Download Magnetic Resonance Imaging Physics and Instrumentation

Coronary angiography
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Intracranial angiography
Magnetic Resonance Imaging
Physics and Instrumentation
Orlando “Lon” Simonetti, PhD
Cardiac function and tissue characterization
Professor of Internal Medicine and Radiology
Director of Cardiac MRI and Cardiac CT Research
The Ohio State University
Columbus, OH
Orthopedic Imaging
Myocardial Perfusion
Neuro Imaging
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MRI in a nutshell
Day One: Origins of the MR Signal
& Protons, spin, and magnetization
& Precession and the Larmor Equation
& Longitudinal and transverse magnetization
& The MR signal
& Longitudinal and transverse relaxation
Cardiovascular MRI : physical principles to practical protocols / Vivian S. Lee ; Lippincott Williams & Wilkins, c2006
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MRI in a nutshell
MRI in a nutshell
& Step 1 – Magnetization is created
% Excess 1:2,000,000 protons align with1.5T B0 field
% Alignment takes about 5xT1 to complete
& Step 2 - Magnetization is perturbed
% RF pulse applied through transmitter coil
% The protons in a selected slice of tissue are “excited” by the RF pulse
& Step 3 – Magnetization relaxes back to equilibrium state
% After excitation, magnetization immediately begins relaxation back to
equilibrium.
% Signal decay dependent on T2.
% Spatial localization by application of magnetic field gradients.
% RF signal detection through receiver coil or coils.
& Step 4 – Repetition of the process for every line of raw data
% Raw data is acquired in “k-space” or Fourier space.
& Step 5 – Fourier transform “reconstruction” of the image from raw data
% Image contrast depends on tissue properties, as well as specifics of pulse
sequence used to excite and acquire signals.
Cardiovascular MRI : physical principles to practical protocols / Vivian S. Lee ; Lippincott Williams & Wilkins, c2006
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Spin
Basis of MRI
& Proton has a unit positive charge, equal and opposite to the
electron charge, and the nuclear “spin” produces a magnetic
dipole.
& NMR
% = Nuclear Magnetic Resonance
& Neutron is electrically uncharged, but subnuclear charge
inhomogeneities result in a magnetic field of opposite direction
and approximately equal strength to proton.
% Atoms with odd total # of protons and neutrons have noninteger nuclear spin with an associated magnetic moment.
& MRI
& Magnetic moment describes the magnetic field properties of the
nucleus.
% = Magnetic Resonance Imaging
% Based on the phenomenon of NMR
% What is imaged: Hydrogen nucleus (single proton)
& If total number of protons and neutrons is even, essentially no
magnetic moment.
% Body: 80% - 95% H2O (a lot of signal source)
& If total number of protons and neutrons is odd, the non-integer
nuclear spin generates a magnetic moment.
& Composition of an H atom
% 1 proton + 1 electron
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Spin
Spin
& Spin: purely quantum mechanical characteristic of atomic
particles.
& Rotation of a sphere is only an analogy, but a useful one.
& MRI: hydrogen atoms in water and hydrocarbons
& Natural abundance of 1H makes it a practical signal source
for MRI
Magnetic field
direction
m
+
Nucleus
+
Electron
Hydrogen atom
1 proton + 1 electron
Hydrogen proton
Sometimes referred to as “a spin”
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Other MRI Relevant Nuclei
N
S
Spinning proton behaves like a small bar magnet
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Magnetic Moment
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Spins and Net Magnetization
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&
&
&
A spin: one H atom
1cc of H2O: ~ 1019 H atoms or “spins”
Aggregate of spins → net magnetization
Net magnetization = vector sum of the effect of spins
m
M
A spin
An aggregate of spins gives net magnetization
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Effect of External Magnetic Field on Spins
Spin Precession
& Spins precess like a top about external field Bo
& Precession frequency (fL or ωL) is called Larmor frequency
& No external magnetic field
% Spins are randomly oriented
% No net magnetization
& With external magnetic field Bo
% Small majority of spins align parallel to the field
% Minority of spins align anti-parallel to the field
% A small net balance parallel to the field
Bo
Bo
=
No magnetic field
External magnetic field
Net Magnetization
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The Larmor Equation
& The Larmor Equation states that the resonance frequency
is proportional to the magnetic field: ω = γ • B0
ω: Larmor frequency
γ: gyromagnetic ratio specific to type of nucleus
γ = 42.577MHz/Tesla for Hydrogen
B0: magnetic field strength
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MRI in a nutshell
Proton Precessional Frequency at
Different Field Strengths
Bo in Tesla
1.0
Precession frequency
(MHz)
42.6
1.5
63.9
3.0
127.7
7.0
298
Cardiovascular MRI : physical principles to practical protocols / Vivian S. Lee ; Lippincott Williams & Wilkins, c2006
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How Spin Dynamics Change in an
oscillating radio frequency (RF) Field (B1)
The Resonance Phenomenon
& Spins reacts to magnetic fields oscillating at the precession
frequency
& The interaction: energy absorbed and precession changed
z
Bo
z’
θ
θ
M
y
B1
M
y’
B1
x
Spin Trajectory
Resultant Spin Motion
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About the B1 (RF) Field
The “Big” Picture
& A time varying magnetic field
& Frequency of oscillation = Larmor frequency
& B1 strength and duration affects degree to which
spins are tipped
& Flip angle = angle that spins are tipped over
& To generate B1:
& Two magnetic fields needed to manipulate spins
% Time varying electric current passed through a coil
% Electric field converted to magnetic field
% Bo aligns the spins
% B1 controls how spins tip
% B1 << Bo
& Definition of terms:
% How spins behave when B1 is turned off – relaxation
% How spins behave when B1 is turned on – excitation
% How to measure signals from spins – signal detection
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z
Some Notations
Mz
& Mz = Longitudinal magnetization
& Mxy = Transverse magnetization
M
Mxy
Mo
Longitudinal magnetization (Mz) is in the
z-direction, along the external magnetic field B0.
