Gradient-echo pulse sequences

4
Gradient-echo pulse sequences




After reading this chapter, you will be able to:



  • Explain how gradient-echo sequences differ from spin-echo.
  • Describe how gradient-echoes are created.
  • Analyze the steady state and why it is important in gradient-echo pulse sequences.
  • Understand the mechanisms of common gradient-echo pulse sequences.
  • Apply what you have learned to understand how images of different weighting are created using gradient-echo pulse sequences.

INTRODUCTION


This chapter discusses the mechanisms, uses, and parameters for each of the common gradient-echo pulse sequences and their advantages and disadvantages. A table is included that compares the common acronyms for gradient-echo pulse sequences for the main manufacturers (Table 4.1). A more comprehensive table is also provided at the beginning of the book. As with Table 3.1 and the acronym table that compares acronyms for spin-echo sequences, these tables are only a guide; they are not meant to compare the performance or specification of each system. The parameters included in this chapter depend on field strength and the nuances of individual systems. However, they should be suitable for most field strengths used in clinical imaging.


Table 4.1 Gradient-echo pulse sequences and their common acronyms.





















































Generic GE Philips Siemens Toshiba Hitachi
Coherent or rewound gradient-echo GRASS FFE FISP SSFP Rephased SARGE
Incoherent or spoiled gradient-echo SPGR T1-FFE FLASH Fast FE RF spoiled SARGE
Reverse-echo gradient-echo SSFP T2-FFE PSIF No sequence Time-reversed SARGE
Balanced gradient-echo FIESTA B-FFE True FISP True SSFP Balanced SARGE
Fast gradient-echo Fast GRASS or SPGR TFE Turbo FLASH Fast FE RGE
Echo planar imaging EPI EPI EPI EPI EPI

Abbreviations used in Table 4.1

































GRASS gradient recalled acquisition in the steady state FLASH fast low angled shot
SPGR spoiled GRASS PSIF reverse FISP
SSFP steady state free precession EPI echo planar imaging
FIESTA free induction echo stimulated acquisition RGE rapid gradient-echo
FFE fast field echo SARGE steady acquisition rewound gradient-echo
FISP fast imaging with steady precession

Gradient-echo pulse sequences differ from spin-echo pulse sequences in two ways:



  • They use variable RF excitation pulse flip angles as opposed to 90° RF excitation pulse flip angles that are common in spin-echo pulse sequences.
  • They use gradients rather than RF pulses to rephase the magnetic moments of hydrogen nuclei to form an echo.

The main purpose of these two mechanisms is to enable shorter TRs and therefore scan times than are common with spin-echo pulse sequences. Let’s explore these strategies in more detail.


VARIABLE FLIP ANGLE


A gradient-echo pulse sequence uses an RF excitation pulse that is variable and therefore flips the NMV through any angle (not just 90°). Typically, a flip angle of less than 90° is used. This means that the NMV is flipped through a lower angle than it is in spin-echo sequences when a larger 90° flip angle is usually applied. As the NMV is moved through a smaller angle in the excitation phase of the pulse sequence, it does not take as long for the NMV to achieve full relaxation once the RF excitation pulse is removed. Therefore, full T1 recovery is achieved in a much shorter TR than in spin-echo pulse sequences. As the TR is a scan time parameter (see Equations (6.7)–(6.9)), this leads to shorter scan times.


GRADIENT REPHASING


After the RF excitation pulse is withdrawn, the FID immediately occurs due to inhomogeneities in the magnetic field and T2* decay. In spin-echo pulse sequences, the magnetic moments of hydrogen nuclei are rephased by an RF pulse. As a relatively large flip angle is used in spin-echo pulse sequences, most of the magnetization is still in the transverse plane when the 180° RF rephasing pulse is applied. Consequently, this pulse rephases this transverse magnetization to create a spin-echo. In gradient-echo pulse sequences, an RF pulse cannot rephase transverse magnetization to create an echo. The low flip angles used in gradient-echo pulse sequences result in a large component of magnetization remaining in the longitudinal plane after the RF excitation pulse is switched off. The 180° RF pulse would therefore largely invert this magnetization into the − z direction (the direction that is opposite to B0) rather than rephase the transverse magnetization [1]. Therefore in gradient-echo pulse sequences, a gradient is used to rephase transverse magnetization instead.


