Jorge Jovicichjovicich@mit.edu

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

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

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

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

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

• 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

• 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

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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