Magnetic Resonance

Introduction

Today you will actually get the basic physics behind MRl and I will introduce you to the nuclear magnetic resnosance. Then, you’ll have to do some work with the very cool simulator, DRCR (Danish Center for MR). Then, we will talk about the image formation. And I think image formation of MR is a little bit complicated, so what we are going to do is first I will give you an explanation that’s close to the book, then you come up with another type of explanation. Finally, we will look at MRI images, and then, look again at the Contrast, Resolution and SNR.

• Basics physics behind MRI
• Nuclear Magnetic Resonance
• Image formation
• MRI images
• Contrast, resolution and SNR.

Recap

Before we then move on with this week, I want to quickly go over what we looked at last class and go through some of the questions.

Which imaging modalities use gamma rays?

SPECT

How is an X-ray image formed?

So it’s basically very similar to taking photographs, but instead of recording the light jumping off of something, you’re shooting light through something, and you recording it on the other side.

How can Computed Tomography images be reconstructed?

Apply Filtered Backprojection algorithm.

Todays Targets

Today we will move away from the X-ray and CT and we’re going to the next one and a very big one of the medical imaging modalities, and that’s MRI.

• Explain the difference between MRI and X-ray/CT
• Describe the principle behind Magnetic Resonance Imaging (MRI)
• List different MRI modalities
• Show the basic concepts behind MRI image formation (slice selection, within slice selection)

Imaging Modalities

So, I showed you this image already last time. What kind of imaging modalities are these? And we basically have those combinations of external and internal and the like. As I showed you already, X-ray and CT is basically external, we’re shooting something through.

And today, we are going to look at MRI and that’s basically the combination of external and internal. And I will show you in the second about what this means.

External and Internal

Why is MRI external and internal?

Why do we say that MRI comes into external and internal sources?

Because it actually uses something from external (radio waves), and what it does is that excites the atomic nuclei that are inside you and actually most of the time, we are using water nuclei. In principle, you can also use something else. Then, we then recording the radio waves that they emit when they relax to regular state back. So that’s why it’s something that’s in between internal and external. I use radio waves to excite and get a resonance in hydrogen nuclei in your body, or other nuclear nuclei, but mostly hydrogen. And then I turn this excitation process off and then I see how radio waves get emitted as those hydrogen nuclei relaxed.

• MRI combines external and internal sources
• it uses an external mechanism (radio waves) to excite atomic nuclei that rotate in a magnetic field (resonance)
• when the atomic nuclei return to their previous energy level, radio waves are emitted (internal) that can be measured

Difference

What makes MRI different from X-ray and CT?

• Provides high-resolution images with excellent soft-tissue contrast superior to X-ray and CT because fo the underlying physics of the imaging process

  Well, compared to X-ray and CT, there is one huge advantage. That is we are actually seeing a lot of soft tissue contrast, what we talked a little bit about it last time. If we take an X-ray or CT image, what we are using is in order to get contrast in the images, the attenuation coefficient. And the attenuation coefficient depends on how dense something is. If you have a bone and air, there is a big difference in density, so you get a big contrast. But if you have fat and muscle, there is not that big difference in contrast. But in terms of water content and kind of what we can see in MR images, we actually get contrast. So it’s very good for soft tissue contrast.

  I don’t know has anyone tried to get an MRI scan of their knee because they maybe torn a ligament I have worked with. So they use this and if you look at this is because there you can really see where are the tendons where are the muscle and so on. I tried to look at my knee actually, I couldn’t understand anything, even though I knew approximately that is bone. But if you’re used to looking at brains, looking at knees like no idea where we are.

• Contrast in the MRI signal is based on the difference of hydrogen protons in the tissue and physiological structures.

  Like I already mentioned so the MRI signal uses the hydrogen atoms and basically it depneds on how they are bound in the tissue, what the physiological properties of these are, how much movable artery in there and how is their distribution.

• Can image anatomical structures as well as biochemical properties based on physiological function, including blood flow and oxygenation.

