Download An introduction to the physics of magnetic resonance imaging.

An Introduction
See index terms
on page 383.
to the Physics
of
Resonance
Magnetic
Stephen
Baiter,
Imaging
Ph.D.
Editors Note:
Meetings
of the RSNA for many years has been the Symposium
on
by a committee
of the American Assoclaflon of Physicists In
with the Program
Committee
of the RSNA RadioGraph/cs
Is pleased to published the symposium
presented
on November
29, 1986 in conjunction
with the 72nd ScientifIc
Assembly
and Annual Meeting of the Society. The symposium, Introduction to the Physics of Magnetic Resonance
Imaging, will appear
serially throughout Volume 7 (1987) of the journal.
The first portion by Dr. BaIter, who chairs the AAPM Symposium Planning committee,
Is presented
here. Radiologists who wish to use this material for group teaching or who, for other reasons, desire It In
an audiovisual
format
are reminded
that this and most previous symposia are available as “slide-tape”
sets that may be ordered
by writing
to RSNA Educational Audio-Visual Materials,
P.O. Box 10168
Chicago, IL 60610, or by calling (312) 943-0450.
A valued
feature
of the Annual
Basic Physics prepared
Medicine in cooperation
and presented
In the 1980s, the technology
magnetic
resonance
emerged
of nuclear
from
the
labora-
tory and became
a major medical
imaging
technique.
The optimum
clinical application
this new entity can only be achieved
when
of
the
physician
understands
enough
of the basic principles to apply
the technique
to the requirements of imaging
an lndMdual
patient. This
essay, and those which will follow in succeeding
Issues of RadioGraph/cs,
will provide
a review of
those physical
and technological
principles
needed
for an adequate
clinical understanding
of magnetic
resonance
imaging
(MRI).
The technique
of nuclear magnetic
resonance (NMR) was initially developed
in the 1940s
by two independent
groups:
Bioch et al. at Stanford and Purcell et al. at Harvard. These groups
discovered that when certain atomic nuclei are
placed
into a strong magnetic
field their magnetic moments will precess around the field with
a known frequency.
A condition called resonance can be observed
by irradiating
the sampie with radio waves and measuring the interaction at the precessional
frequency.
(The terms
used in the preceding
sentences will be defined
and amplified
below.) Thus, the name nuclear
magnetic
resonance
is a short but precise doscription
of the process. NMP is a useful
technique
for analyzing
molecular
structure because the exact resonant frequency
of any
atom in a molecule
is influenced
by the magnetic fields of neighboring
atoms. In addition,
the time sequence
in which atomic nuclei Interact with the external magnetic
field and with the
perfurbing
radio frequency
(RF) field Is influenced by the size and shape of the molecules
as well as by their surroundings.
In the early 1970s, Damadian
introduced
the
concept of deliberately
modulating
the external
magnetic
field so that only one small volume
element
of the sample was in resonance
with
the RF field. By moving either the sensI1ve point
or the sample, he was able to form an Image of
the NMR properties
of his specimen.
In the same
time period, Louterbur devised a method
for
modulating
the
his specimen
field
so that
a line
in
By using back
projection
techniques,
similar to those used in
CT, he also was able to reconstruct
the NMR
properties
of his specimen.
Both groups realized
that deliberate
inhomogeneUles
in the magnetic
field could yield positional
Information.
In oddi-
Dr. Batter is Adjunct Associate Professor of Radiology, Cornell University Medical
Physicist, Philips Medical
Systems, Inc., Sh&ton,
ci.
Address
reprint requests to Stephen
Baiter, Ph.D., Philips Medical
Systems, Inc.,
Volume
magnetic
was in resonance.
7, Number
2
college,
710 Bridgeport
March,
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New Vorlc NV; and
1987
Avenue,
Senior
Shelton,
RadioGraphics
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Medical
CT 06484.
