We can draw this net magnetization as a vector, oriented along the magnetic field, representing the average effect of all these nuclei:
| Note: This lovely manuscript was written by Dr. Weisskoff for a course we taught togethor some years ago, and is included here without his explicit permission. Do not circulate this without first contacting me, or Dr. Weisskoff. |
For "regular" (linear) momentum, the property of a material that relates its speed to its momentum is its mass. The property that relates an object's rotational rate to its angular momentum is its "moment" or its spin. While it may take a leap of faith, it turns out that this spin is, just like mass, an intrinsic part of sub-atomic particles, even though there really isn't anything spinning (at least, not that we know of). Even more remarkable, this sub-atomic angular momentum can only come in discrete chunks, or quanta. That is, just like charge is only found in integral units of the charge on the electron, angular momentum, too, comes only in quantized bundles.
Why is this important for NMR? It turns out that particles with spin interact with a magnetic field: an applied magnetic field will tend to make the particle line up with the field. The energy saved by an electron lining up with the magnetic field is fairly small. For example, even in the strong 1.5 tesla (T) field used in a high field MRI unit (1 T = 10,000 gauss. The earth's magnetic field is 1/3-1/2 gauss), the energy saved by lining up with the field for an electron is about 1° K. Since room temperature is 300 °K, you'd think this tiny energy difference would be lost. But as we'll see below, MRI depends on detecting changes from nuclei that have 1000 times smaller effects.
One way of expressing this constant is in terms of the energy that would be required to take a particle that was lined up with the magnetic field and flip it so that it was oriented opposite to the field. (This was the 1° K energy mentioned for electrons in a 1.5 T field above) A convenient way of expressing this energy, instead of by temperature, is by frequency. Radio waves, for example, have an energy that is proportional to their frequency. (More precisely, photons, which are quanta of electromagnetic wave energy, have energy which is related to their frequency. A radio wave is made of bundles of these photons) We can thus express the effective magnetic moment in terms of the frequency of radio wave that it would take to totally flip the particle in the magnetic field. For example, for protons:
That is, the nucleus of a hydrogen atom would require the energy in a 63.87 MHz radio wave (around Channel 5 on your TV) to complete re-align the nuclear spin in a 1.5 T magnetic field. This constant, which is different for different nuclei, is called the "Larmor" constant, names after Sir Joseph Larmor, a 19th century English physicist who studied the splitting of atomic emission lines in strong magnetic fields.
Frequency is more than just a convenient way to speak about the nuclear magnetic energy. Because the proton's angular momentum is quantized, it turns out that an individual proton can either be aligned with the magnetic field or against the magnetic field: those are its only choices, and there is no "in-between." This may seem strange, but the quantum physics that describes the universe at the atomic scale offers the protons no compromises. Since the proton can only make transitions between those two states (aligned with the magnetic field and against the magnetic field), the Larmor frequency represents not just the energy of the transition, but also the ONLY frequency that will cause the protons to "flip" alignment in the magnetic field. MRI is based on observing what happens when we cause the spins to flip between these two states.
We can draw this net magnetization as a vector, oriented along the
magnetic field, representing the average effect of all these nuclei:
The basic dynamics of NMR are very simple: This net magnetization will rotate (or "precess") around the direction of net magnetic field. The rate at which the vector precesses is precisely the Larmor frequency described above. Sitting in a 1.5 T magnet, then, the magnetization vector precesses 64 million times per second.
Unfortunately, in equilibrium, we cannot detect this excess. The
only way to detect the magnetization is to knock it out of equilibrium.
By hitting the system with an intense oscillating magnetic field (radio)
that is perpendicular to the main magnetic field, we can, while this oscillating
field is present, tip the magnetization down. That is, since the
rule is the magnetization rotates in the direction of the net field, the
intense oscillating field gives the magnetization a new direction to nutate
about. For example, if we apply an oscillating magnetic field in
the y direction, we get:
This rf pulse used to tip the spins into the transverse plane is called
a "90°" pulse, because it tipped the spins 90° around the y-axis.
Once it is in the x-y plane, the magnetization can now be detected.
Why? It turns out that any antenna that can create the intense oscillating
field that is perpendicular to the main magnetic field can also pick up
a rotating magnetization vector that is also in that perpendicular plane.
