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Radiologische Physik
Biomedical Magnetic Resonance: 1 Introduction
Principles of Magnetic Resonance Imaging
Klaus Scheffler, PhDRadiological PhysicsUniversity of Basel
University HospitalBasel
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Radiologische Physik
Biomedical Magnetic Resonance: 1 Introduction
Magnetic Resonance Imaging
Contents:
1 Introduction
2 Nuclear Magnetic Moments
3 Motion of Magnetization
4 Excitation and reception
5 Magnetic Resonance Imaging
6 Contrast
University HospitalBasel
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Radiologische Physik
Biomedical Magnetic Resonance: 1 Introduction
Biomedical Magnetic ResonanceHistory:
University HospitalBasel
198119791974
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Radiologische Physik
Biomedical Magnetic Resonance: 1 Introduction
Biomedical Magnetic ResonanceToday:
University HospitalBasel
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Radiologische Physik
Biomedical Magnetic Resonance: 2 Nuclear Magnetic Moments
Nuclear Magnetic Moments
Properties of a nucleus:
University HospitalBasel
Nuclues is charged (multiples of e+)
Some nuclei have a spin angular momentum J:J = ħI (I multiples of ½)
Then, they have a dipolar magnetic moment : = J = ħIFor example: 1H, 13C, 19F, 31P
ħ = Planck‘s quantum constant = gyromagnetic ration
+
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Radiologische Physik
Nuclear Magnetic Moments
Nucleus in a magnetic field:
University HospitalBasel
We assume I=½ (1H, 13C, 19F, 31P)
Then, the magnetic moment along the field is:
z = ħm = ±½ħ
The magnetic moment z is parallel orantiparallel to the field B0
B0 B0
z = ½ħ z = -½ħ
ħ = Planck‘s quantum constant = gyromagnetic ration
Biomedical Magnetic Resonance: 2 Nuclear Magnetic Moments
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Radiologische Physik
Nuclear Magnetic Moments
Nucleus in a magnetic field:
University HospitalBasel
In an external magnetic field,spin up or spin down are associated todifferent energy levels:
Em = -zB0 = -ħB0m, m = ±½.
E = +½ħB0 , E = -½ħB0
E = ħB0
ħ = Planck‘s quantum constant = gyromagnetic ration
Biomedical Magnetic Resonance: 2 Nuclear Magnetic Moments
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Radiologische Physik
Nuclear Magnetic Moments
University HospitalBasel
01/2 1/2 2 B S
n Bn n nk T
01/2 1/2 2 B S
n Bn n nk T
In thermal equilibrium, there are different probabilitiesfor spin up and down occupation (Boltzmann statistics).The difference in occupation n is given by:
kB : Boltzmann constantTS: Temperature
Biomedical Magnetic Resonance: 2 Nuclear Magnetic Moments
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Radiologische Physik
Nuclear Magnetic Moments
University HospitalBasel
Macroscopic magnetization:
Visible magnetization:
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0 0 0 0( )2 4z z S
B S B S
n B nM n B T Bk T k T
0 izi
M
Sum (macroscopic Magnetization along B0):
0(TS): magnetic susceptibilitykB : Boltzmann constant
Biomedical Magnetic Resonance: 2 Nuclear Magnetic Moments
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Radiologische Physik
Biomedical Magnetic Resonance: 3 Motion of Magnetization
Motion of Magnetization
University HospitalBasel
Magnetization and magnetic field:
S
N
= =
M0
N
S
=
N
S
EW=
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Radiologische PhysikUniversity Hospital
Basel
Magnetization and magnetic field:
N
S
B0
N
S
B0
N
S
B0
Motion of Magnetization
Biomedical Magnetic Resonance: 3 Motion of Magnetization
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Radiologische PhysikUniversity Hospital
Basel
Magnetization and magnetic field:
B0
M0
B0
M0
B0
M0
?