Gradients perform many tasks, which are explored fully in Chapter 5. In this chapter, they are discussed specifically in relation to how they are used to rephase or dephase the magnetic moments of hydrogen nuclei.


How gradients dephase


Look at Figure 4.1. With no gradient applied, all the magnetic moments of hydrogen nuclei precess at the same frequency, as they experience the same field strength (in reality they do not because of magnetic field inhomogeneities, but these changes are relatively small compared with those imposed by a gradient). A gradient is applied to coherent (in phase) magnetization (all the magnetic moments are in the same place at the same time). The gradient alters the magnetic field strength experienced by the coherent magnetization. Some of the magnetic moments speed up, and some slow down, depending on their position along the gradient axis. Thus, the magnetic moments fan out or dephase because their frequencies are changed by the gradient (see the watch analogy in Chapter 1).

Diagrams show two cylinders labeled precessional frequency with spins on left and gradient on right. Two meters show all magnetic moments in phase and magnetic moments become dephased.

Figure 4.1 How gradients dephase.


The trailing edge of the fan (shown in purple) consists of nuclei whose magnetic moments slow down because they are situated on the gradient axis that has a lower magnetic field strength relative to isocenter. The leading edge of the fan (shown in red) consists of nuclei whose magnetic moments speed up because they are situated on the gradient axis that has a higher magnetic field strength relative to isocenter. The magnetic moments of nuclei are therefore no longer in the same place at the same time, and so magnetization is dephased by the gradient. Gradients that dephase in this way are called spoilers, and the process of dephasing magnetic moments with gradients is called gradient spoiling.


How gradients rephase


Look at Figure 4.2. A gradient is applied to incoherent (out of phase) magnetization to rephase it. The magnetic moments initially fan out due to T2* decay, and the fan has a trailing edge consisting of nuclei with slowly precessing magnetic moments (shown in purple) and a leading edge consisting of nuclei with faster precessing magnetic moments (shown in red). A gradient is then applied so that the magnetic field strength is altered in a linear fashion along the axis of the gradient. The direction of this altered field strength is such that the slowly precessing magnetic moments in the trailing edge of the fan experience an increased magnetic field strength and speed up. In Figure 4.2, these are the purple spins that experience the red “high end” of the gradient. At the same time, the faster precessing magnetic moments in the leading edge of the fan experience a decreased magnetic field strength and slow down. In Figure 4.2, these are the red magnetic moments that experience the purple “low end” of the gradient. After a short period of time, the slow magnetic moments speed up sufficiently to meet the faster ones that are slowing down. At this point, all the magnetic moments are in the same place at the same time and are therefore rephased by the gradient. A maximum signal is induced in the receiver coil, and this signal is called a gradient-echo. Gradients that rephase in this way are called rewinders.

Diagrams show two cylinders labeled precessional frequency with speeds up on left and slows down on right. Two meters show fast nuclei slow down slow nuclei speed up and back in phase.

Figure 4.2 How gradients rephase.


Whether a gradient field adds or subtracts from the main magnetic field depends on the direction of current that passes through the gradient coils. This is called the polarity of the gradient. Gradient-echoes are created by a bipolar gradient. This means that it consists of two lobes, one negative and one positive. The frequency-encoding gradient is used for this purpose (see Chapter 5). It is initially applied negatively, which increases dephasing and eliminates the FID. Its polarity is then reversed, which rephases only those magnetic moments that were dephased by the negative lobe. It is only these nuclei (those whose magnetic moments are dephased by the negative lobe of the gradient and are then rephased by the positive lobe) that create the gradient-echo at time TE (Figure 4.3). The area under the negative lobe of the gradient is half that of the area under the positive lobe [2].

Diagram shows four pulse sequences where first stays at level, second increases, decreases, stays at level, and increases and decreases again. third increases and decreases irregularly.

Figure 4.3 A basic gradient-echo sequence showing how a bipolar application of the frequency- encoding gradient produces a gradient-echo.


Table 4.2 Things to remember – gradient-echo pulse sequences.