371
MRI physics
Balfer
tion, they were both able to scale the size of
their magnets
up to the point at which
the
“specimen”
became
a whole
body, and NMR
imaging
became
a reality. The last decade
has
seen an explosion
of image
acquisition
and
image
reconstruction
techniques.
When the
technique
was introduced
into clinical
practice,
there was public
confusion
beiween
nuclear
magnetic
resonance
imaging
and radionuclide
imaging.
This confusion
has been
minimized,
at
the suggestion
of the American
College
of
Radiology,
by renaming
the former
as magnetic
resonance
imaging
(MRI).
The basic principles
of MRI are shown in Figure I. With one key exception,
these are identical to the technology
of NMR spectroscopy
used
in the laboratory.
In both areas, the sample
is
magnetized.
A strong
radio frequency
(RF) signal, at the resonant
frequency,
is used to inject
the energy
needed
to excite
atomic
nuclei
in
the sample.
These nuclei
then emit an RF signal
for a brief period
of time. The use of controlled
nonuniformities
in the magnetic
field distinguishes
NMR from MRI. In the NMR laboratory,
great care Is taken to provide
an absolutely
uniform magnetic
field, and in many cases, the
sample
is rotated
during
the measurement
to
average
out any residual
magnetic
field inhomogeneities.
In MRI, deliberate
spatial
and
temporal
inhomogeneities
are introduced
into
the magnetic
field to provide
the information
needed
to form an image.
It Is appropriate
that we review
some elementary
physics
before
proceeding
to the details of MRI. First, is the concept
of magnetic
flux
density
(Figure 2). Magnetic
lines of force are
pictured
as vectors
emerging
from the north
pole of a magnet
and entering
the south pole
of the same magnet.
The strength
of the magnet
is described
by the number
of lines of force
crossing
a measuring
area between
the poles.
In the SI system of measurement,
the unit of
magnetic
flux density
is the tesla (T). Figure 2
gives some indication
of the relative
strengths
of
different
magnets.
The next principle
is that of
electromagnetic
induction
(Figure 3). A moving
charge
creates
a magnetic
field. If the charge
moves
in a straight
line, the lines of magnetic
flux wrap
around
the direction
of motion.
If the
charge
moves
in a circle,
the lines of flux com-
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bine so that they are perpendicular
to the plane
of motion
at the center
of the circuit. This motion
produces
a magnetic
dipole
or more descniptively a “bar magnet”.
Conversely,
if a magnet
is
moved,
it will generate
current
flow in a nearby
circuit
if the moving
lines of magnetic
flux “cut”
across the circuit.
Magnetic
1. Piace
2.
Resonance
patient
Perturb
Imaging
into uniform
equilibrium
Magnetic
magnetization
Field
with
RF Fieid
3. Observe
RF Emissions
from
perturbed
nuclei
Figure 1
If one looks at the classical
model
of a hydrogen
atom, there are three souces of moving
electrical
charge.
These are the motion
of the
electron
in its orbit, the intrinsic
motion
of charge
within the orbital
electron
as it spins, and the intrinsic motion
of charge
within the proton
(nudeus) as It spins. Each of these motions
gives rise to
an atomic
scale magnetic
dipole
(Figure 4). Nature tends to organize
itself so as to minimize
the
build up of effects
such as magnetic
fields; more
complex
atoms
possess atomic
magnetic
moments that are of the same general
strength
as
hydrogen,
or they may possess no net magnetic
moment
at all. This is due to the occurrence
of
atomic
and nuclear
spins in antiparallel
pairs;
each
member
of the pair cancels
the other’s
field. Nuclei
possessing
a net magnetic
dipole
must have an odd number
of protons
or an odd
number
of neutrons.
Nuclei
of biological
significance
with net nuclear
spins are shown in Table
I. It may be important
to remind
patients
that
these are all radiochemically-stable
isotopes
of
their respective
elements.
7, Number
2
MRI physics
Balfer
Magnetic
Flux
Density
Figure 2
Magnetic lines of force are pictured as vectors emerging
from the north pole of a magnet and entering the south
pole of the same magnet. A strong magnet is represented
by many lines of force. The magnetic flux density (B) is a
vector quantity; the arrow above the (B) is a reminder
that direction and magnitude are both important in a
vector.
