has proved very successful in the early years of diffusion imaging. The following sections describe an overview of the principles of magnetic resonance imaging and measurement of the diffusion signal.
2.2
Magnetic Resonance Imaging
Magnetic resonance imaging (MRI) utilises the quantum mechanical spin properties of atomic nuclei in a magnetic field. Typically MRI uses hydrogen protons in tissue to provide contrast although other substances can be used. These contain a non zero spin angular momentum which induces a magnetic moment (µ) equivalent to a microscopic magnetic dipole along their axis of rotation.
In general these axes are randomly orientated, but in the presence of a static external field (B0), their
moments feel a torque causing them to precess about the field with frequency:
ω = γB0 (2.3)
Here ω is known as the Larmor or resonance frequency and γ is the gyromagnetic ratio, which de- scribes the relation between spin angular momentum and its magnetic moment. This leads to a net magnetisation (magnitude Mz) of the spins in the direction of the applied field (defined by the z-axis,
figure 2.2 )
10 Chapter 2. Diffusion Imaging and Tractography
Magnetic resonance works via injection of an oscillating radiofrequency (RF) pulse at the resonant frequency, in a plane perpendicular to the static field B0. This generates a time varying magnetic
field B1 in the transverse plane and causes spins to precess simultaneously around B0 and B1 (figure
2.3 a). The combined effect can be simplified by viewing the system in a rotating frame of reference (x0,y0,z) (figure 2.3 b). This rotates about the z-axis at the Larmor frequency. In this frame we can ignore the contribution to the precession from the B0, and assume the B1 field is constant along x0.
The result is a rotation of the net magnetisation vector about about B1, where the angle of rotation
is proportional to the length of the RF pulse. This leads to an increase in transverse magnetisation
Mxy. Spins now precess in phase.
a) Laboratory frame b) Rotating frame
Figure 2.3: Simultaneous precession of spin magnetisation about a static magnetic field B0and a time
varying field B1
However, when the pulse is removed, the nuclei gradually return to their original state, releasing energy in the form of an RF pulse from which the MRI image is built up. The nuclei experience two key forms of relaxation: spin-lattice (T1) relaxation:
Mz= Mz0(1 − exp(−t/T1)) (2.4)
This is caused by loss of energy to the surroundings. In addition T2 relaxation:
2.2. Magnetic Resonance Imaging 11
This is caused by loss of coherence of the transverse magnetisation as spins fall out of phase due to spin-spin interactions and inhomogeneities in the static B0 field.
MRI images may be built simply from visualising the contrast due to different water content in different tissues, otherwise known as proton density images. However different tissues in the body also have different T1 and T2 values. Stronger contrast can be seen by weighting image schemes relative to these relaxation times.
2.2.1 Spatial encoding
Images are generated by pinpointing the locations of different frequency signals within the tissue using encoding gradients. Encoding gradients cause position dependent precession of the nuclei in different sections of the body by ensuring each position is subject to a different magnetic field.
There are three encoding gradients applied in a conventional slice MRI sequence (Figure 2.4 a): first slice-select gradients (GSS) are applied coincidentally with the RF pulse so as to ensure MR interac-
tions are restricted to a two-dimensional slab in the x-y plane. Following this individual locations in each slice are identified via repetitions of frequency and phase encoding. First a phase encoding (GP E) gradient is applied in an orthogonal direction to the slice select gradient. This causes spin to precess at position dependent frequencies until the gradient is turned off, whereby spins return to precess at the same rate but retain differences in phase. Then frequency encoding (GF E) gradients are applied
in the third direction, enforcing position dependent frequencies along the remaining dimension.
Data is measured during the application of the frequency encoding gradient but after phase encoding. The whole process is repeated with different magnitudes of phase encoding gradient (shown by dotted lines figure 2.4 a and b). This provides each position along the phase encoding axis with a unique rate of change of phase, or synthesised frequency1. 2-dimensional Fourier transforms of the signal can
then be used to reconstruct the image.
12 Chapter 2. Diffusion Imaging and Tractography
a) Standard sequence b) Spin echo sequence
Figure 2.4: Pulse diagrams for gradient sequence MRI imaging sequencies: a) In the conventional MR gradient echo sequence a 90◦ RF frequency pulse is applied simultaneously with a slice select gradient
applied in the z direction. This ensures that spins are only selected for rotation within a thin slice through the object. Positions in x and y are identified through phase and frequency encoding. b) Spin echo sequences apply an additional 180◦ RF pulse prior to frequency encoding. This causes spins
that are phase advanced to phase delayed and vice versa leading to a partial recovery of the signal following T2 decay
2.2.2 The spin echo sequence
Spin echoes (see Figure 2.4 b) provide image contrast by weighting images relative to T2 relaxation times. In these sequences loss of phase coherence is counteracted by the application of a second 180◦
pulse which flips the magnetization, causing spins which are phase advanced to become delayed and vice versa. As the spins continue to de-phase according to the local field this leads to a recovery of alignment and partial recovery of signal. If the 180◦ pulse is applied at a time t after the original RF
signal then alignment is recovered at time 2t. Therefore by using a series of spin echo sequences and measuring the signal height at each echo time, T2 can be approximated. The principles of spin echo