IRM-Principes de base

Nuclear Magnetic Resonance
 Basic Principles
 NMR Imaging  Functional NMR Imaging & Spectroscopy
Pierre CARLIER ([email protected])
Laboratoire de RMN AFM/CEA
Institut de Myologie Bâtiment Babinski
Groupe Hospitalier Pitié-Salpêtrière
Paris
Cours 1 : Principes de la RMN
1. Magnétisme nucléaire
1.1. Atome
1.2. Moment cinétique
1.3. Moment magnétique
1.4. Rapport gyromagnétique
1.5. Comportement en l’absence et dans un champ statique
1.6. Équation de Larmor
1.7. Noyaux d’intérêt biologique
2. Résonance magnétique nucléaire
2.1. Principe
2.2. Modèle classique (équilibre, excitation)
2.3. Angle de bascule
2.4. Modèle quantique
2.4. Signal de RMN : signal d’induction libre (FID)
3. Phénomène de relaxation
3.1. Relaxation
3.2. Longitudinale (T1)
3.3. Transversale (T2)
3.4. Notion de T2*
4. Mesure du signal RMN
4.1. Aimant/sonde RMN
4.2. FID
4.3. Inversion-récupération : mesure du T1
4.4. Écho de spin: mesure de T2
5. Contraste tissulaire
5.1. contraste T1
5.2. contraste T2
5.3. contraste densité de protons
6. Spectroscopie RMN
6.1. déplacement chimique
6.2. l’exemple de la RMN du P31
Magnetic properties of the nuclei
Matter is made of atoms. Atoms are made up
of electrons and nuclei. Each atomic nucleus
has four important physical properties: mass,
electric charge, magnetism and spin.
spin
Magnetic properties of the nuclei
Matter is made of atoms. Atoms are made up of electrons and
nuclei. Each atomic nucleus has four important physical
properties: mass, electric charge, magnetism and spin.
Spin is a quantum mechanical intrinsic property of elementary particles. It is
very difficult to imagine this property, and the notion of actual rotation can be
somewhat helpful. However, it is wise to separate this notion of a spinning
particle from the quantum mechanical property we call "spin".
Magnetic properties of the nuclei
Matter is made of atoms. Atoms are made up of electrons and
nuclei. Each atomic nucleus has four important physical
properties: mass, electric charge, magnetism and spin.
Spin is a quantum mechanical intrinsic property of elementary particles. It is
very difficult to imagine this property, and the notion of actual rotation can be
somewhat helpful. However, it is wise to separate this notion of a spinning
particle from the quantum mechanical property we call "spin".
Although spin is a form of angular momentum, an elementary particle with
spin does not mean it is rotating; particles with spin simply have spin. The
concept of a particle rotating around its own axis is helpful, but it is
intellectually sterile; for example, at absolute zero temperature when all
motion ceases, a particle still has "spin".
Moment cinétique
Cette rotation individuelle induit ceque l’on appelle un moment cinétique de
spin ou moment angulaire noté j
n
Moment cinétique:
j
r
v
  
j rp
 
 m.r  V

 m.r.V .n
Avec
Proton:
•Charge =  e
•Masse : m= 1.673x10-27 kg

p quantité de mouvement
V vitesse de rotation,
r vecteur position,
n axe de rotation
Moment magnétique
Moment magnétique:
Si la particule en rotation est chargée, alors la
rotation de sa distribution de charge induit ce
que l’on appelle
 un moment magnétique de
spin, noté µ
n



  S .I .n
N 

; V   .r
2 .
I  e. N  e .
j
V
2 .r
Avec
r
v

I courant équivalent
S surface apparente
V vitesse de rotation,
 pulsation,
n axe de rotation , normale à la
Proton:
•Charge =  e =1.6x10-19 C
2

r
•Surface apparente: S=
surface S
N nbre de tours par seconde
(fréquence de rotation)
Rapport gyromagnétique
On obtient:

j
Moment magnétique:

r
v
q.V .r 

.n
2
Moment cinétique:


j  m.r.V .n

Les protons s’apparient entre
eux de sorte que leurs
aimantations s’annulent 2 à 2.
Seuls les atomes à nombre de
nucléons impairs (=> 1 nucléon
non apparié) possèdent un
moment magnétique intrinsèque
non nul.
e

j
2m

Rapport gyromagnétique,
propre à chaque noyau
Comportement en l’absence de champ magnétique externe