B
Earth’s
Field
Household
Magnets
MR Magnets
-c
501i.T
mT
0.1 -4T
Motion
k1iiiIIIIIIi:
#{182}IjIII::
Figure 3
The principles of electromagnetic
induction: A moving
charge induces a magnetic field. The direction of the
field is determined by the direction of motion. Also, a
moving magnetic field can induce charges to move (a
current) in a circuit.
Proton
Electron
Intrinsic
Intrinsic
Electron
Orbital
Spin
Spin
Motion
Figure 4
Each of the motions present in an atom gives rise to a
magnetic dipole. In the hydrogen atom these motions
are the proton’s intrinsic spin, the electron’s intrinsic spin,
and the electron’s orbital motion. In a more complex
atom, the pairing of the electron and nuclear spins and
electron orbital motions largely cancels these effects.
TABLE I
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373
MRI physics
Balfer
When an atom with a net magnetic
moment is placed
in a magnetic
field, all of its
magnetic
moments
(electron
and nuclear)
will
try to align themselves
with the field. Because
the components
of the atom each
have
mechanical
angular
momentum,
they cannot
come
into complete
alignment
with the field.
The individual
components
of the atom will precess around
the direction
of the field, each
separate
component
of the atom will rotate
at
its own precessional
frequency.
The precessional
motion
of the magnetic
moment
around
the direction
of the external
field looks like the motion
of a spinning
top as it circles
the vertical
line
representing
the gravitational
field. To simplify
the discussion
and the drawings,
we will consider
only The nuclear
magnetic
dipole
and The precession
of The nucleus
about
The external
field
(Figure 5). The precessional
frequency
is given
by the Larmor
equation.
It is proportional
to the
strength
of the magnetic
field. It is also proportional
to the mechanical
and electrical
charge
distribution
of the nucleus.
The constant
of proportionalily
is called
the gyromagnetic
ratio. The
gyromagnetic
ratios of useful isotopes
are also
shown
in Table I. Thus, in any given
magnetic
field, each of the usable
nuclei will precess
at a
different
frequency.
The Larmor
equation
is
exactly
satisfied
at all times; any change
in the
field produces
an instantaneous
change
in the
precessional
frequency.
The ability
to change
precessional
frequency
by changing
field
strength
is critical
to image
reconstruction.
Also
shown in Table I are the relative
concentrations
of different
nuclei
in a typical
tissue. Perusal
of
this table
shows that hydrogen
is not only the
most abundant
nucleus
in tissue, but it produces
the strongest
signal for each
atom
present.
It
comes,
therefore,
as no surprise
that hydrogen
is the most important
nucleus
for MRI. It may be
worthwhile
to remember
the value for the gyromagnetic
ratio of hydrogen
is 42.#{243}
MHz/tesla.
When a patient
is placed
In a magnetic
field, each
individual
hydrogen
atom
will try to
align its magnetic
moment
along
the direction
of the external
field. In a classical
physics sense,
this alignment
is disturbed
by random
thermal
motions
of the atoms.
There is a continuous
activily of alignment
and disturbance.
An equilibrium is reached
that is dependent
on temperature and magnetic
field strength.
At body temperature
(300 K), only a few hydrogen
atoms per
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Larmor
Equation
to
=
Bo
y
=
Gyromagnetic
Ratio
Bo
=
Magnetic
Density
Flux
for ‘H
i_
2vr
=426M
T
rN
Figure 5
Because of the mechanical spin of the proton, its dipole
can not completely line up with the external field. The tip
of the dipole’s vector (represented by the arrow through
the proton) describes a circular motion about the vector
representing the external field (Bo). This motion is called
precession. The relation between the precessional frequency and the external field strength is given by the
Lanmor Equation.
