Physics of MRI

Physics of MRI - Detailed

Magnetism is a property of matter that is a result of the orbiting electrons in atoms. The orbiting electrons cause the atoms to have a magnetic moment associated with an intrinsic angular momentum called spin. Spin will be discussed in more detail a little bit further down. It's convenient to imagine the electron spinning on its axis with the up and down orientations. However, in reality the electron is not physically spinning!

The body is largely composed of water molecules. Each water molecule has two hydrogen nuclei or protons. MRI takes advantage of the high prevalence of hydrogen in the body and the magnetic properties of the proton in a hydrogen atom. Hydrogen atoms induce a small magnetic field due to the spin of this atom's proton. When a person goes inside the powerful magnetic field of the scanner, the magnetic moments (the measure of its tendency to align with a magnetic field) of some of these protons changes, and aligns with the direction of the field.

The magnetic field in an magnetic resonance imaging (MRI) scanner is generated by surrounding a coil of wire with super cooling fluids (liquid helium and liquid nitrogen) lowering the temperature to about 10°K (-263°C or -441°F). Electrical current in the coil moves very fast creating the extremely large magnetic field.

Magnetic field strengths are measured in units of gauss (G) and Tesla (T). One Tesla is equal to 10,000 gauss. The earth's magnetic field is about 0.5 gauss. The strength of electromagnets used to pick up cars in junk yards is about the field strength of MRI machines (1.5 to 2.0T). The B_o in MRI refers to the main magnetic field and is measured in Tesla (T). The majority of MRI systems in clinical use are between 1.5T and 3T. Altering the field strength will affect the Larmour frequency at which the protons precess.

The protons placed in a magnetic field have the interesting property in that they will absorb energy at specific frequencies, and then re-emit the energy at the same frequency. To measure the net magnetization in a brain scan, a coil can be placed around the head can be used to both to generate electromagnetic waves and measure the electromagnetic waves that are emitted from the head in response.

Proton density (PD) is the concentration of protons in the tissue in the form of water and macromolecules (proteins, fat, etc). The T1 and T2 relaxation times define the way that the protons revert back to their resting states after the initial RF pulse. The most common effect of flow is loss of signal from rapidly flowing arterial blood.

So when the patient is first placed in the static magnetic field that the machine creates, MRI takes advantage of that high prevalence of hydrogen in the body and the magnetic properties of the proton in a hydrogen atom. Hydrogen atoms induce a small magnetic field due to the spin of this atom's proton. Hydrogen protons within the patient's body will then align to the magnetic field which is typically 30 to 60 thousand times stronger than the magnetic field of the earth.

A radio frequency (RF) pulse is then emitted from the scanner, tuned to a specific range of frequencies at which hydrogen protons precess. This results in some of the hydrogen protons being "knocked" 180° out of alignment with the static magnetic field and being forced into phase with other hydrogen protons. The echo time refers to time between the application of RF excitation pulse and the peak of the signal induced in the coil and is measured in milliseconds.

As the energy from the RF pulse is dissipated, the hydrogen protons will return to alignment with the static magnetic field. The MRI signal is derived from the hydrogen protons as they move back into alignment with the magnetic field, and fall out of "phase" with each other. The actual process is much more complicated, but is broken down into T1 relaxation and T2 decay. The MRI signal is then broken down and spatially located to produce images.

Magnetic Resonance

A MRI is an image from a scanner that actually measures "magnetic resonance." A strong magnetic field is placed across the tissue along the direction of the bore of the magnet and is referred to as B_o. The magnetic moments within the tissue will tend to align towards B_o, although because of molecular vibrations and collisions, they will remain mostly randomly distributed. After some time, the magnetic moments will reach an equilibrium with a small amount favoring the direction of B_o. While magnetic resonance can apply to a large number of different atoms (or even molecules), in clinical MRI we are looking at the magnetic moments of the hydrogen nuclei (protons), in the tissue. Hydrogen is used, once again, because it has a very high abdundance in the body, among other characteristics.

Nuclei have an intrinsic quantum property called spin. When a magnetic field is imposed on the nucleus of an atom, this nuclear spin will orient itself according to this field, and so our z-axis can now be the direction of the magnetic field, for convenience.

Spin

In classical physics, a rotating object possesses a property known as angular momentum. Angular momentum is a form of inertia, reflecting the object's size, shape, mass, and rotational velocity. It's typically represented as a vector (L) pointing along the axis of rotation.

Spin is a quantum mechanical intrinsic property of elementary particles. It's very difficult to imagine this property, and the notion of actual rotation can be somewhat helpful. However, it's wise to separate this notion of a spinning particle from the quantum mechanical property we call spin. Although spin is a form of angular momentum, an elementary particle with spin doesn't mean it's rotating; particles with spin simply have spin. For example, although an electron has mass, it's indicated to be a "point particle", occupying no volume of space at all.

