Kap 8 Image quality, signal, contrast and noise

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1 4/5/ FYS-KJM 474 contrast SNR MR-teori og medisinsk diagnostikk Kap 8 Image qualit, signal, contrast and noise resolution vailable MRparameters speed Main source of noise in MRI: Noise generated within the reciever RF electronics Brownian motion of electrons within the bod (in conducting tissue) Signal induced in received coil with N turns (ignoring effect of sequence parameters) S( t) = ωn M ( r)exp( jk( t) r) dr + n( t) v N=number of turns in receiver coil n(t)=complex noise term NB: M MR signal B = ω γ so S(t) / B ω Noise-independent signal from a voxel of volume V h (Macovski. Magn Reson Med 996) M sig = ω NχVh / γ M(r)=χB Signal-Noise ratio (single voxel, one measurement) SNR = ω NχV h kt R / T r N=No of coil terms, χ=tissue susceptibilit, k=boltzmanns const, T=temp, Tr=read-out time (time to record echo), R=coil resistance, Does SNR scale with B o? (probabl not in realit) Coil resistance R, complex function of B o SNR also function of sequence parameters and Q-factor of coil (Q=ωL/R) SNR QB N S N N s V S(TR,TE, α,t,t, T*, ρ) BW 3 = h =constant (susceptibilit, temp, object geometr, size etc) BW=pixel bandwidth=/t r NS=number of averages N=number of phase encoding steps; Ns=number of slice enc steps (= for D)

2 4/5/ Pixel bandwdth (receiver bandwidth): measured signal includes also noise receiver bandwidth receiver bandwidth increasing the bandwidth sampling time sampling time of echo number of samples number of samples receiver bandwidth = = sampling timeof echo number of samples dwell time sampling time of echo receiver bandwidth and gradient strength noise and frequenc encoding head frequenc rbw frequenc encoding gradient faster rephasing due to gradient; i.e. echo forms faster frequenc encoding gradient receiver bandwidth noise frequenc/ total amount of signal of signal per voxel is unchanged, khz bigger difference of resonance frequencies inside the voxel but : total amount of noise is increased!!! Signal vs contrast (T.GRE) Signal vs contrast CNR = SNR SNR B S( ) S( B) = σ σ = image noise (assumed position independent) Rel SI, Rel CNR Flip angle (deg) T=9 T=3 CNR

3 4/5/ Signal vs contrast (SE) TR opt T T = ln( T / T ) T T.5.5 Rel signal, rel CNR.5 Rel signal, rel CNR TR (ms) T=9 T=3 CNR TR (ms) T=9 T=3 CNR Practical measurement of SNR Effect of NS on SNR σ 5 5 S a Sb Number of averages Effect of BW on SNR Partial k-space sampling k B p* p* k x p p BW=75 Hz BW=55 Hz 3

4 4/5/ Half-scan (partial Fourier) example: half fourier phase partial fourier k FOVx, : 56 mm matrix= 56 x (8+8) pixel size: ( x ) mm acquisition time : ca. 5 % (56 x 56) SNR (relative) =./.4 k x phase error due to inhomogeneit of B 8 further steps required for phase correction k Partial echo Rectangular field of view (rfov) α α k p TE TE G x T acq T acq SNR QB N S N N s V S(TR, TE, α,t, T, T*, ρ) BW 3 = h Working examples: Ref scan: FoV 56 x 56; BW= Hz/px; V=xx mm 3. 75% rfov. Half-scan (partial fourier) 3. Reduced phase sampling (reduced N) 4. Reduced BW =BW/ 5. Increased TR (SE sequence) 6. Increased F (GRE sequence) 7. Partial echo Parallel imaging Basic concepts: Man small coils give better overall SNR than one large Phased arra technolog: parallel processing of signal from multiple coils Requires fast data handling and high processing capacit due to parallel processing of multiple data streams Use of signal sensitivit profile from each coil element to reconstruct corrected undersampled image 4

5 4/5/ Use of multiple receive coils Reduced K-space sampling From Larkman & Nunes; Phs Med Biol (7) From Larkman & Nunes; Phs Med Biol (7) Sensitivit Encoding (SENSE) The concept of parallel imaging Extent of k-space (resolution ) unchanged Distance between adjacent k-space lines increased b factor r Results in signal components from r locations overlap in the (undersampled) image Provided the coil sensitivt is different for each coil element, the correct signal distribution in the whole image can be reconstrcuted from the aliased image if the coil sensitivit profile for each coil element is known. From Larkman & Nunes; Phs Med Biol (7) SENSE The concept of parallel imaging S(x,) =SI in the sub-sampled (alisased) image C(x,) = coil sensitivities at the location of the two aliased pixels ρ = signal (spin densit) from the object at the two locations (x,) and (x, +FoV/) From Larkman & Nunes; Phs Med Biol (7) 5

6 4/5/ SENSE SENSE does not affect spatial resolution but reduced SNR: => In matrix notation: r= SENSE factor g= g-factor and is a function of coil geometr, noise profile and r Where ψ=receive noise matrix From Larkman & Nunes; Phs Med Biol (7) Extraction of coil sensitivit data: r= r=3 r=4 g-factor images SOS = sum of squares From Larkman & Nunes; Phs Med Biol (7) From Larkman & Nunes; Phs Med Biol (7) pplications of SENSE (and similar PI techniques): Phase contrast angiograph (PC) Reduced scan-time (all sequence tpes) Reduced geometric distortion and signal loss in EPI sequences r= ( min) r= (6 min) r=3 (4 min) From Larkman & Nunes; Phs Med Biol (7) 6

7 4/5/ Echo Planar Imaging (EPI) EPI echo modulation: RF G x e e S( P) = kmax / P( k ) exp( jk ) dk kmax / Exp T*-deca =>Lorentzian kernel G B B C D E F k e / W S(, T *) = + j / W W=δ. /π (ETL. ES/T*) Δ= pixel dim in phase enc-dir C F e D E T -relaxation k x Re l. Inte nsit k P ixe l position () EPI damping factor in k-space: r= r=.4 /T * = /T + /T /T = inhomogeneit induced SE-EPI (3 T) TE ( k k, d( k ) = rect( k ) exp T min ) / v k k, exp T ' min / v V = average k-space speed in -direction, which is proportional to SENSE reduction (r-) factor Jaermann et al MRM (6) 7