What referring physicians need to know about MRI physics

What referring physicians need to know about MRI physics
Magnetic resonance imaging is
rooted in a chemical technique known
as nuclear magnetic resonance (NMR).
Although this use of the word “nuclear”
has nothing to do with radioactivity, the
medical community has dropped that
emotion-laden word to become simply,
MRI. In this article, we will look at the
basic physical principles that make MR
imaging possible.
A moving electric charge produces a
magnetic field. The faster it moves or
the larger the charge, the greater the
magnetic field it produces. The nucleus
of a hydrogen atom, a single proton,
has a small positive electric charge and
is spinning very fast, thereby producing
a small, but measurable, magnetic field.
Think of a proton as a small magnet.
Water is the biggest source of protons
in the body, followed by fat. Normally,
the direction that these tiny magnets
point is randomly distributed.
Just as a compass aligns with the
earth’s magnetic field, a spinning proton
(often referred to as a spin) placed near
or within a large external magnetic field
(called Bø) will align with the external
field. But it’s not quite so simple. At the
atomic level, a little more than half of
the protons align with the field and a
little less than half actually align against
the field, canceling out most (but not
all) of the magnetic fields of those
aligned with the field. The number of
spins in excess, defined as the vector
Mø, is directly related to the strength of
the magnetic field. At 0.5 tesla, roughly
three protons out of 2 million will be in
excess. At 1 tesla it’s six out of 2 million
and at 1.5 tesla it’s nine out of 2 million.
All of the signal that is used to produce
MR images comes from these few
excess protons. This why high-field
scanners (1 tesla and above) have a
greater signal-to-noise ratio than midand low-field scanners (0.5 tesla and
If the MR signal comes from so few
excess protons, how is it possible to
detect the signal? A single voxel
(volume pixel) of water with
dimensions 2 x 2 x 5 mm3 (0.02ml) has
a total of 1.2 x 1022 total protons. Of
those, 6.02 x 1015 are in excess, or 6
million billion! So, even though a
spinning proton is a very poor magnet
and the excess fraction aligned with the
field is only a few parts per million, the
total number is still so large that an
appreciable signal is detectable.
A proton’s spin can be compared to
a toy top. Spin a top when orbiting in
the space shuttle (no gravity), and it will
spin cleanly about its axis. Spin a top on
the moon, where there’s little gravity,
and it will wobble or precess slowly
about the axis defined as the force of
gravity. Here on Earth the same top will
wobble more. Spinning protons also
wobble, or precess, about the axis
defined by the external Bø field. The
frequency of the precession is directly
proportional to the strength of the
magnetic field and is defined by the
Larmor equation:
ωø = у Bø
ωø is known as the precessional,
Larmor, or resonance frequency. y is the
gyromagnetic ratio and is a constant
unique to every atom. At the magnetic
field strengths used in clinical MRI
systems, .05 to 3 Tesla, the resonance
frequency of hydrogen ranges from 2.13
MHz to 128 MHz.
If an electromagnetic radio frequency
(RF) pulse is applied at the resonance
frequency, the protons can absorb that
energy (picture shining a light on
phosphorescent paint). At the quantum
level, a single proton jumps to a higher
energy state. At the macro or classical
level, to an observer in the external
laboratory frame of reference, the
magnetization vector, Mø, (roughly 6
million billion protons) initially pointing
in the Z direction, spirals down toward
the XY plane. If you could somehow
jump aboard Mø, just like a merry-goround, the laboratory would be rotating
around you. In this rotating frame of
reference, Mø would seem to tip
smoothly down. The tip angle, , is a
function of the strength and duration of
Magnetic Resonance Update
the RF pulse. Once the RF transmitter
is turned off, three things begin to
happen simultaneously:
1. The absorbed RF energy is
retransmitted (at the resonance
2. The excited spins begin to return
to the original Mz orientation (T1
recovery to thermal equilibrium).
3. Initially in phase, the excited
protons begin to diphase (T2 and T2
Once Mø (a magnetization vector)
has been tipped away from the Z axis,
the vector will continue to precess
around the external Bø field at the
resonance frequency ωø. A rotating
magnetic field produces electromagnetic
radiation. Since ωø is in the radio
frequency portion of the
electromagnetic spectrum, the rotating
vector is said to give off RF waves. So,
just like phosphorescent paint glows in
the dark, the absorbed RF energy is
now being retransmitted, thereby
producing the NMR signal.