How can we imagine an electron rotating? Diagrams and explanations of spin and its consequences can help, but we must be careful not to confuse quantum mechanical (quantized angular momentum) and classical (rotating particle) explanations of MRI.

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Atomic and subatomic particles posses a corresponding property known as spin or spin angular momentum. Protons, neutrons, whole nuclei, and electrons all possess spin and are often represented as tiny spinning balls. Although inaccurate, this isn't a terribly bad way to think about spin as long as you don't take the analogy too far.

Several key differences should be recognized:

•	The particle is not actually spinning or rotating.
•	Spin, like mass, is a fundamental property of nature and doesn't arise from more basic mechanisms.
•	Spin interacts with electromagnetic fields whereas classic angular momentum (L) interacts with gravitational fields.
•	The magnitude of spin is quantized, meaning that it can only take on a limited set of discrete values.

The spin of a nucleus can be compared to a gyroscope.

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Precession

In MRI, we are looking at the behavior of millions and millions of proton-magnets. The net direction of their moments is referred to as the net magnetization vector M. In equilibrium, since more protons are pointing along B_o, M points in the direction of B_o. This direction is typically referred to as the z-axis. There is no net polarization in the x- or y-axes. However, the protons actually rotate round that axis (known as precession), so that any one particular proton at any moment in time will be pointing in some direction in the xy plane.

The simplest version of an MRI sequence involves a so-called 90° pulse. This pulse of energy is exactly enough to rotate the protons 90°, so the net magnetization is rotate from the z-axis, parallel to B_o, into the xy-plane. At that point, Mz, the magnetization along B_o, is 0.

Note that you can put in less energy to give a rotation of less than 90 degrees, which is often used in gradient-echo sequences. Alternatively, you may want to employ a 180° pulse to 'flip' the M vector into the -z direction; this pulse is twice as long (or strong) as the 90° pulse and is used for inversion recovery sequences.

Nuclei precess around the magnetic field for essentially the same reasons that tops or gyroscopes precess around a gravitational field:

•	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. Objects possessing momentum have a tendency to maintain their motion unless acted upon by an external force, like a speeding truck has a great deal of (linear) momentum and can't easily be induced to change its speed or direction. Angular momentum behaves similarly, conferring on the nucleus or gyroscope a strong resistance to changing its orientation or direction of rotation.
•	Static gravitational and magnetic fields create a torque or "twisting force" acting perpendicular to both the field and the direction of the angular momentum. The gyroscope or nucleus doesn't "tip over" but is instead deflected into a circular path perpendicular to the field.
•	The resultant circular motion is called precession. Precession occurs at a specific frequency denoted either by ωo (called the angular frequency, measured in radians/sec) or fo (called the cyclic frequency, measured in cycles/sec or Hz). Since 2π radians = 360° = 1 cycle (revolution), angular and cyclic frequencies can easily be converted by the equation: ωo = 2 π fo
•	The precession frequency of a gyroscope is a function of the mass and shape of the wheel, the speed of wheel rotation, and the strength of the gravitational field. The precession frequency of a nucleus is proportional to the strength of the magnetic field (B_o) and the gyromagnetic ratio (γ), a particle-specific constant incorporating size, mass, and spin. This is embodied in the famous Larmor relationship, given by the equation: *fo = γ B_o**

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The spin is represented by the arrow. Notice the tip of the arrow precesses similar to the top of the gyroscope. This spin allows absorption of a photon of frequency νL, which is dependent on the strength of the magnetic field applied to the nulceus. The applied magnetic field is the direction that the photons axis will align to when it's strong enough.

Resonance and Larmor Frequency

Protons in a magnetic field have a microscopic magnetization and act like tiny toy tops that wobble as they spin. The rate of the wobbling or precession is the resonance or Larmor frequency (νL). In the magnetic field of an MRI scanner at room temperature, there is approximately the same number of proton nuclei aligned with the main magnetic field B_o as counter aligned. The aligned position is slightly favored, as the nucleus is at a lower energy in this position. For every one-million nuclei, there is about one extra aligned with the B_o field as opposed to the field. This results in a net or macroscopic magnetization pointing in the direction of the main magnetic field. Exposure of individual nuclei to RF radiation (B1 field) at the Larmor frequency causes nuclei in the lower energy state to jump into the higher energy state.

In magnetic resonance, the Larmor frequency and is determined by the gyromagnetic ratio γ of the particular magnetic moment (in this case, we are looking at the hydrogen nucleus, and γ = 42.58 MHz/T):

νL = γ * B_o
Where νL is the frequency, γ is the gyromagnetic ratio γ/(2π) in units of hertz per tesla (Hz/T), B_o is the magnetic field.

