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Magnetic Resonance Imaging (MRI)

Introduction

92 elements occur naturally on earth.
Human body is built of only 26 elements.
Oxygen, hydrogen, carbon, nitrogen elements constitute 96 % of human body mass.
Oxygen is 65 % of body mass; carbon is 18 %, hydrogen 10 %, nitrogen 3.2 %.
Let us ignore all elements but Hydrogen.
The body is largely composed of water molecules. Each water molecule has two hydrogen nuclei or protons.
The composition of the human body can be looked at from the point of view of either mass composition or atomic composition.
To illustrate both views, the adult male human body is approximately 57% water, and water is 10% hydrogen by mass but 67% by count of atoms (i.e. 67 atomic percent).
The percentage of water in infants is much higher, typically around 75-78% water, dropping to 65% by one year of age.
Thus, most of the mass of the human body is oxygen, but most of the atoms in the human body are hydrogen atoms.

Why do we take hydrogen as our MR imaging source?

There are two reasons:

It’s the most abundant element we have. Secondly, in quantum physics there is a thing called Gyro Magnetic Ratio. The largest gyromagnetic ratio of a particle in the body. (the ratio of its magnetic momentum in an atom to its angular momentum).

This gyro magnetic ratio for Hydrogen is 42.57 MHz/Tesla.

For who really wants to know, Hydrogen is not the only element we can use for MR imaging. In fact, any element, which has an odd number of particles in the nucleus, can be used. Some elements, which can be used, are:

MRI Hardware

Main components:

Primary magnet
Gradient coil
Radiofrequency (RF) coil
Computer system

The main characteristics of a main magnet are:

Type (superconducting or resistive electromagnets, permanent magnets).
Strength of the field produced, measured in Tesla (T). In current clinical practice, this varies from 0.2 to 3.0 T. In research, magnets with strengths of 7 T or even 11 T and over are used.
Homogeneity (Homogeneity refers to the uniformity of a magnetic field in the center of a scanner when no patient is present).

Primary magnet

Magnet Types:

Primary magnet
- A permanent magnet consists of a material, which has been magnetized such that it will not loose its magnetic field.
- Permanent Magnets are constructed of blocks or slabs of naturally occurring ferrous material. Increasing the amount of ferrous material increases the weight, size, and field strength.
- Up to 30 tons of iron may be needed, restricting their placement to rooms with a strong enough floor.
- The field strength is usually very low and ranges between 0.06T ~ 0.4T (the unit for magnetic field strength is Tesla. 1 Tesla = 10000 Gauss).

Resistive magnet
- Resistive magnets are very large electro magnets, like the ones used in scrap yards to pick up cars. The magnetic field is generated by a current, which runs through loops of wire.
- Resistance is a property of the wire that can pose as an obstacle. Resistance will convert the current into heat, which requires water-cooling. In order to maintain the magnetic field, there must be a constant current. Resistive magnets come in two flavours: air-core and iron-core.
- The field strength can be up to 0.3 Tesla.
- Used in horizontal or vertical field systems. They usually have an open design.

Superconducting magnet
- Todays most commonly used magnets are superconducting magnets.
- Superconductive MRI magnets use a solenoid shaped coil made of alloys such as niobium/titanium or niobium/tin surrounded by copper. These alloys have the property of zero resistance to electrical current when cooled down to about 4-10 Kelvin (-263º_-269º C). The coil is kept below this temperature with liquid helium.
- Superconducting magnets can achieve very high field strengths, so the FDA has a 4T limit. Generally, clinical scanners range between 0.5T and 3T.
- Most superconducting magnets are bore type magnets.
- Superconductivity allows for systems with very high field strengths up to 12 Tesla.

RF Coils

RF coils are needed to transmit and receive radio-frequency waves used in MRI scanners. RF coils are one of the most important components that affect image quality. Current MRI scanners have a range of RF coils suitable to acquire images of all body parts.
Coils are designed to receive only, transmit only, or transmit and receive.
There are two main types of RF coils use in MRI: 1.Body coil 2.local coils
The body coil located within the bore of the magnet is a transmit and receive (TR) coil.
Local coils can be a transmit/receive coil or a receive only.

There are two types of RF local coils: volume coils and surface coils.

Surface coils

As the name already implies, surface coils are placed close to the area under examination such as the temporo-mandibular joint, the orbits or the shoulder.

Volume RF Coils

The design of a volume coil is usually a saddle shape, which guarantees a uniform RF field inside the coil.

MRI Physic

Introduction

If we look at a bunch of hydrogen protons (as in a molecule) we see, in fact, a lot of tiny bar magnets spinning around their own axes.
In our body these tiny bar magnets are ordered in such a way that the magnetic forces equalize. Our bodies are, magnetically speaking, in balance.
Just as well, otherwise we would attract a lot of metal when we go about.