Remember: the arrow over B0 indicates only that B0 is a vector
it does not indicate the direction of the external field.
quan-
tity;
million
are effectively
aligned
with the field of
the largest
MRI magnets.
(Figure #{243}).
Hence,
even
though
drawings
are made
showing
the patient
converted
into a bar magent,
only a minute
amount
of organization
is imparted
to tissue
when
a patient
is put into even the strongest
imaging
magnet.
(The reader
should
be aware
that these devices
are extremely
powerful
magnets in the conventional
sense and can pose
major safety problems
owing to their intense
attractive
force.
There have been
incidents
reported
in which
patients
and personnel
have
been
injured
because
of missile and torque
effects
in ferromagnetic
materials.
Safety issues
will be discussed
in a subsequent
article
in this
series.)
When the protons
precess
around
the direction of the external
magnetic
field, their angular
position
or phase
may be of importance.
This is
shown
schematically
in Figure 7. The relative
phases
of protons
in different
areas
of the patient are often
used as a portion
of the reconstruction
information.
Proton A is aligned
with its
spin antiparallel
to the field (a position
deliberateIy induced
by the pulse sequence
known
as
7, Number
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MRI physics
Baiter
Figure 6
The number of protons aligned with
the external field is an equilibrium between the alignment forces of the
field and the disruptive effects of thenmal motion. In an MR imagen, the
number of protons aligned is only a
few pen million protons present. Jhe
entire MRI process depends upon
these relatively few protons.
©
S
AB
Figure 7
Representation of phase relations between precessing
protons, Proton A is antiparallel to (Bo), protons B, C, D
are parallel to (Bo). Protons B and C are in phase relative
to each other. Proton D is precessing out of phase relative
to protons B and C.
Remember:
quantity;
the arrow
above
it does not indicate
inversion
recovery).
Protons
B,C,D are aligned
parallel
to the field. Protons B and C are precessing so that they are in phase
with each
other.
Proton
D is out of phase
with B and C.
When
a patient
is placed
in a magnet,
the
small atomic
dipoles
will combine
to produce
a
net magnetic
moment
(Mo). The temporal
growth
of the magnetic
moment
is exponential
because
of the interaction
of magnetic
alignment and thermal
disturbance
forces.
The time
B0 indicates
only that
the direction
of the external field.
B0 is a vector
constant
for this exponential
function
is called
the spin-lattice
relaxation
time or TI. In pure
water, TI is 2.8 seconds.
The value of TI will differ
for different
tissues and for different
pathological states, but it is typically
of the order of a few
hundred
milliseconds.
Nominal
values
of TI for
selected
tissues are shown
in Table 2. (The
reader
might observe
that the values
of TI are
somewhat
dependent
upon the strength
of the
external
magnetic
field.)
TABLE II
Tissue Relaxation Characteristics
nominal relaxation time in milliseconds
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MRI physics
Baiter
Unfortunately,
it is impossible
for an external
observer
to directly
measure
the growth
of the
net tissue magnetization
(Figure 8). This is because
the phases
of the individual
precessing
hydrogen
atoms
are random,
and there is no
net flux produced
that will be available
to cut
across the loop and, thereby,
induce
a signal in
the observer’s
probe. This is modeled
by picturing
the net magnetization
vector to lie in the direction
of the external
field (longitudinal
direction).
If the net magnetization
could
be tipped
(notated)
so that it would
lie at a 90-degree
angle
to the external
magnetic
field, and if
simultaneously
all of the protons
could
be
caused
to precess
in phase,
then the precessional
motion
would
generate
a net moving
magnetic
signal which
could
be measured
by
the observer
(Figure 9). This, in fact, is adcomplished
by irradiating
the patient
with a
burst of radio frequency
energy
at exactly
the
Larmor
precessional
frequency.
The phases
of
the individual
atomic
dipoles
will be synchronized
by the external
RF signal. The amount
of angular
rotation
of the net magnetization
vector
(tip) is controlled
by the amount
of RF
energy
applied
to the patient
(Figure 10). After a
90 degree
tip, the net magnetization
lies in the
plane
perpendicular
to the external
magnetic
field (transverse
plane).
This vector
rotates
in the
transverse
plane
with the Larmon frequency.
It is
noted
that pulse powers
of hundreds
of watts
are required
to tip the spins and that the resulting precessional
signal seen by the observer
has
a strength
of a few microwatts.
Since both the
transmitted
and received
signals
must be at
exactly
the same frequency,
considerable
engineering
design
is needed
to separate
one
from the other. As will be seen, this is achieved
by the temporal
separation
obtained
from a
spin-echo
pulse sequence.
Mo
S
1
M
/\Mo
Figure 8
The net magnetization
of the patient is represented by a vector (Mo). The net magnetization grows exponentially toward its equilibrium
value, Mo, with a time constant, TI. As the mdividual precessing atoms align with the field,
they will have random phase. No net external
signal is produced.
Bo
N
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MRI physics
Baiter
S
Figure 9
The patient’s net magnetization
vector (M) has
been rotated (tipped) into the plane which is
perpendicular
to the direction of the external
magnetic field. This process is done in such a
manner as to align the phases of all of the precessing protons. This is represented as a precession of (M) in the transverse plane. An externally
observable signal is produced.
N
S
Bo
Figure 10
The tip of (M) from the longitudinal direction
into the transverse plane is accomplished
by
irradiating the patient with radio waves at the
Lanmor frequency (as a reminder, the transmitten is given the call letters WLF). The protons
initially will all be in phase relative to each
other.
42.6
MHz
I
N
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MRI physics
Baiter
Under ideal conditions
(i.e., a perfect
magnet), as soon as the observer
detects
the signal,
he observes
that it decays
in an exponential
fashion
with a time constant
T2 (Figure
II). In
most cases, T2 (the spin-spin
relaxation
time) is
less than TI. The loss of signal
is due to Iwo effects: the first is the return of individual
nuclear
dipoles
into alignment
with the main field; the
second,
and usually dominant
process,
is due to
loss of phase
coherence
between
those spins
remaining
in the transverse
plane
(Figure 12).
These activities
are separate
processes.
In a substance
such as pure water
placed
in a perfect
magnetic
field, there is nothing
available
to disturb phase coherence.
In this special
case, TI = T2.
In all other cases, TI is greater
than T2. Nominal
values for T2, for different
tissues, are also given
in Table 2. It can be seen that the values
of TI
and T2 for different
tissues do not have the same
ratio. It can also be seen from the table that this
ratio is dependent
upon magnetic
field strength.
The net spin state of tissue can be manipulated
by controlling
the time of application
of RF
pulses and magnetic
field gradients.
These combinations
are called
pulse sequences.
It is worthwhile to examine
patients
using, at least, Iwo different
pulse sequences;
one, to produce
contrast resulting
from TI differences
between
tissues, and a second
to produce
contrast
resulting
from T2 differences
beiween
tissues. The reader
should
also note that the TI and T2 differences
between
different
tissues are much greater
than
the differences
in proton
density
between
these
tissues. Hence,
MRI is capable
of producing
greaten tissue differentiation
than CT. It cannot
be
overemphasized
that observed
tissue contrast
is a
function
of both the tissue and the technique
used
for imaging.
An inappropriate
technique
can
cause a total loss of contrast
and may even cause
contrast
reversals.
S
I
12
iL’’
I
1
Figure 11
Decay of the observable signal: Under ideal
conditions the observer will note that the signal
decays with an exponential time constant T2.
For most substances T2 < TI.
N
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3
4
5
MRI physics
Baiter
S
Figure 12
ML
The loss of signal is due both to a return of mdividual dipoles to alignment with the external
field and to a loss of phase coherence between
the precessing dipoles remaining in the tnansverse plane. In general, these are separate
processes.
MT
N
In a real magnet,
the net signal decays
even more rapidly
than predicted
by the T2
curve
(Figure
13). The actual
loss of signal
is
known
to have an exponential
form. The time
constant
for this phenomenon
is called
T2*, Because
there are variations
in the external
magnetic field in the parts per million
range,
all of
the protons
in the patient
will not have exactly
the same precessional
frequency.
Those protons
located
in a higher
local field will precess
a tiny
bit faster than those in a lower local magnetic
field. This will alter the relative
phases
of protons
in different
locations.
As time goes by, the minutely different
notation
speeds
will alter the
relative
phases
of protons
in different
locations.
This causes a loss of signal which typically
occurs
in a few milliseconds;
a short time relative
to the
tens of milliseconds
characteristic
of T2 and a
very short time compared
with the hundreds
of
milliseconds
characteristic
of TI.
.1\
1/
(
I
II
III
Figure 13
In a neal magnet, minute variations in the external field cause a rapid exponential loss of
phase coherence with a time constant T2”, In
general T2* << TI. At time I, all of the proton
dipoles are in phase coherence and the extennal signal is at a maximum. At time II, the protons in stronger fields have precessed a bit
more rapidly resulting in a spread in phase and
a weaken external signal. At time III, the spread
has progressed to a point at which the phases
of the protons are uniformly dispensed resulting
in no external signal.
time
,
.
;j,#::II
Tj
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379
MRI physics
Baiter
In Figure 14, one sees the situation
that occurs when the spins are losing phase coherence
because
of variations
in the external
magnetic
field. I, All of the protons
are precessing
in the
transverse
plane,
the observer
is looking
down
on this plane from one of the poles of the magnet. The instantaneous
direction
of each
of the
spins lies somewhere
in the “spin phase
bundle”
beiween
F and S. (For simplicity,
only the leading
and trailing
edges
of the spin phase
bundle
are
shown.)
It is possible
to flip the entire spin phase
bundle
like a pancake,
so that instead
of the
faster spins (corresponding
to protons
in a
stronger
field) being
ahead
of the slower
ones
in relative
phase,
they are behind
them.
2, This
flip is produced
by supplying
an additional
RF
pulse with enough
energy
to flip the spins of
each
of the protons
by 180 degrees.
Eventually,
the faster spins catch
up in phase
with the
slower spins, resulting
in a strong external
signal.
3, This is called
an echo. A little later, the fast
spins have outraced
the slow spins, resulting
in
another
loss of signal, 4. The process
may be repeated
and multiple
echoes
may be observed.
Because
of the T2 decay
of the signal, each
echo
is weaker
than its predecessor.
Eventually,
the loss of phase
coherence
caused
by T2
effects
eliminates
the possibility
of observing
further
echoes.
The description
of the timing
of radio frequency
pulses and magnetic
field gradients
is
called
a pulse sequence.
Clinical
image
contrast is determined
in large part by the selection
of the appropriate
pulse sequence.
It is, therefore, worthwhile
for the clinician
to become
adcustomed
to this notation.
The RF portion
of a
typical
pulse sequence
is shown
in Figure 15. This
example
is called
a spin-echo
sequence
because the clinically
useful data is obtained
from
the echo. It is the most common
sequence
used
for clinical
MR imaging.
The entire
pulse sequence
is repeated
periodically
with a time interval
called
the repetition
time, TR. A clinical
study will involve
repeating
the pulse sequence
several
hundred
to several
thousand
times. The
time between
the start of the initial pulse and
the maximum
echo strength
is called
the echo
time, TE. The center
of the 180 degree
pulse is
located
at time TE/2. In an actual
MRI scanner,
the initial signal, called
the free induction
decay
(FID), is ignored and the clinical data is based
upon the echo. This Is the principal
way in which
the transmitted
stimulation
and the received
signal are isolated
from one another.
Figure 14
CD
I
V
WLF
2F
2
:
3
4
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The formation of a spin echo: At some time (I), the spins
are losing phase coherence due to variations in the external magnetic field. The vectors representing the spins
of individual protons are contained in the arc between F
and S. The vector representing the fastest proton is F, that
representing the slowest is S. The protons are precessing
in the direction of the circular arrow. At time (2), a pulse
of RF energy is injected at the Larmon frequency by the
same transmitter that was previously used to tip the spins.
