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 Email riw2004@med.cornell.edu, 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 Methods Examples Diffusion Restricted Diffusion and Anisotropy Methods Data Acquisition Display of Diffusion Tensor Data Fiber Tracking Problems and Limitations Examples

Diffusion

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

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

Diffusion Imaging of Leukemia

Diffusion Imaging of Leukemia

Spin Echo

Spin Echo

Spin Echo

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

Restricted Diffusion

Diffusion Ellipsoid in White Matter

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

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

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

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

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

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

Vector Plot In-plane Through-plane

Direction of Greatest Diffusion + + + X-component Y-component Z-component Anisotropy Color (Hue) = Direction of highest diffusion Brightness = Degree of 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 time D.K. Jones, S.C.R. Williams, D. Gasston, M.A. Horsfield, A. Simmons, R. Howard Human Brain Mapping 15, 216-230 (2002)

Fiber Tracking – Discrete Case Direction of Greatest diffusion

Fiber Tracking – Discrete Case Direction of Greatest diffusion

Fiber Tracking – Continuous Case Direction of Greatest 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 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…

“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

Fiber Tracking - CST

Fiber Tracking - CST

Combining DTI and fMRI

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

fMRI – Finger Tapping Activations more lateral for finger tapping

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

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?

“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

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

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

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

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   g Gx where where Identical if

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…

Corresponding Tensor mm2/s

Eigenvalues and Eigenvectors of the Diffusion Tensor

Corresponding Tensor mm2/s

Eigenvalues and Eigenvectors of the Diffusion Tensor