kap 8 · 4/5/2011 1 kap 8 image quality, signal, contrast and noise fys-kjm 4740 mr-teori og...

4/5/2011

1

Kap 8Image quality, signal, contrast and noise

FYS-KJM 4740

MR-teori og medisinsk diagnostikk

contrast SNR

speedresolution

Available MR-

parameters

contrast SNR

speedresolution

Available MR-

parameters

Main source of noise in MRI:

•Noise generated within the reciever RF electronics

•Brownian motion of electrons within the body (in

conducting tissue)

)())(exp()()( 0 tndrrtjkrMNtSv

+= ∫ω

Signal induced in received coil with N turns

(ignoring effect of sequence parameters)

n(t)=complex noise term

N=number of turns in receiver coil

NB:2

0

2

000 (t) so / ωγω ∝∝=∝−∝ BSBsignalMRM

Noise-independent signal from a voxel of volume Vh

(Macovski A. Magn Reson Med 1996)

N=No of coil terms, χ=tissue susceptibility, k=Boltzmanns const, T=temp, Tr=read-out time (time to record echo), R=coil resistance,

Signal-Noise ratio (single voxel, one measurement)

r

h

TRkT

VNSNR

/2

2

0

⋅=

χω

γχω /2

0 hsig VNM = M(r)=χB0

Does SNR scale with Bo2 ?

(probably not in reality)

Coil resistance R, complex function of Bo

SNR also function of sequence parameters and Q-factor of

coil (Q=ωL/R)

)T2*, T2,T1,,TE,S(TR,

3

0ρα⋅

⋅⋅= h

sySAV

BW

NNNQBASNR

A=constant (susceptibility, temp, object geometry, size etc)

BW=pixel bandwidth=1/Tr

NSA=number of averages

Ny=number of phase encoding steps; Ns=number of slice enc

steps (=1 for 2D)

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receiver bandwidth

measured signal

includes also noise

timedwellsamplesofnumber

samplesofnumber

echooftimesampling

samplesofnumberbandwidthreceiver

⋅==

sampling time of echo

Pixel bandwdth (receiver bandwidth):

increasing the bandwidth

sampling time of echo

receiver bandwidth sampling time

receiver bandwidth and gradient strength

frequency

frequency encoding gradient

rbw

frequency

encoding

gradient

receiver

bandwidth

faster rephasing due to gradient; i.e. echo forms faster

noise and frequency encoding

frequency/

kHz

noise

-16 16-24 24

head

0

total amount of signal of signal per voxel is unchanged,

bigger difference of resonance frequencies inside the voxel

but : total amount of noise is increased !!!

Signal vs contrast

σ

)()( BSASSNRSNRCNR BA

−=−=

σ = image noise (assumed position independent)

0 25 50 75 1000

0.05

0.1

0.15

0.2

0.25

T1=900T1=300

CNR

Flip angle (deg)

Rel

SI,

Rel C

NR

0 25 50 75 1000

0.05

0.1

0.15

0.2

0.25

T1=900T1=300

CNR

Flip angle (deg)

Rel

SI,

Rel C

NR

Signal vs contrast (T1.GRE)

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0 200 400 600 800 10000

0.5

1

1.5

T1=900

T1=300

CNR

TR (ms)

Rel

sig

nal

, re

l C

NR

0 200 400 600 800 10000

0.5

1

1.5

T1=900

T1=300

CNR

TR (ms)

Rel

sig

nal

, re

l C

NR

Signal vs contrast (SE)

)1/1ln(11

1121

21

21 TTTT

TTTR

opt⋅

−=

0 200 400 600 800 10000

0.5

1

1.5

T1=900

T1=300

CNR

TR (ms)

Rel

sig

nal

, re

l C

NR

0 200 400 600 800 10000

0.5

1

1.5

T1=900

T1=300

CNR

TR (ms)

Rel

sig

nal

, re

l C

NR

Sa Sb

σ2

Sa Sb

σ2

Practical measurement of SNR

0

5

10

15

20

25

0 5 10 15 20 25

Number of averages

Effect of NSA on SNR

Effect of BW on SNR

BW=750 Hz BW=2055 Hz

kx

ky

p1

p*1

p2

p*2

A B

Partial k-space sampling

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kx

ky

‘Half-scan’ (partial Fourier) phase partial fourier

example: half fourier

phase error due to

inhomogeneity of B0

8 further steps required

for phase correction

FOVx,y : 256 mm

matrix= 256 x (128+8)

pixel size: (1 x 1) mm2

acquisition time : ca. 50 % (256 x 256)

