Introduction to MRI Principles
• Hardware
• Contrast: T1 e T2 (T2*) weighting
• Localization: phase coding and k-space
• Localization: volume limiting, slice selection
Struttura e funzione:
dall’avvento dell’imaging diagnostico …
Godfrey N. Hounsfield, CT 1969
Peter Mansfield, MRI
Paul
Lauterbur,
MRI
1973
Paul
Lauterbur
discovered
that
two-dimensional images could b
gradients in the magnetic field. In 1973, he described how additio
magnet made it possible to visualize a cross section of tubes with
heavy water. No other imaging method can differentiate between
Hardware - Scheme of an MRI scanner
(insets: main applications)
B1 63 MHz
B0 1.5T
G = | Gx,Gy,Gz|
Hardware Overview
The magnet produces the Bo field for the
imaging procedure.
The gradient coils for producing a
gradient in Bo in the X, Y, and Z directions.
The RF coil produces the B1 magnetic field
necessary to rotate the spins by 90o, 180o,
or any other value selected by the pulse
sequence. The RF coil also detects the
signal from the spins within the body.
The shield prevents the high power RF
pulses from radiating out through the
laboratory. It also prevents the various RF
signals from television and radio stations
from being detected by the scanner.
Hardware Overview
The heart of the imager is the computer. It
controls all components on the imager. The
RF components under control of the
computer are the radio frequency source
and pulse programmer. The source
produces a sine wave of the desired
frequency.
The Pulse programmer shapes the RF
pulses into apodized sinc pulses. The RF
amplifier increases the pulses power from
milli Watts to kilo Watts.
The computer also controls the gradient
pulse programmer which sets the shape
and amplitude of each of the three gradient
fields. The gradient amplifier increases the
power of the gradient pulses to a level
sufficient to drive the gradient coils.
Clinical system
0.5 – 3 T
Preclinical
system
Up to 11.7 T
NMR spectrometer
Up to 17.5 T
Magnet
The main characteristics of a magnet are:
Type (superconducting or resistive electromagnets, permanent magnets) closed,
tunnel-type MRI or open MRI.
Strength of the field produced, measured in Tesla (T). In current clinical practice,
this varies from 0.2 to 3.0 T. In research, magnets with strengths of 7 T or even 11 T
and over are used.
Homogeneity =
Its primary function is to generate a strong uniform
static field (B0) for polarization of nuclear spins in an
object.
Resistive magnets
Permanent magnets
Superconducting magnets
low field (< 0.15 T)
up to 0.3 T
over than 11 T
The Earth’s magnetic field is approximately equal to
0.5 G
1T = 104 G
Superconducting Magnet
The most commonly used magnets are superconducting electromagnets. These
consist of a coil that has been made superconductive by helium liquid cooling. A
superconducting magnet is an electromagnet made of superconducting wire.
Superconducting wire has a resistance approximately equal to zero when it is cooled
to a temperature close to absolute zero (-273.15o C or 0 K) by immersing it in liquid
helium. Once current is caused to flow in the coil it will continue to flow as long as the
coil is kept at liquid helium temperatures
Old
generation
New
generation
Superconducting Magnet
The length of superconducting wire in the magnet is typically several miles. The
coil of wire is kept at a temperature of 4.2K by immersing it in liquid helium.
The typical volume of liquid Helium in an MRI magnet is 1700 liters
In the event of loss of superconductivity, electrical energy is dissipated as heat.
This heating causes a rapid boiling-off of the liquid Helium which is transformed into
a very high volume of gaseous Helium (quench). In order to prevent thermal burns
and asphyxia, superconducting magnets have safety systems: gas evacuation
pipes, monitoring of the percentage of oxygen and temperature inside the MRI
room, door opening outwards (overpressure inside the room).
Superconducting magnets function continuously. To limit magnet installation
constraints, the device has a shielding system that is either passive (metallic) or
active (an outer superconducting coil whose field opposes that of the inner coil) to
reduce the stray field strength.
Helmoltz Coils for open magnet
Magnet bore creates sever problems: claustrophobia, very limited access to
patient. Open magnet scanners can be constructed by separating the main coil
into an Helmoltz pair. Main applications are in surgery.
Consider two identical circular loop of radius a, separated by a distance d, and
carrying the same current I in the same direction.
magnetic field of loop pair = sum of the two single loop fields.
Bz is uniform around z=0 when the
distance is chosen to be the same as
the radius of the loops.
This configuration has the ability to
generate a uniform field in the vicinity of
its midpoint
Helmholtz Coils (field uniformity)
d>a
d=a
a = 15 cm
a = 20 cm
d< a
a = 25 cm
Shim Coils
To obtain the most homogeneous magnetic field, the magnet must be finely tuned
(“shimming”), either passively, using movable pieces of metal, or actively, using
small electromagnetic coils distributed within the magnet.