Once the intense field is turned off, the magnetization starts precessing
about the original direction of the magnetic field (at the Larmor frequency),
and this precessing magnetization can be picked up with the antenna:
Note that the signal picked up is simply the x-component of the vector, which oscillates in time. The intensity of the signal is proportional to the "transverse" (x-y) component of the magnetization vector. This intensity thus has two parts: more magnetization makes it bigger (for example, more protons), the angle the vector makes between the z axis (the direction of the static magnetic field) or the "longitudinal", and the transverse (x-y) plane.
The important factoids to remember are: (1) the magnetization rotates about the effective magnetic field at the Larmor frequency; i.e., at a frequency proportional to the local magnetic field; (2) only when the magnetization is in the xy, or "transverse" plane can it be detected.
To paraphrase Donne, no proton is an island, entire unto itself, at least as far as NMR is concerned. The local environment determines both the rate at which the nuclei become polarized (i.e., line up with the magnetic field), and the length of time they can usefully precess after an excitation (Figure 4 above). The first time expresses how long it takes the longitudinal magnetization to build up, and is called "T1." Both of these effects are referred to as "relaxation" phenomena, because they describe the process by which magnetization relaxes to its equilibrium state. When the system is excited (tipped into the transverse plane so that we can get a signal on our scanner), T1 expresses the length of time we'd have to wait before we could hit it again and get the same signal. The second time expresses how long the transverse magnetization hangs around, and is called "T2." This section will cover a little more about relaxation, and how it is used to make useful contrast in MRI,
Back to earth, into biological tissue at 37°C. Where do protons get the needed electromagnetic energy to make transitions? The answer is: from other spins in the soup. All molecules are is constant motion, tumbling and vibrating. In a magnetic field, some of these molecules have magnetic moments, like the protons we've been discussing, but also electron clouds can have quite large moments. As these molecules tumble and vibrate and randomly walk through the tissue, the moving magnetic moment produces energy (photons) through the electromagnetic spectra. If there is significant overlap of this energy at the Larmor frequency of the protons, then they can be efficiently relaxed (flipping spins is easily mediated) and T1 will be short. If there is relatively little overlap, then, just as in outer space, T1 can be long.
In solids, for example, where all the spins have crystallized into a lattice, there may be very little relaxation because the vibrational modes of the lattice are much to high in frequency to allow efficient relaxation. In these crystals, T1 can be minutes or even hours long. (Bloch's work was originally done in solids, which is hard NMR work even today! Because he talked about the coupling between the spins and the background "lattice," T1 is sometimes called spin-lattice relaxation, though it is a stretch to think of it this way for biological tissue.) In free water?CSF behaves pretty much like free water?the primary source of relaxation is through the rotation of the water molecules. This rotation is, however, much faster than the Larmor frequency, and thus relaxation in pure water is not particularly efficient, with T1 lying between 3-6 s.
However, for tissues with higher protein concentration, mobile lipids, and other long, floppy molecules, the water protons can be much more efficiently relaxed because the rotation and vibration of these larger molecules is much closer to the Larmor frequency. In addition, the protons on these molecules will also be efficiently relaxed. The T1 of grey and white matter in the brain is around 1.0 and 0.8 s, respectively, and the T1 of fat (though it is made up of several resonances, see "Beyond Water," below) is more like 0.2-0.5 s.
Thus, while the proton density between, say very liquid CSF and necrotic, edematous tissue, on the one hand, and grey and white matter on the other, may be slightly different (no more that 20%), the T1 times may be different by an order of magnitude. How do we exploit this for imaging? The answer lies in one of the MRI "knobs" called TR, which translates loosely as time-between-repetitions. Since T1 represent the time it takes the sample to re-magnetize, if we re-excite the sample before it comes back to equilibrium, we will have less magnetization to tip down into the plane. If we plot the effective magnetization available as a function of this repetition time, TR, for two tissues with different T1's but the same protons density, we find:
In addition to the inherent T1 of the tissue, we sometimes add material that modifies this relaxation time, especially in CNS studies. One such class of materials is the Gadolinium (Gd) chelates (there are three currently on the market). They all work the same way: Gd has a huge magnetic moment because of its unpaired electrons, and this electron cloud behaves in such a way as to provide plenty of energy at the Larmor frequency for protons in a 0.5 - 1.5 T scanner. As a result, the proton T1 will drop precipitously whenever it can get near (right up next to) one of the Gd-chelates. In the brain, it can only do this when the iv-delivered Gd can leak through the blood-brain barrier into the interstitial space, which primarily only happens in pathology. If it does leak through, it can drop the T1 from, say, 1000 ms to 200 ms. As a result, a T1-weighted image taken after injection will show bright spots compared to a pre-injection image wherever the Gd has leaked through.
