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MRI Data Acquisition | Physics of MRI 2: K-Space and Image Formation - Part 1b
MRI Data Acquisition | Physics of MRI 2: K-Space and Image Formation - Part 1b
2012adjacentchapterdatafillfrequencyfull videogenerateimagematrixmeasurementmeasurementsmeasuringmodalitiesMRIprocedurepulserepeatsimplytransformUHN
Gradients - Linear Magnetic Field | Physics of MRI 2: K-Space and Image Formation - Part 1b
Gradients - Linear Magnetic Field | Physics of MRI 2: K-Space and Image Formation - Part 1b
2012chapterentirefieldfull videogradientgradientslinearmagneticsimplyslopestrengthteslaUHNvaries
Pulse Sequence - Positive and Negative Polarity Gradients  | Physics of MRI 2: K-Space and Image Formation - Part 1b
Pulse Sequence - Positive and Negative Polarity Gradients | Physics of MRI 2: K-Space and Image Formation - Part 1b
2012acquirecenterchaptercompletedatafull videogradientslinearmagneticmovemovessingleUHN
Orthogonal Linear Magnetic Field Gradient | Physics of MRI 2: K-Space and Image Formation - Part 1b
Orthogonal Linear Magnetic Field Gradient | Physics of MRI 2: K-Space and Image Formation - Part 1b
2012calledcenterchapterdirectiondirectionsfieldfull videogradientgradientsmagneticmovesorthogonalphasepulsetypicallyUHNvariesvertical
Alternate K Space Trajectories | Physics of MRI 2: K-Space and Image Formation - Part 1b
Alternate K Space Trajectories | Physics of MRI 2: K-Space and Image Formation - Part 1b
2012acquirechapterfull videopossibilitiesregionrotatespiralUHN
Transcript

concepts that relate k-Space and some of the properties of the MR data acquisition and then we're gonna be talking about how those relate to pulse sequences which we introduced in the first lecture. As I mentioned really briefly at the very beginning of the talk, in MRI a key difference between MRI and other imaging modalities is that when we do measurements on the MR scanner, what we're actually

measuring is k-Space data. We're measuring data in this frequency domain, rather than in the image domain. When we're acquiring MR data, the whole purpose is to simply sample different parts of this k-Space data matrix and we have to essentially fill it up in order to generate enough image before we can finally reconstruct the image with a Fourier transform. Just to illustrate that concept,

typically what We'll do is we'll start with an empty data matrix here, and what we'll do is we will then proceed to a particular point in this frequency histogram and make a measurement. Once we make that measurement, we'll then store it in our data matrix. We'll then move over to an adjacent point make another measurement and again store that

data in the adjacent point in our k-Space data matrix. We will then repeat that procedure across the whole series of adjacent points until we fill up a line of this k-Space data matrix. In MRI all we're simply doing is going to different points in the k-Space data or the histogram and we're just making a measurement. I'm not gonna go into the details at this stage of how we make

that measurement, nor I'm I going into at this stage and talk about how we move from one point in the k-Space data to the next. For now just accept the fact that we do. Once we filled up a line of k-Space data matrix, we then repeat that procedure on another line of our frequency histogram. So we make another measurement along that line of the histogram and we fill up another line of

our k-Space data matrix. And we simply repeat that procedure line by line by line until we fill up the complete frequency histogram that you see here. Once we do that, as I mentioned before, all we have to do is apply a Fourier transform to that data to say what is the image that corresponds to those frequency components and that's how we generate our MR image. Again for MRI, all

we're doing is we're making measurements of the k-Space histogram or the histogram, the frequency representation of the image, once we've made all the measurements we need to, we apply a Fourier transform and that generates the image. Now as I mentioned before, the thing I have been overlooking here is how do we move from one point in k-Space to the other. So how do we go from point one

to point two or to different lines in k-Space. So that's the part that I'm gonna address in the next couple of slides. So we're gonna go back to this basic idea of a pulse sequence, which we introduced in

the very first lecture. So as I mentioned before, it's just simply a series of operations that we perform, that are necessary in order to generate our MR image. So as we saw in the first lecture, we have our initial

RF pulse, and the purpose of that is to tip magnetization away from the direction of the external magnetic field. And the reason we do that is because once it's away from the direction of the magnetic field, it spins around the magnetic field very rapidly, and that generates a signal. Now, the next thing we have are this line that I've labelled here as gradients. So the gradients, which

we'll get into in a minute are what allow you to move through k-Space. So the purpose of these gradients is to move you from one point in k-Space to the other, so you can make those measurements at different regions of the frequency histogram. So what are gradients? So gradients just simply are short hand for

linear magnetic field gradient. Now when we first put a person

into the MR scanner as I mentioned earlier the field strength is let's say 1.5 tesla. And the ideal case that field strength is uniform throughout the entire body or at least the entire body or at least the entire region within the MR scanner. So it's 1.5 tesla everywhere. In contrast to that a linear magnetic field gradient is just simply an additional magnetic field that we add on inside the MR scanner.

