In this tutorial on magnetic resonance, we present the basic concepts on Magnetic Resonance Imaging. The presentation is made at varying levels of complexity. Analogy is used extensively at this level. Subsections marked *** present material somewhat more exactly. To proceed further, select one of the options below
The physical principal which determines how an electromagnet works states that a moving
electric charge creates a magnetic field. The form of motion which interests us here is
spin,
and the objects of interest are the particles within the nucleus of an atom,
specifically, protons. All protons are spinning, and therefore, each creates a tiny
magnetic field, which we will call a "magnetic moment".
The Pauli exclusion principle demands that no two subatomic particles in the same atom exist simultaneously in the same state. If the nucleus has an even number of protons, each proton will be accompanied by another of exactly the opposite spin, and the two magnetic moments will cancel each other.
Nuclear particles do not act as classical particles: A classical particle spinning in a magnetic field will, according to Maxwell's equation, radiate electromagnetic energy. These nuclear particles, even though they possess a magnetic moment aligned with the external field, do not emit, until stimulated by the rf pulse described next.
Thus, only if a nucleus has an odd number of protons, will it possess a net magnetic moment. Placing this nucleus in a strong, constant magnetic field will cause it to tend to align with the field.
Understanding that we are only using an analogy, we will continue to refer to the quantum-mechanical property as "spin," and say that the nucleus now spins in such a way that the magnetic moment aligns with the external field.
Now we must consider the rate of spin. Once the external field has been applied, the
spin not only changes its direction, it changes its frequency to obey
fo = g Ho (1) where fo is the frequency of spin, g is a
constant, and Ho is the strength of the applied field.
The constant g depends on two factors: primarily the type of nucleus, and to a lesser extent on the "chemical environment" of the nucleus - including such factors as the type, distance,and number of neighboring atoms. It is the second factor which allows NMR to be of tremendous use to organic chemists who need to determine the structure of molecules. In MRI, however, we are primarily concerned with the first factor.
We will almost always use the nucleus of simple hydrogen, 1H. For the MRI systems currently in use, fo, called the "Larmor frequency", is on the order of 60 MHz(megaHertz), a frequency just slightly lower than the conventional fm radio band. Wake forest radio transmits on 88.5 MHz.
Now let's perform a simple thought experiment: image a rotating barrel with a hole in one
side, and suppose you needed to fill that barrel with water from a garden
hose. (look at
figure 2).
Clearly, to get water into the barrel, we must time our spray from the hose to occur just when the fill hole comes around, thus the squirts of water need to occur at precisely the rotation frequency of the barrel. By analogy then, we "squirt" energy into nucleus by using electromagnetic energy which changes at precisely the Larmor frequency. Furthermore, just as the barrel gets more filled the longer we operate the hose, the nucleus gains more energy as we keep the incident radiation on longer.
We refer to the necessity of matching frequencies of spin and incident radio frequency radiation as "resonance," and emphasize that only those atoms which experience a magnetic field of strength
Now let's consider what happens after we turn off the incident radiation. The barrel
continues to spin, and it sloshes water back out. At first, water is lost rapidly, but as
the water level in the barrel drops, the rate of loss also drops. If we were standing next
to the barrel, we would find ourselves getting wet at precisely the spin rate, but a bit
less wet each time (look at figure 3).
To step from the water analogy to observing an excited nucleus, we observe (using an antenna and rf amplifier), a signal emitted from the nucleus at the Larmor frequency, but diminishing in amplitude,
(now look at figure 4)
The envelope of the amplitude of the rf signal
is exponential, satisfying
Now that we understand NMR, let's see how we get an image using this phenomenon.
You may either proceed to the lesson on parameters, or the lesson on imaging using NMR. 1#
Press here to go back to screen 1
How are MRI images formed
We assume the patient is lying in the MR scanner, on her back. We define the z direction to be along the bore of the magnet. Thus if we were to image a slice through the patient such that the z direction is normal to plane of the slice, we would be taking on "axial" image.
The x direction is horizontal, and slices taken normal to x are "sagittal." Y is vertical, resulting in "coronal" images.
Selecting a Plane to Image
At this time, we consider only obtaining axial images. Sagittal and coronal views are taken by interchanging the roles of the "gradient coils" which are discussed below.
To our huge superconducting magnet, let's add some additional coils. These coils will allow us to vary the strength of the magnetic field as we move along the z axis. Note that these additional coils do not modify the direction of the field - it still points along the z axis; only the strength of the field.
As shown above, when the coil named Gz is on, the effect is to vary the strength of H3 linearly about the static field value. Coils that modify the field strength are called "gradient coils."
In the figure above, the windings of Gz are shown as if their spacing varied. In fact there are various ways to achieve the linear variation in H.
