MRI SIMPLIFIED
Parth Patel
MIV, USC SOM
LET US PROBE INSIDE THE
MAGNET
IT'S ALL ABOUT PHYSICS
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Recall that molecules are made of atoms and
atoms have a standard structure.
Electrons are at the periphery and nucleus is in
the center.
The nucleus contains protons and neutrons.
Electrons, protons and neutrons (elementary
particles) all have unique properties.
ONE OF THESE UNIQUE PROPERTIES IS
SPIN.
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Spin is a quantized phenomena that occurs due
to angular momentum.
Think of it as a planet spinning on its axis or a
spintop.
The spin is mathematically described as a
magnetization vector.
The reason for not manipulating the spin of
electrons is that they are usually paired since
most atoms exist in a stable state in nature.
SPIN WOBBLING EFFECT
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Spins wobble or precess about the plane of
magnetic field (B0).
This spin frequency is called the Larmor
frequency (ω0) and it is directly proportional to
the strength of magnetic field.
ω0 = γ B0
MAGNETIZATION VECTOR
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The spins can be broken down into two
perpendicular components: a longitudinal or
transverse component.
In a B0 magnetic field, the precession
corresponds to rotation of the transverse
component along the longitudinal axis.
RESONANCE
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Resonance relates to the transfer/exchange of
energies between two systems at a specific
frequency.
It is analogous to talking to someone on your
cell phone.
In magnetic resonance, only protons with the
same frequency as the RF pulse will respond.
During RF pulse delivery nuclei become excited
and then return to equilibrium.
During equilibrium, they emit energy in the form
of electromagnetic waves.
ELECTROMAGNETIC WAVES
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In brief, this can be thought of as the light we
see but with different frequencies.
The frequency is directly proportional to the
energy and inversely proportional to the
wavelength.
This is the crux of wireless communications that
we encounter in our daily lives.
EXCITATION
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During excitation, protons “jump” to a higher
energy level.
Also, the net magnetization vector spirals down
to the transverse plane (XY plane).
The degree to which the net vector moves down
is called the flip angle.
The flip angle is a function of strength and
duration of the RF pulse.
RELAXATION
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After excitation, the protons emit RF pulse of
their own.
This is the nuclear magnetic resonance signal
in the form of electromagnetic waves (ie: raw
data)
Longitudinal relaxation and transverse
relaxation are the two different mechanisms by
which this occurs.
RELAXATION - T1
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One can see that T1 measures the duration by
which the magnetization vector reverts to the
natural longitudinal direction in a B0 magnetic
field. This duration measures the degree to
which the spins are being disrupted by the
surrouding tissue (a.k.a. spin-lattice relaxation)
RELAXATION - T2
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One can see that T2 time is the duration in
which the magnetization vector decays in the
transverse direction since the spins interact
with each other causing them to be out of phase
(a.k.a. spin-spin relaxation)
RECEIVING THE SIGNAL
When the protons emit RF signal (Electromagnetic radiation) as they relax,
the signal induces a current in the receiving coil and this is the manner in
which raw data in MRI is obtained.
Recall from physics that changes in magnetic flux induces an electromotive
force (i.e. voltage). This physical law (Faraday's law) absolutely runs our
24/7 economy! We couldn't generate electricity efficiently in a large
magnitude without this law.
Electromagnetic waves have both an electric and magnetic field components
perpendicular to each other. When the EM waves strike the receiver coil in
the MRI machine, the change in magnetic flux induces a current.
SUMMARY OF NMR SIGNAL
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In brief, we apply an initial magnetic field, B0
and the protons align with the field while
processing at a frequency proportional to the
magnetic field strength.
We then send RF pulse in the transverse plane
(like pinging a wine glass) and the protons align
and process accordingly.
Thereafter, protons relax in different two ways
via emitting RF pulses.
This allows us to recognize environmental
differences of protons in a given tissue sample.
MAKING USE OF NMR DATA
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The key to obtaining an MRI image is to impart
spatial resolution, use the data from resonance
to fill up a matrix of voxels, and perform a
mathematical calculation called Fourier
transform.
First let us talk about spatial resolution.
The way we do this is by applying a gradient of
magnetic field in order to obtain spatial
information.
SPATIAL RESOLUTION
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If we didn't have a magnetic field gradient, our
image would just look like one big 'blob' without
obtaining any anatomical information. This would
be called free induction decay. We will learn this a
bit later but one needs to have more than one
frequency peak (shown below) to obtain an image.