Gradient-echo sequences use gradients to rephase the magnetic moments of hydrogen nuclei and usually flip angles less than 90°. Both of these strategies permit a shorter TE and TR than in spin-echo pulse sequences
Low flip angles mean that, as less longitudinal magnetization is converted to transverse magnetization during the excitation phase of the sequence, less time is required for relaxation. This is why a short TR can be used
The speed of rephasing is increased using a gradient. A bipolar application of the frequency-encoding gradient enables magnetic moments of the hydrogen nuclei to rephase faster than when using an RF rephasing pulse. This permits a short TE, which means that a shorter TR can be used for a given number of slices than in spin-echo
Although faster than RF rephasing, inhomogeneities are not compensated for in this type of sequence. Magnetic susceptibility artifacts therefore increase

WEIGHTING IN GRADIENT-ECHO PULSE SEQUENCES


The weighting mechanisms in gradient-echo pulse sequences are quite complex, and this is one of the many reasons why they are hard to understand (and explain!). There are essentially three different processes that affect weighting in gradient-echo pulse sequences, and sometimes all three overlay each other in the image. These are as follows:



  • Extrinsic parameters (TR, TE, and flip angle)
  • The steady state
  • Residual transverse magnetization.

Let’s explore each of these processes in detail.


Weighting mechanism 1 – extrinsic contrast parameters


The influence of the TR and TE on image weighting was explored in Chapter 2. The discussion assumed that the RF excitation pulse flip angle is 90° (as in spin-echo pulse sequences). Under these circumstances, TE controls T2 contrast, and T2 contrast increases as the TE increases. The same is true in gradient-echo pulse sequences except that T2 is termed T2* to reflect the fact that magnetic field inhomogeneities are not compensated for by gradient rephasing. In spin-echo pulse sequences, TR controls T1 contrast, and T1 contrast increases as the TR decreases. This is because short TRs do not permit complete recovery of the vectors, and, therefore, subsequent 90° RF excitation pulses cause saturation. In gradient-echo pulse sequences, the TR and the flip angle control the amount of T1 relaxation and saturation that occurs (Equation (4.1)).










Equation 4.1
SI = PD e-TE/T2* (1-e-TR/T1)
[sin θ /(1 – cos θ e-TR/T1)]

SI is the signal intensity in a tissue


PD is the proton density


TE is the echo time (ms)


T2* is the T2* relaxation time of the tissue (ms)


TR is the repetition time (ms)


T1 is the T1 relaxation time in the tissue (ms)


θ is the flip angle


[sin θ/(1 − cos θ e−TR/T1)] is the flip angle function

This equation shows why the signal intensity from a tissue depends on intrinsic and extrinsic contrast parameters. Compare this equation with Equation (2.4). The flip angle function is added, and T2 becomes T2*. The flip angle function shows how the flip angle, TR, and T1 relaxation time all determine whether a tissue is saturated. If α = 0° or 90°, then sin α = 1 and cos α = 0. This equation is then identical to Equation (2.4) [11]

Apart from the added variable of the flip angle, weighting rules in gradient-echo are the same as in spin-echo (see the heat analogy in Chapter 2).


The trick is to imagine how far the vectors are flipped by the RF excitation pulse (flip angle) and then how long they are given to recover their longitudinal magnetization (TR).



  • If the combination of flip angle and TR causes saturation of the vectors (i.e. they never fully recover their longitudinal magnetization during the TR period), then T1 contrast is maximized.
  • If the combination of flip angle and TR does not cause saturation of the vectors (i.e. they recover most, or all, of their longitudinal magnetization during the TR period), then T1 contrast is minimized.

These rules, along with those of how the TE controls T2* contrast, are used to weight images in gradient-echo pulse sequences.


Using extrinsic contrast parameters in gradient-echo – T1 weighting


To obtain a T1-weighted image, differences in the T1 recovery times of the tissues are maximized, and differences in the T2* decay times of the tissues are minimized. To maximize differences in T1 recovery times, neither fat nor water vectors are given time to recover full longitudinal magnetization before the next RF excitation pulse is applied. To avoid full recovery of their longitudinal magnetization, the flip angle is large and the TR short so that the fat and water vectors are still in the process of recovering when the next RF excitation pulse is applied. To minimize differences in T2* decay times, the TE is short so that neither fat nor water has time to decay (Figure 4.4).

