Fund BioImag 201213-1

13: Advanced MRI Contrast Mechanisms

1. How does moving blood affect the image phase ? 2. What is the effect of self-diffusion on the MR signal ?3. Why is diffusion in vivo not isotropic ?

• Fiber tracking4. How do the different imaging modalities compare ?

• Capabilities• Limitations• Choice• Comparison by examples

After this week you1. Understand the influence of motion on the phase of magnetization2. Understand how random motion leads to echo amplitude reduction 3. Are able to calculate the attenuation of the MR signal due to diffusion 4. Understand how diffusion-weighted MRI signal reflects cellular structure and

how this can be exploited to track nerve fibers, among others5. Have a firm grasp on the premises and limitations of the imaging modalities

covered in this course

Fund BioImag 201213-2

Blood moving with velocity v

timeT 2T0

13-1. Effect of Bulk Motion on the Rephased Signal (Blood Flow)

Freq. Encode (Gx)

TE T T

T xx dtvtxGdtvtxGT0

2)()()2(

T

T x

T

x dttxGdttxGt2

0)()(

2)2( GvTT

x(t)=x0+vt

T

x

tvxtG

0

2

)2

( T

T

x

tvxtG

22

)2

(

f(t)

For transverse magnetization at point (x,y):

xtikxdttGixx eeyxm )()(

),(

Phase f of the magnetization:

)()0()( tieMtM

(Gradient along x)

f does not depend on x

Entire echo has phase f at TE

2

2),(

TE

Gvii eeyxm

f(TE)

t

x dttxtGt0

')'()'(

Fund BioImag 201213-3

13-2. Effect of self-Diffusion on the MR signal

<r> = 20 mmD = 0.1 s

<r> = 45 mmD = 0.5 s

<r> = 63 mmD = 1 s

Dr 6

Einstein random walk:

D: self diffusion coefficient

<r>: root mean square displacement after D seconds

Fund BioImag 201213-4

Effect of random motion on magnetization phase

when applying pulsed gradient

RF

G

90°

a

b

c

d

a b c d

Static magnetization:

Magnetization in motion:

stationary

spins

Displacedspins

net transverse magnetization

c: Particle displaces by r

Fund BioImag 201213-5

Effect of Diffusion on MagnetizationPhase f of Mxy

Inco

here

nt m

otio

n

Absence of incoherent motion: Echo formation

timeT

TG(t)

f(t) All in-phase: max. echo formation

f(t)

Not all in-phase: reduced echo amplitude

No diffusion

With diffusion

f

Fund BioImag 201213-6

gradient echo, i.e. sensitive to T2*

Effect of diffusion on the MRI signalMathematical description

Degree of echo signal reduction1. Strength of the diffusion process (D)

2. Delay between dephasing and rephasing gradient (D)

3. Area of the dephasing gradient (strength G, duration d) D

d

G

bDoeSbS )( 3/2 Gb

Attenuation of the signal (echo amplitude) due to diffusion in the direction of G

D: apparent diffusion coefficient (ADC)

D

d

GG

1800

RF

Equivalent sequence (spin echo, i.e. sensitive to T2)

Fund BioImag 201213-7

13-3. Imaging Anisotropic Water Diffusion

Consider structure along (myelinated) axon (or myofibril)

Anisotropic mean displacement Anisotropic diffusion coefficient

Diffusion coefficient depends on gradient orientation

→ Diffusion tensor Dij

zzzyzx

yzyyyx

xzxyxx

DDD

DDD

DDD

D

Motion (diffusion) of water molecules:

Restricted by cell membranes

Corpus callosum

CSF (isotropic)

GxGz Gy

Fund BioImag 201213-8

Diffusion tensor imaging (DTI)imaging anisotropic diffusion

λ3

λ1λ2

3

2

1

00

00

00

DT

Diffusion tensor symmetric: Dij = Dji

3 orthogonal Eigenvectors

→ Eigenvalues li

For each voxel determine direction of principal eigenvector (largest l):

Pseudocolor directionality

Mean diffusivity (trace Dij)

Fractional Anisotropy

(l1-l3)

Fund BioImag 201213-9

Application: Fiber Tracking using Diffusion MRI

from diffusion anisotropy to connectivity1. Image of diffusion anisotropy

2. Directionality of water diffusion connects adjacent voxels (spaghettis)

3. Establish fiber tracks

Fund BioImag 201213-10

13-4. Bio-imaging modalities comparison

I. contrast and limitations

Major limitationsstrong e- density differences (bone)

Ionizing radiation

g emitters available

non-uniform spatial resolution & sensitivity

sensitivity

time-consuming & motion-sensitive

complex methodology

does not penetrate hard objects (e.g. bone)

Major limitationsstrong e- density differences (bone)

Ionizing radiation

g emitters available

non-uniform spatial resolution & sensitivity

sensitivity

time-consuming & motion-sensitive

complex methodology

does not penetrate hard objects (e.g. bone)

Contrast mechanismsContrast mechanisms

CT e- density, Z

MR (Spin concentration)

Relaxation of magnetization

Fat/Water (chemical shift)

Diffusion

(etc …)

SPECT

PETTracer distribution in tissue

USBoundaries of tissues with different mechanical properties

Fund BioImag 201213-11

Comparison IISNR, reconstruction, contrast agents

Image reconstructionImage reconstruction

CT

SPECT

PET

Directionality of photon

→Radon transform

Projection reconstruction

MRprecession of M (gradient G)→ Frequency analysis Fourier transform

Contrast agents(contrast modifiers)

Contrast agents(contrast modifiers)

CT, x-ray Compounds with high Z

MR Compounds shortening relaxation times (T1, T2, or T2*)

Maximize SNRMaximize SNRCT Increase radiation dose

MR Increase magnetic field

SPECT

PETIncrease tracer dose

Limited by

Effective radiation dose

Equilibrium magnetization(Boltzmann distribution)

Scatter noiseRadiation dose

Fund BioImag 201213-12

Which bioimaging modality is right for you ?

Rapid and least invasive assessment of tissue close to surface

Contrast between air-tissue or bone-tissue

Rapid scan with high spatial resolution

Image receptors, glucose metabolism, transport, perfusion

Biochemical information of tissue

Exquisite soft tissue contrast with mm spatial resolution (rodent 100µm)

Functional information

US

X-ray, CT

SPECT, PET

NMR spectroscopy

MRI

MRI

Immobile spins

BoneAir

Air-Tissue

interface

multiple exposures

(ionizing radiation)

Metallic implants

& devices

Moving blood (angiography)MRI (multiple means)CT (contrast agents)

Doppler US

Fund BioImag 201213-13

13-5. Comparison of imaging modalities: Brain

Skull gets in the way of X-ray imaging:– Bone scatters X-rays much more than soft tissue– MRI radio waves pass unimpeded through bone

Images have been “skull stripped”

Same patient

FBPA-PET

PETMRI (T1)

Contrast agents

CT

MRI

pre post

MRI (T1)

MRI (T2)

TE=30 ms TE=80 ms

FDG-PET MRI (T1)

MRI (T2)

post

High grade astrocytoma

Fund BioImag 201213-14

http://www.eradimaging.com/site/article.cfm?ID=327

PET MRI

SPECT

MRI

Heart

Lung LiverWhole body

CT

MRI

US

3D CT of mouse

Comparison of modalities: Body