Once Gz is energized, we have a magnetic field which varies spatially.
To take the next conceptual step, recall that unless a nucleus is in resonance, it will not absorb energy. Therefore, if we apply a pulse of rf energy at a particular frequency, fo,
ONLY the atoms in the plane where
, a plane normal to the
z axis, will resonate. Thus if we turn on our receiver immediately after an
rf pulse, we will detect signals only from atoms lying in a particular (axial) plane.
0.3 Selecting a Line Within the Plane
Before we can explain the selection of a line, we must introduce the concept of "phase."
Let's go back to the spinning barrel analogy for a moment, and imagine that we have two barrels, side by side, spinning at precisely the same rate. Furthermore, imagine that the holes are aligned in the same direction. Then, as they spin, water sprays from both barrels in the same direction at the same time. See Figure __.
Now, for just a moment, let's increase the rotational velocity of one of the two barrels, and then let it return to its original velocity. During the period of acceleration, the one barrel will get slightly ahead of the other. After the deceleration, both are still spinning at the same rate, and exhibit a "phase difference" relative to each other.
There is no such thing as absolute phase. One may only consider relative phase. If one describes the rotation of one barrel by a sine wave
(1) 
where 
then the second barrel may be decided by adding a constant phase term.
(2) 
We note that the phase is really an angle, which may be measured in degrees or radians.
Caption:The phase difference may be viewed as an angle.
Having described the concept of phase, we now go back to atoms, and impose a phase difference on atoms, a difference which will vary in the y direction. Recall, so far, we imposed a gradient in the z direction, and while that gradient was active, we provided an rf pulse and excited the nuclei in a plane. Now, we turn Gz off, and turn on Gy, a field which varies in the y direction.
In this way, the atoms at the top of the scanner see a stronger magnetic field than those at the bottom. But here's the trick: We only leave G y on for a short time. Those nuclei at the top accelerate to spin at the higher Larmor frequency demanded by the higher field at the top of the magnet. When we turn off Gy, all return to their original spin rate, but now, those at the top are ahead in phase of those at the bottom.
We illustrate the pulse sequence in the timing diagram below.
Thus, if we can (somehow) detect the phase of the signal emitted from our patient, we can uniquely specify the z coordinate (since only those were excited) and the y coordinate. All that remains is to determine x.
0.4 Selecting a Pixel Within a Line
After turning Gy off, we now apply Gx, and, while Gx is on, we record the signal from the patient, a signal which is a function of time.
Let's suppose at coordinates [x,y] we have a atom emitting, then the signal emitted by just that atom at time tx (measured from the start of Gx) will be (ignoring, for a moment, the exponential decay over tx).
(3) 
where the term ωx involves the strength of Gx, (which in itself encodes the coordinate x)
(4) 
and &thetas;y is the phase term discussed earlier
(5) 
Of course, our antenna doesn't pick up JUST the signals from the point x,y; we receive emissions from all the atoms in the selected slice
At this point, we recognize a familiar form in Equation (9) - a representation of a signal as a sum of sinusoids. With this recognition, we know how to determine the axy's: the Fourier transform. The transform will allow us to determine the axy if we make one other modification to our pulse sequence: we need a set of &thetas;y's, not just one. So now, our pulse sequence looks like this:
and read out during the time Gy is asserted. We then increase Gy slightly, and repeat the entire sequence, one repeat for each line of the image.
Use of the Fourier Transform
We rewrite EQ (9) using complex exponentials and the definition from Equation (α) and (ρ)
(7) 
(8) 
We now make f a two dimensional function key varying Gy. That is, we repeat the entire sequence of pulses shown in Figure ( ), changing Gy slightly each time.
We denote the mth value of Gy by Gy(m), and write
(9) 
finally, we note that the term preceding the summation is a known, pre-computable constant, which, although important, may be lumped a simple multiplier
(10) 
and defining
(11) 
and
(12) 
we have
(13) 
We now have a form which is exactly the Fourier transform representation, and we may find the coefficients Axy by taking the 2-0 Fourier transform of f.
A Complication: The Non-zero Bandwidth of the Excitation Pulse
We stated earlier that selection of the plane, we used a pulse of a particular frequency. It should be clear that we might interchange the roles of Gx and Gy and obtain a plane perpendicular to the y axis - a coronal view. Thus, we will henceforth refer to this first pulse as the "slice-select" pulse. If the rf pulse truly contained only one frequency, then the slice would be of zero width, and very few atoms would resonate. Few atoms means a signal too small to measure. Therefore, we want an rf pulse which covers a range of frequencies, and excites "slab." Common connection refers to this as the "slice thickness," and values of 1-3 mm are common.
