Einstein on Brownian Motion 1905 five important papers DTI Basics – Water Diffusion

Conventional T 2 WI DW-EPI Why MRI : Detection of Acute Stroke “Diffusion Weighted Imaging (DWI) has proven to be the most effective means of detecting early strokes” Lehigh Magnetic Imaging Center Sodium ion pumps fail, water goes in cells and can not diffuse.

Tumor T2 (bright water) DWI (x direction) (T2 (bright water)+(diffusion)) T1 + Gadolinium

Why MRI (more recently): Fiber Tracking Why MRI (more recently): Fiber Tracking

Diffusion Weighted Image X direction David Porter - November 2000 Artifact or Abnormality  Higher diffusion in X direction  lower signal 1 st level of complexity

Pulse Sequence: Gradient-Echo Diffusion Weighting in X direction 90 o Excitation Image Acquisition RF Gx Gy Gz G -G-G EPI (T2) diffusion gradients

Gradient Coils

RF Gx Gy Gz - Time NO DIFFUISION with DIFFUISION y x protons (Hydrogen) signal loss

RF Gx Gy Gz - Time (gradient strength) T2T2 + diffusion T2

DIFFUSION MAPS (used to remove spin density, T1, T2, TR, and TE effects) (used to remove spin density, T1, T2, TR, and TE effects) S=S 0 e (-bDxx) Ln(S) = Ln(S 0 ) – bD xx or D xx = (Ln(S 0 ) – Ln(S))/b Ln(S) = Ln(S 0 ) – bD xx or D xx = (Ln(S 0 ) – Ln(S))/b S 0 ( T2 * EPI) S (T2* EPI + weak Diffusion in X direction) D xx Most Important image weak

2nd Level of complexity DWI : 3 Direction courtesy of Dr Sorensen, MGH, Boston David Porter - November 2000  single-shot EPI diffusion-weighted (DW) images with b = 1000s/mm 2 and diffusion gradients applied along three orthogonal directions  Higher diffusion  lower signal D zz D xx D yy

X Diffusion-Weighting Y Diffusion- Weighting Z Diffusion-Weighting G FE G PE G SS RF A Little More Detail SS PE FE x z y y x z

Apparent Diffusion Coefficient ADC (AKA TRACE) ADC = (D xx + D yy + D zz )/3 Z Diffusion-Weighting X Diffusion-Weighting Y Diffusion Weighting Orientation independent used in clinical stroke, tumor, etc No directional information (ie direction of greatest diffusion)

3rd level of complexity Diffusion Tensor Imaging Basics Measures water diffusion in at least 6 directions – we use 12 Echo-planar imaging (fast acquisition) Collecting small voxels (1.8x1.8x3mm), scanning takes about 10 minutes

Useful for following white matter tracts  Higher diffusion  lower signal

IsotropicAnisotropic Adapted from: Beaulieu (2002). NMR in Biomed; 15:  Higher diffusion  lower signal

x y z DTI ellipsoid measure 6 directions to describe no diffusion

Pierpaoli and Basser, Toward a Quantitative Assessment of Diffusion Anisotropy, Magn. Reson. Med, 36, (1996) Ellipsoid Image Tract Information available through DTI

Tract tracing problems (fiber crossing)

Tractography Zhang & Laidlaw: Superior view color fiber mapsLateral view color fiber maps

Diffusion Tensor Imaging data for cortical spinal tract on right side blue = superior – inferior fibers green = anterior – posterior fibers red = right – left fibers Note tumor is darker mass on left side of axial slice axial sag cor MRISC

But what is a diffusion tensor ? It is a mathematical description of the ellipsoid. y x z no diffusion D xx D xy D xz D yx D yy D yz D zx D zy D zz z -xz y-z xz y-z xy-xy

What is diffusion “Tensor” (D)? D xx D xy D xz D yx D yy D yz D zx D zy D zz D x’x’ D y’y’ D z’z’ S=S 0 exp(-bD) difussion gradient direction vector = (mathematical manipulation) Calculate FA (fractional anisotropy) Fiber track y ellipsoid reference framelab reference frame