Vecteur aimantation macroscopique M   
B0 = 0
Mx = My
= Mz = 0
Les moments magnétiques (µ) des atomes soumis à un
très faible champ magnétique extérieur ont des
orientations aléatoires: L’aimantation macroscopique
résultante est nulle.
Comportement dans un champ magnétique externe B0
B0 intense  l’orientation des spins parallèlement à B0. En fait,
B0 impose un couple  au moment magnétique  :
  
   X B0
Ils se séparent en 2 populations
tournant autour de B0 avec un
B0  0
angle fixé (PRECESSION), soit
Mx =My=0
dans la même direction que lui
Mz = M0
(parallèle) soit dans la direction
opposée (antiparallèle), en raison
de phénomènes relevant de la
Sous l’action d’un champ B0  0 appliqué dans la
mécanique quantique.
direction Z, tous s’alignent selon Z, répartis dans
le sens parallèle UP ou anti-parallèle DOWN de
sorte que l’aimantation résultante est non nulle.
Interaction with the magnetic field B0
Spin precession
The direct relationship between the magnetic moment (μ) and the spin angular
momentum (J) is, from experiment


  J
When this magnetic moment  is in the presence of an external magnetic field
B0 it experiences a torque and precesses around the B0 field with an angular
frequency 0 (the “Larmor frequency”):

 
 d 

     B0
 dt 
 B0  0
Équation de Larmor
La pulsation ou vitesse de précession dans un champ
magnétique statique est définie par la relation de Larmor:
 0  B0
Interaction with the magnetic field B0
Spin precession
 B0  0
Interaction with the magnetic field B0
Spin precession
spin
Interaction with the magnetic field B0
A selection of nuclear isotopes and their properties.
Interaction with the magnetic field B0
© 2006 Denis Hoa et al, Campus Medica. www.e-mri.org
Modèle quantique

A L’EQUILIBRE dans un champ B0
D’un point de vue énergétique:
état UP
état DOWN
(parallèle)
(anti-parallèle)
=
Basse
énergie
E
E= hB0
=
Haute
énergie
E2=+hB0/2
Excédent =M0
E1 =-hB0/2
Macroscopic magnetization
Quantum Description:

Bo > 0
E  0

Bo
When placed in an external magnetic field, the direction of
angular momentum arising from nuclear spin is quantized
(it can only take certain values). This results in discrete
energy states. (Without an external magnetic field these
states collapse into one state.)
Note that Zeeman splitting is a quantum mechanical
effect, and without it MRI and NMR would not exist.
Macroscopic magnetization
The equivalent population difference which occurs between the two energy
states results in the net magnetization in a sample.
N   N  0  B0


spin excess 
N   N  2kT
2kT
  1.05  10 34 Joule  s
k  1.38 10  23 Joule/K
N  N
10

 10 ppm
N   N  1000000
T  300 K
B0  3 Tesla
  2.68 10 rad/s
8
M0 
 0 2  2
4kT
B0
Continuous wave (CW) experiment
Continuous wave (CW) experiment
Continuous wave (CW) experiment
Continuous wave (CW) experiment
40 MHz
900MHz, 21.2 T NMR Magnet at
HWB-NMR, Birmingham, UK being
loaded with a sample
Interaction with B1
Classical Description
Rotating Frame
0
To simplify the vector description, the X,Y axis rotates
about the Z axis at the Larmor frequency 0
Interaction with B1
Classical Description
Rotating Frame
B1 << B0

B1
x’
y’
B1 is an oscillatory magnetic field with angular frequency = 1
B1 is stationary in the rotating frame
Interaction with B1
Classical Description
Rotating Frame

µ
B1 << B0

B1
x’
y’
In the presence of an external magnetic field B1,
 experiences a torque (in the rotating frame)

 
 d 

     B1
 dt 
'
Interaction with B1
A B1 field applied for a finite time is called an “rf pulse”. Suppose the rf field in
turned on (quickly) to a constant value B1x’ for a time interval  and the is
rapidly turned off. In the rotating frame, the net magnetization will rotate
through the angle  :
   B1 
For example, the size of B1 required for a 90° flip angle over 1.0 ms is 5.9 T
for protons.
Interaction with B1
Classical Description
A B1 field applied for a finite time is called an “rf pulse”. Suppose the rf field in
turned on (quickly) to a constant value B1x’ for a time interval  and the is
rapidly turned off. In the rotating frame, the net magnetization will rotate
through the angle  :
   B1 
Mz
+
Mxy
Modèle quantique
EXCITATION
Déséquilibrer le système
induire des transitions
de l’état bas (E2)
vers l’état haut (E1)
Fournir l’énergie nécessaire via une onde
électromagnétique: E=hr=E
transition d’état + MISE EN PHASE des spins
E= hB0
E
E2
E1