But unlike this mean magnetic field, the external magnetic field, this linear magnetic field gradient varies from one position to the next. In particular it varies linearly as a function of position. We can vary the strength of the gradient so the size of the gradient just simply varies how steep this slope is. So if we increase the strength of gradient. That increases the slope of the line. We can also have gradients of

different polarity so this gradient has a negative polarity and that just simply means that the slope of the gradient lies in the opposite direction. Now as I mentioned gradients are responsible for moving your through k-Space, and I'm just gonna illustrate

an example of that here. Let's say initially we start at this position in k-Space here, so we start in the lower left hand corner. If

we turn our gradient on, what that does is it moves us through k-Space. It moves us from one point in the frequency histogram to the next. Again we can take a measurement at each point if we so desire. As long as we keep that gradient on, we're going to continue to move through k-Space in that same direction. As long as we keep that gradient on, we can keep moving from one point

in k-Space to the next. If we reverse the polarity of the gradient all that simply does is it reverses the direction with which that we travel through k-Space. In the first case, we were travelling from left to right with a positive polarity gradient. When I invert the polarity of the gradient the negative polarity gradient, we now travel from right to left. Now with this bit of information,

we can then go back into our description of pulse sequences that

that we didn't have in that lecture. Again we have our initial RF pulse which we now know tips down the magnetization away from the direction of the external magnetic field. And as we saw earlier the reason for this is because it causes the magnetization to rotate

about the magnetic field and that emits a signal. After we've done our RF pulse, now we're then ready to apply our gradients which we now know the purpose is to move us through different regions of a k-Space. Now one point to emphasize here is that after we play out our initial RF pulse, and before we turn on any gradients, we always start at the very

center of k-Space. Our first position is always at the very center of k-Space, at the origin of k-Space. Once we turn on our negative polarity gradient, that moves us out from the center of k-Space out towards the left edge of the k-Space data matrix. We then put on our positive polarity ingredient and that moves us in the opposite direction. Now in this case because our ingredient is twice as long

that means we're gonna move twice as far in k-Space, so you can see in this case we sweep out a complete line. And it's at this point when we actually acquire our data which I've indicated by the asterisks here in the image. Now you could ask the question why don't we also acquire data on when we're playing out this negative polarity when we're moving from the center out. You could do that, however

as you'll see in later lectures, the problem is that acquiring this data multiple times in this manner could make it more difficult to interpret the image that we ultimately get. So typically we really only acquire data, or make measurements, when we're sweeping across a single line of k-Space, or a single direction. Now, that essentially gave

us a single line of k-Space, as you see here. But as I mentioned before, we have to make measurements at the complete histogram so that raises a question. How do we cover the other lines in k-Space? Because at this point, all I can do is move back and forth in one direction in k-Space, but I can't move out the other lines in the k-Space matrix, which I will need to generate a complete

image. So the way we do that, is we actually add in an additional set of linear magnetic field gradients but these linear magnetic

field gradients now lie in the orthogonal direction to our first one. So typically we have built in x gradient. So that's a linear magnetic field gradient, that varies as a function of x position, and we also have a y gradient. So the strength of this magnetic

field varies linearly as a function of the y position. And it's the combination of these two gradients that allow us to move in orthogonal directions in k-Space. So we have orthogonal gradients, can move in orthogonal directions in k-Space. So just to put that together. So after we do our RF pulse we know we lie again at the origin of k-Space, center of k-Space. If we

turn on our y gradient. So what this does is it now moves us in the vertical direction of k-Space as opposed to the x gradient which moved us in the horizontal direction. So this moves up to a different position along the vertical direction. We then turn on our X gradient and proceed as before. So the negative polarity gradient moves us out to the edge of k-Space, positive polarity gradient just twice

as long moves us out to a sweep out a complete line of k-Space. So we've now acquired a single line of k-Space. Typically what we then do is we then go make another measurement. But we don't do it right away but rather we wait some period of time called the TR or the repetition time. Following that we again begin the process all over again, so again we turn on our RF pulse and that as before starts

us at the center of k-Space. We then turn on Y gradient again, but in this case we have one that has a different amplitude. So in this case it's a larger amplitude. And as we know the larger the amplitude, the further we are gonna move in k-Space. So this is going to push us up to a higher line along the vertical direction because our gradient is now stronger and then we can then repeat the same process

of reading out this other line. Now another bit of MR drug that we are gonna introduce here is the X direction is often called the readout or the frequency encode direction because essentially we're reading out the k-Space data. That's why it's called the readout direction. The Y direction is called the phase encode direction and I have to admit I've never actually been sure why

they call it that because you're actually encoding phase in both the x and y directions but nonetheless that's the jargon that's used. Now in general, what I've shown you here is one possible k-Space

it up each time until we cover the entire extent of k-Space and

we apply our Fourier transform and generate our image. But in general it really doesn't matter how we cover that region of k-Space. In other words if we could measure that k-Space in any order we want. As long as we make measurements at the same points in k-Space, when we apply our Fourier transform, we will get out the same image. In general, there's really an infinite number of possibilities

for different directions where different orders that you could acquire the k-Space again, and the specific order of k-Space data you acquire is called the k-Space trajectory. So here we just have a couple of other examples so this is called a spiral k-Space trajectory, so this is where we start at the origin k-Space and spiral outwards like you see here.

So this is the k-Space trajectory, and these are the gradients, as you can see here that are necessary to produce that trajectory. Here we have another example of a different type of k-Space trajectory, this one's called propeller. So this one is starts out similar to the one we talked about earlier and we just acquired one line after another, so here we acquire a series of lines so you can see what the shaded region here, but then instead

of proceeding and acquiring the rest of k-Space we actually rotate the region of k-Space we acquire. So we acquire essentially of series of these strips at different rotation angles. So it looks kind of like the bladed propeller as you rotate it around. And again the gradients that produce this sort of k-Space trajectory look like this. So as I said there is an infinite number of possibilities for which order you can

acquire k-Space and this is often a research from many different groups to finding different types of k-Space trajectories with which to acquire data. So that brings us to the end of the discussion on k-Space MR data acquisition as well as pulse sequences. And that

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