Einstein on Brownian Motion

1905 five important papers

DTI Basics – Water DiffusionDTI Basics – Water Diffusion

Conventional TConventional T22 WI WI DW-EPIDW-EPI

Why MRI : Detection of Acute StrokeWhy 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.

TumorTumor

T2 (bright water)DWI (x direction)

(T2 (bright water)+(diffusion))

T1 + Gadolinium

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

Diffusion Weighted Image X directionDiffusion Weighted Image X direction

David Porter - November 2000

Artifact or Abnormality

Higher diffusion in X direction lower signal

1st level of complexity

Pulse Sequence: Gradient-EchoPulse Sequence: Gradient-EchoDiffusion Weighting in X directionDiffusion Weighting in X direction

90o

Excitation

Image

Acquisition

RF

Gx

Gy

Gz

G

-G EPI (T2)

diffusion gradients

GradientCoils

RFGxGyGz

-

Time

NO DIFFUISION

with DIFFUISION

y

x

protons (Hydrogen)

signal loss

RFGxGyGz

-

Time

(gradient strength)

T2T2 + diffusion

T2

DIFFUSION MAPSDIFFUSION MAPS

(used to remove spin density, T1, T2, TR, and TE effects)(used to remove spin density, T1, T2, TR, and TE effects)S=SS=S00ee(-bDxx)(-bDxx)

Ln(S) = Ln(SLn(S) = Ln(S00) – bD) – bDxxxx or D or Dxxxx = (Ln(S = (Ln(S00) – Ln(S))/b) – Ln(S))/b

S0 (T2* EPI) S (T2* EPI + weak Diffusion in X direction)

Dxx

Most Important image

weak

2nd Level of complexity2nd Level of complexityDWI : 3 Direction DWI : 3 Direction

courtesy of Dr Sorensen, MGH, Boston

David Porter - November 2000

single-shot EPI diffusion-weighted (DW) images with b = 1000s/mm2 and diffusion gradients applied along three orthogonal directions Higher diffusion lower signal

Dzz Dxx Dyy

X Diffusion-WeightingX Diffusion-Weighting Y Diffusion-Y Diffusion-WeightingWeightingZ Diffusion-WeightingZ Diffusion-Weighting

GGFEFE

GGPEPE

GGSSSS

RFRF

A Little More DetailA Little More Detail

SS

PE

FEx

z

y

y

x

z

Apparent Diffusion Coefficient ADC (AKA TRACE)

ADC = (Dxx + Dyy + Dzz)/3

Orientation independent

used in clinical stroke, tumor, etc

No directional information (ie direction of greatest diffusion)

3rd level of complexity3rd level of complexityDiffusion Tensor Imaging BasicsDiffusion Tensor Imaging Basics

Measures water diffusion in Measures water diffusion in at least 6 at least 6 directionsdirections – we use 12 – we use 12Echo-planar imaging (fast acquisition)Echo-planar imaging (fast acquisition)Collecting small voxels (1.8x1.8x3mm), Collecting small voxels (1.8x1.8x3mm), scanning takes about 10 minutesscanning takes about 10 minutes

• Useful for following white matter tracts

Higher diffusion lower signal

Isotropic Anisotropic

Adapted from: Beaulieu (2002). NMR in Biomed; 15:435-455

Higher diffusion lower signal

x

yz

DTI ellipsoidDTI ellipsoidmeasure 6 directions to describemeasure 6 directions to describe

no diffusion

Pierpaoli and Basser, Toward a Quantitative Assessment of Diffusion Anisotropy, Magn. Reson. Med, 36, 893-906 (1996)

Ellipsoid Image

Tract

Information available through DTI

Tract tracing problems (fiber crossing)Tract tracing problems (fiber crossing)

TractographyTractography

Zhang & Laidlaw: http://csdl.computer.org/comp/proceedings/vis/2004/8788/00/87880028p.pdf.

Superior view color fiber maps Lateral view color fiber maps

Diffusion Tensor Imaging data forcortical spinal tract on right side

blue = superior – inferior fibersgreen = anterior – posterior fibersred = right – left fibers

Note tumor is darker mass on leftside of axial slice

axial

sag

corMRISC

But what is a diffusion But what is a diffusion tensortensor?? It is a mathematical description of It is a mathematical description of the ellipsoid. the ellipsoid.

y

x

z

no diffusion

Dxx Dxy Dxz

Dyx Dyy Dyz

Dzx Dzy Dzz

z-xz

y-zxz

y-z

xy -xy

What is diffusion “Tensor” (D)?

Dxx Dxy Dxz

Dyx Dyy Dyz

Dzx Dzy Dzz

Dx’x’ 0 00 Dy’y’ 00 0 Dz’z’

S=SS=S00exp(-bD)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 (fractional anisotropy)

FA = ((Dx’x’-Dav)2 + (Dy’y’-Dav)2 + (Dz’z’-Dav)2)0.5

(Dx’x’2+Dy’y’

2+Dz’z’2)0.5

Dx’x’

Dy’y’

Dz’z’

FA = 0

FA = 0.9

FA (fractional anisotropy) MAP

FA + colorFA + color (largest diffusion direction)(largest diffusion direction)

red = right – leftgreen = anterior – posteriorblue = superior - inferior

probably no useprobably no use

TractographyTractography

Zhang & Laidlaw: http://csdl.computer.org/comp/proceedings/vis/2004/8788/00/87880028p.pdf.