  What we can also do is we can image some physiological process. So if you look at X-ray or CT, they are very good at showing you the structure. If we look at SPECT and PET on Thursday, they’re very good at showing you function because we can target functions in the body by using SPECT and PET. MRI can do a little bit of both. It can definitely do structure because it can show you different contrasts for different tissue types. But it can also show you function, for example, there are something that is called the bold response that’s blood oxygenation response. What we look at this, we can basically see where in the brain, for example, is a lot of oxygen consumed and this we associate with neuronal activity. So this is how we get to functional MRI and you’ll see example later.

Reason

What makes MRI different from X-ray and CT?

• MRI is harmless as it does not use ionzing radiation, in contrast to ordinary X-ray or Computer Tomography

  And then, one of the biggest advantages is of course that MRI is harmless. So in CT or X-ray, we’re actually using ionizing radiation. So we’re giving you some radiation and there’s a limit how much radiation we can put you through per year. That’s why usually so here in Denmark, it’s centrally recorded, but in a lot of other countries, you have an X-ray pass where it basically states the X-rays that you’ve gotten throughout your life. So you’re sure that you are not getting too many radiation. And in MRI, we don’t have this, it’s basically using magnetism, and there have been quite a few studies and there are no long-term effects of lying in the MRI scanner.

• BUT patients with magnetic metal in the body or a pacemaker cannot be examined with MRI due to the strong magnetic field, and patients with clastrophobia may have difficulties undergoing MRI.

  But there is a big caveat if you have any kind of metal in your body, or you for example, have something electric like a pacemaker or a deep brain simulation could also be an issue, you can unfortunately not be scanned. And that’s because of we have this huge static magnetic field, and this basically mean you’re getting put into a huge magnet. Now if you have something magnetic in your body, it’s going to react to it. And some of the stuff that is welded in your body, for example, you’ve had a broken arm and usually they use titanium, it may be fine to go in, but the other thing is that, because titanium is not magnetic, but if you’re in there and you have a metal, what it will change is to susceptibility of the magnetic field, and it will actually make a big black hole in image.

Different Types of MRI

If we look at different types of MRI images, I just brought you some here. Does anyone has a clue what they are?

Below are some examples of the brain, white is the white matter of the brain. The gray parts on the outside is the cortical ribbon, so that’s where all our neurons are located. Our gray matter and then the black parts are basically our ventricles.

And I will just quickly go through. We have structural MRI.

This could happen with different contrasts. In the clinic, we use so called T1 and T2 weighted, sometimes diffusion images, but mostly, T1 and T2 weighted. And they have different contrasts. The contrasts is flipped. And in T1 image, the white matter is light brighter and the gray matter darker. In the T2, it’s the other way around.

In Functional MRI, what you see here is exactly changes in the blood oxygenation levels, and this means basically, we think there is some brain activity going on here.

And then, we have diffusion weighted MRI (DWI). Diffusion MRI can be used in order to look at basically how are the neuronal tracts formed. So we look at water diffusion inside the brain and then we can do that we call track tography to show you what to connections are between different areas of the brain.

Then, there is perfusion weighted (PWI). Imagine here we are very interested when we for example, have a stroke. To use something like this.

Finally, we have MR spectroscopy. You can look at the chemical properties over a piece of tissue, for example, we are looking at some necrotic tissue and we’re looking at the composition there, at the chemical composition. That’s also a thing.

So, you can actually do a lot of different things with MRI, it’s quite versatile.

Basic Physics NMR

Proton

So, let’s go to the basic physics.

MRI uses the nuclear magnetic resonance (NMR) property of the matter of the object.

What is NMR?

This basically means that, when I have an atom, for example, the hydrogen atom, and I look like it in a more crude view, not a quantum mechanic view or something. What I can see it looks like a small magnet with the north and south pole. And that’s because our little proton of the hydrogen has what we call spin and that induces a magnetic moment. So I have a small magnet, you can think of it like the picture below.

The atomic nucleus of hydrogen (a proton) behaves like a small magnet with a north and a south pole (a magnetic dipole).

So this is basically our small hydrogen proton, and this is what we call a spin or basic space exisiting induced magnetic moment. And this is what we assume has been.

Compass

What we are using now is this property that it’s basically a small magnet. So, if we think about our hydrogen atom, like a compass. So I drew a compass here.

So you have a north and a south pole on the outside. There’s an external magnet and here you have a north and South pole, this is our hydrogen atom.

