Transcript Document

Basic Physical Principles
of MRI
James Voyvodic, Ph.D.
Brain Imaging and Analysis Center
Synopsis of MRI
1) Put subject in big magnetic field
2) Transmit radio waves into subject [2~10 ms]
3) Turn off radio wave transmitter
4) Receive radio waves re-transmitted by subject0
5) Convert measured RF data to image
Many factors contribute to MR
imaging
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•
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Quantum properties of nuclear spins
Radio frequency (RF) excitation properties
Tissue relaxation properties
Magnetic field strength and gradients
Timing of gradients, RF pulses, and signal
detection
MRI uses a combination of Magnetic
and Electromagnetic Fields
• NMR measures magnetization of atomic nuclei in the presence
of magnetic fields
• Magnetization can be manipulated by manipulating the
magnetic fields (this is how we get images)
• Static magnetic fields don’t change (< 0.1 ppm / hr):
The main field is static and (nearly) homogeneous
• RF (radio frequency) fields are electromagnetic fields that
oscillate at radio frequencies (tens of millions of times per
second)
• Gradient magnetic fields change gradually over space and can
change quickly over time (thousands of times per second)
Radio Frequency Fields
• RF electromagnetic fields are used to manipulate the
magnetization of specific types of atoms
• This is because some atomic nuclei are sensitive to
magnetic fields and their magnetic properties are tuned to
particular RF frequencies
• Externally applied RF waves can be transmitted into a
subject to perturb those nuclei
• Perturbed nuclei will generate RF signals at the same
frequency – these can be detected coming out of the subject
Electromagnetic Radiation Energy
X-Ray, CT
MRI
What kinds of nuclei can be used
for NMR?
• Nucleus needs to have 2 properties:
– Spin
– charge
• Nuclei are made of protons and neutrons
– Both have spin ½
– Protons have charge
• Pairs of spins tend to cancel, so only atoms with
an odd number of protons or neutrons have spin
– Good MR nuclei are 1H, 13C, 19F, 23Na, 31P
Hydrogen atoms are best for MRI
• Biological tissues are predominantly 12C, 16O, 1H,
and 14N
• Hydrogen atom is the only major species that is
MR sensitive
• Hydrogen is the most abundant atom in the body
• The majority of hydrogen is in water (H2O)
• Essentially all MRI is hydrogen (proton) imaging
Nuclear Magnetic Resonance Visible Nuclei
Why do protons interact with a
magnetic field?
• Moving (spinning) charged particle
generates its own little magnetic field
• Spinning particles with mass have angular
momentum
A Single Proton
There is electric charge
on the surface of the
proton, thus creating a
small current loop and
generating magnetic
moment m.
m
+
+
+
J
The proton also
has mass which
generates an
angular
momentum
J when it is
spinning.
Thus proton “magnet” differs from the magnetic bar in that it
also possesses angular momentum caused by spinning.
Magnetic Moment
B
B
I
L
W
L
F
F = IBL
Force
t = IBLW =
IBA
Torque
m = tmax / B
= IA
t=mB
= m B sinq
Angular Momentum
J = mw=mvr
J
m
v
r
The magnetic moment and angular
momentum are vectors lying along the
spin axis
m =gJ
g is the gyromagnetic ratio
g is a constant for a given nucleus
Vectors and Fields
•
Magnetic field B and magnetization M are vectors:
–
–
–
–
Quantities with direction as well as size
Drawn as arrows ....................................
Another example: velocity is a vector (speed is its size)
Vector operations:
dot product AB cosq
cross product AB sinq
• Magnetic field exerts torque to line magnets up in a
given direction
– direction of alignment is direction of B
– torque proportional to size of B [units=Tesla, Gauss=10–4 T]
How do protons interact with a
magnetic field?