We achieve non-zero bandwidth by using a sinc pulse, as shown below.
In fact, this figure is only correct to first order. Modern scanners use additional compensation techniques to shape the spectrum of the rf pulse.
But now, we have a problem: since our slice has significant thickness, atoms of opposite sides of the slice experience different Gz fields. Those with higher Gz will rotate slightly faster, and a phase difference will accumulate, just as occurs in the application of Gy. However, in the case of Gy, we deliberately induced the phase difference. Here, a phase difference in the z direction could compromise our resolution in y. For this reason, we modify the pulse sequence as shown below.
Press here to go to the first screen
Let's consider for a moment, the timing of the gradient pulses.
Although we have not discussed it yet, it turns out that some overlappnig of the gradients is permissable, and that we actually require only about 20 ms for the sequence.
In figure 4 we illustrated that the signal emitted from out excited nuclei diminished expo- nentially with time. This process of loss of measured signal is referred to as T2 and it requires about 10 ms for the signal to be totally gone. However, we probably won't even get the x gradient turned on for 30ms or so.
Whoops! The signal we are trying to measure has decayed away to zero before we ever measured it. (Remember - we measure while Gx is on). Oh well, MRI was a good idea, but it will obviously never work. Let's give up and open a McDonald's concession in Paupan- New Gunea...No, wait! Let's just make the gradient pulses shorter!
No. Sorry. J.C. Maxwell says you can't shorten those pulses too much. To deliver suffi- cient magnetization to the patient, you must keep the area of the gradient pulse constant. A shorter pulse means a higher pulse. A higher pulse means a shorter rise time, and more rapid rise times mean is larger. A rapidly changing magnetic field induces voltages, and subsequently currents in the patient, particularly in areas of high conductivity (such as metals, like ECG leads). There is a clear lower limit to the duration of a pulse.
We have only two choices: we can try to UNDERSTAND why the signal drops so rapidly, and try compensate for that, or, we can buy those tickets for PNG.
Assuming we choose the first option, we must abandon our spinning barrel analogy, because it is simply not sufficiently descriptive, and resort to the analogy most often used in the literature - a precessing top. So lets model the nucleus as a top, spin- ning about the Bo field.
After being hit by the pulse of rf radiation, the top no longer has its axis aligned with Bo, but is now precessing about Bo. (precessing is what a top does when it starts to slow down; it continues to spin, but wobbles also)
A sufficiently long rf pulse will rotate the top until it rotates totally in the x-y plane. The rf pulse required to achieve this much rotation is referred to as a "90 degree pulse". The amount of signal which we measure from this nucleus will be proportional to how much of its rotation lies in the x-y plane.
If an rf pulse results in a "flip angle" of 90 degrees, we will detect a maximal signal. Gradu-
ally, the nucleus will lose energy, returning to alignment with Ho and emitting nothing. Now here's the
interesting part. (Pay attention! This is important.) The reason T2 is so short is
because of local interactions. (Huh? Is this political science or what?).
Remember: each atom produces a magnetic field, and every atom senses not only
the big Ho field, but the field from neighboring atoms as well. Therefore the
resonant frequency of each atom is not just fo (due to Ho), but some other
frequency,
f = fo + something,
where the something is due to the NEIGHBORHOOD the atom finds itself in. Now,
since the individual atoms are precessing at slightly different rates, they
rapidly get out of phase. (remember phase?)
Unfortunately, we can't measure the signal from individual atoms, but on from rather large collections of atoms. As the individual atoms get out of phase, the signal which we measure, a sort of average of the individuals, rapidly drops off to nothing. We call this process "interference".
So here's the trick: (and a clever trick it is). Kick all the (selected) atoms with a 90 degree rf pulse. Let them dephase for a while. That is, those which sense a locally stronger field will precess slightly faster, and get ahead of those which sense a lower field. Now, give them all a 180 degree pulse, which turns the tops right upside down. (You need to have a sort of wierd floor for the top to spin on at this point, but I think you can imagine it. The top is now upside down). Those atoms which were behind in phase now start to catch up (because the direction is reversed), and after a while, they all catch up and are in phase again, and we measure a nice strong signal. That signal is called an "echo". Of course, it's not an echo at all, but the result of dephasing and the rephasing.
Now, move on to the discussion of parameters of MRI imaging. Press here to go back to screen 1 and a choice of other options
After a proton has been excited, it emits energy as it begins to decay back toward alignment with the main magnetic field. This signal, if we could measure it, would be called the "free inducation decay", and would be a decaying sinusoid. We can't, of course, measure the emission from a single atom; instead, we must consider collections of atoms in a neighborhood of tissue. As this collection emits energy, the energy emitted also declines exponentially with time, following a time constant known as T1.
