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RUPRECHT-KARLS-UNIVERSITY HEIDELBERG
Computer Assisted Clinical MedicineProf. Dr. Lothar Schad
12/9/2008 | Page 1Master‘s Program in Medical Physics
Chair in Computer Assisted Clinical MedicineFaculty of Medicine Mannheim University of HeidelbergTheodor-Kutzer-Ufer 1-3D-68167 Mannheim, GermanyLothar.Schad@MedMa.Uni-Heidelberg.dewww.ma.uni-heidelberg.de/inst/cbtm/ckm/
Physics of Imaging Systems
Basic Principles of Magnetic Resonance Imaging III
Prof. Dr. Lothar Schad
RUPRECHT-KARLS-UNIVERSITY HEIDELBERG
Computer Assisted Clinical MedicineProf. Dr. Lothar Schad
12/9/2008 | Page 2
Relaxation
Relaxation
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RUPRECHT-KARLS-UNIVERSITY HEIDELBERG
Computer Assisted Clinical MedicineProf. Dr. Lothar Schad
12/9/2008 | Page 3Magnetization: Mz and Mxy
longitudinal magnetization: Mz
transversal magnetization: Mxy
transversal magnetization: Mxy- phase synchronization after a 90°-pulse- the magnetic moments μ of the probe startto precede around B1 leading to a synchronizationof spin packages → Mxy
- after 90°-pulse Mxy = M0
RUPRECHT-KARLS-UNIVERSITY HEIDELBERG
Computer Assisted Clinical MedicineProf. Dr. Lothar Schad
12/9/2008 | Page 4Movie: Mz and Mxy
source: Schlegel and Mahr. “3D Conformal Radiation Therapy: A Multimedia Introduction to Methods and Techniques" 2007
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RUPRECHT-KARLS-UNIVERSITY HEIDELBERG
Computer Assisted Clinical MedicineProf. Dr. Lothar Schad
12/9/2008 | Page 5Longitudinal Relaxation Time: T1
after 90°-pulse:- N-1/2 = N+1/2 and Mz = 0, Mxy = M0
after RF switched off:- magnetization turns back to thermal equilibrium- Mz = M0, Mxy = 0
→ T1 relaxationlongitudinal relaxation time T1spin-lattice-relaxation time T1
thermal equilibrium excited state
RUPRECHT-KARLS-UNIVERSITY HEIDELBERG
Computer Assisted Clinical MedicineProf. Dr. Lothar Schad
12/9/2008 | Page 6Physical Model of T1 Relaxation
- in a real spin system (tissue) every nucleiis surrounded by intra- and intermolecularmagnetic moments
- thermal motion (rotation, translation, oscillation)leads to an additional fluctuating magnetic field Bloc(t)with typical spectral distribution J(ω)
- longitudinal components of J(ω) at ω0 allow energytransfer hω0 from the spin system to the “lattice”
→ T1 relaxation
- trajectory of the tip of magnetization vector in thelaboratory system
source: Liang and Lauterbur. “Principles of Magnetic Resonance Imaging” 2000
J(ω) ⊥ B0
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RUPRECHT-KARLS-UNIVERSITY HEIDELBERG
Computer Assisted Clinical MedicineProf. Dr. Lothar Schad
12/9/2008 | Page 7Phenomological Description of T1 || B0
the longitudinal magnetization Mz relaxesexponential to the equilibrium state Mz = M0with a typical time constant T1
dMz/dt = (γ x B)z + (M0 – Mz)/T1 : Bloch equation with T1
with Mz = 0 at t = 0:
Mz(t) = M0 (1 – exp(-t/T1)) → solution of Bloch equation
repetition time TR [s]
0 1 2 3
norm
aliz
ed s
igna
l: M
z(t) /
M0 1.0
0.5
T1
0.63
(1-e-t/T1) typical T1-values intissue:100 - 2000 ms
RUPRECHT-KARLS-UNIVERSITY HEIDELBERG
Computer Assisted Clinical MedicineProf. Dr. Lothar Schad
12/9/2008 | Page 8Movie: T1 Relaxation
© Plewes DB, Plewes B, Kucharczyk W. The Animated Physics of MRI, University Toronto, Canada
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RUPRECHT-KARLS-UNIVERSITY HEIDELBERG
Computer Assisted Clinical MedicineProf. Dr. Lothar Schad
12/9/2008 | Page 9Transversal Relaxation Time: T2
after 90°-pulse:- N-1/2 = N+1/2 and Mz = 0, Mxy = M0
after RF switched off:- magnetization Mxy starts to rotate in thex,y-plane at Larmor frequency
- all transversal components J(ω) of thefluctuating magnetic field Bloc(t) result in adephasing of Mxy → spin-spin interaction
- mainly static frequency components J(ω) of thefluctuating magnetic field Bloc(t) at ω = 0 are contributing
- no energy transfer in the spin system (entropy ↑)- no influence of T2 on T1, they are independent !