For many biological systems, the net result of this "transverse" relaxation
is a simple, exponential decrease of coherent, transverse magnetization:
In solids, back in the early days of NMR, this effect was described as the effect that one spin locked in the lattice had on its neighboring spins (as opposed to the effect of the lattice itself), which could be quite strong. Thus this type of relaxation historically was called "spin-spin" relaxation. In solids, the T2's can be very short, measured in microseconds. While, the perturbations are no weaker in biological systems, the effect of random motion in a fluid or gel that describes most soft tissues averages out much of the dephasing, and thus T2's tend to range from 10's to 100's of milliseconds.
We have another knob on our MR scanner to exploit T2 differences between
tissues. This knob is called TE (roughly translates to "time-'til-echo"),
and is used to vary the time after the excitation that we measure the magnetization:
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The idea is very simple. After exciting the protons with a 90°
pulse, wait some time, T, and then apply a 180° pulse; that is, an
RF pulse at the Larmor frequency that is twice as intense. For example,
if we applied the 90° pulse so the protons rotated about the y-axis,
we can apply the 180° pulse so that they rotate about the x-axis.
If between time 0 and T, protons experiencing one magnetic field precessed
D degrees, then the 180° pulse will flip them to D degrees back the
other side of the x-axis. Between time T and 2T then, the protons
will continue to precess in the same direction, making back the distance
D degrees and reach the origin (0°) at time 2T.
They do this because their local magnetic field does not change between
time 0 and 2T. In fact, no matter what static field the protons experience,
they will all return to 0° at 2T, and we will get back a large signal.
This signal is called an "echo" because it seems to grow out of nowhere,
echoing the original excitation and signal. Note that this won't happen
for true T2 relaxation. The loss of coherence there depends solely
on random spin-spin interactions, which, because they are random, can't
happen the same way between 0 and 2T. As a result, this "spin echo"
will still have T2-weighting, and the amplitude of the spin echo will be
decreased by e-2T/T2. For spin echo imaging, 2T is called "TE" and
thus it is the knob we use to dial in T2 contrast.
There are also imaging modes that simple use the 90° excitation
pulse with no additional 180° pulse, imaging the original signal.
That original signal (as opposed to the echo) is called the "free induction
decay" or FID, so these are sometimes called FID-images. These images
have an intensity that decreases like e-TE/T2*. FID-images are used
in a variety of contexts in MRI. While beyond the scope of this introduction,
they are particularly useful for making faster MR images, especially when
T2* contrast or T1 contrast is desirable. In addition, specifically
in the head, FID images are particularly sensitive to distortions in the
magnetic field caused by biological material, especially deoxygenated blood
that would be present from a sub-acute hemorrhage. Imaging blood
will be described in a later talk in this series.
An allied field of MR imaging is MR spectroscopy (MRS) which seeks to exploit these chemical differences. For example, it is possible to image the protons in various metabolites, which are all present in trace quantities (at least, compared to water) in the cells. Many researchers who work in MRS believe that metabolic imaging is the next great application of NMR in clinical practice, primarily because of the increase in diagnostic power that may be available by imaging the functional constituents of the brain instead of the mere spectator, water.
In addition to hydrogen nuclei, many other nuclei have NMR resonances. (Remember, any nucleus with "spin" will have resonances.) There are nuclei with no spin, 12C, the next most abundant nucleus in the body, for example, and thus are not useful for NMR. However, many others are, though they are usually not the most abundant isotopes in the body: 13C, 23Na, 19F,31P, etc. Carbon and Phosphorus spectroscopy have numerous applications to the study of metabolism, and have been exploited in countless physiological experiments in basic neurology, cardiology, etc. Like proton spectroscopy, though, large scientific triumphs have yet to translate into large clinical acceptance, currently because of the added difficulty and cost associated with such exams, though proponents of such techniques believe that these are mere reflections of the current technology. Ultimately, the best NMR image you'll ever see is likely to be of a corpse: there is no motion artifact and the contrast between grey and white matter is exquisite. However, there is really no way to tell whether the image came from a live person or a dead corpse, setting, perhaps, limits on what MRI can tell us. MRS, no doubt, could distinguish the two.