protected], Telephone 212 746-5781

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.

Outline• Background

– Diffusion– Restricted Diffusion and Anisotropy

• Methods– Data Acquisition– Display of Diffusion Tensor Data– Fiber Tracking– Problems and Limitations

• Examples

Diffusion

Diffusion Equation

Dtr 62

r = Displacement (mm)D = Diffusion constant

(mm2/s)t = Time (mm)

Distance ScalesQuestion: What distance do protons travel during an EPI readout time?

Assume: Diffusion constant ~ 10-3 mm2/sTime ~ 100 ms = 0.1s

1.0106

63

2

Dtr

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

Diffusion Imaging of Leukemia

Diffusion Imaging of Leukemia

Spin Echo

Spin Echo

Spin Echo

Data Acquisition – Spin Echo

TE

time

90º 180º

RF

Gx

Diffusion Gradients

Echo

bDeSS 0 where 3222 gb

g

Restricted Diffusion

Diffusion Ellipsoid in White Matter

Anisotropy

Isotropic:Having the same properties in all directions

Anisotropic:Not isotropic; having different properties in different directions

Webster’s Dictionary

Data Acquisition – Spin Echo

TE

time

90º 180º

RF

Gx

Gy

Gz

Linear combination of gradients - measure component of diffusion in any direction

Echo

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

zzyzxz

yzyyxy

xzxyxx

DDD

DDD

DDD

D

Calculated Quantities…

T2-Weighted Image “Average” Diffusion*

Diffusion along X Diffusion along Y Diffusion along Z

Degree of Anisotropy*

* Various definitions

1. (Approximately) Isotropic Diffusion

How a blob of ink would spread out

2. Anisotropic Diffusion

How a blob of ink would spread out

Vector PlotIn-plane

Through-plane

Direction of Greatest Diffusion

+++

=

Color (Hue) = Direction of highest diffusionBrightness = Degree of anisotropy

X-component Y-component Z-component Anisotropy

Diffusion Tensor – Colour Map

Left-Right

Anterior-Posterior

Superior-Inferior

DTI – Color Map

Diffusion Tensor – 3D Colour Map

Left-Right

Anterior-Posterior

Superior-Inferior

How Many Measurements?

Which Directions?

Isotropic resolution diffusion tensor imaging with whole brain acquisition in a clinically acceptable timeD.K. Jones, S.C.R. Williams, D. Gasston, M.A. Horsfield, A. Simmons, R. HowardHuman Brain Mapping 15, 216-230 (2002)

Fiber Tracking – Discrete Case

Direction ofGreatest diffusion

Fiber Tracking – Discrete Case

Direction ofGreatest diffusion

Fiber Tracking – Continuous Case

Direction ofGreatest diffusion

Mori et al, 1999

Fiber Tracking – Where to Start

• Everywhere: Seed points distributed evenly throughout volume

DTI Tractography

Fiber Tracking – Where to Start

• Within a plane: All fibers within or crossing a selected plane are tracked

Fiber Tracking – Corpus Callosum

Fiber Tracking – Corpus Callosum

Fiber Tracking – Where to Start

• Within a small volume

Fiber Tracking - CST

“Human Neuroanatomy” Carpenter & Sutin 1981

Upper Extremity

Trunk

Lower Extremity

“Human Neuroanatomy” Carpenter & Sutin 1983

Upper ExtremityTrunk

Lower Extremity

Fiber Tracking - CST

Fiber Tracking - CST

Combining DTI and fMRI

fMRI – Feet Movement

Feet

-4

-3

-2

-1

0

1

2

3

4

1 8 15 22 29 36 43 50 57 64 71 78 85 92 99 106

Acquisition Number

Sig

nal

Ch

ang

e (%

)

fMRI – Finger Tapping

Fingers

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

2.5

3

1 8 15 22 29 36 43 50 57 64 71 78 85 92 99 106

Acquisition Number

Sig

nal

Ch

ang

e (%

)

fMRI – Tongue Movement

Tongue

0

1

2

3

4

5

6

1 8 15 22 29 36 43 50 57 64 71 78 85 92 99 106

Acquisition Number

Sig

nal

Ch

ang

e (%

)

Results – fMRI – Feet, Fingers, Tongue

“Images of Mind”, Posner and Raichie, 1999

Fiber Tracking - CSTSubject 1 Subject 2 Subject 3 Subject 4

Crossing Fibers

Tongue movementFeet movement

Corticospinal Tract

Longitudinal Fasciculus

Cingulum

CorpusCallosum

DTI – Tracking below SLF

TongueFeetFingers

Lower

TrunkUpper

DTI Tractography – Clinical Example

DTI Tractography – Clinical Example

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

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, 216-230 (2002)

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

DTI – Tracking below SLF

DTI – Tracking below SLF

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, 837-843 (2002)

• White matter mapping using diffusion tensor MRI– C.R. Tench, P.S. Morgan, M. Wilson, L.D. Blumhardt

– Magn. Res. Med. 47, 967-972 (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, 265-269 (1999)

• Diffusion tensor imaging: Concepts and applications– D. Le Bihan et al

– J. Magn. Res. Imaging 13, 534-546 (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. 42 1123-1127 (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, 352-361 (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, 804-813 (1999)

References• Imaging cortical association tracts in the human brain using diffusion-tensor based axonal

tracking– S. Mori et al

– Magn. Res. Med. 47, 215-223 (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, 216-230 (2002)

• Diffusion tensor imaging and axonal tracking in the human brainstem– B. Stietjes et al

– NeuroImage 14 723-735 (2001)

• Tracking neuronal fiber pathways in the living human brain– T.E. Conturo et al

– Proc. Natl. Acad. Sci. 96 10422-10427 (1999)

• The future for diffusion tensor imaging in neuropsychiatry– K.H. Taber et al

– J. Neuropsychiatry Clin. Neurosci. 14 1-5 (2002)

• Tensorlines: Advection-diffusion based propogation through diffusion tensor fields– D. Weinstein, G. Kindlmann, E. Lundberg

The Diffusion Tensor

gDgb T

eSS 0

0 where 3

220

b

gGx

bDeSS 0 where 3222 gb

Identical if

D

D

D

DDD

DDD

DDD

D

zzyzxz

yzyyxy

xzxyxx

00

00

00

How Many Measurements?

gDgb T

eSS 0

0

zzyzxz

yzyyxy

xzxyxx

DDD

DDD

DDD

D

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…

310

649.0074.0064.0

074.0709.0075.0

064.0075.0638.0

D

Corresponding Tensor

mm2/s

Eigenvalues and Eigenvectors of the Diffusion Tensor

31 10814.0

509.0

709.0

488.0

1v

32 10603.0

615.0

696.0

371.0

2v

33 10578.0

603.0

111.0

790.0

3v

310

606.0085.0022.0

085.0620.1775.0

022.0775.0115.1

D

Corresponding Tensor

mm2/s

Eigenvalues and Eigenvectors of the Diffusion Tensor

31 10185.2

036.0

809.0

586.0

1v

32 10651.0

823.0

309.0

476.0

2v

33 10506.0

566.0

500.0

656.0

3v