t1& #magne*za*on#transfer - national institutes of health · 2015. 8. 24. · 1 t 1&...
TRANSCRIPT
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T1 & Magne*za*on Transfer
Peter van Gelderen AMRI, LFMI, NINDS, Na-onal Ins-tutes of Health,
Bethesda, MD, United States
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T1 & MT
Outline
•T1 and T2 •Relevance for MRI •Measuring T1 •Magnetization Transfer (MT) •Measuring MT •Sources of T1 contrast: T1 & MT
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T1 & MT
MagneBzaBon
Nuclear spins polarize in a magnetic field
Energy: B0
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T1 & MT
MagneBzaBon
Nuclear spins polarize in a magnetic field
B0B0=0
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T1 & MT
MagneBzaBon
Nuclear spins polarize in a magnetic field
Energy: B0N-‐
N+
N-‐/N+= e-‐hγB0/kbT≅1-‐ hγB0/kbT= 1-‐ 6.5x10-‐6B0
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T1 & MT
MagneBzaBon
Nuclear spins polarize in a magnetic field, but how fast? Change in polarization requires energy transfer to different species.
Pure water: no energy transfer -‐> no (change in) polarization
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T1 & MT
MagneBzaBonTime course: -‐ every spin has certain probability to transition -‐ P-‐ for P+ for where P-‐ slightly higher than P+ (due to ΔE)-‐ # spins : N-‐P-‐, : N+P+-‐ M= N+ -‐N-‐
-‐ change in M= dM= (N-‐P-‐ -‐N+P+)-‐ dM= 0 for equilibrium (M0), N+0/N-‐0= P-‐/P+-‐ M= M0 + Δ, N-‐= N-‐0 -‐ Δ/2, N+= N+0 + Δ/2,-‐ dM= ((N-‐0 -‐ Δ/2)P-‐ -‐(N+0 + Δ/2)P+)= N-‐0P-‐ -‐N+0P+-‐ Δ/2(P-‐+P+)=-‐ Δ/2(P-‐+P+)-‐ dM/dt= -‐k(M-‐M0), k= R1=1/T1
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T1 & MT
MagneBzaBon
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T1 & MT
MagneBzaBon
dMz/dt= -‐R1*(Mz-‐ M0) Mz= M0-‐ (Mz(0)-‐ M0)e-‐R1t
Mz/M
0
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T1 & MT
MagneBzaBon
Mz= M0-‐ (Mz(0)-‐ M0)e-‐R1t T1 = 1/R1
Mz/M
0
T1
1/e
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T1 & MT
T1-‐RelaxaBon in MRI
Mz not directly measured, M needs to be transverse:
RF
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T1 & MT
T2-‐RelaxaBon
M rotates around B0 Frequency: γB0
B0
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T1 & MT
T2-‐RelaxaBon
M rotates around B0 Frequency: γB0 B0 not the same everywhere: dispersion
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T1 & MT
T2-‐RelaxaBon
Mt in rotating frame:
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T1 & MT
T2-‐RelaxaBon
Mt/M
0 Mt= Mt(0)e-‐R2t
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T1 & MT
T2-‐RelaxaBon
T2 is dispersion of M in transverse plain caused by frequency differences, from -‐ spin-‐spin interactions (true T2) -‐ field inhomogeneity from magnet or local susceptibility (T2*)
No energy transfer, can be (much) faster then T1
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T1 & MT
T1-‐RelaxaBon
MR measurement:
RF T2 T1
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T1 & MT
T1-‐RelaxaBon
Relevance for MR Imaging
RF T2T1
Mt=0, Mz= 1 Mt=0, Mz= 0Mt=1, Mz= 0
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T1 & MT
T1-‐RelaxaBon & MRI
RF RF RF RF RF
Mz
TR
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T1 & MT
T1-‐RelaxaBon & TR
TR
Mz
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T1 & MT
T1-‐RelaxaBon & Flip Angle
90°
45°
Mz
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T1 & MT
T1-‐RelaxaBon & Flip Angle
90°
22.5°
45°
Mz
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T1 & MT
T1-‐RelaxaBon & Signal
Flip= 90°
Mz, M
t
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T1 & MT
T1-‐RelaxaBon & Signal
Flip= 45°M
z, M
t
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T1 & MT
T1-‐RelaxaBon & Signal
Flip= 22.5°
Mz, M
t
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T1 & MT
T1-‐RelaxaBon: Signal CalculaBon
RF
Ma MbMaMb
Mb= cos(α)Ma
Ma= 1-‐(1-‐Mb)e-‐TR/T1=1-‐(1-‐Mb)E1
Solution: Ma= (1-‐E1)/(1-‐cos(α)E1) Signal: Mt= sin(α)Ma
Mz=
RFTR