SPATIAL RESOLUTION CONT'D.
Spatial resolution achieved through gradient field
is nicely depicted in this figure below.
FILLING UP K-SPACE
Simply put, k-space is a matrix usually 512x512
that is used to store data acquired from magnetic
resonance of protons. The math is complex but
there is an analogy to this.
Recall that CT scan uses a similar matrix and then
calculates the numbers to add up photons
received in both x and y planes.
K-SPACE
The k-space is filled up in iterations by using the
resonance data obtained from magnetic field
gradients.
First, we select a slice (in millimeters) by applying a
field gradient in the horizontal plane.
Within this slice we try to map out objects in both x
and y planes by collecting raw data in these planes.
The y-plane is called phase encoding direction. To
obtain this one has to apply field gradient in the
vertical (or y-plane) direction.
The x-plane is called frequency encoding direction.
To obtain this one has to apply field gradient in the
horizontal (or x-plane) direction.
K-SPACE
This is an example of how the matrix is filled with
data during each slice.
K-SPACE
The top image shows process of slice selection, and bottom
left shows the phase encoding data where as bottom right
shows frequency encoding data.
K-SPACE
The phase encoding direction acts as a sieve which is
sensitive to only vertically distributed data. In real life, the
filters will obviously be many more than depicted in the last
slide.
Vice-versa, the frequency encoding direction acts as a sieve
which is sensitive to only horizontally distributed data.
One can imagine that if we continued to do this for slices
upon slices then we would get a stack of data which we can
scroll through hence creating a vivid image.
K-SPACE → IMAGE FORMATION
Now that we have completed the daunting task of obtaining
data in different planes, how can we make an
image?...Fourier transform, of course!
I would like to briefly talk about music since this analogy
eases the pain of learning Fourier transform rigorously.
Imagine the following: say, we have a sound tracing of a
song and we know what instruments (including the voice
box) were involved in making the final song. Suppose we
wanted to know what instruments were being played at what
time in the sound tracing so that we could create a mental
picture of how the music was composed (i.e. arrangement)
FOURIER TRANSFORM (FT)
ANALOGY
Observe the sound tracing below. Each tracing
corresponds to a different harmonic (or frequency).
Instruments are 'tuned' to different frequencies and when
various instruments are played in unison, our brains
perceive it as melody. We have to use FT in order to
dissect the sound tracing into its corresponding
harmonics
FOURIER TRANSFORM
Fourier transform is an efficient method to convert time
domain data into frequency domain. Meaning that you
give me any kind of a curve (tracing in this case) and I
can transform or represent the curve into its sine and
cosine wave components.
That's it! Now, we won't get into how this is done for this
lecture.
Now, the MR data obtained in our magnificent k-space
can be transformed into wave functions representing
different frequencies to give us a high-resolution image of
the body.
IMAGE FORMATION
One can see this being done in the axial brain image
below. We can even do this with counting photons (in the
visible range) and perform Fourier transform to make an
image. Your digital camera does something similar but
with a different method!
THE SECRET IS IN THE K-SPACE
One can see below that the center of k-space is where
the contrast information is stored. The periphery is where
the fine details of the images are stored. This is nicely
depicted in the airplane images below.
RECALL RELAXATION
Recall the two types of relaxation T1 and T2. Here's a
diagram to help you. Z = longitudinal axis corresponding
to T1 relaxation Y= transverse axis corresponding to T2
relaxation.
B0 vector is shown in the initial magnetic field direction.
MRI SEQUENCES
Now that we know how images are formed, let us talk
about how we can create different images to view
pathologies by using various sequences.
For simplicity, we will only talk about basic T1, T2, STIR,
and FLAIR sequences.
Note: There are hundreds of pulse sequences (each
manufacturers even have their own!) that you don't need
to know about unless you want to be an expert at MRI.
TISSUE COMPOSITION
Hydrogen atoms are ubiquitous in nature as well as in
our body. Fats whether in the form of triglycerides,
cholesterol, fatty acids all contain hydrogen atoms.
Indeed the same applies for water.
It turns out that fat has shorter T1 time (100-150 ms) and
longer T2 time (10-100 ms) compared to water.
Conversely, water has longer T1 time (1.5-2.0 s) and
longer T2 time (40-200 ms)range compared to fat.
This turns out to be crucial in distinguishing different
pathologies and it will be discussed at the end of this
lecture.