• Moving (spinning) charged particle
generates its own little magnetic field
– Such particles will tend to line up with external
magnetic field lines (think of iron filings
around a magnet)
• Spinning particles with mass have angular
momentum
– Angular momentum resists attempts to change
the spin orientation (think of a gyroscope)
[Main magnet and some of its lines of force]
[Little magnets lining up with external lines of force]
Ref: www.simplyphysics.com
Net Magnetization
Bo
M
Bo
M =c
T
Net magnetization
• Small B0 produces small net magnetization M
• Larger B0 produces larger net magnetization M,
lined up with B0
• Thermal motions try to randomize alignment of
proton magnets
• At room temperature, the population ratio of antiparallel versus parallel protons is roughly 100,000
to 100,006 per Tesla of B0
The Energy Difference Between
the Two Alignment States
D E = 2 mz Bo
DE = hn
n = g/2p Bo
known as larmor frequency
g/2p = 42.57 MHz / Tesla for proton
Resonance frequencies of common nuclei
To measure magnetization we
must perturb it
• Need to apply energy to tip protons out of
alignment
– aligned with magnetic field is lowest energy
– aligned opposite magnetic field is next lowest
energy state
• Amount of energy needed depends on
nucleus and applied field strength (Larmor
frequency)
Basic Quantum Mechanics Theory of MR
The Effect of Irradiation to the Spin
System
Lower
Higher
Basic Quantum Mechanics Theory of MR
Spin System After Irradiation
Precession
 If M is not parallel to B, then it precesses clockwise around
the direction of B.
“Normal” (fully relaxed) situation has M parallel to B, and
therefore does not precess
This is like a gyroscope
Derivation of precession frequency
t = m × Bo
t = dJ / dt
J = m/g
dm/dt = g (m × Bo)
m(t) = (mxocos gBot + myosin gBot) x + (myocos gBot - mxosin gBot) y + mzoz
This says that the precession frequency is the
SAME as the larmor frequency
RF Coil: Transmitting B1 Field
• To tip spins in the static B0 field we apply (transmit)
a magnetic field B1 that fluctuates at the precession
frequency and points perpendicular to B0 (how do we
achieve this? – by making a coil)
 The effect of the tiny B1 is
to cause M to spiral away
from the direction of the
static B0 field
 B110–4 Tesla
 If B1 frequency is not close to
resonance, B1 has no effect
A Mechanical Analogy: A Swingset
• Person sitting on swing at rest is “aligned” with
externally imposed force field (gravity)
• To get the person up high, you could simply
supply enough force to overcome gravity and
lift him (and the swing) up
– Analogous to forcing M over by turning on a huge
static B1
• The other way is to push back and forth with a
tiny force, synchronously with the natural
oscillations of the swing
– Analogous to using the tiny RF B1 to slowly flip M
over
g
NMR signal decays in time
• T1 relaxation – Flipped nuclei realign with the magnetic
field
• T2 relaxation – Flipped nuclei start off all spinning
together, but quickly become incoherent (out of phase)
• T2* relaxation – Disturbances in magnetic field (magnetic
susceptibility) increase rate of spin coherence T2
relaxation
• NMR signal is a combination of the total number of nuclei
(proton density), minus the T1 relaxation and T2 relaxation
components
Different tissues have different
relaxation times
Relaxation times are important
for generating image contrast
• T1 - Gray/White matter
• T2 - Tissue CSF
• T2* - Susceptibility (functional MRI)
MRI Scanner
Things needed for a typical MRI scanner
Strong magnetic field, usually from
superconducting magnets.
RadioFrequency coils and subsystem.
Gradient coils and sub-system.
Shimming coils and sub-system.
Computer(s) that coordinate all subsystems.
MRI scanner components
Using NMR signals for imaging
• Need to prolong and amplify the
decaying signal
• Need to know the spatial location of the
tissue generating the signal
The decaying NMR signal can be
recovered by realigning spins
Spin Echo
Imaging
Gradient Echo
Imaging
Spatial location is identified by using
spatially varying magnetic fields
Proton resonance with
uniform magnetic field
Proton resonance with
axial field gradient
It is actually spatial frequency, not
physical location, that is scanned
• Gradients cause spins to spread out and realign at
different times
• Bands of tissue with uniform spacing will realign
together
• MRI scanning systematically samples the strength
of the signal at different spatial frequencies
Horizontal sampling (Kx)
Vertical sampling (Ky)
MRI scanner collects spatial
frequency data (in k-space)
Horizontal spatial frequency density
Vertical
spatial
frequency
density
A 2-dimensional Fourier transform
mathematically converts from spatial
frequency to reconstructed MR images
The versatility of MRI arises from the
different types of tissue contrast that can
be generated by manipulating parameters
• TR – adjusting the time between acquisitions affects T1
relaxation
• TE – adjusting the time between refocusing pulses
affects T2 and T2* relaxations
• Timing of gradients affects sampling in k-space
• Additional gradient pulses before the RF pulse can
enhance specific tissue properties
• Chemical agents can further enhance image contrast