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T1 & MT
T1-‐RelaxaBon & Signal
Flip Angle
Signal
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T1 & MT
Inversion
More RF than excitation
RF
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T1 & MT
Inversion Recovery
Mz
T10.7T1
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T1 & MT
T1 Measurement
T1 can be measured in two ways: -‐ saturation -‐ inversion recovery
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T1 & MT
T1 MeasurementSaturation
RF
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T1 & MT
T1 Measurement
SaturationM
z
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T1 & MT
T1 Measurement
SaturationSignal
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T1 & MT
T1-‐RelaxaBon & Signal
Flip Angle
Signal
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T1 & MT
T1 MeasurementInversion Recovery
RF
90° 90° 90° 90°180° 180° 180°
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T1 & MT
T1 Measurement
Inversion Recovery
RF
Mz
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T1 & MT
T1 Measurement
Inversion Recovery
RF
Mz, M
t
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T1 & MT
T1 Measurement
Inversion Recovery Hybrid: MPRAGE
RF
10°180° 180° 10°
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T1 & MT
T1 Measurement
Mz, M
tInversion Recovery Hybrid: MPRAGE
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T1 & MT
T1 Measurement
Mz, M
tMPRAGE: T1 contrast
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T1 & MT
T1 Measurement
Mz, M
tMPRAGE: T1 contrast
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T1 MeasurementComplications
Signal depends on T1, but also on: -‐ T2(*) -‐ RF (flip angle): Transmit coil, Dielectric effects, Calibration -‐ Receive sensitivity: Coils, System amplification -‐ Proton density
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T1 MeasurementChoosing a method
Inversion Recovery: best quantification, slow Saturation: fast, but mixed with RF and some T2 MPRAGE: fast and useful contrast, hard to quantify, and potential for spatial blurring. MPRAGE with second scan (MP2RAGE) can compensate some of the coil contrast etc.
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T1 & MT
T1 MeasurementExamples: 7T IR with EPI
REF TI: 7 64 145 256 1200 ms
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T1 & MT
T1 MeasurementExamples: MPRAGE, MP2RAGE
Curtesy of Pascal Sati, NINDS
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T1 & MT
T1 MeasurementExamples: 7T 0.5mm MP2RAGEHealthy(brain(
7T(((T1w(MP2RAGE((voxel(size(=(0.5(mm(isotropic(
Curtesy of Pascal Sati, NINDS
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T1 & MT
T1 MeasurementExamples: 7T, MPRAGE, Gd-‐injection
Pre-‐injection 5min post-‐injection
Enhancing lesion due to open blood -‐brain barrier
Curtesy of Pascal Sati, NINDS
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T1 & MT
T1: Sources
Pure water: no net energy transfer -‐> no relaxation
Interaction with other molecules required: in the brain, mostly lipids and protein
Interaction: Magnetization Transfer (= part 2)
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T1 & MT
MT: T2Average field = 0 : long T2
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T1 & MT
MT: T2
C CC C
C CC C
H
H
H HH
HH H
HH HH
HH HH
Lipid has more structure
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T1 & MT
MT: T2Average field ≠ 0: short T2
C CC C
C CC C
H
H
H HH
HH H
HH HH
HH HH
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T1 & MT
MT: T2Short T2
T2 << 1 ms : not visible in MRI
But: ‘hidden’ magnetization interacts with water
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T1 & MT
MT: T2Lipid and Exchange
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T1 & MT
MT: T2Lipid and Exchange
Lipid Membrane Water
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T1 & MT
MTLipid and Exchange
Lipid Membrane Water
Exchange: -‐ Magnetic -‐ Chemical
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T1 & MT
MTLipid and Exchange