The process of giving off RF energy
occurs as the spins go from a highenergy state to a low-energy state,
realigning with Bø. The RF emission is
the net result of the Z component (Mz)
of the magnetization recovering back to
Mø. Some of the energy does not make
it out of the patient but instead is
reabsorbed by the surrounding tissue,
referred to as the lattice. This type of
spin-lattice interaction is the result of
the excited system returning to thermal
equilibrium. In the classical description,
the Mz component begins to grow at
the expense of the Mxy component.
The time course whereby the system
returns to thermal equilibrium, or Mz
grows to Mø, is mathematically
described by an exponential curve. This
recovery rate is characterized by the
time constant T1, which is unique to
every tissue. At a time t=-T1 after the
excitation pulse, 63.2% of the
magnetization has recovered alignment
with Bø. At t=3T1, 95% of Mz as
recovered, and at t=5T1, more than
99% of Mz recovery has occurred.
MR imaging can use these
differences in Mz recovery rates to
differentiate between different types of
tissue. Acquiring an MR image requires
multiple “excitation-data collect” cycles.
The time between each cycle is known
as the repeat or TR time. The key
concept here is that it is only possible to
excite spins (and, hence, produce a
signal) that have an Mz component. Fat
has a very short T1 while CSF has a
very long T1. If our repeat time is fairly
short, say around 400 msec, then fat
will have recovered roughly 80% of its
Z magnetization and will appear bright
while CSF will have recovered only
10% and will appear dark.
When the spins (all 6 million billion
of them) are first tilted down to the XY
plane, they are all in phase. Think of a
playground with a million swings. If all
of the children are going up and down
together, at exactly the same rate, then
they are swinging in phase. Assuming
that all the children are pumping their
legs with the same force and frequency,
then they will stay in phase. But if one
child stops pumping for a few seconds
and another child pumps a little harder
or a little faster, then they will start to
get out of synch with everyone else.
The same type of thing happens to
precessing protons. For reasons
discussed below, some protons spin a
little faster while others spin a little
slower. Very quickly, they move out of
phase relative to each other, causing their
individual signals to interfere or cancel,
resulting in the NMR signal fading
How fast a proton wobbles or
precesses depends on the magnetic field
that it experiences. An isolated proton,
far from any other protons (or
electrons), is only affected by the main
Bø field. As protons (or spins) move
together due to random motion or
vibration, their magnetic fields begin to
interact. If the field from one proton
increases the field that the second
proton experiences, then the second
proton will precess at a slightly faster
rate. Similarly, if the first field opposes
the main field then the second proton
will precess more slowly. As soon as the
protons (or spins) move farther apart,
their fields no longer interact and they
both return to the original frequency,
but at different phases. This type of
random spin-spin interaction causes a
cumulative loss of phase across the
excited spins, resulting in an overall loss
of signal.
Similar to T1 relaxation, the signal
decay resulting from transverse or spinspin relaxation is described
mathematically by an exponential curve,
identical in concept to radioactive decay
with a half-life measured in tens of
msecs. The value T2 is the time after
excitation when the signal amplitude
has been reduced to 36.8% of its
original value (or has lost 63.2% - this is
the opposite of T1 where 63.2% of Mz
is recovered in one T1 period.) T2
values are unique for every kind of
tissue and are determined primarily by
the chemical environment with little
relation to field strength. Spins that
interact frequently, such as hydrogen
protons bound closely to proteins, will
have short T2 time constants while
spins in nearly pure water such as CSF
will have very long T2 time constants.
After the RF transmitter is turned
off, the protons immediately begin to
re-radiate the absorbed energy. If
nothing is affecting homogeneity of the
magnetic field all of the protons will be
spinning at the same resonance
frequency. The initial amplitude of the
signal is determined by the portion of
the magnetization vector (Mø) that has
been tipped onto the XY plane. This, in
turn, is determined by the sine of the
flip angle, a. The maximum signal is
obtained when the flip angle is 90.
(Remember, sin(0) = 0, sin(90) = 1.0)
The signal unaffected by any gradient is
known as the Free Induction Decay
(FID). The time constant that
determines the rate of decay is called
T2. An FID has no positional
For reasons that will be discussed
later, the time after exciting the spins
when the NMR signal is sampled or
recorded is called the echo time, or TE.
Imaging that emphasizes the differences
in tissue T2 values is accomplished
using long repeat times (TRs on the
order of 2500 to 6000 msec) to
eliminate T1 differences, and long echo
times, on the order of 80 to 120 msec.
This allows time for the signal from
tissues with short T2 values to decay
while not so long that the signal from
tissues with long T2 values is also lost.
There is a third tissue parameter that
also affects image contrast: the
concentration or density of protons.