Bo
Mz
Mz = Mo·cosα
Mxy = Mo·sinα
α
Transverse magnetization (Mxy) is in the
x-y plane, perpendicular to the external magnetic
field.
Mxy
Spins must be in the x-y plane in order for us to
receive MR signal.
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z
z
H
90°
180°
Flip Angle (α) is the total amount of deflection of the
magnetization after the end of an applied RF pulse.
A 90°-pulse flips the magnetization into the x-y
plane.
The stronger the energy of the applied RF pulse, the
greater the flip angle.
A 180°-pulse flips the magnetization into exactly the
opposite direction.
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The MR Signal
Signal Detection
• Only
&
&
&
&
spins tipped into the transverse plane can induce a signal.
• RF coils are used to receive the MR signal.
z
• The simplest example of an MR signal is the
free induction decay (FID).
B1 field on/off creates a change of Mxy
Change of Mxy is time varying (at Larmor frequency)
Change of Mxy detected by a coil
Time varying Mxy → Electromagnetic induction
→ time varying electrical signal
y
RF coil
S
x
S
z
N
M
N
θ
Detector coil
y
x
B1
Free Induction Decay
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Tissue Contrast in MRI
Magnetic Relaxation
•Proton Density
& Bo is always on
& When RF current to coil is turned off
% B1 field is off
•T1
% Mz goes back to Mo
Each tissue has a
unique set of T1, T2 and
PD
Mo
Mz
•T2
α
α
Mxy
MT
Mo
Mz
M0
% Mxy reduces to 0
Mxy
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Longitudinal Magnetization
Relaxation Time Constants
T1 (Spin-Lattice) Relaxation Time - The characteristic time for the
longitudinal spins to align themselves in the main magnetic field.
The longitudinal magnetization vector will regain 63% of its
maximum value in the time T1.
T2 (Spin-Spin) Relaxation Time - The characteristic time for the
loss of phase coherence among the spins oriented in the
transverse direction. The transverse magnetization vector will loss
63% of its value in the time T2.
T2* Relaxation Time - The characteristic time for the loss of phase
coherence among the spins oriented in the transverse direction.
This time constant accounts for such non-idealities as field
inhomogeneities. The T2* time constant is always smaller than the
T2 time constant (i.e. the signal decays faster).
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Longitudinal Relaxation
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Longitudinal Relaxation in Tissues
& In body, T1 is between 100ms and 2s
& T1 fat < T1 myocardium < T1 blood
Mz
1.2
T1 relaxation for different tissues at 1.5T
Mo 1.0
0.8
0.63Mo 0.6
blood
fat
myocardium
0.4
0.2
0.0
Mz = 1-exp(-T1/t)
0
500
1000
1500
2000
2500
3000
Time (ms)
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Transverse Relaxation
Transverse Relaxation: T2 and T2*
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&
&
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Also called spin-spin relaxation
Cause: mutual interaction among spins
Local magnetic field of spins differ
Spin precession frequencies differ from each other
Spins disperse or “dephase” on the transverse plane
Relaxation time constant = T2
Spins on
transverse plane
(at resonant freq)
Net
magnetization
Time course
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Transverse relaxation
Transverse Relaxation: T2
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T2 relaxation is due to spin - spin interaction.
T2 decay is the destruction of transverse magnetization.
T2 relaxation is faster than T1 relaxation.
In body, T2 is between 20ms to 1.5s
Mxy
Mo
M xy (t ) = M 0e− t / T2
0.63Mo
0.37Mo
time
T2
B1 field off
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Field inhomogeneity: changes spins’ precession frequency
More dispersion of spins over the transverse plane
Faster decay of transverse magnetization
Relaxation time constant = T2*
T2* < T2
& Transverse relaxation due to
spin dephasing
& T2 irreversible dephasing
& T2/ reversible dephasing
& Combined effect
M x(t)/M x(0)
Transverse Relaxation: T2*
&
&
&
&
&
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Transverse Relaxation: T2*
Mxy
Mo
T2 decay
M xy (t ) = M 0e − t / T2
T2* decay
time
*
0.8
0.6
0.4
0.2
1 1 1
= +
T2* T2 T2/
M ⊥ (t ) = M ⊥ (0)e
1.0
0.0
0
1
2
*
t/T2
3
4
5
−t / T2*
B1 field off
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The MR Signal
T1 and T2 in tissues
• Only
spins tipped into the transverse plane can induce a signal.
• RF coils are used to receive the MR signal.
z
• The simplest example of an MR signal is the
free induction decay (FID).
y
RF coil
x
S
N
Tissue
T1
T2
T2/T1
Blood
1250 msec
250msec
(arterial)
1/5
Myocardium
900 msec
50 msec
1/18
Fat
180 msec
90 msec
1/2
Muscle
900 msec
40 msec
1/22
Free Induction Decay
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Contrast dependent on T1 and T2
The “Big” Picture
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Bo field aligns spins
B1 field tips spins to transverse plane
Signal from spins detected by a coil that picks up Mxy
Spins return to original state by:
% T1 relaxation – magnetization relaxes back to
longitudinal equilibrium
% T2 & T2* relaxation – coherent spins dephased
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Day Two: Echoes and Image Encoding
& Spin echoes
& Echo Time (TE) and Repetition Time (TR)
& Image contrast
& Gradients
& Slice selection
& In-plane image encoding
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