BASIC PHYSICS OF MAGNETIC RESONANCE IMAGING:
DRAW-A-LONG LECTURE NOTES.
by James Thompson, PhD
1. PROTONS & PRECESSION
Atoms are made up of different combinations of protons, neutrons, and electrons.
For example, the most common isotope of the most abundant element in the
universe, hydrogen (1H), is made up of a single proton.
Protons have a positive charge
They spin around on an axis, like the way the earth spins around on its North-
The positive charge on a
proton spins around with
it, creating an electrical
current. As we all know,
an electrical current also
generates a magnetic
Protons are normally aligned randomly. However, if you place them in an
external magnetic field (also called B1), they will align themselves with it. Some
will be in a low energy state, and align themselves parallel to the external
magnetic field. Others will be in a high energy state, and align themselves anti-
parallel to the external magnetic field.
At the normal temperature of the Earth’s surface, there will be close to even
numbers aligned parallel
and anti-parallel. Slightly
more will be parallel than
will be anti-parallel:
100,007 parallel for every
For every anti-parallel
proton, there is a parallel
one that cancels it out. As
there are slightly more parallel protons, the net magnetization of all these
protons will be in the direction parallel to the external magnetic field.
I lied a little – protons don’t quite line up with the external magnetic field.
Instead, they move around the axis of the external magnetic field like a spinning
top. This is called precession.
The frequency () at which they spin around the direction of B1 depends its
strength (B0) (measured in T or Tesla) and the gyromagnetic ratio () for protons.
This is the Lamour equation:
Protons in a 1 Tesla magnetic field precess at around 42MHz (that is, about 42
million times per second).
2. LONGITUDINAL MAGNETIZATION
It helps to describe the
precession of protons in an
external magnetic field using a
system. In this, the z direction
is the direction of the external
All of the spinning protons
have a magnetic field, which is
aligned in the z-direction, either parallel or anti-parallel. As the parallel magnetic
fields cancel out the anti-parallel ones, we end up with net magnetization in the z-
In theory, we can get this by summing the vectors that represent the magnetic
fields of all the protons that
are positive in the z-
At this point, all the protons
are precessing out of phase
with each other. This means
if we sum all the vectors in
the x- and y-directions we get
a big fat zero.
The magnetic field in the z-direction is known as longitudinal magnetization.
It’s just like longitudinal co-ordinates on a globe (remember, lat is flat, long goes
from North to South).
Unfortunately, we can’t measure longitudinal magnetization directly, because it is
in the same direction as the external magnetic field. Instead we need to perturb the
system in some way and then see how the field changes.
3. TRANSVERSE MAGNETIZATON
To perturb protons, we add a high-frequency pulse of energy, known as a
radio frequency (RF) pulse. This RF pulse exchanges energy with the protons,
causing some of the low energy (parallel) protons to go into a high energy
(anti-parallel) state. We call this excitation.
In order to transfer energy to the protons, the frequency of the RF pulse must
be as close as possible to the frequency at which they are precessing around
the z-axis. This is called resonance.
One effect of making some of the parallel protons go anti-parallel is to reduce
the longitudinal magnetization
Another effect is to make all the protons precess in phase with each other.
Now if we sum the x- and y-vectors we get something more than zero. This is
called an increase in transverse magnetization.
If we pick a point
on the x- and y-
plane and measure
magnetic field of
the protons as they
all precess past in
phase at the
frequency. This signal is one of the things that contributes to our images.
4. LONGITUDINAL RELAXATION
However, just turning the RF signal on and leaving it on doesn’t give us a lot
of information, because all the protons will act similar to each other,
regardless of what environment they are in.
Instead, we send a pulse of RF. When it is turned off, the protons will start to
go back to their original state.
First, those protons
that switched to the
when the RF pulse
was switched on
will start to go back
to their original
longitudinal magnetization in the z-direction will start to increase. This is
called longitudinal relaxation. If we plot longitudinal magnetization as a
function of time, we get a curve.
When longitudinal magnetization reaches 63% we get a value called T1
The process of going from high-energy back to low-energy involves emitting
energy to the surrounding environment. This environment is called the lattice.