Lungs have almost no water, bone has
very little, tissue has quite a bit and CSF
has a lot. T1-weighted imaging is done
with echo or data sampling times as
short as possible to minimize T2 decay
differences. T2-weighted imaging is
done with long TR times to minimize
T1 differences. If we simultaneously
minimize T1 and T2 differences by
using long TRs and short TEs, we are
left with images where the tissue
contrast comes from differences in
proton density.
T2 decay is caused by the random
interactions between spins temporarily
causing a change in the resonance
frequency of the interacting spins. The
underlying assumption here is that the
main external Bø field is absolutely
homogenous. In reality, there are many
factors creating imperfections in the
homogeneity of a magnetic field. The
main magnet itself will have flaws in its
manufacture. Every tissue has a
different magnetic susceptibility that
distorts the field at tissue borders,
particularly at air/tissue interfaces.
Patients may have some type of metal
on or in them such as dental work, clips
or staples. The sum of all of these
random and fixed effects is called
T2(pronounced T – Two star).
To summarize, T2 decay comes from
random causes while T2comes from a
combination of both random and fixed
causes. There is nothing that can be
done to prevent or compensate for
random losses in phase, but losses from
fixed effects can be compensated.
Consider the following race. The
contestants are a turtle, a bicyclist, you
in the pace car, an airplane and a rocket.
At the start of the race, everyone is
together (in phase). Once the race starts
(at t = 0), the contestants all move out,
each at their fastest pace. Soon, there is
a noticeable separation between them.
After some time, let’s call it TE/2, a
signal is given for everyone to turn
around and go back. Assuming all
contestants are still going at the same
rate as before, then after an additional
time, TE/2, they all arrive at the
starting/finish line together.
In terms of MR imaging, at the time
TE (TE/2 + TE/2) all the spins are
back in phase, producing a large signal.
This large signal is called a spin echo
and the time TE is called the echo time.
Here we present the principle of spin
echo formation in the rotating frame:
At time = ø, immediately after a 90 RF
pulse, Mø points along the Y’ axis. At
time of TE/2 is allowed to elapse while
the spins dephase (T2 mechanisms).
At t = TE/2, a 180 RF pulse is given
which flips the dephased vectors about
the X’ axis. Another TE/2 time is
allowed to pass while the vectors
rephrase. At t = TE, the vectors have
rephased and an echo of opposite sign
As described above, a 180 pulse can
be used to reverse the T2 dephasing
process and thereby produce a spin
echo. As soon as the spins all come
back into phase at the echo time, they
immediately start to go out of phase
again. A second 180 pulse will generate
a second echo. This process can be
repeated many times, producing many
echoes, as long as the pure T2 decay
mechanisms have left some signal to
work with. The ability to produce
multiple spin echoes after a single
excitation is the principle underlying the
technique known as fast spin-echo
imaging, which is beyond the scope of
this article.
MR imaging sequences can be
divided into two general categories, spin
echo and gradient echo. Spin echo
techniques always have an excitation RF
pulse, usually 90, followed by one or
more 180 refocusing pulses. The MR
signal is acquired at a spin echo time
chosen for the desired contrast. Spin
echo image sequences usually take one
to ten minutes, depending upon the TR
and number of averages. As already
stated, image contrast depends upon the
physical parameters of the tissues being
imaged. Due to its motion, blood is an
exception. The signal from blood can
be either strong or weak depending
upon a complex interaction of the TE
phase of the cardiac cycle and imaging
plane orientation. Usually, we try to
tailor spine echo sequences to produce
dark blood images.
As discussed earlier, any
inhomogeneity in the magnetic field
causes the spins to diphase. In gradient
echo imaging, a linear magnetic gradient
is intentionally applied for a brief time
causing the spins to diphase a known
amount. The direction of the gradient is
then reversed causing the spins to
rephrase and produce what is called a
Gradient Reversal Echo (GRE).
Without the 180 RF pulse, gradient
echo times are much shorter, usually on
the order of 2 to 8 msec, minimizing
the effects of T2 dephasing and also
resulting in bright blood. The excitation
RF pulse is usually much smaller than
90 which means less time is needed for
T1 recovery which means that TR times
are shorter which in turn leads to much
shorter imaging times, anywhere from
half a second to 20 or 30 seconds for
one or more images.
Magnetic resonance imaging is more
complicated than all other imaging
modalities combined. This article
touches on only a small part of the
physics of MR imaging. With that
complexity, however, comes an
amazing flexibility making MRI one of
the most important diagnostic tools
available to today’s clinicians.
References available upon request.
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