Now if a really high magnetic field is present, this precession is in the RF portion of the spectrum. The atoms are placed in a non-uniform magnetic field. The nuclei of these atoms will have a different Larmor frequency of spin as a result of the equation above. As the RF electromagnetic radiation is sent through the patient, the atomic nuclei in the body will absorb the energy. This absorption of energy causes nuclei to change the direction of their spin. You can intuitively understand this with the model shown above.

If you transmit energy into the system at the resonant frequency, you can change turn protons away from pointing along B_o. After some time, these protons will "relax" and give off energy to return to the lower energy state. This energy will be given off at the same frequency, and it's this signal that we measure.

Radiofrequency

On a macroscopic level, exposure of an object or person to RF radiation at the Larmor frequency, causes the net magnetization to spiral away from the B_o field. In the rotating frame of reference, the net magnetization vector rotate from a longitudinal position a distance proportional to the time length of the RF pulse. After a certain length of time, the net magnetization vector rotates 90° and lies in the transverse or x-y plane. It's in this position that the net magnetization can be detected on MRI. The angle that the net magnetization vector rotates is commonly called the 'flip' or 'tip' angle. At angles greater than or less than 90° there will still be a small component of the magnetization that will be in the x-y plane, and therefore be detected.

The recovery of longitudinal magnetization is called longitudinal or T1 relaxation and occurs exponentially with a time constant T1. The loss of phase coherence in the transverse plane is called transverse or T2 relaxation. T1 is thus associated with the enthalpy of the spin system, or the number of nuclei with parallel versus anti-parallel spin. T2 on the other hand is associated with the entropy of the system, or the number of nuclei in phase.

When the RF pulse is turned off, the transverse vector component produces an oscillating magnetic field which induces a small current in the receiver coil. This signal is called the free induction decay (FID).

The RF signal has a frequency equal to the unique resonant frequency of the nuclei, the Larmor frequency. Once the RF signal is turned off, three basic processes occur:

•	Absorbed RF Energy is Emitted Nuclei that have absorbed the radio frequency energy will not remain in their excited state for a long time. They return to their initial state, emitting a radio frequency signal to their surroundings. These signals are picked up by detectors that are placed all around the body. The signals are then compiled using Computed Tomography (CT) techniques into an image. The following two nuclear processes are used to assemble a MRI.
•	Spin-Lattice Relaxation When a nucleus absorbs a photon at its Larmor frequency, its spin state changes. However the nucleus will not stay in this state. It will return to its original state after emitting a photon. The time it takes to do this is called the spin-lattice relaxation time, and is given by the constant T1.
•	Spin-Spin Relaxation Another type of relaxation used in MRI is spin-spin relaxation. Because the magnetic field varies, the nuclei's Larmor frequency will vary. Since they spin at different frequencies, the nuclei will gradually end up out of phase, or spin at different times. MRIs use the loss of signal due to the phase-difference between these nuclei to assist in creating the image.

Relaxation

The various types of MRI scans that are used (most commonly the T1-weighted scan and the T2-weighted scan) measure this relaxation time differently. Computer programs translate the data into cross-sectional pictures of the water in human tissue. The layer of myelin that protects nerve-cell fibers is fatty and therefore repels water. In the areas where the myelin has been damaged by MS, the fat is stripped away. With the fat gone, the area holds more water, and shows up on an MRI scan as either a bright white spot or a darkened area depending on the type of scan that is used. Gadolinium (gd) can be injected intravenously to further enhance the sensitivity of the T1-weighted MRI scan.

MRI image contrast is influenced by several characteristics of tissues and other materials including: T1, T2 and T2* relaxation as well as spin density, susceptibility effects and flow effects. Relaxation is the process in which spins release the energy received from a RF pulse.

T1 and T2 relaxation rates affect the SNR in an image. Improvement in the SNR is seen when the TR is increased significantly to about 3 to 5 T1 times. Changing the TR time will also affect the T1 weighting of the image and the acquisition time. T1 weighting occurs in a short TR spin echo sequence because of incomplete recovery of longitudinal magnetization.

The T1 relaxation time, also known as the spin-lattice relaxation time, is a measure of how quickly the net magnetization vector (NMV) recovers to its ground state in the direction of B_o. The return of excited nuclei from the high energy state to the low energy or ground state is associated with loss of energy to the surrounding nuclei. Nuclear magnetic resonance was originally used to examine solids in the form of lattices, hence the name "spin-lattice" relaxation. Two other forms of relaxation are the T2 relaxation time (spin-spin relaxation) and T2* relaxation.