This flips each of the spins by 180 degrees in phase so
that now the fasten spins are behind the slower ones. At
time (3), the faster protons have overtaken the slower
ones resulting in a regrowth of coherence and a
reemergence
of the external signal (the echo). At a
further time (4), the fasten protons have passed the slower
protons causing another loss of phase coherence and
another loss of the external signal.
7, Number
2
Baiter
MRI physics
18
iaO#{176}
Figure 15
Spin-Echo Pulse Sequence: This is a representation of the RF portion of a common
clinical sequence. The entire sequence is
repeated periodically (several hundred to
several thousand times) during the course of
a study. The time interval between one repetition of the sequence and the next is called
TR. It is usually measured between the 90degree RF flip pulses. The time between the
90-degree pulse and the peak of the echo
is TE.The 180-degree flipping pulse occurs at
time TEI2. Note that exactly twice as much
RF energy is required for the 180-degree as
for the 90-degree pulse. The flipping sequence is shown again in this illustration,
900
900
echo
TR
=
TE
=
Repetition
Echo time
time
4
‘Lt
e
k*:E?
*E
The received
signal can be characterized
by its frequency
and phase
as well as by its intensily. The frequency
and phase
information
are used to localize
the source
of the signal spatially. The signal
intensity
itself, in turn, is a function of the number
of accessible
protons
in the
measuring
volume,
the flow of protons
through
the volume,
the presence
of natural
or enhanced
concentrations
of paramagnetic
nuclei,
and the relaxation
constants
TI and T2. The contnibution
of the relaxation
constants
of each tissue to the received
signal strength
is critically
influenced
by the pulse sequence
used for scanning. To repeat:
The available
MR signal, and the
contrast
in MR signals beiween
tissues is dependent both on intrinsic tissue properties
and upon
all of the operating
parameters
of the scanner.
The details
of these processes
will be the subject
of later articles
in this series. The selection
of the
appropriate
pulse sequence
required
for the
examination
of an individual
patient
involves
the
use of careful
clinical
judgment
coupled
with a
firm understanding
of the technology.
This will
also be discussed
in a separate
article.
The distinguishing
feature
beiween
magnetic resonance
imaging
and NMR spectrosdopy
is the use of deliberate
magnetic
field gradients
for spatial
localization
of the signal. This is adcomplished
by appropriately
shaping
the magnetic field and by a corresponding
selection
of
the frequency
content
of the RF pulse. The
simplest
example
of the use of magnetic
gradients
is slice selection
(Figure 16).
Figure 16
Slice Selection Gradient: The magnetic field is made slightly nonuniform
in the axial (7) direction. The 90-degree
flipping pulse is given a limited frequency content. Only those protons
that satisfy the Lanmor equation are
flipped. In this case, this selection conresponds to a transverse plane
through the patient.
higher precessKn frequency
precession
frequency
excitation
frequency
=
lower precession frequency
single excitation
frequency
Volume
7, Number
2
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#{149}
381
MRI physics
Baiter
In this example,
the magnetic
field is made
slightly nonuniform
along the patient’s
longitudinal axis (i.e., the Z direction)
b,’ supplying
power
to a gradient
electromagnet.
If the RF pulse contains only one frequency,
then only one transverse plane
in the patient
will meet the requirements
of the Lanmor equation.
Only the protons
in this plane
will absorb
the energy
from The
transmitter
and will be flipped
into the emitting
position.
The emitted
signal can come
only from
protons
in that plane.
This still leaves
the problem of deciding
where
on the plane
any panticular
portion
of the signal originates.
The next
step is to apply
a second
magnetic
field gradient in the active
plane only during
the readout
of the echo.