What happen to the hydrogen protons, when we put a person in a magnet:

They align with the magnetic field. This is done in two ways, parallel or anti-parallel. You could call this also Low and High Energy State.

Bo is the indication for the magnetic field of the MRI scanner
There are more protons aligned parallel or low energy state than there are anti-parallel or high energy state.
The excess amount of protons aligned parallel within a 0.5T field is only 3 per million (3 ppm = parts per million), in a 1.0T system there are 6 per million and in a 1.5T system there are 9 per million. (That is also the reason why 1.5T systems make better images than systems with lower field strengths)

They precess or wobble due to the magnetic momentum of the atom.

Both gyroscopes and nuclei possess angular momentum. For the gyroscope, angular momentum results from a flywheel rotating about its axis. For the nucleus, angular momentum results from an intrinsic quantum property (spin). Momentum is also sometimes called inertia.
Protons spin around the long axis of the primary magnetic field = precession rate is termed Larmor frequency.
The Larmor frequency Precession can be calculated from the following equation:

If we have a MRI system of 1.5 Tesla then the Larmor or precessional frequency is: 42.57 x 1.5 = 63.855 MHz. The precessional frequencies of 1.0T, 0.5T, 0.35T and 0.2T systems would work out to be 42.57 MHz, 21.285 MHz, 14.8995 MHz and 8.514 MHz respectively.
We need the Larmor frequency to calculate the operating frequency of the MRI system.

Excitation

Before the system starts to acquire the data it will perform a quick measurement (also called pre-scan) to determine at which frequency the protons are spinning with just the static magnetic field (the Larmor frequency).
Once the centre frequency is determined the system will start the acquisition.
Let us assume we work with a 1.5 Tesla system.
The centre or operating frequency of the system is 63.855 MHz.
In order to manipulate the net magnetization we will therefore have to send an Radio Frequency (RF) pulse with a frequency that matches the centre frequency of the system: 63.855 MHz.
This is where the Resonance comes from in the name Magnetic Resonance Imaging. Only protons that spin with the same frequency as the RF pulse will respond to that RF pulse.
If we would send an RF pulse with a different frequency, lets say 59.347 MHz, nothing would happen.
By sending an RF pulse at the centre frequency, with a certain strength (amplitude) and for a certain period of time it is possible to rotate the net magnetization into a plane perpendicular to the Z axis, in this case the X-Y plane.
We just flipped the net magnetization 90º. But there is a parameter in our pulse sequence, called the Flip Angle (FA), which indicates the amount of degrees we rotate the net magnetization.
It is possible to flip the net magnetization any degree in the range from 1º to 180º. For now we only use an FA of 90º.

Relaxation

We rotated the net magnetization 90º into the X-Y plane. (We could also say that we lifted the protons into a higher energy state, same thing.)
This happened because the protons absorbed energy from the RF pulse and this is a situation that the protons do not like.
they prefer to align with the main magnetic field or, in other words, they would rather be in a low energy state.
Now something happens that is referred to as Relaxation. The relaxation process can be divided into two parts: T1 and T2 relaxation.

T1 Relaxation and Curves

T1 relaxation describes what happens in the Z direction.
T1 relaxation is also known as Spin-Lattice relaxation, because the energy is released to the surrounding tissue (lattice).
T1 relaxation happens to the protons in the volume that experienced the 90º-excitation pulse. However, not all the protons are bound in their molecules in the same way.
The curve shows at time = 0 that there is no magnetization in the Z-direction right after the RF-pulse. But immediately the Mz starts to recover along the Z-axis. T1 relaxation is a time constant. T1 is defined as the time it takes for the longitudinal magnetization (Mz) to reach 63 % of the original magnetization.
Each tissue will release energy (relax) at a different rate and that’s why MRI has such good contrast resolution.

T2 Relaxation and Curves

First of all, it is very important to realize that T1 and T2 relaxation are two independent processes.
T1 relaxation describes what happens in the Z direction, while T2 relaxation describes what happens in the X-Y plane. Thats why they have nothing to do with one another.
When we apply the 90º RF pulse something interesting happens. Apart from flipping the magnetization into the X-Y plane, the protons will also start spinning in-phase.
In the meanwhile the whole lot is still rotating around the Z-axis in the X-Y plane.
This process of getting from a total in-phase situation to a total out-of-phase situation is called T2 relaxation.
Just like T1 relaxation, T2 relaxation does not happen at once. Again, it depends on how the Hydrogen proton is bound in its molecule and that again is different for each tissue.
Right after the 90º RF-pulse all the magnetization is flipped into the XY-plane. The net magnetization changes name and is now called MXY.
At time = 0 all spins are in-phase, but immediately start to de-phase. T2 relaxation is also a time constant. T2 is defined as the time it takes for the spins to de-phase to 37% of the original value.

