[Cat 1] Discuss the significance and the uniqueness of the Larmor frequency for a nuclear species.
[Cat 1] Describe the origin of the Free Induction Decay and discuss the key factors which determine its strength.
[Cat 1] Describe the origin of the T1 and T2 relaxation mechanisms.
[Cat 1] Describe the behaviour of T1 and T2 as the strength of the static field is changed.
[Cat 1] Describe the spin-echo and inversion recovery pulse sequences – including multiple spin echo and STIR.
[Cat 1] Outline the advantages and characteristic features of Gradient Echo, Fast Spin Echo, Echo Planar Imaging (EPI) and other fast imaging techniques.
[Cat 1] Discuss the physics behind the chemical shift phenomenon.
[Cat 1] Describe how gradients may be applied to spatially encode the NMR signal.
[Cat 1] Describe interleaved multislice imaging and indicate why it is utilised.
[Cat 1] Discuss quality features of MR images including artifacts.
[Cat 1] Discuss safety issues (patient and environmental) and contra-indications in the use of MRI.
[Cat 2] Discuss the role of the Fourier Transform (FT) in MR image reconstruction.
[Cat 2] Describe 2D-FT reconstruction methods in terms of the three time intervals (slice selection, phase encoding and frequency encoding).
[Cat 2] Compare the 3D-FT reconstruction technique with the 2D-FT method.
[Cat 2] Discuss the advantages of the Gradient Echo, Fast Spin Echo, Echo Planar Imaging (EPI) and other fast imaging techniques.
[Cat 2] Explain the effects of preparatory inversion pulse on image contrast.
[Cat 2] Compare and contrast fat suppression obtained by spectral, IR GRE and subtraction methods.
[Cat 2] Identify the biomolecular species which may be analysed in clinical MRS.
[Cat 3] Describe the general construction and mode of operation of MRI scanners.
[Cat 3]Describe in simple terms the effects of blood flow on MR image data.
1. Introduction
Magnetic resonance imaging is a technique that uses strong magnetic fields, magnetic field gradients and radio waves to generate images of the organs in the body. The following information is a simplified explanation of a complex phenomenon.
1.1. Nuclear magnetic resonance
Atomic nuclei with odd numbers of protons and/or neutrons, such as the hydrogen (1H) atom, demonstrate the ability to absorb and re-emit radio-frequency energy when placed in a strong magnetic field. The 1H nucleus comprises a single proton which possesses two important quantum mechanical properties that gives rise to the phenomenon of nuclear magnetic resonance:
- Spin – an intrinsic form of angular momentum carried by atomic nuclei.
- Magnetism – the spin of the positively charged proton give rises to a magnetic field oriented along the axis of rotation, termed the nuclear magnetic dipole/moment.
The human body is composed of 70% H2O, thus making hydrogen ideal for nuclear magnetic resonance imaging.
1.2. Precession
Normally, the magnetic moment of a 1H nucleus is randomly oriented due to thermal energy. However, when placed in a strong, homogeneous and static external magnetic field B0, the magnetic moment attempts to align parallel (‘spin up’) or anti-parallel (‘spin down’) with the magnetic field. There’s a slight preponderance (i.e. 3 per million) for the 1H nuclei to naturally align parallel (low energy) rather than the anti-parallel (high energy) to B0.
Due to the angular momentum of the nucleus, the magnetic moments rotate around the general direction of B0, with the line of the vector tracing a cone, in a motion termed precession. At this stage, all hydrogen atoms are precessing at a frequency determined by the Larmor equation but not in synchronisation with each other, i.e. the magnetic moments precess out of phase
.In clinical imaging, the B0 is established along the bore (i.e. Z-axis) of the MRI scanner.
1.3. Larmor equation
ω = γ·B0
measured in Hz, where ω = the precession frequency, γ = the gyromagnetic ratio and B0 = static magnetic field strength.
Note, the gyromanetic ratio γ for hydrogen is 42.58 MHz/T.
1.4. Net Magnetisation Vector
At thermal equilibrium, as there is partial alignment of magnetic moments with B0 field a net magnetisation vector (Mz) aligned with the longitudinal plane (Z-axis) is formed. The strength of MZ depends on the strength of B0 and the temperature.
2. Resonance
Applying a transverse or 90º magnetic field B1 in the form of a radio-frequency pulse will cause:
- The longitudinal magnetisation vector MZ to be rotated towards the XY plane, creating a transverse magnetisation vector Mxy
- The precessing nuclei to resonate coherently in phase if the RF pulse matches the Larmor frequency.
As Mxy rotates around the Z-axis, it creates an sinusoidally-oscillating magnetic flux which will induce an electromotive force in coils placed perpendicular to its movement (by Faraday’s Law of Induction).
Generally, Mxy decays faster than Mz recovers to its maximum, i.e. T2 relaxation is faster than T1 relaxation.
T2 relaxation
As nuclei seek to return to a lower energy state, Different tissues possess different
T2 relaxation describes the exponential process by which the transverse components of magnetisation (MXY) decays as the rotating nuclear magnetic moments lose phase coherence.
This occurs due to interaction of their magnetic fields, a process termed spin-spin interactions, which slightly modifies their precession rate. Over time, this causes cumulative loss of phase coherence resulting in the decay of the transverse net magnetisation.
The exponetional decay rate is characterised by a tissue-specific time constant termed T2. After time T2, transverse magnetisation has lost 63% of its original value.
T2 relaxation describes the loss of transverse magnetization (Mxy) due to the loss of phase coherence. Under ideal conditions, the loss of phase coherence is a simple exponential decay process where the detectable signal S decreases from its initial maximum S0 towards zero.
Note: T2 is the time-constant of the exponential decay, not the rate of signal decay. Also, transverse relaxation is faster than longitudinal relaxation.
T1 relaxation
T1 relaxation describes the exponential recovery of Mz (i.e. longitudinal magnetisation along B0) towards its thermal equilibrium with time, i.e. the partial re-alignment of nuclear magnetic moments with the primary magnetic field B0.
It occurs due to energy exchange between the spins and the surrounding lattice, a process also termed spin-lattice relaxation, thus re-establishing thermal equilibrium. As the spin states transition from a high energy state to its preferred low-energy state, radiofrequency energy is released into the surrounding lattice.
The exponential recovery rate is characterised by the tissue-specific time constant termed T1 (approximately ranges from 200ms to 3000ms). After time T1, the longitudinal magnetisation has returned to 63% of it’s final value.
Mz = 1 – e–t/T1
M = M0 (1 – e-tT)
The stronger the external magnetic field B0, the longer the T1 relaxation times.
Free induction decay
Refers to the sinusoidal electromagnetic signal which appears following a 90o RF pulse. If the magnetization vector has a non-zero component in the xy plane, then the precessing magnetisation will induce a corresponding oscillating voltage in a detection coil surrounding the sample.
A free induction decay signal (FID) decays due to both true T2 effects (tissue-specific spin-spin relaxation) and magnetic field inhomogeneity.
Dephasing occurs due to spin–spin interactions (T2) and local magnetic field
inhomogeneities. Spin–lattice (or T1) relaxation is responsible for realignment of
magnetic dipoles with the external magnetic field.
Change in magnetic flux induces a voltage (Lenz’s Law) in the gradient coil
Increasing magnetic field strength increases and frequency amplitude of signal detected as it is proportional of precession frequency and therefore also y and B
Magnetic Resonance Imaging
Superconducting electromagnet
Shimming coils
Gradient coils
Radiofrequency coils
MRI Sequences
Spin-echo imaging (SE)
A spin-echo sequence requires a 90° RF excitation pulse and a 180° RF rephasing pulse.
The FID signal decays due to loss of precessional phase coherence. Some of this loss is due to irreversible true T2 processes, and some is due to field inhomogeneity resulting in nuclei in different regions of our ‘sample’ having different precession rates
The MR scanner can only detect signal (magnetization) in the transverse plane. We discussed a way to produce transverse magnetization, the 90-degree pulse, above. This produced a free induction decay signal, with the signal decreasing according to T2* effects. There are two disadvantages of this approach: (1) The signal decays very rapidly, requiring an extremely fast scanner to detect it before it dies out; and (2) The signal depends on T2*, not T2, so it is very susceptible to local magnetic field inhomogeneity. In order to combat both of these challenges, we can add another pulse to generate an “echo” that occurs later in time and happens to reverse the T2* effects to leave us with T2 only. This is referred to as the spin echo.
Fixed magnetic field inhomogeneities do not change over time. They lead to fixed differences in proton precession speed across the tissue. The clever solution (discovered by Dr. Erwin Hahn) is to ‘reverse’ the proton precession so that the faster and slower precessing protons refocus. The often cited analogy is the tortoise and hare race. Imagine the tortoise and hare starting on a race; the hare gets much farther. Then, at a certain time, we tell them both to turn around and come back. They will reach the starting line at the same time – remember that even though the hare is farther out, it is that much faster. In reality, instead of reversing the direction of precession, we rotate the protons with a 180-degree pulse; they continue precessing in the same direction but will refocus along the -y axis, as shown below.
Multiple refocusing 180 pulses can be applied following one excitation, and
multiple echoes (albeit of decreasing amplitude due to T2 relaxation) can be
obtained. This is the basis of fast (turbo) spin–echo sequences
The 180° RF pulse reverses dephasing due to static field inhomogeneities (T2* effects) but not random spin-spin relaxation (T2 effects, tissue-specific).
The best contrast between tissues with different T1s is obtained with short repetition
times (TRs) and short echo times (TEs). T1 weighting is obtained with a short TR, usually between 300 and 800 ms (close to the T1s of the tissues being imaged). With increasing TR, the longitudinal
magnetization in all tissues would recover more, diminishing the T1 contrast. Short
TEs are used to reduce the effect of T2 relaxation on contrast (see below).
Gradient-echo imaging
Gradient-echo imaging involves sampling the signal formed during the FID.
This is why gradient-echo images have a T2
weighting
Summary
1. At thermal equilibrium, there is an net alignment of 1H magnetic moments parallel with B0 creating a net magnetisation vector.
2. Application of a 90o RF pulse B1 at the Lamor Frequency ω = γ·B0 induces phase coherence of the nuclear magnetic moments and applies a torque on the NMV rotating it into the XY-plane.
3. T2 relaxation – Magnetic field inhomogeneity from B0 and spin-spin interactions results in gradual loss of phase coherence due to difference precession rates with a time constant T2*. A sinusoidal FID signal can be detected in a coil surrounding the sample.
4. Application of a 180o RF pulse along X-axis flips the nuclear magnetic moments in the XY-plane, resulting in gradual recovery of phase coherence which can be detected as a spin echo signal with reduced amplitude due to irreversible loss of phase coherence due to true T2 relaxation.
Quiz
Recall that the spin of an unpaired proton (positively charged) will induce a magnetic field. As Carbon 12C and Oxygen 16O have even numbers of protons and neutrons, they do not possess a net magnetic moment and therefore cannot be polarised.