Gradients

A MRI sequence produces signal from all the tissue in the scanner that's within the transmit/receive coils. Without a means of spatial localization, all you would get is a single number for the entire body. Drs. Lauterbur and Mansfield discovered a way to separate signal from different parts of the body. In order to understand how they did it, and how MR scanners work, you need to understand magnetic gradients.

While the main magnetic field of the scanner (B_o) can't change, additional smaller magnetic fields can be added with changing electrical fields. If you remember physics classes, a changing electrical field produces a magnetic field which is the basis of electromagnets. Each MR scanner has 3 sets of spatial encoding electrical coils to produce magnetic fields in the x, y, and z directions. These coils can be adjusted to produce not a constant field but a gradient, in other words a magnetic field that changes in strength depending on your position.

These magnetic fields are much weaker than B_o and vary linearly across the x, y, or z direction. They can even be turned on in combinations to create a linear gradient in any arbitrary direction in space.

Slice-Selection

Now that we have gradients, we can separate different parts of anatomy by frequency. We will start with the simplest type of separation: the imaging slice. Remember that protons only exchange energy efficiently if the frequency of the energy matches their precession frequency. Thus, the 90° and 180° pulses must be sent at the Larmor frequency of the proton. We can combine this with gradients to select a slice of the body to image.

By turning on the magnetic field gradient, the protons at each position in the body experience a slightly different magnetic field - slightly more or less than B_o. Thus, we get a gradient of precession frequencies along the body that differ. By then altering the frequency of our 90° and 180° pulses, we will excite different protons. The magnetic field gradients are close to the order of several hundredths of a percent over a couple centimeters, so an extremely small frequency change will move the position for the next image slice.

The scanner can select the particular slice to image by turning on the slice-select gradient and then altering the frequency of the excitation pulses (90, 180, and any inversion pulse) to match the frequency at the desired slice position. Protons not in the slice will not get excited since their Larmor frequency will not match the frequency of the pulse, thus they won't efficiently receive energy from the pulse.

Fourier Transform

In order to understand how to determine spatial localization within a slice (frequency and phase encoding) we need to look at the Fourier transform. Fourier, a French mathematician, realized that all signals, or oscillating functions, can be represented as a combination of simple sine and cosine waves. Each sine and cosine corresponds to a particular frequency in the signal. High frequencies correspond to rapidly changing features, while low frequencies (including zero, a constant signal) correspond to slowly changing features in the original signal. Fourier devised a method for transforming a signal in time, such as music, into the set of frequencies that compose it, and this is known as the Fourier transform.

MRI Measurement

The MRI Measurement consists of the following:

•	Alignment of the protons in the body with the large magnetic field of the MRI scanner. After a few seconds in the scanner the protons in the patient are aligned with the magnetic field.
•	A RF pulse is used to tip the protons out of alignment with the scanner's magnetic field.
•	Once out of alignment the magnetic moment of the hydrogen protons can be measured as they rotate past measurement coils (loops of wire) inducing an electrical current.
•	The protons are pulled back into alignment with the main magnetic field decreasing the measurable signal. The rate at which this occurs determines the T1 properties of a tissue. If the protons in a tissue return to alignment faster than all other tissues then this tissue will be brightest on a T1-weighted scan.
•	While rotating the protons gradually become out of phase with one another decreasing the measurable signal. The rate at which this dephasing occurs determines the T2 properties of a tissue. If the protons in a tissue remain in phase with one another longer than all other tissues then this tissue will be brightest on a T2-weighted scan.
•	A proton density (PD) scan minimizes both T1 and T2 contrast to produce an image in which brightness is determined by the number of protons in a voxel.

Tissue Contrast

The contrast on the MRI can be manipulated by changing the pulse sequence parameters. A pulse sequence sets the specific number, strength, and timing of the RF and gradient pulses. The two most important parameters are the TR and the TE. The TR is the time between consecutive 90° RF pulse. The TE is the time between the initial 90° RF pulse and the echo.

Two controls determine tissue contrast: TR (repetition time) and TE (echo time) of the scan.

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Repetition time (TR) is the time from the application of an excitation pulse to the application of the next pulse or the time between successive RF pulses. A long repetition time allows the protons in all of the tissues to relax back into alignment with the main magnetic field. A short repetition time will result in the protons from some tissues not having fully relaxed back into alignment before the next measurement is made decreasing the signal from this tissue. It determines how much longitudinal magnetization recovers between each pulse. It's measured in milliseconds.

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Echo time (TE) is the time between the application of RF excitation pulse and the peak of the signal induced in the coil. A long echo time results in reduced signal in tissues like white matter and gray matter since the protons are more likely to become out of phase. Protons in a fluid will remain in phase for a longer time since they are not constrained by structures such as axons and neurons. A short echo time reduces the amount of dephasing that can occur in tissue like white matter and gray matter. It's measured in milliseconds.