Motion of Magnetization
Biomedical Magnetic Resonance: 3 Motion of Magnetization
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Hi
Radiologische PhysikUniversity Hospital
Basel
Nuclues is charged (multiples of e+)
Some nuclei have a spin angular momentum J:J = ħI (I multiples of ½)
Then, they have a dipolar magnetic moment : = J = ħI
ħ = Planck‘s quantum constant = gyromagnetic ration
+
Magnetization and magnetic field:
ΣM0
=
Motion of Magnetization
Biomedical Magnetic Resonance: 3 Motion of Magnetization
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Hi
Radiologische PhysikUniversity Hospital
Basel
M0
=
Magnetization and magnetic field:
N
S
B0
M0
Motion of Magnetization
Biomedical Magnetic Resonance: 3 Motion of Magnetization
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Radiologische PhysikUniversity Hospital
Basel
Magnetization and magnetic field:gravity
N
S
B0
N
S
B0
gravity
B0
M0
Motion of Magnetization
Biomedical Magnetic Resonance: 3 Motion of Magnetization
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Radiologische PhysikUniversity Hospital
Basel
Motion of magnetization: precession
( )d Bdt
Motion of Magnetization
Biomedical Magnetic Resonance: 3 Motion of Magnetization
B
d
d Bdt
d
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Radiologische PhysikUniversity Hospital
Basel
Motion of magnetization: precession
Motion of Magnetization
Biomedical Magnetic Resonance: 3 Motion of Magnetization
( )d Bdt
d Bdt
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Radiologische PhysikUniversity Hospital
Basel
Motion of magnetization: precession ( )d Bdt
Motion of Magnetization
Biomedical Magnetic Resonance: 3 Motion of Magnetization
d Bdt
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Radiologische PhysikUniversity Hospital
Basel
B0 B0
Bx(t) = 2B1cos(t)
B0
Excitation and Reception
Biomedical Magnetic Resonance: 4 Excitation and Reception
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Radiologische PhysikUniversity Hospital
Basel
FID: free induction decay
B0
precession of magnetization
a) on-resonance, b) off-resonance, c) spectrum
Excitation and Reception
Biomedical Magnetic Resonance: 4 Excitation and Reception
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Radiologische Physik
Biomedical Magnetic Resonance: 5 Magnetic Resonance Imaging
University HospitalBasel
Imaging = spatial discrimination
Magnetic Resonance Imaging
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Radiologische PhysikUniversity Hospital
Basel
Magnetic Resonance Imaging
Biomedical Magnetic Resonance: 5 Magnetic Resonance Imaging
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Radiologische PhysikUniversity Hospital
Basel
Magnetic Resonance Imaging
Biomedical Magnetic Resonance: 5 Magnetic Resonance Imaging
Bloch equation
= B
dMdt
M B ( )
Larmor equation
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Radiologische PhysikUniversity Hospital
Basel
Magnetic Resonance Imaging
Biomedical Magnetic Resonance: 5 Magnetic Resonance Imaging
Magnetic Field Gradients
x
B 0 = B0
B0
Sample in a homogenous magnetic field B0
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Radiologische PhysikUniversity Hospital
Basel
Magnetic Resonance Imaging
Biomedical Magnetic Resonance: 5 Magnetic Resonance Imaging
Magnetic Field Gradients
x
B(x) = B0 + xGx
B0
Sample in a magnetic gradient field B0 + B
am
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Radiologische PhysikUniversity Hospital
Basel
Magnetic Resonance Imaging
Biomedical Magnetic Resonance: 5 Magnetic Resonance Imaging
BB
xx
yyMagneticMagnetic fieldfield IsoIso--FluxFlux GraphGraph
Problem: 2D Problem: 2D oror higherhigher -- FrequenciesFrequencies ambiguousambiguous
xx
yy
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Radiologische PhysikUniversity Hospital
Basel
Magnetic Resonance Imaging
Biomedical Magnetic Resonance: 5 Magnetic Resonance Imaging
Magnetic Field Gradients
Swichable, linear magnetic field gradientsindependently in x, y and z direction
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Radiologische PhysikUniversity Hospital
BaselMagnetic Resonance Imaging
Biomedical Magnetic Resonance: 5 Magnetic Resonance Imaging
Spatially resolved reception
GradientGradient
x2x2
x1x1
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Radiologische PhysikUniversity Hospital
BaselMagnetic Resonance Imaging
Biomedical Magnetic Resonance: 5 Magnetic Resonance Imaging
Spatially resolved reception
Spatial encoding: the Fourier Transform
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Radiologische PhysikUniversity Hospital
BaselMagnetic Resonance Imaging
Biomedical Magnetic Resonance: 5 Magnetic Resonance Imaging
Spatially resolved reception
RF excitation
z gradient
x gradient
GradientGradient
x2x2
x1x1
MR signal
FT
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Radiologische PhysikUniversity Hospital
