MRI SIMPLIFIED

Parth PatelMIV, USC SOM

LET US PROBE INSIDE THE MAGNET

IT'S ALL ABOUT PHYSICS

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. 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 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 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 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 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 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 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

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

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 SIGNALWhen 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 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

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 RESOLUTIONIf 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-SPACESimply 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-SPACEThe 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-SPACEThis is an example of how the matrix is filled with

data during each slice.

K-SPACEThe top image shows process of slice selection, and bottom

left shows the phase encoding data where as bottom right shows frequency encoding data.

K-SPACEThe 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 FORMATIONOne 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 RELAXATIONRecall 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 DIAGRAMUsually 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 ECHOThis 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 IMAGEIn 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 IMAGEIn 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 FLAIRSTIR (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 T2-weighted 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!).”