Superior view color fiber maps Lateral view color fiber maps

G

18090

G

echoTE

At the echo time TE, NMR signal is decayed by, - T2 decay (spin-spin diffusion) - diffusive motion

ijij2 DbTTEoij eeSbTES /),(

b D G D Gij ij i ij j ( / )

b G2 ( / )

For any set of diff. gradient pulses

Signal loss Signal loss : : by intra-voxel phase dispersionby intra-voxel phase dispersion

DTI Scalar ParametersDTI Scalar Parameters

TraceTrace: Magnitude of : Magnitude of diffusion in a voxel.diffusion in a voxel.– Increases in damaged white Increases in damaged white

mattermatter

Fractional Anisotropy (FA)Fractional Anisotropy (FA): : Measure of directionally-Measure of directionally-restricted diffusion.restricted diffusion.– Decreases in damaged white Decreases in damaged white

mattermatter

Rosenbloom M, et al. (July 2004). NIAA pubs; http://www.niaaa.nih.gov/publications/arh27-2/146-152.htm

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

Diffusion Vector (Colour) MapDiffusion Vector (Colour) Map

The three magnitudes The three magnitudes of the diffusion ellipsoid of the diffusion ellipsoid can be shown using can be shown using three colours (RGB).three colours (RGB).– Red = Left – RightRed = Left – Right– Green = Ant. – Pos.Green = Ant. – Pos.– Blue = Sup. – Inf.Blue = Sup. – Inf.

Map of major directions Map of major directions of water movement in of water movement in the brain.the brain.

Fibre TractographyFibre Tractography

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

without hindrance

with hindrance

Hindered Diffusion(diffusion ellipsoid)

WILSON

Information available through DTI – Orientation of λ1

• Useful for following white matter tracts

D)(

21A D

Information available through DTI -- Aσ

• Related to the shape of the ellipsoid

• Independent of Dav (normalized)

• Zero for a sphere, positive for other shapes

• Sensitive to myelination and cortical development

av

Diffusion Tensor Imaging (Diffusion Tensor Imaging (AA))Normal Adult Brain

(A maps)

Higher diffusion lower signal

Tissue Sample ATissue Sample A Tissue Sample BTissue Sample B

Freely Diffusing Water = DarkFreely Diffusing Water = Dark Larger DLarger D

Restricted Diffusion = BrightRestricted Diffusion = Bright Smaller DSmaller D

CELLCELL

EXTRA-CELLULAR SPACEEXTRA-CELLULAR SPACE

FREELY DIFFUSING WATER INFREELY DIFFUSING WATER INEXTRA-CELLULAR SPACEEXTRA-CELLULAR SPACE

K-space view of the spin echo imaging

Kx

Ky

123.......n

X Diffusion-WeightingX Diffusion-WeightingY Diffusion-Y Diffusion-WeightingWeighting Z Diffusion-WeightingZ Diffusion-Weighting

GGFEFE

GGPEPE

GGSSSS

RFRF

Diff. Grad. along different axisDiff. Grad. along different axis

SS

PE

FE

DTIDTI (Diffusion Tensor Imaging) (Diffusion Tensor Imaging)

courtesy of Dr Sorensen, MGH, Boston

David Porter - November 2000

single-shot EPI diffusion-weighted (DW) images with b = 1000s/mm2 and diffusion gradients applied along three orthogonal directions Higher diffusion lower signal

Conventional TConventional T22 WI WI DW-EPIDW-EPI

Detection of Acute StrokeDetection 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.

TumorTumor

T2 (bright water)DWI (x direction)

(T2 (bright water)+diffusion)

T1 + Gadolinium

90o

Excitation

Image

Acquisition

RF

Gx

Gy

Gz

G

-G

Do X, Y , and Z at the same timeDo X, Y , and Z at the same time

The Diffusion Tensor, DThe Diffusion Tensor, DDiffusion is not equal in all directionsDiffusion is not equal in all directions

(anisotropic).(anisotropic).Use this to probe brain structure!Use this to probe brain structure!Diffusion ellipsoid for each voxelDiffusion ellipsoid for each voxel

x

yz

ijij2 DbTTEoij eeSbTES /),(

b D G D Gij ij i ij j ( / )b G2 ( / )

DTI Scalar ParametersDTI Scalar Parameters

TraceTrace: The magnitude of diffusion in a : The magnitude of diffusion in a voxel.voxel.

Fractional Anisotropy (FA)Fractional Anisotropy (FA): The extent to : The extent to which diffusion is directionally restricted.which diffusion is directionally restricted.