Giving energy from spinning protons to the lattice is called spin-lattice
We mentioned above that in order for the RF pulse to transmit energy to
protons it must be at the same frequency as the protons are precessing. We
called this resonance. Well, it doesn’t need to be exactly the same frequency,
but the further away it is, the less efficiently is the energy transfer. The same
goes for protons giving off energy during spin-lattice relaxation.
If the lattice is spinning at the same frequency as the protons, then the energy
transfer will be fast and the protons will return to a low-energy state faster and
have a short T1. For example, carbon bonds in fat have a frequency close to
the precession frequency. Thus, the T1 of fat is relatively fast.
If the lattice is spinning at a different frequency to the protons, then the energy
transfer will be slow. Water spins much faster than the protons, so energy
transfer is less
efficient and the
relaxation to the
low energy state
resulting in a
Therefore, at the
T1 for fat we will
have more longitudinal magnetization coming from protons in fat than we will
from protons in water.
At higher external magnetic field strengths, protons spin faster and energy
transfer is less efficient. This leads to longer T1’s than at lower field strengths.
6. TRANSVERSE RELAXATION
As well as going from high-energy to low-energy, the protons do something else.
Remember that when the RF pulse was switched on, the protons all started
precessing in phase. Now, if we switch the RF pulse off, the protons will all start
to go back to being out of phase with each other. This is called dephasing.
Just like how putting
the protons in phase
led to an increase in
dephasing leads to a
magnetization in the
x- and y-direction. This is called transverse relaxation.
As it involves spins going out of phase with each other, we also call it spin-spin
Like T1, we can also plot transverse relaxation as a function of time. In this case,
it decreases as a function of time. The point at which the transverse magnetization
reaches 37% is called T2.
T2 relaxation is determined by two variables. One is minor variations in field
strength across the external magnetic field – called B0 inhomogeneity. The other
is local differences in the magnetic properties of different types of tissue.
If local magnetic fields are homogenous, such as water molecules that spin fast
and in a random fashion,
then it takes a long time
for the protons to go out
of phase. In these
circumstances, T2 will be
If local magnetic fields
are inhomogenous, such
as viscous, impure liquids
like blood, or fat, then protons go out of phase more quickly. This leads to
relatively shorter T2.
8. GETTING AN MRI SIGNAL
When we send in an RF pulse, we don’t just send in any type of pulse. To flip
some of the protons over to the high-energy state, we need flip the vector that
makes up longitudinal magnetization over by 90o. To do this, we need a pulse
with a flip angle of 90o.
Imagine we have 6 protons in the low-energy state contributing to longitudinal
magnetization. These are precessing out of phase with each other, giving us zero
We send in an RF pulse
that flips 3 of these protons
into the high-energy state
and also makes them
precess in phase with each
other. This reduces our
to zero, but gives us
The vector that gives us transverse magnetization looks like we have just flipped
the z-axis by 90o.
Now when we switch off the RF pulse, two things happen. The protons in the
high-energy state return to their low-energy state (longitudinal relaxation), and all
the protons start to go out of phase with each other (transverse relaxation. These
things happen simultaneously but independently from each other.
While the increase in longitudinal magnetization and the decrease in transverse
magnetization happen independently, we can represent the sum of longitudinal
magnetization and transverse magnetization as a sum vector. The horizontal
plane of this vector is determined by transverse magnetization, and the vertical
plane is determined by longitudinal magnetization.
This sum vector is what gives
us our MR signal. If we have
an antenna (or receiver coil)
nearby, we can record a
signal that oscillates at the
9. TR AND T1 CONTRAST
We know from earlier that different properties of the environment (or lattice)
affect the T1. So, we just wait for the longitudinal relaxation to reach the point of
maximum difference between two environments (e.g., tissue types), right? Well,
If we just send a pulse in and wait, we are going to get both longitudinal (T1) and
transverse (T2) relaxation contributing to our signal. Remember also that we can’t
just measure longitudinal magnetization – we need transverse magnetization to
get a signal.
To get a signal that gives us the best T1 contrast, we want to do things that
maximize the contribution of longitudinal relaxation differences. First, we send a
90o RF pulse. This flips the longitudinal magnetization vector by 90o. Then we
wait for some relaxation to occur.