MRI characteristics in black and white images

Acquisition

During the relaxation processes the spins shed their excess energy, which they acquired from the 90º RF pulse, in the shape of radio frequency waves.
In order to produce an image we need to pick up these waves before they disappear into space.
This can be done with a Receive coil. The receive coil can be the same as the Transmit coil or a different one. An interesting, but ever so important, fact is the position of the receive coil.
The receive coil must be positioned at right angles to the main magnetic field (B0).
The signal is called: Free Induction Decay. The FID is the signal we would receive in absence of any magnetic field.

Figure below shows the entire process graphically.

More Physics

if we assume we have a 100% homogeneous magnetic field (which it is not), then all the protons in the body would spin at the Larmor frequency.
This also means that all protons would return signal. How do we know whether the signal is coming from the head or from the foot? Well, we do not. If we would leave things as they are then we wouldn’t get a pretty picture; certainly not one we would expect. It would have nothing but undecipherable blobs.
The solution to our problem can be found in the properties of an RF-wave, which are: phase, frequency and amplitude.
First we will divide the body up into volume elements, also known as: voxels. Then we are going to code the voxels such that the protons, within that voxel, will emit an RF wave with a known phase and frequency.
The amplitude of the signal depends on the amount of protons in the voxel.
The answer to our problem is: Gradient Coils.

Gradient Coils

Gradients are loops of wire or thin conductive sheets on a cylindrical shell lying just inside the bore of an MR scanner ,which enable us to create additional magnetic fields, which are, in a way, superimposed on the main magnetic field B0.
When current is passed through these coils a secondary magnetic field is created.
This gradient field slightly distorts the main magnetic field in a predictable pattern, causing the resonance frequency of protons to vary in as a function of position.
The primary function of gradients, therefore, is to allow spatial encoding of the MR signal.

There are three sets of gradient coils in MR systems: the x-, y-, and z-gradients.
Each coil set is driven by an independent power amplifier and creates a gradient field whose z-component varies linearly along the x-, y-, and z-directions, respectively.
The design of the z-gradients is usually based on circular (Maxwell) coils, while the transverse (x- and y-) gradients typically have a saddle (Golay) coil configuration.
These coils that are used to vary the intensity of the magnetic field:
In the left to right direction is the X gradient coil.
In the anterior to posterior(top to bottom) direction is the Y gradient coil.
In the head to foot direction is the Z gradient coil.

Even More Physics

A journey into k-Space

The MRI data prior to becoming an image (raw or unprocessed data) is what makes up k-space.

Synonyms for k-space are matrix and time time-domain. Same things. The reason why the phrase k-space is used and not the others are because everybody uses it in the literature.

Question: Why is k-space so important?

Answer: It helps us to understand how an MRI image is acquired and how various pulse-sequences work.

Figure (1) shows a square. This is a representation of k-space, matrix, time-domain or whatever you would like to call it. We see two lines, X and Y, which divide the box such that both left, right and top, bottom are symmetrical. In this box we are going to put our MRI data before it gets reconstructed into an image.

The acquired data (also known as raw data) is put into this box such that signals with low frequencies go in the centre and those with high frequencies are spaced around the centre.
Signal with low frequencies contain information about signal and contrast, while high frequencies contain information about spatial resolution (sharpness).
Raw data can be reconstructed in two ways. Figure (1B) shows one way of reconstruction we are not very familiar with. This is what we call a raw data image. It is just a different representation of the image data.
The image shows very clearly that the data is spaced around the centre. You can also see that the centre contains high and low signal as well as contrast information. Spaced around the centre you see rings, which make up information regarding spatial resolution. Furthermore, it can be seen that k-space is symmetrical both from left to right and from top to bottom.
The other way of reconstructing raw data will give us an image, which we recognize immediately (Figure 3). This image is reconstructed from the same raw data set.
Engineers use the raw data image (Figure 2) to obtain more information regarding image artifacts. Image artifacts are usually caused by wrong frequencies.

To illustrate the fact that information about signal/noise and contrast is stored in the centre of k-space we can do the following experiment. Have a look at Figure 4. Here we only reconstructed the central part of k-space (Figure 4A).
The resulting image (Figure 4B) shows contrast, but the image is very blurred. This is because we left out the information regarding spatial resolution, which is stored in the outside of k-space.
We can do the same thing, but this time we only reconstruct the outside of k-space (Figure 5A).
The resulting image (Figure 5B) shows sharp contours, but almost no contrast information.