Diagram shows graph for full recovery not possible as TR is short, short TE little dephasing on 110 degree flip of saturation.

Figure 4.4 T1 contrast in gradient-echo.


Using extrinsic contrast parameters in gradient-echo – T2* weighting


To obtain a T2*-weighted image, differences in the T2* decay times of the tissues are maximized, and differences in the T1 recovery times are minimized. To maximize differences in T2* decay times, the TE is long so that fat and water vectors have had time to dephase. To minimize differences in T1 recovery times, the flip angle is small and the TR long enough to permit full recovery of the fat and water vectors before the next RF excitation pulse is applied. In practice, small flip angles produce such little transverse magnetization that full longitudinal recovery occurs even if the TR is short (Figure 4.5).

Diagram shows graph for small flip angle, long TE maximum dephasing on 110 degree flip of saturation on time scale with no saturation can occur.

Figure 4.5 T2* contrast in gradient-echo.


Using extrinsic contrast parameters in gradient-echo – PD weighting


To obtain a PD-weighted image, both T1 and T2* processes are minimized so that the differences in proton density of the tissues are demonstrated. To minimize T2* decay, the TE is short so that neither the fat nor the water vectors have had time to decay. To minimize T1 recovery, the flip angle is small and the TR long enough to permit full recovery of longitudinal magnetization before the next RF excitation pulse is applied.

Image described by caption and surrounding text.

Figure 4.6 T1 weighting in gradient-echo and the heat analogy.

Image described by caption and surrounding text.

Figure 4.7 T2* weighting in gradient-echo and the heat analogy.

Image described by caption and surrounding text.

Figure 4.8 PD weighting in gradient-echo and the heat analogy.


Table 4.3 Comparison of extrinsic parameters – spin-echo and gradient-echo.


































Sequence TR TE Flip angle
Spin-echo Long 2000 m s+ Long 70 m s+ 90°
Short 300–700 m s+ Short 10–30 m s+ 90°
Gradient-echo Long 100 m s+ Long 15–25 ms Small 5°–20°
Short less than 50 ms Short less than 5 ms Medium 30°–45°
Large 70 °+

Table 4.4 Things to remember – weighting mechanism gradient-echo pulse sequence.













TR and flip angle control whether the NMV is saturated. Saturation is required for T1 weighting only
TE controls T2* weighting
For a T1-weighted gradient–echo, the flip angle and TR combination ensures that saturation occurs. The flip angle is large and the TR short to achieve this. In addition, the TE is short to minimize T2*
For T2*-weighted gradient-echo, the flip angle and TR combination prevents saturation. The flip angle is small and the TR long to achieve this. In addition, the TE is long to maximize T2*
For PD-weighted gradient–echo, the flip angle and TR combination prevents saturation. The flip angle is small and the TR long to achieve this. In addition, the TE is short to minimize T2*

Weighting mechanism 2 – the steady state


The steady state is a term referred to in Chapter 2 but is commonly associated with gradient-echo sequences. It has a significant impact on image weighting in these pulse sequences. The steady state is generically defined as a stable condition that does not change over time. For example, if a pot of water is placed on a stove, the heating element of the stove gradually heats it up. Heat energy is lost through processes of conduction, convection, and radiation. If the amount of heat energy gained from the heating element of the stove equals the amount of heat energy lost by convection, conduction, and radiation, the temperature of the pot and water remains constant and stable. This is an example of the steady state because the energy “in” equals the energy “out,” and, therefore, the temperature of the whole system remains unchanged for a time.


This analogy works well in MRI. The RF excitation pulse gives energy to hydrogen nuclei, and the amount of energy applied is determined by the flip angle. Energy is lost by hydrogen nuclei through spin-lattice energy transfer, and the amount of lost energy is determined by the TR. Therefore, by selecting a certain combination of TR and flip angle, the overall energy of the system remains constant, as the energy “in” as determined by the flip angle equals the energy “out” as determined by the TR (Figure 4.9). As RF has a low frequency and hence low energy, for most values of flip angle very short TRs are required to achieve the steady state. In fact, the required TRs are shorter than the T1 and T2 relaxation times of tissues. Therefore, unlike spin-echo, where even with short TRs some transverse magnetization decays, in gradient-echo there is no time for transverse magnetization to decay before the pulse sequence is repeated. This magnetization influences weighting as the receiver coil is positioned in the transverse plane.

