Transcription
Hello everybody and welcome back. Today, we are going to be looking at chemical shift and the chemical shift artifact. Now, up until now, we've been thinking about hydrogen atoms in isolation, unbound to other atoms and not forming parts of larger molecules. And we've seen that because the hydrogen atom has a non-zero spin, if we were to place it in an external magnetic field, it would align with that magnetic field and precess at a specific frequency. And we can calculate that precessional frequency using the Larmor equation.
Now, the Larmor equation states that the precessional frequency is a product of both the gyromagnetic ratio, which is specific for the atom we're looking at, and the strength of the external magnetic field. And the stronger we make the external magnetic field, the faster that precessional frequency of the hydrogen atom.
Now, in MRI imaging, we are comparing generally signal from fat and water. And it's the differences in signal between fat and water that give us contrast within our image. Now, the hydrogen atoms in fat, as opposed to the hydrogen atoms in water, exist in very different molecular structures. And it turns out the local environments mean that there's a difference in this precessional frequency. And it's that difference that we term chemical shift.
So let's have a look at these hydrogen atoms within both water and fat molecules. We can see that within water, two hydrogens are bound to a single oxygen atom, H2O. And the way any chemical bond forms is a sharing of a valence electron. A hydrogen proton has one valence electron, or just one electron in the atom. And that hydrogen's electron will then fill a vacancy within the outer shell of the oxygen's electron orbitals, and a chemical bond will be formed.
Now, because oxygen is larger than the hydrogen and has more electrons, the probability, if we were to take a snapshot and say where is that single electron at any given point in time, the probability of that electron being closer to the oxygen as opposed to the hydrogen is higher. In general terms, that electron is spending more time around the oxygen than it is around the hydrogen. And that leaves that hydrogen atom relatively exposed or unshielded by that electron.
If we were to look at the molecular structure of fat, I've drawn a triglyceride here, where we've got fatty acids joined to a glycerol backbone. Here we've got hydrogens that are bound to a chain of carbon atoms here. And then in our glycerol backbone, we've got both carbon, oxygen, and hydrogen atoms. In this case, the electrons, relatively speaking compared to water, are spending more time around those hydrogen protons.
Now, when we apply an external magnetic field and we use this Larmor equation to calculate the precessional frequency, the magnetic field is what we're using to calculate that precessional frequency. Now, this is slightly incorrect. It's actually the local, at the atomic level, the local magnetic field strength. And there are predominantly two factors that determine that local magnetic field. By far and away, the main magnetic field is the main contributor to that local magnetic field.
Now, there's a separate magnetic field that is created by the electron orbiting the hydrogen atom. We've seen when we looked at electromagnetic induction, the movement of charge creates an electromagnetic field. An electron is negatively charged orbiting a hydrogen atom. That movement of charge creates a minute electromagnetic field around that hydrogen proton that opposes the external magnetic field. This is very, very small compared to that external magnetic field, but it is significant. It has enough effect to change ever so slightly that precessional frequency.
So when we use the Larmor frequency, we want to change this B naught, the main magnetic field, to be local. What is the local magnetic field? It turns out that the local magnetic field, or the electron shielding, that's another term for that electromagnetic field induced by that electron spinning around the hydrogen proton, electron shielding, turns out electron shielding is slightly more in fat than it is in water, making the net magnetic field slightly less in fat, reducing that precessional frequency of the hydrogen protons ever so slightly compared to water.
So let's have a look at what this looks like in more detail. We've changed the Larmor equation here to the precessional frequency being a product of the gyromagnetic ratio and the local magnetic field. So let's look in water. What the local magnetic field is, the local magnetic field is the B naught, the main magnetic field, the large magnetic field that we apply across our patient, minus the electron shielding, that local electromagnetic field that is created around the hydrogen atom. And in water, that's very small. That electron is predominantly around the oxygen atom here. So we get a precessional frequency that is pretty much a product of the gyromagnetic ratio and our main magnetic field.
Now, we can't go and actually calculate this here. It's difficult. This is such a small value here. It's difficult to put actual numerical values in here. What we can do is generate an image and then make assumptions as to what the difference is in local magnetic fields are within water and within fat.