SNR (relative) = 1./1.41

α

TE

α

Tacq

TE

Tacq

Gx

‘Partial echo’ky

p1

kyky

Rectangular field of view (rFoV)

)T2*, T2,T1,,TE,S(TR,

3

0ρα⋅

⋅⋅=

h

sySAV

BW

NNNQBASNR

Working examples:

Ref scan: FoV 256 x 256; BW=1000 Hz/px; V=1x1x1 mm3

1. 75% rFoV

2. Half-scan (partial fourier)

3. Reduced phase sampling (reduced Ny)

4. Reduced BW =BW/2

5. Increased TR (SE sequence)

6. Increased FA (GRE sequence)

7. Partial echo

Parallel imaging

Basic concepts:

•Many small coils give better overall SNR than one large

•Phased array technology: parallel processing of signal from

multiple coils

•Requires fast data handling and high processing capacity due to

parallel processing of multiple data streams

•Use of signal sensitivity profile from each coil element to

reconstruct corrected ’undersampled’ image

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From Larkman & Nunes; Phys Med Biol (2007)

Use of multiple receive coils


Reduced K-space sampling

Sensitivity Encoding (SENSE)

•Extent of k-space (resolution ) unchanged

•Distance between adjacent k-space lines increased by factor r

•Results in signal components from r locations overlap in the

(undersampled) image

•Provided the coil sensitivty is different for each coil element,

the correct signal distribution in the whole image can be

reconstrcuted from the aliased image if the coil sensitivity

profile for each coil element is known.

The concept of parallel imaging


SENSE

S(x,y) =SI in the sub-sampled (alisased) image

C(x,y) = coil sensitivities at the location of the two aliased

pixels

ρ = signal (spin density) from the object at the two

locations (x,y) and (x, y+FoV/2)

The concept of parallel imaging


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SENSE

In matrix notation:

=>

Where ψ=receive noise matrix


SENSE does not affect spatial resolution but reduced

SNR:

r= SENSE factor

g=’g-factor’ and is a function of coil geometry, noise profile and r

r=3r=2 r=4

’g-factor’ images


SOS = sum of squares

Extraction of coil sensitivity data:


Applications of SENSE (and similar PI techniques):

•Reduced scan-time (all sequence types)

•Reduced geometric distortion and signal loss in

EPI sequences

r=1 (12 min) r=2 (6 min) r=3 (4 min)

Phase contrast angiography (PCA)


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ky

kx

0

AB

C D

EF

e1

e2

A

RF

Gx

Gy

e1

e2

B C D E F

ky

kx

0

AB

C D

EF

e1

e2

ky

kx

0

AB

C D

EF

e1

e2

A

RF

Gx

Gy

e1

e2

B C D E FA

RF

Gx

Gy

e1

e2

RF

Gx

Gy

e1

e2

B C D E F

Echo Planar Imaging (EPI)

ky

T2-relaxation

50 55 60 65 70 75 800

5

10

15

20

25

30

35

40

P ixe l pos ition (y)

Re

l. I

nte

ns

ity

ky

T2-relaxation

ky

T2-relaxation

50 55 60 65 70 75 800

5

10

15

20

25

30

35

40

P ixe l pos ition (y)

Re

l. I

nte

ns

ity

∫−

−=

2/

2/

max

max

)exp()()(

k

k

yyy dkjkkPPS

Wyj

WTyS

/21

/1*)2,(

+=

EPI – echo modulation:

Exp T2*-decay =>Lorentzian kernel

W=δy.2/π (ETL . ES/T2*)

Δy= pixel dim in phase enc-dir

−−

−−−⋅=

'

/|,|exp

/),(exp)()(

2

min

2

min

T

vkk

T

vkkTEkrectkd

yyyyyy

yy

EPI – ’damping factor’ in k-space:

Vy = average ’k-space’ speed in y-direction, which is

proportional to SENSE reduction (r-) factor

1/T2* = 1/T2 + 1/T2’1/T2’= ’inhomogeneity induced’

r=1 r=2.4

SE-EPI (3 T)

Jaermann et al MRM (2006)

kap 8 · 4/5/2011 1 kap 8 image quality, signal, contrast and noise fys-kjm 4740 mr-teori og...

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