This readout
gradient
is applied
in
the X direction
in Figure 17. This gradient
will
cause the protons
to precess
at a slightly higher
frequency
where
the field is stronger
and at a
slightly
lower frequency
where
the field is
weaker.
Remember
that only those protons
in
the previously
selected
slice are emitting
a signal. This signal will now contain
a band
of frequencies,
and the RF intensity
at each frequency
will correspond
to the protons
found
in one line
of tissue in the preselected
slice. By electrically
notating
the direction
of the readout
gradient
and repeating
the process
many times, one obtains enough
information
to reconstruct
the patient’s cross section
using CT mathematics.
Many MRI scanners
use the phase
information present
in the emitted
RF echo to obtain
still further
information
about
the distribution
of
signal
in the patient.
If a third orthogonal
gradient, i.e., in the V direction,
is applied
during
the
time of the initial free induction
decay,
it is possible to speed
up the the precession
of the protons proportional
to their V coordinate
(Figure
18). When the V gradient
is switched
off, each
proton
returns to precessing
at the original
frequendy,
but, because
of the previous
speedup,
the phases
of spins now differ along
the V axis.
A brief analogy
may be appropriate
to demonstrate the use of frequency
and phase
information for spatial
localization.
A small choir is shown
in Figure 19. We would
like to know how loud Jim
is singing.
If we happen
to know that Jim is a
tenor, then we know that he is in the column
with
all of the other tenors.
But, how do we know
which tenor is Jim? If the choir is singing
a round
Gz
phase-encoding
mae
gradient
/
p-on
G x
gradnt
G
frequency
/
/
frequencies
fres
onginal
frequency
hher
frequencies
frequency
Figure 17
Frequency Encoding: By applying a gradient in the X direction during the readout process, protons in different lines in
the selected plane are caused to emit their signal at different frequencies.
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Volume
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frequendes
Figure 18
Phase Encoding: By applying a gradient in the V direction
during the initial free induction decay, the relative precessional phases of protons are made proportional to the V
coordinate in the selected plane. Different magnitudes of
this gradient are required for different pulses in a complete
pulse sequence.
7, Number
2
Bolter
MRI physics
(i.e., Three Blind Mice),
each
row will be singing
a different
portion
of the round. That is to say,
each
row will be singing
in a different
phase.
If
we now happen
to know which
phase
Jim is
singing,
then we have him uniquely
identifiedhe is the only tenor singing
the third phase
of
three
blind mice. Although
the mathematics
of
image
reconstruction
is more complex
than our
simple
analogy,
the principle
of isolating
a pixel
by using its phase
and frequency
information
are identical.
In conclusion,
let us review
a typical
pulse
sequence
(Figure 20). The magnetic
field gradients
lGx, Gy, Gz) are used to reconstruct
the
positions
of MR emitters
in the patient
and the
relative
strengths
of the signals
are determined
by the pulse timing
parameters
TR and TE. The
optimum
strategy
for examining
patients
requires that the technical
parameters
must be
related
to the clinical
question.
In addition,
due
consideration
must be given to safety as well as
efficiency.
Future articles
in this series will cover
all of this material
in detail.
S
A
T
B
Jim
2
iE;E
Figure 19
Analogy of Frequency and Phase Encoding: How loud is Jim
singing? Jim is a tenor, so he must be in the tenon’s column
of the choir. He is also singing the third pant (phase) of Three
Blind Mice so he must be in the third now. Jim is now uniquely
identified among the members of the choir.
Figure 20
A more complete spin-echo pulse sequence.
The magnetic field gradients are shown, Gz is
the slice selection gradient, Gy is the phase encoding gradient (different intensities are applied at different times during the study), and
Gx is the frequency encoding gradient. Note
the relationships between the various magnetic
field gradients, the RF pulses, and the observed
signal intensity 5(t). Note that IR is not drawn to
scale.
RadloGraphlcs
index terms:
Magnetic
Resonance
Imaging
physics
Magnetic
Resonance
Imaging
radIation
physics
cumulative
Magnetic
physics
Index terms:
resonance
(MRI),
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