Methods for Medical Imaging– Prof. G. Baselli

2012

Diffusion weighted MRI and DTI tractography

Maria Giulia Pretimaria.preti@mail.polimi.it

MRI contrasts

Contrast between two tissues A and B CAB = abs (IA – IB ) / IREF

NB: MRI offers several contrast types, they dipend on weighing (T1, T2, T2*, Proton Density, Diffusion, etc.)

Definition:

T1

T2

Diffusion weighted imaging, DWI

Normally, acquisition sequences are designed to enhance a specific diffusion weight (e.g., T1, T2, DWI)

Liquor

White Matter, WM

Gray Matter, GM

The amount of motion of water molecules diffusing within tissues is observed

Molecular Diffusion

MOLECULAR DIFFUSION: caotic motion of molecules, due to their thermal agitation (Brownian motion)

Definition (Einstein, 1905)

free diffusion

= equal displacement probability in all directionsISOTROPIC DIFFUSION

D = DIFFUSION COEFFICIENT(mass, viscosity, temperature)

Diffusion Weighted Imaging (DWI)

Dr 62

Isotropic Diffusion

Distribution of displacementsGaussian

r = displacement of molecules from time t1 to time t2

Dr 22Meand squard displacement

in 1DIn 3D:

Δ = diffusion time (t2–t1)

Diffusion in biological tissues

In tissues, water diffusion finds barriers: it is hindered The apparent diffusion coefficient (ADC) is lower and

depends on microscopic structure

Higly hindered Less hindered

ISOTROPIC NON ANISOTROPIC

3D description by the Diffusion Tensor (DT)

RephasingDephasing

RephasingDephasing

RephasingDephasing

Slice selection

Gz

Gy

Gx

Phase Encoding

Frequency Encoding

SignalTE

90° 180°

Diffusion weighted spin-echo EPI

Addition of a bipolar gradient pulse

Δ

δ

G

y

Diffusion weighing by bipolar gradient pulse

G

position dependent dephasing

y

-G

Dephasing

Rephasing

)( 2121 xxG The final phase shift of spins requires displacemnt

Phase t=0 Phase t=Δ Position t=ΔPosition t=0

x1=x2 (NO DIFFUSION) NO Dephase, NO signal attenuation

G gradient pulse amplitude

δ= duration of gradient pulse

Δ = Δt between the two pulses = diffusion time

γ = gyromagnetic ratio

Dephasing

Δ

δ

G Rephasing

Diffusion weighing by bipolar gradient pulse

Rephasin

g

Dephasin

g

90° 180°

B0

Diffusion weighing by bipolar gradient pulse

Dephasin

g

90° 180°

B0

Diffusion weighing: low diffusion

Rephasin

g

Dephasin

g

90° 180°

B0

Diffusion weighing: high diffusion

DWI Contrast

DWI:

MORE DIFFUSIONE LESS SIGNAL

(DARKER)

b-value DIFFUSION WEIGHING INDEX

Liquor >diffusion <signal

SIGNAL ATTENUATIONDIFFUSION

Stejkal andTanner’s equation

Diffusion weighing in the gradient direction

ADCbADCGee

S

S

)3(

0

222 b=0 imge weithed byT2 onlyb≠0 weighted by T2 and by diffusion DWI

ADC estimate by log ratio of T2 and DWI:

ADCbSS )ln(

0

Signal attenuation:

DWI

G gradient pulse amplitude

δ= duration of gradient pulse

Δ = Δt between the two pulses = diffusion time

γ = gyromagnetic ratio

Apparent Diffusion Coefficient (ADC)

ADC Map Image of diffusion voxel by voxel.

A refernce (S0) and a DWI are necessary(or a low b and a high b DWI)

b=0

S0

b=1200 sec/mm²

SPeri-tumoral edema area has the same intensity than other tissues

ADC=-1/b ln(S/S0)

ADC mapEdema area is enhanced

ADCbSS )ln(

0

Diffusion Tensor Imaging (DTI)

Orderly oriented structures:

Preferential diffusion parallel to fibers, hindered or even restricted in the orthogonal directions. NOTE: DTI model does not distinguish restricted diff. (not Gaussian)

WHITE MATTER (WM)

IN THE CNS

Exploration in the 3D space

Description in each voxel by a 3x3 symmetric matrix:

DIFFUSION TENSOR

xx xy xz

xy yy yz

xz yz zz

D D D

D D D

D D DD

DTI

NON ISOTROPIC DIFFUSION in a preferred direction along fibers

Calcolo del tensore di diffusione

Diffusion Tensor (DT) symmetry 6 independent components each scan requires ad at least 6 DWI acquisitions along maximally distant directions +1 reference image (b=0)Often, more directions are acquired: 12 and more

Minimal set acquisition

and gradient components

(1) (1) (1) (1) (1) (1)1

( ) ( ) ( ) ( ) ( ) ( )

ln 2 2 2

.....

.....

ln 2 2 2

xx xx yy yy zz zz xy xy xz xz yz yz

N N N N N NN xx xx yy yy zz zz xy xy xz xz yz yz

A b D b D b D b D b D b D

A b D b D b D b D b D b D

Least squares solution of a system of Stejkal andTanner eq.

Z

X

Y

ijijDbeS/SA 0

xx xy xz

xy yy yz

xz yz zz

D D D

D D D

D D DD

i,j = x,y,zBij = (ɣδ)2 (Δ - δ /3) Gi Gj

1. PRINCIPAL DIFFUSION DIRECTION: eigenvector (e1) of the largest eignevalue

xx xy xz

xy yy yz

xz yz zz

D D D

D D D

D D DD

3DM 321 λλλ

23

22

21

23

22

21 )()()(

2

3

DMDMDMAF

The DT of each voxel provides the eigenvalues and eigenvectors

2. MEAN DIFFUSIVITY: diffusion averaged over all directons

3. FRACTIONAL ANISOTROPY: measure of ordered directionality

Diffusion Tensor Imaging (DTI)

e1

e2

e3

fiber

Tensor eigen-vectors oriented parallel (e1) and orthogonally (e2, e3) to fibers

scanner reference system

Isotropic Non Isotropic

Non Isotropic

1 2 3, , autovettorie e e

Reconstruction of fibers following the principal direction voxel through voxel

2 STOPPING RULES:

o Minimum AF

o Maximum bending angle from voxel to voxel

Start from: seed points[ ROI of seed points ]

ASSUMPTION ASSUMPTION

Principal direction = average fiber orientation

AF < threshold

X

angle > threshold

X

Diffusion Tensor Tractography (DTT)

ILF ARCUATE

UNCINATE

CINGULATE

CORPUS CALLOSUM

IFOF

WHOLE BRAIN

Tractography: reconstructed bundles or fascicles

Positioning of ROI for seed points

ROI of seed points - ideally: anatomical region crossed by all fascicle fibers and not crossed by other fascicles.

Locate usual on the FA map good contrast of fbers.

FA

Example: 3 ROIs for identifying 3 portions of corpus callosum (CC) (genu-body-splenium) ROIs on the central sagittal plane CC extends from ROIs to the emispheres

Afferent and efferent fibers not distinguish One single principal direction per voxel, no distinction of fibers

with different directions (see below) Partial volume effects (e.g. GM); particularly severe the effect of free

water (isotropic) in edema FA drop fiber reconstruction stops Low resolution for SNR and acquisition time

DT Tractorgraphy limitations

In case of mixed directions the principal directions is actually the average direction

“kissing”, “crossing” and “diverging” fibers.