Basic Principles of Magnetic Resonance -...
Transcript of Basic Principles of Magnetic Resonance -...
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Jorge [email protected]
Basic Principles of Magnetic Resonance
I) Historical Background
Contents:
II) An MR experiment - Overview - Can we scan the subject? - The subject goes into the magnet - Brief RF pulses are applied - The MR signal - Summary
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Overview of a MRI procedure
Magnetic field
Tissue protons align with magnetic field(equilibrium state)
RF pulses
Protons absorbRF energy
(excited state)
Relaxation processes
Protons emit RF energy(return to equilibrium state)
NMR signaldetection
Relaxation processes
Repeat
Spatial encodingusing magneticfield gradients
Subject
Safety screening
RAW DATA MATRIX Fourier transform IMAGEJ. Jovicich, MIT
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Can we scan the subject? Safety Issues
• Not everybody can undergo a MR examination
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• Screening is mandatory to ensure safety / quality during the MR examination
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A typical MRI scanner
The main magnetic field:
• is VERY strong ( 3T ~ 30,000 times the earth’s magnetic field)
• is A L W A Y S O N !! (superconducting currents)
• it’s strength decays ~ 1 / r3 (r is the distance from the center)
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Can we scan the subject? Safety Issues
• Risks:
- Ferromagnetic materials (unsafe)
- will be subject to force / torque in the main magnetic field
- risks associated with motion / displacements
- active biomedical implants may not function properly
From: www.symplyphysics.com/flying_objects.htmlJ. Jovicich, MIT
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Can we scan the subject? Safety Issues
- Non ferromagnetic materials (safe but give image distortions)
• Risks:
- Ferromagnetic materials (unsafe)
Sagitall MRI of a normal
female subject
With hair rubber band* Without hair rubber band
* The two ends of the rubber band are joined by a ~ 2 mm cooper clamp.J. Jovicich, MIT
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• Risks:
- Ferromagnetic materials (unsafe)
- Non ferromagnetic materials (safe but give image distortions)
- Claustrophobia (subject unhappy → image distortions)
Can we scan the subject? Safety Issues
J. Jovicich, MIT
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• Risks:
- Ferromagnetic materials (unsafe)
- Non ferromagnetic materials (safe but give image distortions)
- Acoustic protection (mandatory)
- Claustrophobia (subject unhappy → image distortions)
- Movement during examination (potential problem for dynamic studies)
Can we scan the subject? Safety Issues
J. Jovicich, MIT
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Overview of a MRI procedure
Subject
Safety screening
Magnetic field
We will introduce the following concepts:
• equilibrium magnetization
• dynamics of the magnetization
• rotating coordinate system
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The subject goes into the magnet...
O
HH
Water molecules
Hydrogen nucleus:magnetic moment
r
: uniform static magnetic field : static macroscopic magnetization
r B 0
r
M 0
Two energy states:
Low energy
state
High energy
state
Anti-parallel Parallel
Precession frequency:
o = Bo
Bo
(E1) (E0)
∆E = E1 − E0
∆E = h 0
Y
Bo
Mo
Singlenucleus
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The subject goes into the magnet… (continued)
A group of protons
Mo
Net magnetization Mo
Equilibrium magnetization Mo: - Mz aligned with Bo - Mxy = 0
Y
Bo
Mo
N1
N0
= exp − h B0
kT
N1 = # of protons in state E1
N0 = # of protons in state E0
k : Boltzmann’s constantT : temperature
Spin states distribution
E1
Eo
Energy statesBo
ωo = γ Bo
∆E = h 0
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Reminder of three main steps in MRI
0) Equilibrium (Mo along Bo)
1) RF excitation (tip Mo away from equil.)