BaselMagnetic Resonance Imaging
Biomedical Magnetic Resonance: 5 Magnetic Resonance Imaging
Spatially resolved reception
Back projection: imaging sequence
RF excitation
z gradient
x gradient
y gradient
Signal acquisition sinogram
FT
recon
k
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Radiologische PhysikUniversity Hospital
BaselMagnetic Resonance Imaging
Biomedical Magnetic Resonance: 5 Magnetic Resonance Imaging
Imaging in k-space
2DFT2DFT
k-space image
i2 kxS(k) (x) e dx -i 2(x) S(k) e dkkx
S(k) = S(k(t)) = S(t)
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Radiologische PhysikUniversity Hospital
BaselMagnetic Resonance Imaging
Biomedical Magnetic Resonance: 5 Magnetic Resonance Imaging
Properties of k-space
kx
ky
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Radiologische PhysikUniversity Hospital
BaselMagnetic Resonance Imaging
Biomedical Magnetic Resonance: 5 Magnetic Resonance Imaging
Properties of k-space
8 x 8512 x 512
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Radiologische PhysikUniversity Hospital
BaselMagnetic Resonance Imaging
Biomedical Magnetic Resonance: 5 Magnetic Resonance Imaging
Imaging in k-space
k-space
i2 kxS(k) (x) e dx
S(k) = S(k(t)) = S(t)
RF excitation
z gradient
x gradient
y gradient
Signal acquisition
t
0
1( ) (t) dt2
k t G
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Radiologische PhysikUniversity Hospital
BaselMagnetic Resonance Imaging
Biomedical Magnetic Resonance: 5 Magnetic Resonance Imaging
Imaging in k-space: gradient echo (GE) sequence
k-space
i2 kxS(k) (x) e dx
S(k) = S(k(t)) = S(t)
RF excitation
z gradient
x gradient
y gradient
Signal acquisition
t
0
1( ) (t) dt2
k t G
37
Radiologische PhysikUniversity Hospital
BaselMagnetic Resonance Imaging
Biomedical Magnetic Resonance: 5 Magnetic Resonance Imaging
Imaging in k-space: gradient echo (GE) sequence (EPI)
k-space
i2 kxS(k) (x) e dx
S(k) = S(k(t)) = S(t)
RF excitation
z gradient
x gradient
y gradient
Signal acquisition
t
0
1( ) (t) dt2
k t G
38
Radiologische PhysikUniversity Hospital
BaselMagnetic Resonance Imaging
Biomedical Magnetic Resonance: 5 Magnetic Resonance Imaging
Imaging in k-space: gradient echo (GE) sequence (spiral EPI)
k-space
i2 kxS(k) (x) e dx
S(k) = S(k(t)) = S(t)
RF excitation
z gradient
x gradient
y gradient
Signal acquisition
t
0
1( ) (t) dt2
k t G
39
Radiologische PhysikUniversity Hospital
BaselMagnetic Resonance Imaging
Biomedical Magnetic Resonance: 5 Magnetic Resonance Imaging
Imaging in k-space: spin echo (SE) sequence
k-space
i2 kxS(k) (x) e dx
S(k) = S(k(t)) = S(t)
RF excitation
z gradient
x gradient
y gradient
Signal acquisition
t
0
1( ) (t) dt2
k t G
90°
40
Radiologische PhysikUniversity Hospital
BaselMagnetic Resonance Imaging
Biomedical Magnetic Resonance: 5 Magnetic Resonance Imaging
Imaging in k-space: spin echo (SE) sequence
k-space
i2 kxS(k) (x) e dx
S(k) = S(k(t)) = S(t)
RF excitation
z gradient
x gradient
y gradient
Signal acquisition
t
0
1( ) (t) dt2
k t G
90°
180°
41
Radiologische PhysikUniversity Hospital
BaselMagnetic Resonance Imaging
Biomedical Magnetic Resonance: 5 Magnetic Resonance Imaging
Imaging in k-space: spin echo (SE) sequence
k-space
i2 kxS(k) (x) e dx
S(k) = S(k(t)) = S(t)
RF excitation
z gradient
x gradient
y gradient
Signal acquisition
t
0
1( ) (t) dt2
k t G
90°
180°
42
Radiologische PhysikUniversity Hospital
Basel
Contrast
Biomedical Magnetic Resonance: 6 Contrast
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Radiologische PhysikUniversity Hospital
BaselContrast
Relaxation in living tissue
T1: recovery of longitudinal magnetization
T2* : loss of phase coherence of transverse magnetization
T2`
staticdephasing
randomdephasing
T2
T2*
x
z
T1 T2*
M
2
2
1
/
/
/0 0( )
t Tx xi
t Ty yi
t Tz zi
M M e
M M e
M M M e M
Biomedical Magnetic Resonance: 6 Contrast
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Radiologische PhysikUniversity Hospital
Basel
Spin Echoes
Biomedical Magnetic Resonance: 5 Magnetic Resonance Imaging
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Radiologische PhysikUniversity Hospital
Basel
Relaxation in living tissue
Contrast
Biomedical Magnetic Resonance: 6 Contrast
46
Radiologische PhysikUniversity Hospital
Basel
Contrast of imaging sequences
k-space RF excitation
z gradient
x gradient
y gradient
Signal acquisition
Repeat hundreds of times
Contrast
Biomedical Magnetic Resonance: 6 Contrast
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Radiologische PhysikUniversity Hospital
Basel
Contrast of imaging sequences:TR~T1>T2
t
MzM0
0 1 2 3 4 5 6 7 8
M0cos
Mt
M0sin
RF (flip angle )
Contrast
Biomedical Magnetic Resonance: 6 Contrast
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Radiologische PhysikUniversity Hospital
Basel
200 500 1000 3000 6000
10
40
70
100
TRTE
Contrast
Biomedical Magnetic Resonance: 6 Contrast