Radiofrequency (RF) pulse sequences for MRI 

The FID is one of four basic types of NMR signals. The other three are: Spin echo (SE), Stimulated echo (STE) and Gradient Echo (GRE) (ref1), (ref2). An MRI pulse sequence is a set of pulses and gradients that result in a desired result. Each sequence has a series of parameters such as time to echo (TE), time to repetition (TR), inversion pulse(s) etc. Pulse sequences are broadly categorized as: spin echo sequences, gradient echo sequences, inversion recovery sequences etc.

Spin echo (SE) is the refocusing of spin magnetization mediated by a second RF pulse

The notion of “echo” suggests the reappearance or repetition of a signal. Following the end of the 90° RF pulse and the decay of the Mxy magnetization (Figure 1C), upon the application of another RF pulse e.g. a 180° RF pulse (Figure 1D), it is possible to refocus or rephase the spins (Figure 1E) in order to mediate the regrowth of magnetization and thereby generate another signal (Figure 1F and Figure 2), which is termed a “spin echo” (SE) or simply “echo” (ref.3) (ref.4). It is noted that a spin echo is the result of a second pulse is magnetic resonance (it is the result of two pulses). The time between the middle of the first RF pulse and the peak of the spin echo is called the time to echo or echo time (TE).  

Figure 1: A first 90° RF pulse followed by a 180° RF pulse results in the refocusing of the spins and the regrowth of the transverse magnetization which provides an “echo”. The red dot indicates the temporal evolution of the process. Figure from Wikipedia (an animated version is also provided at this link). 

Figure 2:  "Spin echo" or "echo". Image: Allen D. Elster, MRIquestions.com (ref.)

Stimulated echo (STE) is the refocusing of spin magnetization mediated by three (or more) RF pulses

Following the decay of the Mxy magnetization, upon the application of a second 90° RF pulse, the spin system will be tipped or rotated in the z plane where Bo, the main magnetic field of the scanner is present. The Bo will tend to make spins parallel to its magnetic field lines (cf. pointing to the same direction). Let us consider a system of four spins, a to d as presented in Figure 2. Spins a and b will move closer to each other as Bo tries to make them parallel to it, while spins c and d will move further apart from each under the same influence from Bo (they will tend to align to the Bo). If a third 90° RF pulse is applied, spins will be tipped and then refocused and a transverse magnetization will be generated resulting in the creation of an echo, which is in this case is called a “stimulated echo” (ref.). It is noted that a stimulated echo (STE) is the result of three or more pulses in magnetic resonance.

Figure 2: Stimulated echo. Image: Allen D. Elster, MRIquestions.com (ref.)

A Gradient Echo (GRE) is a manipulation of the FID using a bipolar gradient

A gradient echo (GRE) is a manipulation of the FID signal which consists of the application of (ref.):

1. a dephasing magnetic field gradient that accelerates the FID

2. a rephasing magnetic field gradient of an opposite polarity that reverses the previous one and refocuses the spins.

Please refer to the pictures in the above reference.

A pulse train in magnetic resonance can generate a steady-state magnetization resulting in a sustained magnetic resonance signal emitted from the subject

Introduction

In accordance with what was mentioned previously, one pulse generates an FID, two pulses a spin echo (SE) and three or more pulses a stimulated spin echo (STE).

Let us consider a pulse train which consists of evenly spaced pulses with a repetition rate TR. The first 90° RF pulse rotates the longitudinal magnetization Mz and converts it to transverse magnetization Mxy. This will be followed by spin dephasing which represents T2 relaxation and subsequently the longitudinal magnetization Mz will start recovering towards reaching its maximal value Mo in an exponential fashion with time constant T1 (T1 relaxation).

(Effect on Mz) If the TR is sufficiently longer than T1, then Mz recovers fully to Mo

If the time between pulses (repetition rate) is sufficiently long, in practice four to five times longer than T1 (4x-5x T1), then the longitudinal magnetization Mz will have time to recover fully to its initial value Mo before the next pulse is applied (Figure 3, left panel).

(Effect on Mz) If the TR is shorter than T1, then Mz does not recover fully to Mo but a new steady state is established

If the time between pulses is shorter than T1, then the longitudinal magnetization Mz will not have time to recover fully to its initial value Mo but will be recovering to an intermediate value. After a few pulses, a new steady-state longitudinal magnetization will be established, Mss < Mo  as represented in Figure 3, right panel.

Figure 3:  (Left) For a pulse train with long TR, Mz recovers to maximal value Mo. (Right) For a pulse train with short TR (shorter than T1), Mz does not recover to  maximal value Mo, but instead a new steady-state longitudinal magnetization is established, Mss < Mo. Image: Allen D. Elster, MRIquestions.com (ref.)

(Effect on Mxy) If the TR is sufficiently longer than T2, magnetization will be on and off

If the time between pulses (TR*) is longer than T2, the dephasing will be complete and the Mxy magnetization will have fully decayed before the next pulse. The transverse magnetization will be disappearing and reappearing. The FID will have been completed before the SE/STE start (Figure 4).

Figure 4: TR>> T2. The FID is completed before the SE/STE start. Image: Allen D. Elster, MRIquestions.com (ref).

(Effect on Mxy) If the TR is shorter than or equal to T2, magnetization will be constantly on and a Transverse Steady State or Steady State Free Precession (SSFP) is established

If the time between pulses (TR*) is shorter or equal to T2, the dephasing will not be complete and the Mxy magnetization will not have fully decayed before the next pulse. The FID will not have been completed before the SE/STE start and as a result their tails will be merged. In this case the transverse magnetization never disappears but is sustained and a Transverse Steady State or Steady State Free Precession (SSFP) is established (Figure 5).

Figure 5: TR< T2 or TR=T2. The FID has not been completed before the SE/STE start and as a result their tails are merged. Image: Image: Allen D. Elster, MRIquestions.com (ref).

Steady-state free precession (SSFP) imaging