Now, we can plot these precessional frequencies on a graph. You can see that water has a slight range of precessional frequencies and gives off a certain amount of signal. How much water is in our image in the slice that we're imaging? Now, we're not getting one set frequency. There are obviously local changes in water. Water can exist in CSF, relatively free. It can exist in the cytoplasm within a cell. There are slight changes, and that's why we get a slight range in precessional frequencies. It's not one set frequency.
Then, if we look at fat, we can calculate the precessional frequency of fat. Now, I've said that the shielding, the electron shield, that induced magnetic field around the hydrogen proton, is slightly more in fat. That makes our B local, which is our main magnetic field minus that shielding, slightly less in fat than it would be in water. The magnetic field experienced by the hydrogen protons in fat, because of its molecular structure, is slightly less than the magnetic field experienced by hydrogen protons in water. They're the same hydrogen protons, but the local magnetic fields are slightly different. That slight reduction in B local, the local magnetic field, results in a slight reduction in precessional frequency in fat. We can see there's a difference now in precessional frequencies between water and fat. And that difference is very, very small.
Now, that difference is what we call chemical shift. And it's set when we're comparing water and fat. There's not anything that we can do to change the ratio between water and fat precessional frequencies. That's chemical shift. Because of those frequencies, when we go and create an image and perhaps misregister where water and fats are within an image and create an artifact, the artifact that we see in the image is called chemical shift artifact. And you'll see there are changes that we can make to reduce chemical shift artifact. We're not reducing chemical shift itself, we're reducing the artifact. It's an important difference to make in your mind.
Now, we represent chemical shift via this symbol here. And what we can do is take the frequency of our reference sample. We use water as a reference. That's the closest to a free hydrogen proton that we'll get. And we find what is the difference between the frequency of the hydrogen atoms within fat compared to our reference sample, compared to water. There's going to be an ever so slight difference because of those local magnetic field changes. And we divide it by our reference frequency, the Larmor frequency of hydrogen protons within water. That gives us a ratio known as the chemical shift. And the difference between water and fat is 3.5 parts per million.
Now, what does parts per million mean? Well, when we're talking about precessional frequencies within our MRI, we're generally talking about megahertz. We've seen that the gyromagnetic ratio of hydrogen atoms at one Tesla is about 42.5 megahertz. So for every million Hertz, there's going to be a 3.5 Hertz difference between water and fat. For every megahertz that these are precessing, there's going to be a 3.5 Hertz difference, a very, very small difference between water and fat.
Now, what changes those megahertz values? What changes those precessional frequencies? It's the strength of the external magnetic field. The stronger we make that external magnetic field, the faster these hydrogen atoms will precess, the more megahertz they will precess. And for each megahertz that we add on to the precessional frequency, we're going to introduce an absolute difference of 3.5 Hertz between water and fat. So hopefully you can see that as we increase our external magnetic field, the absolute difference in frequency between water and fat is going to get higher.
If we were to take a 1.5 Tesla machine, our external magnetic field is 1.5 Tesla. We know that the gyromagnetic ratio of hydrogen is 42.58 megahertz per Tesla. We times that by 1.5, by our main magnetic field, our hydrogens in water are going to precess at 63.87 megahertz, 63.87 times 10 to the power of 6 Hertz megahertz there. We know that for every megahertz, for every million parts per million, there are 3.5 Hertz difference between water and fat. So for every million, there's 3.5 Hertz difference. Because the water is precessing at 63.87 megahertz, we are going to calculate the difference between water and fat as 223.5 Hertz difference. For every megahertz, there's 3.5 parts per million difference. Our fat is going to precess slower than water by just 223.5 Hertz.
Now, what would happen if we were to increase the magnetic field strength? We were to double the magnetic field strength to three Tesla. The precessional frequency of hydrogen in water is going to double. As we double this main magnetic field, we double the precessional frequency. A doubled precessional frequency means that the hydrogen atoms in water are now precessing at 127.74 megahertz. The difference now between water and fats, in terms of absolute difference, is 447.1 Hertz. By increasing the magnetic field strength, we have increased the absolute difference in precessional frequencies. So we can see that increasing the magnetic field strength could increase chemical shift artifact within our image.