→ T2 relaxationtransversal relaxation time T2spin-spin-relaxation time T2
- although technical in homogeneities of B0 causedephasing of Mxy → T2* (effective relaxation)
J(ω) || B0
J(ω=0)
RUPRECHT-KARLS-UNIVERSITY HEIDELBERG
Computer Assisted Clinical MedicineProf. Dr. Lothar Schad
12/9/2008 | Page 10Physical Model of T2 Relaxation
thermal equilibrium
Mz
xy
z
xy
z
Mxy = 0
B0
y
RF90°- pulse
x
z
Mxy
timesign
al in
tens
ity
Mxy
yx
z
Mxy
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RUPRECHT-KARLS-UNIVERSITY HEIDELBERG
Computer Assisted Clinical MedicineProf. Dr. Lothar Schad
12/9/2008 | Page 11Movie: Spin Dephasing
© Plewes DB, Plewes B, Kucharczyk W. The Animated Physics of MRI, University Toronto, Canada
RUPRECHT-KARLS-UNIVERSITY HEIDELBERG
Computer Assisted Clinical MedicineProf. Dr. Lothar Schad
12/9/2008 | Page 12Phenomological Description of T2 ⊥ B0
the transversal magnetization Mxy relaxesexponential to Mxy = 0 with a typical time constant T2
dMxy/dt = (γ x B)xy – Mxy/T2 : Bloch equation with T2
with Mxy = M0 at t = 0:
Mxy(t) = M0 exp(-t/T2)) → solution of Bloch equation
T2
0.37
e-t/T2
norm
aliz
ed s
igna
l: M
xy(t)
/ M
0 1.0
0.5
0 50 100 150 200
echo time TE [ms]
typical T2-values intissue: 50 - 100 mswater: ~1000 ms
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RUPRECHT-KARLS-UNIVERSITY HEIDELBERG
Computer Assisted Clinical MedicineProf. Dr. Lothar Schad
12/9/2008 | Page 13
T2*-decay
T1-recovery
time
transversal: dephasing of spin ensemblelong
itudi
nal:
rela
xatio
n to
ther
mal
equ
ilibriu
m T1- and T2*- relaxation are simultaneous processes
T2* < T1
Simultaneous T1 and T2 Relaxation
RUPRECHT-KARLS-UNIVERSITY HEIDELBERG
Computer Assisted Clinical MedicineProf. Dr. Lothar Schad
12/9/2008 | Page 14Movie: T1 and T2 Relaxation
source: Schlegel and Mahr. “3D Conformal Radiation Therapy: A Multimedia Introduction to Methods and Techniques" 2007
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RUPRECHT-KARLS-UNIVERSITY HEIDELBERG
Computer Assisted Clinical MedicineProf. Dr. Lothar Schad
12/9/2008 | Page 15
0,79 ± 0,130,68 ± 0,120,54 ± 0,0992 ± 22white matter
0,92 ± 0,160,81 ± 0,140,66 ± 0,11101 ± 13 grey matter
0,26 ± 0,070,24 ± 0,070,21 ± 0,0684 ± 36fata
0,78 ± 0,150,68 ± 0,130,54 ± 0,1062 ± 27spleen
0,65 ± 0,180,59 ± 0,160,50 ± 0,1358 ± 24kidney
0,50 ± 0,110,43 ± 0,090,33 ± 0,0743 ± 14liver
0,87 ± 0,140,75 ± 0,120,58 ± 0,0957 ± 16myocardium
0,87 ± 0,160,73 ± 0,130,55 ± 0,1047 ± 13skeletal muscle
T1 [s] at 1.5 T
T1 [s] at 1.0 T
T1 [s] at 0.5 T
T2 [ms]tissue
a more than one exponential component
T1 and T2 Relaxation Times in-vivo
- T1 increases with B0- T2 nearly independent of B0
Bottomley et al. Med Phys 1984
RUPRECHT-KARLS-UNIVERSITY HEIDELBERG
Computer Assisted Clinical MedicineProf. Dr. Lothar Schad
12/9/2008 | Page 16
19481948
Harvard Nicolaas Bloembergen
Robert Pound
Edward Purcell
• characterized the relaxation times of the nuclear response signal in detail
excitation pulse