The purpose of shim coils on a spectrometer is to correct minor spatial
inhomogeneities in the Bo magnetic field. These inhomogeneities could be caused
by the magnet design, materials in the probe, variations in the thickness of the
sample, sample permeability, and ferromagnetic materials around the magnet. A
shim coil is designed to create a small magnetic field which will oppose and cancel
out an inhomogeneity in the Bo magnetic field.
Gradient Coils
They produce a linear variation in magnetic field intensity in a direction in space. This
variation in magnetic field intensity is added to the main magnetic field, which is far more
powerful. The variation is produced by pairs of coils, placed in each spatial direction.
This modifies resonance frequency, in proportion to the intensity of the magnetic field to
which they are submitted (in accordance with Larmor’s equation: the stronger the field,
the faster they precess). This variation in Larmor frequency also causes a variation and
dispersion of spin phases.
IMPORTANT: the linearly varying field added by gradients is in the z direction, that
of B0. Keep in mind that gradient direction (which can be any, by combining x, y, z
gradients) refers to field “changes”, not to field direction.
Gradient characteristics
Gradient performances are linked to:
• their maximal amplitude (magnetic field variation in mT/m), which determines
maximal spatial resolution (slice thickness and field of view)
• their slew rate, corresponding to their switching speed: high slew rates and low rise
time are required to switch gradients quickly and allow ultra-fast imaging sequences
such as echo planar (EPI)
• their linearity, which must be as perfect as possible within the scanning area.
Gradient Coils
Assuming the standard magnetic resonance coordinate system, a gradient in Bo in
the Z direction is achieved with a Maxwell type of coil. Current in the two coils flow in
opposite directions creating a magnetic field gradient between the two coils. The B
field at one coil adds to the Bo field while the B field at the center of the other coil
subtracts from the Bo field.
Maxwell Coils for z-Gracdient
If the currents in the two loops are in opposite directions, the magnetic field along
the z-axis is then
When the distance is chosen to be
times of the radius of the loops,
Bz around z=0 is linear along z.
Helmholtz Coil
Maxwell Coil
Transverse (x & y) Gradient Coils
The X and Y gradients in the Bo field are created by a pair of coils (Golay Coils). The X
axis coils create a gradient in Bo in the X direction due to the direction of the current
through the coils. The Y axis coils provides a similar gradient in Bo along the Y axis.
Gradient Coils
RF Coils
RF coils create the B1 field which rotates the net magnetization in a pulse sequence.
They also detect the transverse magnetization as it precesses in the XY plane.
RF coils can be divided into three general categories:
1) transmit and receive coils (transceiver)
2) receive only coils and
3) transmit only coils.
An imaging coil must resonate, or efficiently store energy, at the Larmor frequency. All
imaging coils are composed of an inductor, or inductive elements, and a set of
capacitive elements. The resonant frequency, ν, of an RF coil is determined by the
inductance (L) and capacitance (C) of the inductor capacitor circuit.
There are many types of imaging coils:
Volume coils surround the imaged object
Surface coils are placed adjacent to the imaged object.
An internal coil is one designed to record information from regions outside of the
coil, such as a catheter coil designed to be inserted into a blood vessel.
RF Surface Coils
Surface coils are very popular because they have a good signal-to-noise ratio for
tissues adjacent to the coil. In general, the sensitivity of a surface coil drops off as the
distance from the coil increases. Here is an example of an image of the lower human
spine obtained with a surface coil.
RF Volume Coils
Radio frequency coil that surrounds either the whole body, or one specific region, such
as the head or a knee. Volume coils have a better RF homogeneity than surface coils,
which extends over a large area. The most commonly used design is a (birdcage) bird
cage coil.
Alderman-Grant Coil
Phased array coils
RF Coils – Surface vs. Volume
Surface Coil
vs
.
FOV
SENSITIVITY
SNR
Volume coil
24
RF Coils
25
In accordance with Kirchoff law, we obtain
The current is given by
If R=0
From which it is obvious that
I→Inf when
This phenomenon is called resonance and
frequency
is called the resonant
Tuning and matching
26
Variations in the size and tissue composition of the anatomy placed in an imaging coil
affect the amount of RF energy getting into and the amount of signal detected from
the imaged anatomy.
Tuning the probe entails adjusting two
types of capacitors on the RF probe
The matching capacitor matches the
impedance of the coil with imaged object to
that of the 50 Ohm cable coming from the
spectrometer.
The tuning capacitor changes the
resonance frequency of the RF coil.
Magnetic resonance – physical principles
27
In classical mechanics, spin I can be represented with a
rotation of the nucleus around an internal axis.
A rotating charge produces a magnetic moment m = I
where  is the gyromagnetic ratio of the nucleus. The
modulus is:
h
m =
I ( I  1) where h=Planck constant
2
Nuclei can be
considered as
magnetic dipoles.
Magnetic resonance – physical principles
28
• Magnetic moments corresponding to
1H take a pointing up (parallel to B ) or
0
a pointing down (antiparallel to B0)
orientation.