Graph shows transverse component held steady for next repetition on horizontal axis versus longitudinal component held steady on vertical axis where diagonal and vertical lines are drawn.

Figure 4.9 The steady state.


The number of TR periods needed to reach the steady state depends on the TR, flip angle, and the relaxation times of tissues [3]. However, in gradient-echo sequences, a short TR is deliberately used to minimize the scan time. As the TR is so short, magnetization in tissues does not have time to reach its T1 recovery or T2 decay times before the next RF excitation pulse is applied. Therefore, in the steady state, image contrast is not due to differences in the T1 recovery and T2 decay times of tissues but rather due to the ratio of T1 recovery time to T2 decay time. In tissues where T1 recovery and T2 decay times are similar, signal intensity is high, and where they are dissimilar, signal intensity is low. In the human body, fat and water have this parity (fat, very short T1 recovery and T2 decay times; water, very long T1 recovery and T2 decay times); therefore these tissues return high signal intensity in steady state sequences (Table 4.5). Tissues such as muscle do not have this parity (very short T2 decay time and very long T1 recovery time), so they return a low signal in steady state sequences.


Table 4.5 T1 and T2 relaxation times and signal intensity of brain tissue in the steady state at 1 T.


































Tissue T1 time (ms) T2 time (ms) T1/T2 Signal intensity
Water 2500 2500 1
Fat 200 100 0.5
Cerebral spinal fluid 2000 300 0.15
White matter 500 200 0.2

Typically, TRs less than 50 ms are considered appropriate to maintain the steady state. The optimum flip angle is determined by the Ernst angle equation (Equation (4.2)). The Ernst angle is the flip angle that provides optimum signal intensity for a tissue with a given T1 recovery time scanned using a given TR. Figure 4.10 illustrates typical Ernst angles for three tissues in the brain using a TR of 30 ms. The optimum signal intensity in all three tissues is about 12°, but to obtain good contrast between them, larger flip angles between 30° and 45° are required. As contrast generation is important, medium flip angles in the range shown in Figure 4.10 are common.










Equation 4.2
Ernst = cos-1 [e(-TR T1)]

Ernst is the Ernst angle in degrees


TR is the repetition time (ms)


T1 is the T1 relaxation time of a tissue (ms)

This equation determines the maximum signal intensity for a tissue with a certain T1 relaxation time at different TR values. When the flip angle is larger than the Ernst angle, saturation and therefore T1 contrast increase. When the flip angle is less than the Ernst angle, contrast relies more on PD
Graph shows flip angle in degrees versus signal intensity where curves CSF, white matter, and grey matter steeply increase and gradually decrease.

Figure 4.10 Ernst angle graphs in the brain using a TR of 30 ms.


Weighting mechanism 3 – residual transverse magnetization


In the steady state, there is coexistence of both longitudinal and transverse magnetization. The transverse component of magnetization does not have time to decay and builds up over successive TRs. This transverse magnetization is produced because of previous RF excitation pulses but remains over several TR periods in the transverse plane (see learning tip below). It is called residual transverse magnetization, and it affects image contrast, as it induces a voltage in the receiver coil. Tissues with long T2 decay times (i.e. water) are the main component of this residual transverse magnetization and enhance T2 contrast.


Figure 4.11 demonstrates a typical image acquired using a gradient-echo sequence in the steady state. The extrinsic contrast parameters (TR, TE, and flip angle) are selected to generate the steady state and to enhance T2* contrast. However, the influence of the other two weighting mechanisms is also evident. The effect of residual transverse magnetization is seen from the high signal from water in the stomach. Water is also hyperintense in this image because water has a good parity between its T1 recovery and T2 decay times. Fat is also bright on this image for the same reason. Muscle is hypointense because it does not have a parity between its T1 recovery and T2 decay times.

Image described by caption and surrounding text.

Figure 4.11 Axial steady state image.

Mar 9, 2019 | Posted by in MAGNETIC RESONANCE IMAGING | Comments Off on Gradient-echo pulse sequences
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