refocusingpulse
excitation pulse
refocusingpulse
© Yves De Deene. University of Gent, Belgium
NMR History: Relaxation Times
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RUPRECHT-KARLS-UNIVERSITY HEIDELBERG
Computer Assisted Clinical MedicineProf. Dr. Lothar Schad
12/9/2008 | Page 17
- no bones
+ best soft tissue contrast
+ no radiation
CTWM: 1025 HuGM: 1035 Hu } Δ = 1%CSF: 1000 Hu
T2 T1 MRIWM: 90 ms 550 msGM: 100 ms 1000 ms } Δ = 100%CSF: >1000 ms 2000 ms
ρ T2 T1
CT
patient: astrocytoma grade II
Comparison: CT and MRI
RUPRECHT-KARLS-UNIVERSITY HEIDELBERG
Computer Assisted Clinical MedicineProf. Dr. Lothar Schad
12/9/2008 | Page 18
1
0
2
))(()()()()(
TkMtM
TjtMitM
tBMdt
tMd zzyx
rrrrr
r−
−+
−×⋅= γ
11
2
2
Tt
zTt
0z
0x0yTt
y
0y0xTt
x
e)0(M)e1(M)t(M
))tsin()0(M)tcos()0(M(e)t(M
))tsin()0(M)tcos()0(M(e)t(M
−−
−
−
⋅+−⋅=
⋅ω⋅−⋅ω⋅=
⋅ω⋅+⋅ω⋅=
00 B⋅= γω
Bloch Equations with T1 and T2
dMz/dt = (γ x B)z + (M0 – Mz)/T1
dMxy/dt = (γ x B)xy – Mxy/T2
rotating system:
laboratory system:
complex signal:
M⊥ = Mx + iMy
M⊥ = M0 exp(-iωLt – t/T2)
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RUPRECHT-KARLS-UNIVERSITY HEIDELBERG
Computer Assisted Clinical MedicineProf. Dr. Lothar Schad
12/9/2008 | Page 19Complex Signal: Simulated FID
absorptionMx: real part FTMx(ω) = M0 T2
1 + (ω - ωL)2 T22
dispersionMy: imaginary part FTMy(ω) = M0 T22 (ω - ωL)
1 + (ω - ωL)2 T22
light dispersion
FID
complex FT
2T2
2T2
ωL
ωL
exp(-t/T2)
source: Liang and Lauterbur. “Principles of Magnetic Resonance Imaging” 2000
RUPRECHT-KARLS-UNIVERSITY HEIDELBERG
Computer Assisted Clinical MedicineProf. Dr. Lothar Schad
12/9/2008 | Page 20Macroscopic Effect: Diamagnetism
- Lenz’s law: the induced current produces an own magnetic moment μ in a conductor opposite to B0
- most of biological tissues have diamagnetic propertiessince the electron magnetization Me of the electron sheath is opposite to B0 due to Lenz’s law:B = μ0(H + Me)Me = χ H with μ0 = 1.257 10-6 Vs/A magnetic field constant
χH2O = -0.72 10-6 magnetic susceptibility
- weaker B-field inside a diamagnetic sphere due toe--shielding which is very effective since γe- = 658 γp
- intersection of different tissues creates additionallocal field inhomogeneities of B0can be “homogenized” by additional shim coils
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RUPRECHT-KARLS-UNIVERSITY HEIDELBERG
Computer Assisted Clinical MedicineProf. Dr. Lothar Schad
12/9/2008 | Page 21Microscopic Effect: Chemical Shift
- precession frequency of nuclei bound in a specific molecule is determined by the local magnetic field Bloc:
Bloc = B - δBωloc = γ Bloc = γ(1 - δ)B
with δ = 106 (ω - ωref)/ω0the relative chemical shift [ppm]
- δ ~ 10 ppm for 1Hδ ~ 100 ppm for 13C, 19F, and 31P
- high resolution spectrum at B0 > 1.5 T with ΔB/B0 < 0.1 - 0.5 ppm show multiplet splitting due to spin-spin coupling→ domain of MRS
- in MRI only protons of water are imaged,chemical shift is not relevant !exception: δfat = 3.5 ppm (220 Hz) at 1.5 T