Macro Molecular Protons Water Protons
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T1 & MT
MTParameters
MP WP
R1MP
T2MP
R1WP
T2WP
f1-‐f
kMW
kWM
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T1 & MT
MT
MP WP
R1MP
T2MP
R1WP
T2WP
f1-‐f
kMW
kWM
saturation: S= 1-‐ Mz
d SWP / dt = -‐R1wp SWP -‐ kWM SWP + kWM SMP
d SMP / dt = -‐R1mp SMP -‐ kMW SMP + kMW SWP
f kMW = (1-‐f) kWM
SWP(t) = a1e-‐λ1t + a2e-‐λ2t
Equations
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T1 & MT
MTSaturation SWP(t) = a1e-‐λ1t + a2e-‐λ2t
S WP(t)= 1-‐ M
z(t)
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Pulse Design
α
-‐2α
2α
-‐2α
α
T1 & MT
Short T2
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Pulse Design
α
T1 & MT
T2
Effective flip angle α≅γB1T2 Mz= cos(α)=1-‐ α2/2 PW/T2 times
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0 2000 4000 6000-1.0
-0.5
0.0
0.5
1.0
0 2000 4000 6000-0.04
-0.02
0.00
0.02
0.04
0 2000 4000 60000.70
0.75
0.80
0.85
0.90
0.95
1.00
0 2000 4000 6000-0.3
-0.2
-0.1
0.0
0.1
0.2
0.3
0 2000 4000 60000.0
0.2
0.4
0.6
0.8
1.0
0 2000 4000 60000.0
0.2
0.4
0.6
0.8
1.0
Pulse Effect
My
Mz
Short T2 Intermediate T2 Long T2
T1 & MT
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Pulse Design
Approximate Transitions:
Short T2: (γB1)2PW/2
Long T2: sin(α)2PW/2
100 101 102 103 104 105
T2 [µs]
0.0
0.2
0.4
0.6
0.8
1.0
Satu
ratio
n
T1 & MT
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T1 & MT
T1 MeasurementInversion Recovery
RF
90° 90° 90° 90°180° 180° 180°
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T1 & MT
MT MeasurementMT Saturation Recovery
RF
90° 90° 90° 90°
MT MT MT
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MT Recovery
Normalized difference with reference
T1 & MT
TI: 7 64 145 256 380 ms
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MT measurements0996
0 100 200 300 400 500 600Td [ms]
0.05
0.10
0.15
0.20
0.25
Satu
ratio
n
16.2 27.0‘ 90 0.11 0.99 8.0 40.0‘ 30 0.08 0.93 4.0 60.0‘ 10 0.06 0.86 2.1 105.0‘ 3 0.05 0.79
PW α N Sf Sb
100 101 102 103 104 105
T2 [µs]
0.0
0.2
0.4
0.6
0.8
1.0
Satu
ratio
n
PW N 16.2 90 8.0 30 4.0 10 2.1 3
T1 & MT
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T1 & MT
T1 MeasurementSaturation
RF
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T1 & MT
MT MeasurementMT Saturation Equilibrium
RF
MT Saturation in balance with T1
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T1 & MT
Inversion & MTIR and Exchange
MP WP
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T1 & MT
Inversion & MTIR and Exchange
MP WP
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T1 & MTT1 & MT
Inversion & MTIR and Exchange
In an IR experiment initial saturation of MP depends on RF power Early part of IR dominated by exchange
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Inversion & MTT1 & MT
IR double exponential and RF dependent
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Inversion & MTT1 & MT
Calculated T1 as function of TIHigh RF Low RF
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T1 & MT
MT
MP WP
R1MP
T2MP
R1WP
T2WP
f1-‐f
kMW
kWM
d SWP / dt = -‐R1WP SWP -‐ kWM SWP + kWM SMP
d SMP / dt = -‐R1MP SMP -‐ kMW SMP + kMW SWP
f kMW = (1-‐f) kWM
SWP(t) = a1e-‐λ1t + a2e-‐λ2t λ1𐅽 (1-‐f)R1WP +fR1MP
Equations
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Inversion & MTT1 & MT
λ1 f kwmf
R1eff = λ1𐅽 (1-‐f)R1WP +fR1MP
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T1 & MTT1 & MT
T1 & MTSummary
-‐ Pure water has a very long T1 -‐ Main source of T1 relaxation is semi-‐solid lipids & other macro molecules through MT between water and MP
-‐ Consequences: :: MT and T1 contrast both measure MP :: T1 relaxation (at least) bi-‐exponential
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T1 & MTT1 & MT
T1 & MTSummary
Reality more complex: -‐ multiple pools of water (intra-‐, extra-‐ cellular, myelin) -‐ multiple kinds of MP, each with R1, T2 etc.
Two pool T1 generally sufficient, fast component more important at higher field
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T1 & MTT1 & MT
T1 & MT
The End