At some point, the longitudinal magnetization vectors from the different tissue
types will be different. Then we send another 90o pulse, again flipping the
longitudinal magnetization vector by 90o. The difference in magnetization
between the two tissue types that was reflected in longitudinal magnetization will
now be reflected in the transverse magnetization, giving us MR signal differences
between the two tissue types. This is called T1-dependent contrast, and is the
basis of most anatomical MR scans.
If we wait to long
before repeating the 90o
pulse, both tissue types
will have reached
relaxation and we wont
be able to tell them
apart. Thus, for T1-
dependent contrast you
need to use a short
repetition time, or TR. As a rule of thumb, a long TR is around 1-2 seconds (the
time it takes for recovery of longitudinal magnetization) while a short TR is
10. TE AND T2 CONTRAST
T2 –dependent contrast is a little more difficult to explain. Remember, if we send
in a 90o pulse, not only do we flip the longitudinal magnetization by 90o, we also
make all the protons precess in phase.
Once we turn the pulse off, they start to go out of phase. The time it takes them to
get out of phase depends on B0 inhomogeneities and local magnetic
inhomogeneities depending on the properties of the tissue the protons are part of.
So different tissue types will show different rates of dephasing, this different rates
of transverse relaxation.
Protons that are
will be showing
Now, to get a signal
in which the
contribution comes from transverse magnetization and not longitudinal
magnetization, we need to be clever. Rather than sending in a second 90o pulse,
which gives us the T1 signal, we send in an 180o pulse.
There are no net effects to the MR signal from longitudinal relaxation, as it has
just been flipped upside down and doesn’t contribute to the transverse
The 180o pulse acts like a rubber wall, as it sends the protons spinning in the
opposite direction – back from where they came. At some point they will go back
in phase with each other and give us transverse magnetization.
The effect of this 180o pulse on spins is like an echo, that’s why we call it the
spin-echo. The time from the 90o being switched off until the 180o pulse is
switched on is one half of the echo time or TE. The full echo time is the time it
takes for all the protons to come back into phase after the 180o pulse.
occurs at a much faster
time scale than
Its on the order of a
Therefore, TEs tend to be
around 10 to 40msecs.
We can send as many 180o pulses as we want. One reason we might want to send
lots is because the effects of these pulses only acts to reverse dephasing due to B0
inhomogeneities. It doesn’t reverse the dephasing due to local tissue effects.
Therefore, while the 180o pulses will send the dephasing protons back into phase
and restore the transverse magnetization, eventually the signal will decrease after
multiple echos over an extended period of time. This is called T2 effects.
Different tissue types will show different T2 effects, giving us T2-dependent
11. T2* (pronounced T2-star)
We don’t need to send in a 180o pulse to view effects on transverse
magnetization. The dephasing that occurs after the 90o pulse, which is due to both
B0 inhomogeneity and local tissue inhomogeneity will contribute to this
dephasing. This is called the T2* –dependent contrast. T2* effects occur at a
much faster time scale than T2 effects – in the order of tens of milliseconds.
It’s not very good at
different tissue types, but is
good at measuring changes to
the local magnetic properties
(susceptibility) of a location.
So, just say you measure the
T2* from one point in space,
and then something happens
to change the local magnetic susceptibility of that point (like, for example, an
influx of oxygenated blood that has different magnetic susceptibility to the
deoxygenated blood). You will get a change in T2* signal. This forms the basis of
the blood oxygen level-dependent (BOLD) signal.
12. SLICE SELECTION
OK, so now we can get our MR signals from our different tissue types and
separate T1 and T2 effects. But at the moment we only have a 1-dimensional
signal. How can we localize things in the brain?
First thing is to be able to select brain slices. These are slices across which we are
going to form a 2 dimensional image describing the magnetization at every
horizontal and vertical location. We call these locations that make up an image
Selecting a slice is actually
pretty easy. Remember
that protons precess at a
frequency that is described
by Lamour’s equation. In
essence, this tells us that
the precession frequency
will vary as a function of
the strength of the external
magnetic field B0.
And remember that the transfer of energy from the RF pulse, called excitation,
depends on the match between the precession frequency and the RF frequency.
We called this resonance.