Now, how does this actually then go about leading to chemical shift artifact in an image, and what exactly is chemical shift artifact? When we take the analog signal from a single slice, we take that analog signal and Fourier transform it, split it into multiple different frequencies. And we use those frequencies to plot where that signal is coming from along the frequency encoding direction of our image. We use this gradient, this frequency encoding gradient, along the frequency encoding direction to then plot those different frequencies and put the signal in the right x-axis location.
If we have an image like this, the dark gray representing water, the light gray representing fat. Now, the water is going to precess at a set frequency, and the fat is going to precess at a frequency that is slightly less than that water. Now, the machine itself has no way to know, is the signal coming from fat or is it coming from water? It can only tell the signal amplitude and the frequency at which that signal is coming from. That's the only two variables it has to go and plot the signal. We can't differentiate water and fat.
So what is going to happen is when this fat signal comes back and we Fourier transform, splitting those frequencies and placing them along the x-axis, we are going to falsely place the fat signal slightly to the left on this image, at slightly lower frequencies than the surrounding water. So the first difference in our chemical shift is that we get a shift to the left here of fat. Now, why is the signal brighter here? Well, underlying this, we've got water giving off signal at this frequency, at this location on the x-axis, and those signals are then combined by the MRI machine, by that Fourier transform. So we get a bright rim surrounding our fat. We've misregistered that fat along the frequency encoding direction.
Now, the opposite is also true. The fat here is going to precess at a slightly lower frequency than we expect, than the surrounding water, and it's going to be misregistered along the x-axis this way. Now, we get a dark band forming on this part of the fat because there's no underlying water here spinning at this frequency for this x-axis location. It's giving us no signal. And the fat that is actually here, truly in the anatomy of the patient, is being misregistered at a different place. And we get no signal at this part of the fat-water interface. This is essentially what the chemical shift artifact is. And it predominantly happens in the frequency encoding direction. Chemical shift is a difference in frequencies, and we misregister those differences in frequency, leading to this chemical shift artifact.
Now, what is creating this gradient here? It's our frequency encoding gradient. Now, what determines that frequency encoding gradient? This is why I'm including the chemical shift artifact here. We've been talking about field of view and bandwidth for the last couple of talks. Even aliasing required a bandwidth. The bandwidth set that Nyquist limit and determined whether we would get aliasing or not, combined with our field of view here. The gradient field strength is a product of the field of view that we've selected, as well as the bandwidth that we selected. The MRI machine then goes about creating a gradient that will ensure that we have a specific bandwidth along that field of view.
So let's take an example here. A 20,000 Hertz bandwidth. We've got a difference in frequency of 20,000 Hertz across this slice here. Now, if we were to think about that slice being split into 256 different pixels, we can represent those pixels with these blocks here. Obviously, I don't have 256 pixels, but say we're zooming into the pixels. Each pixel is going to represent a slight range of frequencies. Our 20,000 Hertz has been divided into 256 pixels. It's going to be a range of frequencies represented by each one of those pixels.
So in this example, let's calculate what that range of frequencies is. The range of frequencies is our bandwidth, the total range of frequencies across our field of view, divided by the number of pixels. And we see in this example, the range of frequencies that are bucketed into one pixel is 78.1 Hertz. And we've seen that at a 1.5 Tesla field strength, this is what we calculated earlier. The difference in precessional frequencies between water and fat is 223.5 Hertz. Say the edge of this pixel here was 64 million Hertz, 64 megahertz. The other edge of this pixel here will be 64 million 78.1 Hertz. There will be a 78.1 Hertz difference across here.
Now, if we were to take the signal from fat, let's put fat in our image here. If we were to take the signal from fat being produced here, it's going to be 223.5 Hertz less than the signal from water that we use to plot our signal along the x-axis. We're going to misregister these factors actually being in this pixel here. It's about 3 pixels. The range of pixels here is 78.1. We're going to misregister three pixels across to the left. What our image is actually going to look like is this. We're combining the fat signal and the underlying water signal in this region. The one pixel that had fat in it is still in the area that there is fat. There's no water underlying there, so we get true fat signal here. And we're getting no signal in these pixels here. There's no water truly in this anatomical location, and we've misregistered the signal coming from the fat there as being at a different place in the x-axis location.
