Gradient and Spin Echo Pulse Sequences

There are two broad classes of pulse sequences used: gradient-echo and spin-echo methods. Gradient-echo sequences use a simpler pulse and acquire acquisition, while spin-echo sequences use an additional RF refocusing pulse that eliminates the effects of off-resonance that are often undesirable.

Learning Goals

1. Describe how various types of MRI contrast are created

   • Describe the difference between gradient and spin echo contrast

2. Understand the most popular pulse sequences and their acronyms

   • Identify gradient echo and spin echo pulse sequences

3. Identify artifacts and how to mitigate them

   • Understand the effects of off-resonance and T2* on contrast

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Gradient Echo Pulse Sequence (GE or GRE)

The building block of a gradient-echo (GE) pulse sequence includes an RF excitation pulse followed by imaging gradients. A complete 2D imaging sequence is

It is called a “gradient-echo (GE)” since the frequency encoding imaging gradients, shown on \(G_X\), are refocused or canceled out at the echo time (more in Spatial Encoding section). Another name for these sequences is a “gradient-recalled echo (GRE)”.

And using a simplified diagram for the gradient echo sequence:

The gradient-echo pulse sequence exhibits \(T_2^*\) contrast, which is explained below

\[S_{GE} \propto M_0 \exp(-TE/T_2^*)\]

Off-resonance

Ideally, the magnetic field is uniform in the absense of any applied gradients. However, in practice there are unavoidable variations in the magnetic field that lead to changes in resonance frequency. These magnetic field variations are referred to as “off-resonance”, and can be represented as

\[\Delta f_r(\vec{r}) = \bar \gamma \Delta B_0(\vec{r}) \]

These are due imperfections in the main \(B_0\) magnet as well as subject-specific changes in the magnetic field that are largely due to magnetic susceptibility effects.

Effects of Off-resonance and T2*

Ideally, the MRI signal decays with a time constant of \(T_2\), the transverse decay rate. However, in practice every imaging voxel contains off-resonance that leads to changes in the signal decay. We characterize this change in signal decay with \(T_2^*\).

The smallest size we can measure with MRI is an imaging voxel, so our image measurements are a sum of the transverse magnetizations across the voxel, including both \(T_2\) and off-resonance:

\[\begin{split}\begin{align} s_{\mathrm{voxel}}(t) & = \int_{\mathrm{voxel}} M_{XY}(\vec{r},0) \exp(-t/T_2(\vec{r})) \exp(-i 2 \pi \Delta f_r(\vec{r})) \ d\vec{r} \\ & \approx M_{XY}(\vec{r},0) \exp(-t/T_2^*(\vec{r})) \end{align}\end{split}\]

(Note that any effects of applied gradients are removed during the image reconstruction process.)

The mechanism of this decay is that, across an imaging voxel, the transverse magnetizations across the voxel precess at slightly different rates. This is called “de-phasing”, and means that when the transverse magnetization is averaged across the voxel it’s overall magnitude is reduced. This is illustrated in the examples below (generated by t2star_spinecho_illustration.m)

No off-resonance, \(T_2 = 80\) ms
Mild off-resonance, \(T_2 = 80\) ms	Severe off-resonance \(T_2 = 80\) ms

\(T_2^*\) is an approximation of these dephasing effects, and depends on the voxel size and location. It is often broken up as follows to separate out the additional dephasing rate, \(1/T_2'\):

\[ \frac{1}{T_2^*} = \frac{1}{T_2}+\frac{1}{T_2'}\]

\[ T_2^* \leq T_2\]

Refocusing off-resonance

The effects of off-resonance can be reversed by applying a 180-degree flip angle “refocusing” RF pulse. This has the effect of inverting the phase accumulation of off-resonance net magnetizations, after which the off-resonance phase begins to cancel out. This is most easily illustrated in the voxel decay illustrations below:

Spin-echo with No off-resonance, \(T_2 = 80\) ms
Spin-echo with Mild off-resonance, \(T_2 = 80\) ms	Spin-echo with Severe off-resonance \(T_2 = 80\) ms

The spin-echo does not make any difference when there is no off-resonance.
Can you identify when the 180-degree refocusing pulse was applied? This is when the \(M_{XY}\) reverts its phase.

Simulation for Visualization of refocusing off-resonance

To simulate and visualize off-resonance, including various refocusing pulse flip angles, try

• Visit http://drcmr.dk/BlochSimulator/

• Scene: Inhomogeneity

• Apply 90x hard, then 180y hard - what happens to the dephasing spins?

• Apply 90x hard, then 180x hard - this applies the 180-degree pulse at a different angle. Is there still a spin-echo?

• Apply 90x hard, then repeated 180s - can multiple spin-echoes be created?

Spin Echo Pulse Sequence (SE)

The building block of a spin-echo (SE) pulse sequence has an additional 180-degree refocusing pulse between the excitation and data acquisition in order to refocus the effects of off-resonance and create pure T2-weighting:

It is called a “gradient-echo (GE)” since the spins are all refocused at the echo time, TE.

This is a simplified diagram for the spin echo sequence:

Because of the refocusing, a spin-echo sequence gives pure T2 contrast:

\[S_{SE} \propto M_0 \exp(-TE/T_2)\]