If a signal is described by an exponential function of the form
s(t) = exp (- t/T),
the denominator, T, is known as the "time constant". The longer the time
constant, the longer it takes for this decaying signal to reach zero. Here are
some typical values of T1 for several tissues:
These are times, measured in milliseconds.
T1
White matter 390
Gray matter 520
CSF 2000
Skeletal Muscle 600
Fat 180
Liver 270
Renal medula 680
Renal cortex 360
Blood 800
Notice the VERY long decay time for water (what is CSF, after all?)
Now let's learn about T2.
Remember that the rate of precession of a nucleus is dependent on the magntic field which that atom senses. This magnetic field is due to several things:
Item 3 is the factor that interests us here, because it is a characteristic of tissues, not the scanner. This is the time we refer to as T2. Here are some T2 values for those same tissues:
T2
White matter 90
Gray matter 100
CSF 300
Skeletal Muscle 40
Fat 90
Liver 50
Renal medula 140
Renal cortex 70
Blood 180
Remember the screen on spin echo? Let TE be the time from the original
exciting 90 degree rf pulse until the 180 degree pulse. Furthermore, let's
repeat this entire process every TR seconds. Thus, TE and TR are settings for
the MR scanner, whereas T1 and T2 are properties of the local tissue. T1 and
T2 differ, of course, as you go from one place in the body to another. These
four parameters are related by an equation (of course...)
S = PD exp(-TE/T2) (1 - exp(-TR/T1)) (n)
(No, I dont remember what the equation number should be either)
In this equation, S is the brightness (signal) measured at some particular point in the image--at some particular "pixel"; PD is "Proton Density", the number of hydrogen atoms in the region corresponding to that pixel; and T1 and T2 are the corresponding time constants for that pixel.
Lets look at that equation for a moment: An exponential with a negative argument has the property that if the argument is large (that is, more negative than about -5), the value of the exponential is very small. A short TE, say about 10 ms, and a moderate TR, say about 500ms results in a "T1-weighted image". That is, visible differences in contrast are due to variations in T1 more than variations in the other parameters. You can work this out for yourself if you plot the two curves for two different tissues. Similarly, a moderate TE, say about 50ms, and long TR, say 2 seconds, results in a "T2-weighted image". Finally, a short TE and a long TR results in a "PD-weighted image".
One last observation (which the mathematically inclined can also derive from
the above equation):
Tissues which have a short T1 will be bright on a T1-weighted image.
Tissues which have a long T2 will be bright on a T2-weighted image.
Now that you understand all that, Im putting up a program for you to play with. This is an image of a healthy brain, and you may, by moving sliders around, see what this image would look like if you used various TE and TR settings.
*************************READ THIS**************************************** The following instructions are regarding an implementation of an MRI simulator. Chances are you dont have that program on your computer, so most likely, you will just want to skip this part. **************************************************************************
Press here to skip to the material on visualizing pathology in MRI
Press here to skip to the beginning
Things I want you to learn from this is 1) Set TE and TR to create a T1-weighted image. What features of the brain are bright? Which are particularly dark? In what sense does this agree with the list of long and short T1 and T2 values I have you earlier? 2) Re-do this for a T2 weighted image. 3) Look at the right (as you view it) end of the brain. Set TE to 6 and TR to 1700. Now do you see a very bright spot? (yes, I know it's green. Just ignore the color and think of it as very bright). What is that? (Hint: Where does the dura have two levels, and what is between those levels?) Now that you have that answered, can you identify the bright spot on the lower left? 4) What are those dark areas in the middle of the image? Is TE = 6, TR = 1700 a T1-weighted image or a T2-weighted image? If you can identify those dark areas, and know what's in them, what are the T1 and T2 responses of this material? NOTE: when you are finished with this other program, exit from it by pulling down the menu under minus sign at the upper left of THAT window (please, please don't close my window). While you are playing with that program, I am going to take a nap. When you exit from the other program, it will awaken me. Please don't press any of my buttons while I am snoozing. Thanks. Press here to start the MRI simulator running#msym# msym#Please dont bother me. I'm snoozing#F/usr/users/wes/forks/frwd -i \ /usr/users/wes/forks/f0 /usr/users/wes/forks/f1 /usr/users/wes/forks/f2 -o \ junk# 2# If you were puzzeled by the wave-like artifacts at the left-side of the brain, press here.#ringing# Press here to start overPathology in MRI images
(thanks to Dr. Allen Elster for the information in this section)
Virtually everything of clinical significance in an MRI image (tumors, MS, infection, etc.) get bright on T2-weighted images and darker on T1 weighted images. This is due to the fact that all these things have increased water content.
Exceptions: Things you might be interested in that are--
A: Things that are bright on T1: