Magnetic Resonance Imaging

Learning Objectives

• Nuclear Spin
• Magnetic Field and Magnetism
• Resonance Effect, Excitation, Signal Reception
• Image Formation (Gradients, k-space and spatial encoding)

Introduction

MRI is 30 000 times stronger than the Earth’s magnetic field. There are lots of advantages and disadvantages of MRI:

Nuclear Spin

An electron orbits the nucleus and is essentially a loop of current. This loop of current creates a perpendicular magnetic field known as a magnetic moment.

Quantum Spin Stern-Gerlach Experiment

The Stern-Gerlach experiment is where silver atoms are fired out and pass through a non-uniform magnetic field to a screen. Originally the classical theory predicted random orientation of angular momentum of silver atoms when they reached the screen. However quantum theory predicted the opposite, that the silver atoms land in two discrete orientations (now known as spin up, spin down). The results of the experiment agreed with quantum prediction not the classical one. The quantum property causing the deflection of silver atoms is known as the inartistic angular momentum or spin.

Nuclei with non-zero spin

The following are a group of nuclei with no nuclear spin:

Not only is Hydrogen extremely sensitive to magnetic fields but it is also the most abundant element in the human body (as well as the planet!).

in vivo biomedical nuclei

Hydrogen Nucleus

The most common isotope of hydrogen (1H) is simply a single proton. It is the most sensitive to external magnetic fields (42.56 MHz T^-1), therefore almost all biomedical MRI makes use of 1H nuclei. Other nuclei are studied in MR Spectroscopy.

Magnetisation

In the presence of an external magnetic fields, the spins tend to align either parallel or anti parallel, with a small bias towards the parallel (low-energy) state.

Note: How magnetisation is sensitive to temperature, easier to increase the magnetic field than keep the patient cool

Because of this slight bias, the patient will have a net magnetisation (very small). If all these magnetisation elements are added together they become the ‘bulk’ magnetisation vector.

As you can see, the degree of magnetisation is tiny, but at just 20 ppm (protons per million) this is enough to make detailed images of the body.

Static Magnetic field

Clinical MRI scanners have field strength of 1.5 T or 3 T usually. The Earth’s magnetic field is ~50 µT. Ferromagnetic objects can become missiles at 0.3 mT and active implants such as pacemakers can fail at 0.5 mT.

Resonance

Precession

This is where, like the Earth’s axis, each spin is tilted slightly away from the bore’s magnetic field. This leads to a precession around the bore axis at the Larmor frequency. This natural frequency is defined by field strength and is also known as the resonant frequency.

Excitation

A second temporary (B1) magnetic field is turned on perpendicular to the main B field. This short pulse at the resonant (Larmor) frequency flips the M (magnetisation) vector into the transverse plan towards the higher energy anti-parallel state. The degree of the flip angle, α, is defined by the length and amplitude of the pulse.

Longitudinal and Transversal Magnetisation

The flipped M vector now has two components, M_z (still exists, but can go to zero) and M_xy transverse magnetisation (which didn’t exist before). This movement of transverse magnetisation produces the change in magnetic field. However now M_z and M_xy want to return to their original state, a process known as relaxation.

Relaxation

The relaxation of the two Mz and Mxy components are separate, and during the process causes induced current in the RF coil.

Note: usually the same RF coil produces the pulse and picks up the change in magnetic field, although they can be different

T1 longitudinal spin-lattice

M_z wants to return to the parallel state, its full peak to M₀. This is an interaction of the hydrogen spin with the lattice surrounding it. Depending on the lattice structure around the spin, the relaxation happens at different exponential rates. Relaxation of M_z tends to 63% ($ 1-\frac{1}{e} $). Different tissue types have different T1 values with fat having the fastest rate, then Muscle, with Blood being the slowest.

EQUATION SHOULD BE KNOWN!

$ M_z = M_0(1-e^{\frac{-t}{T_1}}) $

T2 transverse spin-spin

M_xy wants to disappear through decoherence or dephasing. M_xy is at a maximum when the flip angle is at 90° This is a result of spin-spin interaction, i.e. hydrogen nuclei with other hydrogen nuclei. Again different tissue types have different T2 values with M_xy starting at 37% ($\frac{1}{e} ​$).

$ M_{xy}(t) = M_{xy}(0) e^{\frac{-t}{T_2}} $

T1 & T2 Values

Notice that T2 is largely insensitive to field strength. CSF takes the longest time to relax because it is the most liquid, having free movement and little time for interaction with the lattice or with other spins

RF Reception

Faraday’s law means that a fluctuating magnetic field will induce currents. Receiving RF coils are tuned to the expected signal from the rotating M vector. Electronic components (ADC, bandpass filtering, gain etc) digitise signal for image formation.

RF Coils and Excitation

Any electrically-conductive material exposed to RF will have currents induced, leading to resistive heating. Heating of the body is measured in W/kg, aka SAR (Specific Absorption Rate). MR scanner estimates SAR for every sequence and this is limited by FDA/IEC regulations

At 3T effects can occur in current loops as small as 30cm, such as the touching of arms and or legs with the body. Therefore patients are advised to touch their body parts together. Otherwise, the patients may get burnt at the point of contact as there is an increase in resistance at that point, causing the skin to warm up.

Imaging

Gradients

While the main magnetic field of the scanner (B₀) cannot change, we can add additional, smaller magnetic fields with changing electrical fields. As you may remember from physics, a changing electrical field produces a magnetic field; this 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 B0 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, ‘tilted’ in space. By the Larmor equation, f = γ * B, so that if the magnetic field varies across space, the precession frequency of the protons will vary as well.

Slice Selection

The thickness of the slice is determined by the intersection of the gradient and the bandwidth. A region of spins are excited by an RF pulse. The thinner the slices the less signal you receive resulting in worse image quality. A bit like when you cut an onion in two it becomes a bit see through, there is not enough there.

Filling K-Space

The white plots in the middle of the K space (frequency domain) are low frequency, and slowly varying. There is conjugate symmetry in the K space matrix.

K Matrix size: 256 x 256 = 256 samples and 256 phase-encoding steps. Fourier Transform of K-space returns matrix in image space of exact same size. For a fixed field of view, increasing the matrix size increases the resolution.

Safety procedures noise

Time-varying magnetic fields induce currents in electrically conductive materials. This can lead to nerve stimulation. The Control of Noise at Work Regulations (2005) require that hearing protection is available if staff noise exposure exceeds 80 dB(A). Groups of particular concerns are children and neonates, the foetus, unconscious patients, and those with pre-existing hearing problems.

Localisation is performed by spatially varying the phase and frequency of a frequency-selected slice.

Pulse sequence

A pulse sequence is a series of RF and gradient field pulses used to acquire an MR image. Altering pulsed fields timing and strength, results in changes to the information content of the resulting image. Different pulse sequences are designed to encode different kinds of information into NMR signal.

Free Induction Decay FID

This is a sinusoidal wave which oscillates a Lamor frequency. The signal received from the RF coil is a function of the precession and decay of the transverse magnetisation. Measuring T2 from the FID is difficult due to the technical limitations. The transverse magnetisation is ‘refocused’ in order to produce an echo.

LEARN THIS BLOODY FUCKER!

$ M_{xy}(t) = M_0 exp(iw_0 t) \dot exp \bigg( \frac{-t}{T_2} \bigg) $

The signal received from the RF coil is a function of the precession and decay of the transverse magnetisation. Measuring T2 from the FID is difficult due to the technical limitations. The transverse magnetisation is ‘refocused’ in order to produce an ‘echo’.

Gradient Echo T2

The spin (RF) echo refocuses relaxation due to inhomogeneity but not spin-spin interactions. Gradient echo uses the gradient not, NOT RF, to refocus FID but cannot undo the effect of inhomogeneity. The transverse magnetisation is ‘refocused’ in order to produce an ‘echo’.

GRE Pulse Sequence

Echo is produced by inverting the FE gradient. Flip angle usually less than 90, leads to faster imaging and reduced SAR (Specific Absorption Rate). Sensitive inhomogeneity, can be plus or negative depending on the context.

Contrast in Gradient Echo

The echo time (TE) represents the time from the center of the RF-pulse to the center of the echo. For pulse sequences with multiple echoes between each RF pulse. The repetition time (TR) is the length of time between corresponding consecutive points on a repeating series of pulses and echoes.

Important Points

• Major MRI components (Static coils, gradient coils, RF coils), their roles and safety considerations
• Origin of the MRI signal, why we sue a certain nuclei, why we excite it and how we get image formation
• Spin echo and gradient echo. The differences in between them and about inversion recovery and why we use that. Signal suppression
• How to calculate acquisition in time and how to speed it up
• SNR and how to speed it up.

Problems

Which equation describes the Larmor frequency of a magnetic moment exposed to an external magnetic field?
$f = 2 \pi \gamma B_0$

What mathematical technique is required to transform a signal from the time domain into the frequency domain?
Fourier Transform

Which of these is NOT an advantage of MRI over CT?

• Excellent soft tissue contrast
• No use of ionising radiation
• Can image in arbitrary planes
• Good visualisation of skeletal structure (solution)

Which nuclei is the primary nuclei studied in biomedical MRI
1H

At what field strength to ferromagnetic objects become a missile risk?
3mT

Which tissue has a very long T1 relaxation time?
CSF

What risks are associated with the RF coils?
Heating of the body

What is the image size of an MRI slice if the K-Space matrix is 128x128?
128x128

What impact on SNR does halving the slice thickness (delta z) have on the SNR?
It halves the SNR, but increases spatial resolution in the z direction.

In an axial conventional spin echo image of the brain, the skull fat is brightest, followed by the white matter, followed by the gray matter. The CSF is dark. What weighting does this image have?
T1

Generally, how is the SNR different in SE (Spin Echo) vs GRE (Gradient Echo)?
SNR is higher than in GRE.