If B0 is uniform, then the RF will excite all the protons in whatever is in the
magnetic field equally. However, we can vary the magnetic field slightly
producing a gradient in B0. At one point in this gradient, the B0 will be slightly
lower, making the protons in that area of the field precess slightly slower. At other
points B0 will be higher, making the protons in that area of the field precess
Now, if we use an RF pulse that matches the slightly slower precession
frequency, we can excite only those protons spinning at that particular frequency.
This allows us to select that particular area of the field. If we use another, slightly
faster RF frequency, we can select another part of the field.
The thickness of the slices, and the spatial resolution of the images in the other
two directions, will be
determined by the
steepness of the various
gradients used. Steeper
gradients lead to larger
frequencies across a
given distance, thus
13. FREQUENCY ENCODING
The slice selection gradient allows us to select a slice in one direction. This
occurs at the point of excitation, when the RF pulse is turned on. For example,
for a person this might be across their body or head. A gradient that allows us to
choose this slice would run from head to toe. Now we want to locate the voxels
that make up that slice.
To do this, we can apply another gradient in a different direction, for example
from left to right. This will make the protons located from left to right spin at
different frequencies. This is called frequency encoding.
This time, unlike with slice selection, we are not exciting protons that are
spinning at a particular frequency. Instead, we are taking the ones we have
excited (go from low-energy to high-energy) and make them precess at different
This gradient is applied at the data acquisition stage, after we have done the
fancy things with RF pulses.
Remember that when we are recording the signal, the antenna (actually the
receiving coil) picks up a
signal being transmitted at
the precession frequency. We
can then use information
about the frequency that the
protons are precessing in
order to localize them in the
13. PHASE ENCODING
So we can select a slice in the head to toe direction by selectively exciting only a
slice of voxels by combining a gradient field with the RF pulse. And we can
localize voxels within this slice in the left to right direction by applying a
frequency encoding gradient and localizing these frequencies with the receiving
coils. Now we just need one more piece of information - that is the location of
voxels in the front to back direction.
Luckily, there is one more piece of information we can manipulate to localize
voxels. If we apply a brief, third gradient field in the front to back direction, the
protons will speed up to different extents depending on were they are in relation
to the gradient.
When this gradient is turned
off, they will go back to the
frequency determined by the
other gradients but will now
differ in phase across the
direction of the phase
encoding gradient. We can
then use this phase
information to determine
where voxels are in the front to back direction.
Like with frequency encoding, the phase encoding gradient is turned on and off at
the data acquisition stage.
It is important to note that the directions I have used here are arbitrary and could
all the swapped around. So you could select slices in the front to back direction,
use frequency encoding in the head to toe direction, and phase encoding in the left
to right direction etc etc…
We now end up with a slice which is made up of a 2-dimensional image
containing the frequency information on one axis and the phase information on
the other axis. The intensity of each data point in this image reflects the MR
signal strength at each frequency and phase.
The steepness of the slice
determines the slice
thickness. The steepness of
the frequency and phase
determines the in-plane
resolution (ie the size of
The 2-D Fourier transform takes any 2-D image and treats it as a combination of a
series of sinusoids and determines the amplitudes of the various frequencies and
their phases. The Inverse Fourier transform does the opposite, taking a series of
frequencies and phases and transforms them into a series of sinusoids. These can
make an image.
To get an image of the brain, we take the Inverse Fourier transform of the k-space
image and get a brain!
14. 3-D IMAGING AND GRADIENT ECHO SEQUENCES
While the procedure described above works great for anatomical images in which
we can collect 2-D data slice by slice over a 7-8 minute period, it’s not so good if
we want to collect data from the whole brain in a second or two.
More rapid techniques can collect 3-D data essentially all in one go, rather than
slice by slice. For example, methods used to measure changes in BOLD use 3-D
imaging methods. Briefly, rather than selecting a thin slice in the slice selection
stage, a thick slab or volume is selected.
Then, during the data acquisition stage, a second phase encoding gradient is used
to encode voxels in the slice direction. Because we also use phase encoding for
in-plane spatial encoding, this process can be a little tricky!
Also, while methods based on T2* effects don’t use the spin-echo methods
described earlier, they often use gradients to generate signal echo. Gradient echo
methods allow you to generate signal echo (send the protons back towards being
in phase) without losing sensitivity to local field susceptibility differences.