2) Precession of Mxy induces signal (dephasing for a time TE)
3) Return to equilibrium (recovery time TR)
Dynamics of magnetization
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Dynamics of the magnetization
• Equation of motion of in external
• Classical mechanics formalism
• First, model a single nucleus
• Then, add up for sample
• Finally, consider relaxation (Bloch equations)
r
M r B ext
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• Mechanical moment ⇔ angular momentum (spin)
• Magnetic moment ⇔ spin
• Magnetic moment and magnetic field interaction
r T = d
r L
dt
r =
r L
r T = r ×
r B ext
Equation of motion for a single nucleus:
r
d
r ( t )
dt= r
( t ) ×r B ext ( t )
Bext
Precession of about with frequency r
r B ext
= Bext
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Equation of motion for the magnetization vector:
• Assuming no interaction between nuclei
r
M = r 0 + r
1 + r 2 + ... = r
i∑
r
M
d
r M ( t )
dt=
r M ( t ) ×
r B ext ( t)
Bext
Precession of about with frequency
r B ext
= Bext
• And since for each nuclei
d
r i( t )
dt= r
i (t ) ×r B ext ( t )
(spin excess)
r
M
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To describe the magnetization we needto choose a coordinate systems
z
x
y
z = z’
x’
y’
Laboratory coordinate system Rotating coordinate system
ωo = γ Bo
ωo = γ Bo
M(t) M’(t)
with: Bext(t) = B0 + B1(t) with: Beff(t) = B1’(t)
Bo Bo
d
r M ( t )
dt=
r M ( t ) ×
r B ext ( t)
dr
M ' ( t )
dt=
r M ' ( t ) ×
r B eff ( t )
On-resonance spins: staticOff-resonance spins:
ωo
ωo + ∆ω ∆ω
Example:
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The NMR signal
• We need net transverse magnetization:
- precession of Mxy about B0
- rotating magnetic field
- induces current in a coil: MR signal
Mxy
Bo
• At equilibrium no signal:
- static longitudinal magnetization Mo
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• With an RF pulse on resonance we can rotate M0
The NMR signal (continuation)
Bo
B1’
• Dynamics:
• B1’(t): B’1 constant and ⊥ to B0
• M’ precesses about B1 with ω1= γ B’1
• Flip angle θ:
Rotating frame:
'1B
tγ=
∆θ∆
d
r M ' ( t )
dt=
r M ' ( t ) ×
r B eff ( t )
Beff(t) = B1’(t)
• Signal relaxation, system goes back to equilibrium
Mz → Mo (T1 relaxation)
Mxy → 0 (signal loss, T2 & T2* relaxation)
• Relaxation mechanisms give tissue contrast
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The NMR signal (continuation)
Schematic representation:
Radio-frequency pulse(oscillating B1(t) rotating at ω0)
NMR signal(transverse magnetization decay)
‘Free Induction Decay’
T2* decay
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T1 or spin-lattice relaxation (longitudinal magnetization)• Mz defined by spin excess population between two energy states• Mz recovery → transitions between spin states• transitions → fluctuating transverse field on resonance → molecular motion• exponential recovery (T1 ≈ 100 - 3000 ms, longer for higher Bo)
Relaxation mechanisms
dMz
dt= Mo − Mz
T1
time
Mz
Mo
Mz=0 after 90o RF pulse
Mz=Mo at equilibrium
TR
Repetition time (TR): time allowed for recovery, defines T1 contrast
Bo
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T2 or spin-spin relaxation (transverse magnetization)• incoherent exchange of energy between spins• molecular motion → fluctuations in local Bz → resonance frequency variations• dephasing of transverse magnetization → signal decay• exponential decay (T2 ≈ 70 - 1000 ms)
Relaxation mechanisms (continued)
2T
M
dt
dM xyxy −=
time
Mxy
Mo sinθ
spins dephase
Mxy NMR signal
TE
Echo time (TE): time allowed for dephasing, defines T2 contrast
Mxy maxafter 90o
RF pulse
Mxy =0at equilibrium
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Relaxation mechanisms (continued)
T2* relaxation• dephasing of transverse magnetization due to both:
- microscopic molecular interactions (T2) - spatial variations of the external main field ∆B (tissue/air, tissue/bone interfaces)
• exponential decay (T2* ≈ 30 - 100 ms, shorter for higher Bo)
time
Mxy
Mo sinT2
T2*
1T2 *
= 1T2
+ ∆Β2
tissue
air
B = µ µ0 H
Boundary conditions
Field distortions(∆B)
TE
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dr
M ( t )
dt=
r M ( t ) ×
r B ext ( t) −
(Mxˆ i + My
ˆ j )
T2
*−
(Mz − M0 )
T1
ˆ k
Bloch Equations
• Dynamics of the magnetization + Relaxation effects:
• Geometrical description: damped precession (SUMMARY)
B0
M0
timeEquilibrium
RF
Equilibrium
NMRsignal
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