• Like compass needles, protons tend to align along the direction of an applied magnetic field.

If we put some kind of magnet into an external magnetic field, it will align, just like we have here. Now, let’s say if I push it, I push it, it will swing, but the external magnetic field will lead it to align again. So it were kind of oscillate and then it will come to rest. Visualization is below.

• If a compass needle in rest is given a push, it will oscillate about the north direction before it eventually comes to rest.

Here, a little bit of the really basic physics comes again. When I have a magnet that is oscillating and then I put a coil next to it. What can I measure? $\implies$ You introduce an electric signal into the coil. That’s also how an electromoter partially works, right? You mechanically turn something and you turn magents around a coil and you get electricity out. That’s how regular electromoter works.

• As long as the needle oscillates, it will generate an oscillating magnetic field (emit radio waves).

So here, we can try and push thing like I said before. And when it oscillates and util it relaxes, if we have a coil next here, we can actually measure an electric signal.

And basically what we can do is instead of pushing it, we can subject it to an oscillating field from the outside, and if that oscillating field is at the right frequency, we get the compass needle to swing and swing and swing more until it basically filps over and then I take my oscillating field away and then I can measure how it swings back to the neutral position.

• The reverse process occurs if the compass is subject to an oscillating field from an external source that push an initially resting needle in synchrony with its natural oscillation frequency: The needle will start swinging and the oscillation will gain amplitude.

• Explore Below

  Video 1. MRI Compass Example

  Watch link https://www.youtube.com/watch?v=shB8T8cOeas

Spin

We believe that our hydrogen and our spin behaves like a small compass. And again, this is an imaeg what we’re looking at this little ball with an arrow. In principle, and when we look at the spin, instead of a compass needle, that’s swinging right through left. What we have when we look at our magnetic moment is a precession around the north.

So if you try to visualize this where before we had a compass going like this, when you have a spin, what happens is precesses, and then it precesses more like this. So it’s a little bit different quantitation of movement.

• Whereares compass needles will swing through north, the motion of the proton magnetic moment is precession around the north direction (vibration vs. precession)
• This difference between nuclei and normal compass needles is not of fundamental importance for the MR phenomenon, but it is certainly worth keeping in mind.

And it’s not really important that you notice distinction, but it’s worth keeping in mind when you’re thinking about it. But you don’t need to know more about it.

Things we use

Most of the time, we use hydrogen nuclei, why do we do this? Well, human body is what 75% water, so it’s abundant. So we can use that in order to image basically any part of the body. But you can also use other nuclei. For example, you can use helium and this is when they use this hyperpolarization MRI scans. This is mostly used for pulmonary MRI, so you make them inhale something, and then you have a very good contrast in the lung. And as you know, helium as long as you don’t do too much, it’s not hard to just makes you speak in a funny way when you inhale it and of course you need to be sure that there’s enough oxygen in the body. So the helium doesn’t overtake oxygen.

You can also use a floor and nature and so on, there’s a different list and you can look at other nuclei. But in the clinic, I have to say, we don’t use anything else besides a regular water. In research, I would say 95% is a regular water scans. A lot of it is functional scans.

• Most frequently, the MR signal is derived from hydrogen nuclei (meaning the atomic nuclei in the hydrogen atoms). Most of the body’s hygrogen is found in the water molecules.

• Few other nuclei are used for MR:

  
  Figure 11. List for the nuclei that are used for MR

Image Formation

Get the single signal

So basically what you’ve learned now by looking at the simulator and by playing around with it is if I have a single little compass or hydrogen atom. How do I get one signal out? That’s not going to cut it if you’re trying to image the brain or the knee and you have millions of those. So how do we actually get an image out of this?

What we usually do is in X-ray, for example, we have those kind of antennas and we can measure this. So think about like this when I have my X-ray and I shoot X-rays through you and I measure it with my photographic plate on the back. Basically you can think about those photographic plate being small antennas that receives the X-ray signal that goes through, and I can do this because my X-rays are very very small. So I get a good resolution when I shoot X-rays through you. And exactly this way because it’s so small, the resolution is what we call wavelengths limited. This means, we can only measure things that are approximate to the wavelength of the signal we’re looking at. And X-rays and gamma rays, you saw that’s very small, so we can measure very very small things with it. But in MRI, it’s several meters, it’s not like I could see there’s even a human in the scanner if I would try the same approach. So the thing is we have to come up with something completely different. We cannot just put a human in and then excite and then stand and wait for something to come out. Because the signals that come out, if we would just put some kind of a coil around. And just say, oh, I have one coil here, I received one signal. You would get a big blob and that’s it. You wouldn’t get the resolution you need.