1H spectrum of ethanol
MRS
RUPRECHT-KARLS-UNIVERSITY HEIDELBERG
Computer Assisted Clinical MedicineProf. Dr. Lothar Schad
12/9/2008 | Page 22
one isochromate
three isochromates
many isochromates
Summary: FID and MRS
simulated 31P absorption spectrum
PCr
ATP
MRS
simulated isochromates
source: Liang and Lauterbur. “Principles of Magnetic Resonance Imaging” 2000
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RUPRECHT-KARLS-UNIVERSITY HEIDELBERG
Computer Assisted Clinical MedicineProf. Dr. Lothar Schad
12/9/2008 | Page 23
FID signal is the transient response of a spin system after RF excitation;FID is a complex signal with amplitude and phase
FID amplitude is dependent on many parameters like: flip angle, number of spins, and magnetic field strength
FID timing is dependent on the grade of local magnetic field inhomogeneitiescharacterized by T2*:
1/T2* = 1/T2 + γΔBz with T2* < T2
T2*: the effective (local) T2 relaxation timeT2 : the true T2 relaxation time
Summary: FID and MRI
RUPRECHT-KARLS-UNIVERSITY HEIDELBERG
Computer Assisted Clinical MedicineProf. Dr. Lothar Schad
12/9/2008 | Page 24
Saturation-Recovery Sequence
Inversion-Recovery Sequence
Spin-Echo Sequence
Standard Techniques for T1 and T2
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RUPRECHT-KARLS-UNIVERSITY HEIDELBERG
Computer Assisted Clinical MedicineProf. Dr. Lothar Schad
12/9/2008 | Page 25
• saturation-recovery sequence
• 90°-pulse moves the longitudinal magnetization M0 to the x-, y – plane → FID
• transversal magnetization Mxy decays with T2*
• longitudinal magnetization starts to recover to thermal equilibrium → Mz↑ with T1
• after TR actual (reduced) magnetization Mz is moved to the x-, y – plane → FID
• repeat measurement with different TR→ T1 determination by
Saturation-Recovery Sequence
S ~ ρ [1 - exp(-TR / T1)] with TR >> T2*
RUPRECHT-KARLS-UNIVERSITY HEIDELBERG
Computer Assisted Clinical MedicineProf. Dr. Lothar Schad
12/9/2008 | Page 26
• inversion-recovery sequence
• 180°-pulse invert the longitudinal magnetization M0 to –M0 at the z-axes
• longitudinal magnetization starts to recover to thermal equilibrium → Mz↑ with T1
• inversion time TI
• after TI 90°-pulse moves the actual (reduced) longitudinal magnetization Mz to the x-, y –plane → FID
• transversal magnetization Mxy decays with T2*
• repeat measurement with different TI→ T1 determination by
Inversion-Recovery Sequence
S ~ ρ [1 – 2 exp(-TI / T1)] with TR > 5 T1
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RUPRECHT-KARLS-UNIVERSITY HEIDELBERG
Computer Assisted Clinical MedicineProf. Dr. Lothar Schad
12/9/2008 | Page 27
TI0
T1 Measurement: Inversion Recoveryinversion recovery (Mz(0) = -M0):
Mz(t) = M0 (1 – 2 exp(-TI/T1))
with Mz = 0 at TI = TI0:0.5 = exp(-TI0/T1)
→ T1 = -TI0 / ln(0.5) = TI0 / 0.7
RUPRECHT-KARLS-UNIVERSITY HEIDELBERG
Computer Assisted Clinical MedicineProf. Dr. Lothar Schad
12/9/2008 | Page 28How to get rid of “Scanner’s” Dephasing ?
