Prof. Dr. Lothar Schad - uni-heidelberg.de · 1 Seite 1 RUPRECHT-KARLS-UNIVERSITY HEIDELBERG...

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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



12/9/2008 | Page 2

Relaxation

Relaxation

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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



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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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



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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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



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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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)



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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12/9/2008 | Page 11Movie: Spin Dephasing




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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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



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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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



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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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



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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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)




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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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



12/9/2008 | Page 22

one isochromate

three isochromates

many isochromates

Summary: FID and MRS

simulated 31P absorption spectrum

PCr

ATP

MRS

simulated isochromates


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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



12/9/2008 | Page 24

Saturation-Recovery Sequence

Inversion-Recovery Sequence

Spin-Echo Sequence

Standard Techniques for T1 and T2

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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*



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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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



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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12/9/2008 | Page 29Movie: Spin-Echo I




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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12/9/2008 | Page 31Movie: Spin-Echo II




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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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



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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12/9/2008 | Page 35T2 Measurement: Spin Echo

spin-echo (Mxy(0) = M0):

Mxy(t) = M0 exp(-t/T2)

T2 Measurement: Spin-Echo



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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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)



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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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 !



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

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