• So NMR yields signal of a single atomic nucleus, but how do we get an image out of this?
• Try and use antennas that can detect where in the body the radio waves are emitted? “optical” technique such as X-ray
• These approaches are “wavelength-limited”, which means that they cannot be used to acquire images more detailed than approximately one wavelength.
• Wavelengths in MR typically several meters long

So, if we can’t do it like an X-ray and CT, what can we else do?

OK guys, let’s look at some of the ideas that are there.

• Opinion 1 $\implies$ If I could make a lot more measurements then maybe I can get back to what was there.
• Opinion 2 $\implies$ Has something to do with gradient coils.
• Opinion 3 $\implies$ Since there’s no ionizing radiation, we can do as many experiments as we like. We think that by composing many images from different angles we can somehow get a higher precision.

History and Intro

Image formation for MR is actually fundamentally different than what we do in CT and X-ray. And this principle of nuclear magnetic resonance has been around since the 40s by Felix Bloch and Edward Purcell.

Actually, it took another 30 years until someone could use it to make an image and that’s because it’s actually complicated to do this.

Like what we’ve mentioned before, simply using the magnetic field itself is not enough. What we are on top of that needing to use is linear field variations. And with this, we can get by using gradient coils, so we’re introducing a gradient in the magnetic field.

Slice Selection

Let’s say I am lying in the MR scanner, the MR scanner is actually all the way around me this way. So, there’s a magnetic field if I want to image my head this way.

So there’s a static magnetic field that’s going with the north pole and the south pole behind me. I’m lying in there looking at the scanner, but this means I have the same magnetic field in all direction. Let’s say the doctor now only wants to look at the slice that goes right through my nose. So he doesn’t want to look at all of my head but only wants to look at my nose. What I can do is we have these so-called gradient coils. And what I then can do is I can vary my static magnetic field that is now let’s say three Tesla. All the way through me, it is a big plane of three Tesla because I’ve two magnets in the front and in my back if you visualize like this. I call this the x-direction, and in this x-direction, I can put a gradient and what it means is the following, I vary the strength of my big magnetic field (B0) a little bit. And this means if I vary little bit, I also change my resonance frequency. So my resonance frequency changes a little bit from my right ear to my left ear and this means if I hit with the resonance frequency, I can then excite only exactly the plane that goes through my nose. So, that’s one thing. Instead of the whole 3D volume, first thing I need to do is I need to actually excite a certain slice. That means by just putting a gradient in one direction, for example, in what I call x-direction, I can then slect a slice in this x direction, that’s the first thing.

• The magnetic field strength can be controlled so that it, for example, increases from left to right ear, while the direction is the same everywhere (along the body)
• By making the field inhomogeneous in this way, the resonance frequency varies in the direction of the field gradient.
• If we then push the protons with radio waves at a certain frequency, the resonance condition will be fulfilled in a plane perpendicular to the gradient.

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Static Magnetic Field (B0): In MRI, there’s a strong static magnetic field B0, which aligns the nuclear spins of atoms in the body along its direction. This magnetic field is uniform and the same in all directions.

Gradient Coils: Gradient coils are additional coils placed within the MRI scanner. They allow for the manipulation of the static magnetic field along specific directions, typically referred to as $x, y$ and $z$ directions.

Varying Magnetic Field Strength: Within the MRI scanner, they can slightly change the strength of the magnetic field in the $x-$direction. This variation is done very precisely.

Resonance Frequency: The resonance frequency of nuclei (e.g., hydrogen nuclei or protons) is directly proportional to the strength of the static magnetic field (B0).

Selective Excitation: By varing the magnetic field strength along the $x-$direction (using gradient coils), the resonance frequency also varies slightly from one side of the body to the other. This means that the protons in different regions of the body will have slightly different resonance frequencies.