t
90° 180°AQ
TE
180° refocusing pulse
to slow
to fast
to fast
to slow
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RUPRECHT-KARLS-UNIVERSITY HEIDELBERG
Computer Assisted Clinical MedicineProf. Dr. Lothar Schad
12/9/2008 | Page 29Movie: Spin-Echo I
© Plewes DB, Plewes B, Kucharczyk W. The Animated Physics of MRI, University Toronto, Canada
RUPRECHT-KARLS-UNIVERSITY HEIDELBERG
Computer Assisted Clinical MedicineProf. Dr. Lothar Schad
12/9/2008 | Page 30
a) RF impulse schema
b) timing of longitudinal magnetization Mz
c) induced measured signal: spin-echo SE
source: Schlegel and Bille. “Medizinische Physik Bd. 2” 2002
rephasing partof signal
dephasing partof signal
Spin-Echo Schema
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RUPRECHT-KARLS-UNIVERSITY HEIDELBERG
Computer Assisted Clinical MedicineProf. Dr. Lothar Schad
12/9/2008 | Page 31Movie: Spin-Echo II
© Plewes DB, Plewes B, Kucharczyk W. The Animated Physics of MRI, University Toronto, Canada
RUPRECHT-KARLS-UNIVERSITY HEIDELBERG
Computer Assisted Clinical MedicineProf. Dr. Lothar Schad
12/9/2008 | Page 32
1/T2* = 1/T2 + 1/T2´T2* : „effective“ relaxation with T2* < T2T2 : „true“ relaxation due to irreversible dephasingT2‘ : „scanner“ relaxation due to static and constant
field inhomogeneitiessource: Dössel. “Bildgebende Verfahren in der Medizin” 2000
Multi Spin-Echoes
RFexcitation
MTsignal
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RUPRECHT-KARLS-UNIVERSITY HEIDELBERG
Computer Assisted Clinical MedicineProf. Dr. Lothar Schad
12/9/2008 | Page 33
19491949
Erwin Hahn
• discovered a “second” nuclear resonance signal, the spin echo
• achieved T1 and T2 weighting
excitation pulse
refocusingpulse
TE/2 TE/2
The first observed spin echo by E. Hahn (1950)
© Yves De Deene. University of Gent, Belgium
Illinois
NMR History: Spin-Echo
RUPRECHT-KARLS-UNIVERSITY HEIDELBERG
Computer Assisted Clinical MedicineProf. Dr. Lothar Schad
12/9/2008 | Page 34T2 Measurement by Multi Spin-Echo
SE-signal:SI ~ Mxy = Mxy e-t/T2
WM: T2 ≅ 90 msGM: T2 ≅ 100 msCSF: T2 > 500 ms
time t
90°
180°
TE2
180°
signal signal
180°
signal
TE3TE1
90°
TRSI~Mxy
time t
sign
al in
tens
ity
T2 ~ e-t/T2T2*
multi spin-echo techniqueTR: repetition timeTE: spin-echo time
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RUPRECHT-KARLS-UNIVERSITY HEIDELBERG
Computer Assisted Clinical MedicineProf. Dr. Lothar Schad
12/9/2008 | Page 35T2 Measurement: Spin Echo
spin-echo (Mxy(0) = M0):
Mxy(t) = M0 exp(-t/T2)
T2 Measurement: Spin-Echo
RUPRECHT-KARLS-UNIVERSITY HEIDELBERG
Computer Assisted Clinical MedicineProf. Dr. Lothar Schad
12/9/2008 | Page 36
- spin-echo signal is the consequence of refocusing of a large amount ofdephased isochromates
- spin-echo signal has maximum amplitude where isochromates reach new phase coherence
- spin-echo signal is a “two-sided” signal with two mirror-inverted FID’s,both components of the spin-echo increase/decay with T2*,but the amplitude of the spin-echo is T2-weighted
xy
z
My
xy
z
xy
zafter 90°-pulse after 180°-pulseRF
180°-pulse
Summary: Spin-Echo
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RUPRECHT-KARLS-UNIVERSITY HEIDELBERG
Computer Assisted Clinical MedicineProf. Dr. Lothar Schad
12/9/2008 | Page 37Multi-Exponential T2: Tumor Tissue
Schad et al. JCAT 1989
most tissues in MRI:- bi-exponential due to partial volume effect
M0 = ρ
spin density: ρT1 T2m = ρm exp(-t/T2m)
T2b = ρf exp(-t/T2f) + ρs exp(-t/T2s)
RUPRECHT-KARLS-UNIVERSITY HEIDELBERG
Computer Assisted Clinical MedicineProf. Dr. Lothar Schad
12/9/2008 | Page 38Multi-Exponential T1, T2: Fatty Tissue
fatty tissue : bi-exponential in T1 and T2tumor tissue : bi-exponential in T2 due to
partial volume effect with CSF
Schad et al. MRI 1989
T1 T2m
T2f T2s
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RUPRECHT-KARLS-UNIVERSITY HEIDELBERG
Computer Assisted Clinical MedicineProf. Dr. Lothar Schad
12/9/2008 | Page 39MRI – Based Therapy Planning ?
Brix. Dissertation, Heidelberg 1988
tissues in NMR:- multi-exponential with very short T2 relaxationcomponents → invisible at conventional MRI
- measurement of proton densities (e.g. for n-dosimetry, HI-therapy) is not possible !
RUPRECHT-KARLS-UNIVERSITY HEIDELBERG
Computer Assisted Clinical MedicineProf. Dr. Lothar Schad
12/9/2008 | Page 40T1-, T2 – Based Tissue Segmentation
Schad et al. ZMP 1992 Friedlinger et al. Comp Med Ima Graph 1995
tissue characterization tissue segmentation