Information available through DTI av  FA (fractional anisotropy) FA = ((D x’x’ -D av ) 2 + (D y’y’ -D av ) 2 + (D z’z’ -D av ) 2 ) 0.5 (D x’x’ 2 +D y’y’ 2 +D z’z’ 2 ) 0.5 D x’x’ D y’y’ D z’z’ FA = 0 FA = 0.9

FA (fractional anisotropy) MAP

FA + color (largest diffusion direction) red = right – left green = anterior – posterior blue = superior - inferior

probably no use

Tractography Zhang & Laidlaw: Superior view color fiber mapsLateral view color fiber maps

G G echo TE At the echo time TE, NMR signal is decayed by, - T2 decay (spin-spin diffusion) - diffusive motion For any set of diff. gradient pulses Signal loss : by intra-voxel phase dispersion

DTI Scalar Parameters Trace: Magnitude of diffusion in a voxel. –Increases in damaged white matter Fractional Anisotropy (FA): Measure of directionally- restricted diffusion. –Decreases in damaged white matter Rosenbloom M, et al. (July 2004). NIAA pubs;

The Diffusion Tensor, D Diffusion is not equal in all directions (anisotropic). Use this to probe brain structure! Represent the diffusion pattern at each point in the brain using an ellipsoid.

Diffusion Vector (Colour) Map The three magnitudes of the diffusion ellipsoid can be shown using three colours (RGB). –Red = Left – Right –Green = Ant. – Pos. –Blue = Sup. – Inf. Map of major directions of water movement in the brain.

Fibre Tractography In principle, the locations of major white matter fibre tracts in the brain can be mapped using the information in the colour map, by “following the arrows.”

without hindrance with hindrance Hindered Diffusion (diffusion ellipsoid) WILSON

Information available through DTI – Orientation of λ 1 Useful for following white matter tracts

Information available through DTI -- A σ Related to the shape of the ellipsoid Independent of D av (normalized) Zero for a sphere, positive for other shapes Sensitive to myelination and cortical development av 

Diffusion Tensor Imaging ( A  ) Normal Adult Brain (A  maps)

 Higher diffusion  lower signal Tissue Sample A Tissue Sample B Freely Diffusing Water = Dark Freely Diffusing Water = Dark Larger D Larger D Restricted Diffusion = Bright Restricted Diffusion = Bright Smaller D Smaller D CELL EXTRA-CELLULAR SPACE FREELY DIFFUSING WATER IN EXTRA-CELLULAR SPACE

K-space view of the spin echo imaging Kx Ky n n

X Diffusion-Weighting Y Diffusion- Weighting Z Diffusion-Weighting G FE G PE G SS RF Diff. Grad. along different axis SS PE FE

DTI (Diffusion Tensor Imaging) DTI (Diffusion Tensor Imaging) courtesy of Dr Sorensen, MGH, Boston David Porter - November 2000  single-shot EPI diffusion-weighted (DW) images with b = 1000s/mm 2 and diffusion gradients applied along three orthogonal directions  Higher diffusion  lower signal

Conventional T 2 WI DW-EPI Detection of Acute Stroke “Diffusion Weighted Imaging (DWI) has proven to be the most effective means of detecting early strokes” Lehigh Magnetic Imaging Center Sodium ion pumps fail, water goes in cells and can not diffuse.

Tumor T2 (bright water) DWI (x direction) (T2 (bright water)+diffusion) T1 + Gadolinium

90 o Excitation Image Acquisition RF Gx Gy Gz G -G-G Do X, Y, and Z at the same time

The Diffusion Tensor, D Diffusion is not equal in all directions (anisotropic). (anisotropic). Use this to probe brain structure! Diffusion ellipsoid for each voxel x y z

DTI Scalar Parameters Trace: The magnitude of diffusion in a voxel. Fractional Anisotropy (FA): The extent to which diffusion is directionally restricted.