Now, what would happen if we changed our bandwidth? Say we want to increase the bandwidth. What's that going to do to the gradient field strength? It's going to increase the gradient field strength. So let's take an example now where we've increased the bandwidth to 60,000 Hertz. We've had to increase that gradient. What's that done? It's increased the range of frequencies along the frequency encoding direction. That means that the range of frequencies represented by each individual pixel is now 60,000 Hertz divided by 256, if we're doing 256 pixels in our image. The range of frequencies per pixel now has changed. It is now much larger. Each pixel represents a wider range of frequencies because of this deeper gradient field strength.
Now, the differences between the two edges of our pixel is 234.4 Hertz. What hasn't changed is at a 1.5 Tesla field strength, the difference between water and fat precessional frequencies, the chemical shift at 1.5 Tesla, is the same. It's 223.5 Hertz. Now, signal coming from this location on the x-axis from fat is only going to misregister one pixel to the left. The signal coming from here, our machine is going to detect it at a specific frequency. It's going to be 223.5 Hertz less than water, and it's going to register this signal is coming from here. So you can see that the chemical shift, or the degree of chemical shift, has been reduced simply by increasing the bandwidth, increasing the range of frequencies over our set field of view. And how do we increase the range of frequencies? We increase the gradient field strength. That increase in gradient field strength has given us a larger range that is covered by one pixel, a larger range of frequencies represented by each pixel, reducing the chemical shift artifact.
So we've seen that if we reduce the field strength, the main magnetic field strength, we decrease the absolute difference in frequencies between water and fat, ultimately decreasing the chemical shift artifact. We're obviously losing some signal as well as we reduce the main magnetic field strength. We decrease the chemical shift artifact by increasing the bandwidth, as we've just seen in this example. See how the high signal intensity and the dark regional low signal intensity region here are much smaller with this higher bandwidth?
There's one more mechanism that we can use to increase or decrease the amount of chemical shift artifact, and that's by changing the matrix size. If we were to increase the number of pixels here, then the range of frequency covered by each individual pixel will be less. This number would be less if we're dividing by a greater number of pixels here. If we have a smaller range of frequencies represented by each pixel, we are going to get an increase in the chemical shift artifact here. The difference between fat and water that we've calculated at this magnetic field strength is going to be emphasized in our image, increasing chemical shift artifact.
So you've seen that the best way is probably just by increasing the bandwidth. Why then don't we just increase the bandwidth to the maximum that we can and just reduce all of the chemical shift artifact in our image? What we've seen before that increasing the bandwidth comes at a cost. As we increase the bandwidth, we are changing these range of frequencies here. We need a faster sampling rate in order to sample this Nyquist limit that we've calculated, and that sampling rate is inversely proportional to our sampling time. We've seen that increasing the bandwidth, like we see in this example, a higher bandwidth compared to a lower bandwidth, decreases the signal to noise ratio. Our true signal that we get compared to the background noise decreases. And we've seen that signal to noise ratio, see how the noise has been introduced into this image. We've seen that signal to noise ratio is represented by this formula when we're looking at bandwidth. So it comes at a trade-off. A lower bandwidth gives us better signal to noise ratio, gives us better signal in our image, but we are going to increase the amount of chemical shift artifact represented in that image. The same thing goes with increasing our matrix size. We get better resolution by getting smaller pixels, but we're going to get more chemical shift artifact. And these are trade-offs that we need to make when deciding on the parameters that we're going to use in order to acquire this MRI image.
So this nicely rounds off the past four lectures. We spent two lectures looking at bandwidth, field of view, and gradient field strength, and how that affected our image. Then we looked at two artifacts that are specific to the bandwidth that we choose. Aliasing artifact is affected by the bandwidth that we set. We've seen that frequencies outside of our bandwidth are going to be misregistered. And the chemical shift artifact, as we've seen now, is also influenced by our bandwidth and that gradient field strength, especially along the frequency encoding direction. And we've seen that increasing that bandwidth, increasing that gradient, is going to reduce the chemical shift artifact at the cost of signal to noise. So that rounds off this section. Now we're going to move on to the section that many of you have been waiting for, and that is going through the individual pulse sequences. And a reminder, if you're studying for an exam, I've linked a curated question bank in the description below. A great way to test your knowledge that you've learned in these video series, as well as test yourself on actual exam questions that have come up in previous exams. Otherwise, let's move on to pulse sequences. I'll see you all in the next talk. Goodbye everybody.