• The number of parallel magnetic
moments is larger than the number of
antiparallel magnetic moments .
• The magnetic moment orientation
inside the plane orthogonal to B0
(transverse plane) remains random.
• The result is a global magnetization
M0 along B0 (longitudinal
magnetization).
29
Magnetic resonance – physical principles
• The external magnetic field B0, trying to align the
magnetic moment m along the direction of B0, produces a
torque C=m X B0
• Rate of change of angular moment vector:
• Motion equation:
dμ
dt
=  μ  B0
• The result is that the
magnetic moment m
precesses around B0
keeping a constant angle.
dI
dt
= μ  B0
Precession
movement
B0
Spin
movement
Magnetic resonance – physical principles
The same condition subsists when a spinning gyroscope
precesses under the effect of gravity.
30
Magnetic resonance – physical principles
31
• The precession frequency is proportional to the external
magnetic field intensity:
f = 1/2π ·  · B0 Larmor frequency
• For 1H, if B0=1T:
f=42.57 MHz (radiofrequency)
• Precession angular velocity:
W=  · B0
The gyromagnetic ratio  is a characteristic of the nucleus
and represents the ratio between the magnetic moment and
the angular moment.
Nuclear magnetic resonance and signal
Spin up/down
precession
32
RF pulse  rotating transverse
magnetization Mxy
Static bulk magnetization
MZ = M0  no signal
f. Larmor
z
Precession at
f0 = 63 MHz
Larmor freq.
B0
1.5T
M0
B1 63
MHz
x’
Mxy  NMR signal at RF
spin-spin interaction:
RF signal decay  T2
z
y’
Mxy
63 MHz
spin-lattice interaction
MZ saturation recovery  T1
z
z
MZ <M0
y’
y’
y’
Mxy
x’
63 MHz
x’
63 MHz
x’
63 MHz
33
Spin echo
T1 and T2 contrast weight
Mxy
34
Weights in a spin-echo sequence
T2 weighting
M
M0
xy
( r ) =  ( r )  1  exp   TR / T1 ( r )   exp   TE / T 2 ( r ) 
 proton
T1
density
T2B
T2
T2A
TE
t
100 ms
Mz
Mxy
M0
T1A
T2A = T2B
Mz  Mxy
T1B
T1 weight in the
ripetition
 saturation
TR
100 ms
t
TR
100 ms
t
Contrast example: CSF, WM, GM
T1
[ms]
T1 weighted
image
35
T2
[ms]
White Matter (WM)
687
107
Gray Matter (GM)
825
110
Cerebro Spinal Fluid
(CSF)
1500
1500
T2 weighted
image
Example T1 image for GM, WM, liquor
segmentation
36
T1-3D, voxel 1x1x1 mm3, healthy subject, age 24. (Siemens Magnetom
Avanto 1.5T). Contrast of GM, WM, liquor.
Courtesy IRCCS S. Maria Nascente, Fondazione Don C.Gnocchi ONLUS, Milano
LOCALIZATION: PHASE ENCODING AND K-SPACE
37
1 – Gradient on develops phase shifts accumulate through time Tpe
fast
B(r) = B0 + G·r
slow
LOCALIZATION: PHASE ENCODING AND K-SPACE
2 – cosine and sine are developed into the material
Vector k describes
spatial frequncy value
and orientation
38
Acquisition of a Fourier Transform sample
Re
-FOV/2
at frequency
corresponding
to k value
c
39

(r)
-
d
1
Re[M’xy]|
-1
e
1
Im[M’xy]
-1
-FOV/2
X
X
X
X
FOV/2
X
r
amplitude of
NMR
r
|Mxy|(r) = ampiezza
RM
nel at
volume
f
In-phase and quadrature
demodulation samples
g and phase
amplitude
amplitude and
phase
Mxy(r) = ampiezza
e fase
-FOV/2
FOV/2
r
Integrazione
sul volume
fatta dall’antenna
Integration
over all volume
performed
by antenna
S (k ) =

VOL
M
xy
( r )  exp(  2 j k  r )  d r =
F M
Demod.
xy

(r ) (k )
S(k)
Magnetic resonance imaging: slice selection
40
As shown previously, MRI is volumetric and 3D scans are actually used.
However, slice selection greatly reduces acquisition time by reducing reconstruction
problem from 3D to 2D. The 2D FT is the most frequent acquisition protocol.
• A slice selection gradient (e.g, Gz) is switched on during excitation pulse.
• All the protons positioned in zp have Larmor precession frequency
Wzp=(B0+Gzzp)
• An RF pulse with frequency Wzp excites only nuclei with coordinate z=zp.
Magnetic resonance imaging: slice selection
any direction can be obtained
41
2D FT spin echo sequence
42
Slice selection
Phase endcoding – moves to raw ky
Phase endcoding
Spin Echo
Frequency endcoding
Frequency endcoding – gradient x during acquisition
causes progressive movement in kx direction
(note, frequency encoding is used as progressive phase encoding)