PULSE SEQUENCE DIAGRAM
Usually sequences are depicted in the following way. You have the RF
pulse delivery, then the next line shows slice selection gradient, then the
phase gradient, then the frequency gradient and then the readout echo
signal. There are two main parameters in MRI imaging. You can select
the time that you want to repeat your RF pulse delivery called TR
(repetition time) and the time you want the receiver coil to receive the
signal from proton resonance called TE (echo time). Usually, the RF
pulse is at 42.58 MHz, which is the frequency at which proton in the
hydrogen atoms resonate.
Spin Echo Sequence
SPIN ECHO
This is a classic pulse sequence. In Spin Echo, we apply a RF
pulse 90o relative the initial magnetic field, B0 and then apply a RF
pulse 180o relative to the B0 field to obtain our image. The reason
for applying 90o pulse is to dephase proton spins so that we can
'see' the differences in tissues. Moreover, an 180o pulse is applied
to rephase spins of protons so that we can measure an accurate
T2 echo since all spins will be rephased in the transverse axis.
One may ask how can180o pulse rephase spins if they are all out
of phase. Consider a race between a turtle and rat. When the race
starts (relaxation begins), both are in the same place. As the rat
runs faster, the distance between them widens. Then they both
have to turn around and go back (180o pulse) at the same speed to
reach the finish line. Both will arrive at the same time (rephase) to
the finish line.
Remember: Longitudinal axis (T1 relaxation); Transverse axis (T2
relaxation)
SPIN ECHO
One can already see that the echo signal after 90o pulse is
due to T1 and T2 relaxation since protons will attempt to
align with the B0 magnetic field in the longitudinal axis (T1)
as well as show decay in the transverse axis (T2).
Conversely, the echo signal after 180o pulse is due to T2
decay since the spins have been rephased and there is a
net vector of all the spins in the transverse axis. Hence,
180o pulse is applied in order to obtain accurate T2
measurement as stated previously.
Thereafter, the spins will realign in the longitudinal axis and
one can then accurately measure T1 time. In this way, one
can obtain T1 and T2 weighted images based on this spin
echo sequence by modifying the TR and TE time.
T1 AND T2-WEIGHTED IMAGES
As we have already discussed, the origin of T1 and T2
time is due to relaxation of protons in different planes.
If we want a T1 weighted image then the TR and TE time
will have to be short. This image will show fat brighter
relative to water.
If we want a T2 weighted image then the TR and TE time
will have to be long. This image will show water brighter
relative to fat.
T1-WEIGHTED IMAGE
In the figure below, patient on the left is a normal control vs.
patient on the right who has MS. The patient with MS has
significant loss of myelin due to autoimmune destruction.
T2-WEIGHTED IMAGE
In the figure below, one can see the bright CSF signal as well as
a cyst in the arachnoid space.
T2-weighted images are generally a good starting place when
searching for pathology since it has some component of edema.
STIR AND FLAIR
STIR (Short Time Inversion Recovery) is a pulse sequence where
one suppresses the fat signal by applying a pulse 180o relative the
initial B0 magnetic field and then quickly applying a pulse 90o
relative to B0 field direction. The time between is called TI
(Inversion Time).This combination of pulses doesn't allow the fat to
relax in the longitudinal plane hence negating signal from
surrounding tissues containing fat.
FLAIR (Fluid Attenuated Inversion Recovery) is a pulse sequence
where one suppresses signal from fluid to make surrounding
pathology appear brighter. This is used frequently in MS. Since
classic location of plaques in MS is around the ventricles, nulling
the signal from CSF allows for easy visualization of plaques.
FLAIR sequence uses a TI that is long (close to that of T2weighted image) to suppress fluid from CSF and other fluid filled
cavities in the body.
TISSUE CHARACTERISTICS
REFERENCE
Here are the T1 and T2 times for different tissues in the
human body.
THAT'S IT!
Now you should be able to explain MRI in basic terms to someone
who doesn't know anything about obtaining images using magnetic
resonance.
Remember if you forget you can always say this:
“Protons resonate or wobble at a certain frequency and when you
excite them they relax and emit energy in the form of
electromagnetic radiation. The body has different numbers and
location of protons in various tissues. When you receive the
emitted energy you can map the data onto a matrix. Then you can
extrapolate using sine and cosine waves what the body looks like
based on the mapped RF pulses emitted by different numbers of
protons residing in various tissues (kind of like picturing the music
arrangement by looking only at the sound signal on your audio
receiver!).”