Selective Slice Excitation: To image a specific slice (e.g., the one going through the nose) the MRI system sends a radio frequency (RF) pulse at a specific frequency that corresponds to the resonance frequency of the desired slice. This pulse is precisely tuned to match the varing resonance frequency along the $x-$direction.

Resonance and Excitation: When the RF pulse matches the resonace frequency of a specific slice, it excites the protons in that slice. This excitation is like flipping the magnetic spins in that slice temporarily. After the RF pulse is turned off, the excited protons emit radio frequency signals, which are detected and used to create the MRI image.

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Spatial Localization within a Slice

Then, we have a whole slice, and they will all emit radio waves. So then let’s say I have my slice here through my nose. Now I have this whole plane which should be an image, which is a cutout through my brain, and all the radio waves in there. They emit something simultaneously, that’s a problem right? Because now I have a whole 2D plane and I don’t know where something is coming from.

• After the protons in a slice are excited, they will all emit radio waves. We can’t tell them apart.

Then, the tricks come. What we can do is we can create different patterns of magnetization in or throughout the slice with the help of other gradients.

Now I use some gradient variation in $x$, but I can also introduce some gradient variation in $y$ and $z$. So I basically can split up my 2D slice here. And basically the way that it essentially works, if you look at it roughly is I know what kind of gradients I am applying, so just like in my $x$ direction, I know what gradient I am putting, I can use my gradients in my $y$ and $z$ to draw patterns and because I know what I’m putting in, I know what I’m expecting out. Now, how do we draw patterns?

So basically, once after we have put our body in our external magnetic field, all my spins in this plane they look the same way, they rotate or they are aligned with my external magnetic field of the scanner, and they basically start processing at their resonance frequency. So if I say my magnet here was north and south, all my magnetic moments in this plane would be aligned with the external field and they were precessed with the resonance frequency that I made because I made a gradient in $x$ direction.

• Immediately after excitation the spins all point in the same direction perpendicular to the magnetic field.

• They will tereafter precess around the magnetic field, that is, they will rotate in the plane of the parper at a frequency that is dependent on the magnetic field. Insofar as the field is made to increase from left to right by applying a field gradient briefly, the spins will each turn an angle that depends linearly on the nucleus’ position.

如图所示，激发后，所有自旋都会立即指向与磁场垂直的同一方向，即指向纸外。此后，它们将围绕磁场进行前冲，也就是说，它们将以取决于磁场的频率在纸张平面上旋转。只要通过短暂的磁场梯度使磁场从左到右增加，自旋就会各自转动一个角度，这个角度与原子核的位置成线性关系。

Now, what I can do is when they precess like this, I can basically apply some gradients in the $y$ and $z$ direction and when I do this, I can draw a pattern. Just like I used a gradient coil to select the resonace frequency to select the slice, I can also use the gradient coil too then changing kind of the way they are precessing. What we call this is basically a phase roll.

• This is so-called “phase roll” is an example of a spin pattern that can be created in the patient by use of gradients. The word “phase” expresses the direction that the spins point in.

这种所谓的 “相位旋转 “就是上述自旋模式的一个例子，可以通过梯度在患者体内产生。相位一词表示自旋指向的方向。可以看到，相邻的自旋指向几乎相同，但在整个物体中，磁化旋转了几圈。梯度开启的时间越长，产生的磁场变化越大，积累的 “相位旋转 “就越多（单位长度内的旋转次数越多）。

And what it means that I actually create this type of spin pattern by phase. What we mean is if I have a spin that is precessing kind of where, then this is we call the phase. So if you look at a spin that’s rotating from the top, then those arrows would be the projected view. And if they’re all rotating in the same way, so they’re rotating at the same time, you would look into the projection, they’re all looking upwards. If I make some of them have an offset, then the 2D projection looks like this.

And then, even though my neighboring spins here, they look almost the same, if I look, let’s say all the way through my slice in $z$ or in $y$ direction, I see that my magnetization turns several times.

• Neighboring spins point in nearly the same direction, but throughout the object, the magnetization has rotated several turns.

And the longer I have my gradients act on me, the more we accumulate the spin roll. So you can think about it like a spiral, and the more I turned a gradient on to tighter, I wind my spiral.