B1
Le champ externe B0
Il faut générer un champ fort et stable.
Aimant résistif
Aimant supraconducteur
- Consommation courant, B0<0.3T,
+ peu cher
Pour l’IRM in vivo, Bo vaut de 0.5 Tesla
(homme) à 11 Tesla (souris)
-- cher!! Installation/ conso liquides
cryogéniques (He, N2)
+ + stables, B0 élevés, faible conso
de courant
Champ magnétique terrestre b = 5. 10-5 Tesla
Sonde RMN
La sonde RMN va produire le champ RF d’excitation et lire
le signal de relaxation dans le plan transversal (0xy).
z
B0
B1
O
x
y
Circuit d’accord-adaptation
r
Émetteur/récepteur
CM
Re
RF
CT
L
Boucle d’induction
Réglage d’adaptation
C M  CT
r
Re
Réglage d’accord
f circuit 
1
LCT
NMR Signal
A rotating magnetic moment generates a rotating magnetic field. It is possible
to detect this oscillating field using a wire coil.
NMR Signal
The oscillating electric current induced by the precessing nuclear transverse
magnetization is called the NMR signal or free-induction decay (FID)
Signal de précession libre:Free Induction Decay (FID)
90
acquisition
t
S(t)  S0 exp( * )
T2
Relaxation
Return to equilibrium of net magnetization is called relaxation.
Relaxation combines 2 different mechanisms:
Longitudinal relaxation corresponds to longitudinal magnetization recovery
Transverse relaxation corresponds to transverse magnetization decay
M does not simply "rotate" back to M0, because the longitudinal and
transverse relaxation are separate.
Relaxation
Longitudinal relaxation (T1)
Longitudinal magnetization
precessing protons are pulled back into alignment with main magnetic field (B0)
M z (t )  M z (1  e t T1 )
Relaxation
The T1 time is related to the transfer of energy from a nuclear spin
system to its environment ("lattice“).
The transfer of energy to the "lattice" is not spontaneous—T1 "relaxation"
can only occur when a proton encounters an oscillating magnetic field at
(or near) the Larmor frequency. The frequency of the oscillating magnetic
field a molecule produces is dependent on how fast it moves (rotation,
translation, vibration).
The source of such a field is other protons in the same molecule or in
different molecules.
Relaxation
Longitudinal relaxation (T1)
Relaxation
Transverse relaxation (T2)
Transverse magnetization
precessing protons become out of phase leading to a drop in the net magnetic
moment vector
M x (t )  M x e t T2
time
Relaxation
Relaxation
The T2 time is related to the effect of nuclear spins on each other. The spinspin interaction purely refers to the loss of phase coherence of spins as they
interact with each other via their own oscillating magnetic fields. (Phase
coherence means spins are all precessing together.) The slight changes in
magnetic field which a proton experiences causes its Larmor frequency to
change. As a result, the precession of spins moves out of phase and the
overall net magnetization is reduced.
NMR Signal acquisition methods
NMR Signal acquisition methods
1-2
NMR Signal acquisition methods
Écho de spin: principe
90°
e
180°
 t /T2*
e
 t /T2
x
y
L’aimantation M
est basculée
dans le plan xy
Inhomogénéités
fixes de B0=>
déphasage des µ
Inhomogénéités
fixes de B0=> le
déphasage se
poursuit
L’aimantation
est refocalisée
NMR Signal acquisition methods
Contrast
Ability to distinguish different tissues from one another.
Contrast
Ability to distinguish different tissues from one another.
Contrast
T1 weighted images
short T1
Signal
long T1
maximal contrast
TR
Contrast
Signal
T2 weighted images
short T2
long T2
maximal contrast
TE
Contrast
 weighted images
=1
=1
Signal
Signal
 = 0,8
TR
 = 0,8
TE