• The longer time a gradient is turned on, and the greater the field variation that arises, the more “phase roll” is accumulated.

We use these spin patterns and we know what we’re putting into the patient. So we know exactly what spin pattern using in the patient in my $y$ and $z$ direction, and usng this when I then come out and measure, I can then compare the patterns I put in with the patterns I get out.

• So by using gradients we may “draw” spin patterns in the patient. In return, we receive radio waves whose strength reveals the similarity between patient structure and the drawn pattern.

我们通过使用梯度，使自旋以可控的方式指向各个方向，从而同时失去了信号。通过比较上述两种情况就可以看出这一点，因为测得的磁化是各个自旋贡献的总和。当自旋相位相同（即指向同一方向）时，它们会共同产生相当大的磁化，从而发出无线电波。当自旋指向各个方向（如施加梯度时）时，它们的总和就非常小。因此，发出的无线电波相对较弱。

因此，使用梯度的增益可能非常小：我们只是失去了信号。然而，情况并非一定如此。例如，请看下图所示的情况，质子并不是（像上面那样）从左到右均匀分布的，而是含水量有规律的变化。

从图中我们可以看到，在应用与上述相同的梯度之前和之后，自旋的指向是怎样的。前面两幅图的唯一区别是 “洞”，表示缺少质子（局部无水环境–例如骨骼）。

现在我们来考虑一下新情况下的总磁化率和信号。只要自旋全部指向同一方向，即在施加梯度之前，我们接收到的信号就会比之前少，因为对磁化有贡献的自旋数量更少。因此，施加梯度之前的信号就是总含水量的测量值。

另一方面，在施加梯度后，我们接收到的信号比上述类似情况（均匀的水分布）下的信号要多。这可能看起来很奇怪，因为对磁化有贡献的质子减少了。然而，剩余的质子基本上都指向同一个方向，因此它们的磁化总和相对较大。

有结构的物体（含水量不同）在施加梯度后仍能发射无线电波，这是因为相位卷与物体的结构相匹配，可以理解为相位卷的 “波长 “与示例中水坑之间的距离相同。

如果情况并非如此，则会出现磁化的不同贡献相互抵消的趋势。因此，信号是相位滚动模式与物体结构之间 “相似性 “的度量：通过施加梯度在物体中引入相位卷之后，我们收到的信号就是物体中是否存在与相位卷相匹配的结构的量度。

因此，我们现在有了理解磁共振成像的基础：人体中不同的相位滚动模式被一个接一个地绘制出来。由此产生的无线电波信号会被记录下来。根据特定相位滚动模式的信号大小，我们就可以知道该模式是否与人体结构相似。

MRI Images

Image Comments

So brain we often want to use MRI because we want to see soft tissue contrast, so we want to look at the balance between gray and white matter, and also, it’s not so good to shoot ionizing radiation at the brain. So if we can avoid, we don’t do it.

The knee again, often what were doing the MRI is that we have some soft tissue issues. For example, we have a ligament torn or something like this.

At the spine often what they’re using it for is to look for the nerves, to see if there’s anything because in principle, if you’re looking for a discus prolapse. So if you’re looking for a spinal injury, where the discs collapse, then you could talke an x-ray, right? If you think the bonus crush, you look at when x-ray, but if you want to look at injuries of the spinal cord, it’s better than to use an MRI.

MRI Scanner

Pass Through

Contrast, Resolution and SNR

• contrast in MR images comes from the differentiation of MR signal with respect to spin (proton) density, and T1 and T2 relaxation times of the tissue
• resolution in MRI is very high in the range of a millimeter to one - hundredth of a millimeter
• resolution depends on sequence and on the relaxation times of the tissue that is being imaged
• SNR depends on the data collection method (pulse sequence or spatial sampling and signal averaging), imaging parameters (strength of magnetic field, spin density, T1 and T2 relaxation times, coil sensitivity)
• prominent sources of noise and field inhomogeneities that cause artifacts and affect tissue contrast in MR images are RF noise, field inhomogeneities, motion, etc.

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This is the learning note for mia, and all the material above are from the course "Medical Image Analysis" taught by UCPH.