The Basics of MRI

• Introduction
• Multislice imaging
• Oblique Imaging
• Spin-Echo Imaging
• Inversion Recovery Imaging
• Gradient Recalled Echo Imaging
• Image Contrast
• Signal Averaging
• Problems

Introduction

In the previous chapter you learned the principles of Fourier transform magnetic resonance imaging. The examples presented were for a simplified 90-FID imaging sequence. Although the principles were correct, some aspects were simplified to make the presentation easier to understand. Some of these principles will be presented in a little more depth in this section. The 90-FID imaging sequence will be presented as a gradient recalled echo sequence in this section. The principles of multislice imaging and oblique imaging will be introduced. Two new imaging sequences called the spin-echo sequence and inversion recovery sequence will be introduced.

Multislice Imaging

An imaging sequence based on a 90-FID was introduced in Chapter 7. Based on this presentation, the time to acquire an image is equal to the product of the TR value and the number of phase encoding steps. If TR were one second and there were 256 phase encoding gradient steps the total imaging time required to produce the image would be 4 minutes and 16 seconds. If we wanted to take 20 images across a region of interest the imaging time would be approximately 1.5 hours. This will obviously not do if we are searching for pathology. Looking at the timing diagram for the imaging sequence with a one second TR it is clear that most of the sequence time is unused. This unused time could be made use of by exciting other slices in the object. The only restriction is that the excitation used for one slice must not affect those from another slice. This can be accomplished by applying one magnitude slice selection gradient and changing the RF frequency of the 90^o pulses. Note that the three frequency bands from the pulses do not overlap. In this animation there are three RF pulses applied in the TR period. Each has a different center frequency n₁, n₂, and n₃. As a consequence the pulses affect different slices in the imaged object.

Oblique Imaging

Orthogonal imaging planes along the X, Y, or Z axes are easily produced with the imaging sequence presented in the Chapter 7. However what if the anatomy of interest does not lie along one of the three orthogonal imaging planes? This is where the concept of oblique imaging comes in. Oblique imaging is the production of images which lie between the conventional X, Y, and Z axes. Oblique imaging is performed by applying linear combinations of the X, Y, and Z magnetic field gradients so as to produce a slice selection gradient which is perpendicular to the imaged plane, a phase encoding gradient which is along one edge of the imaged plane, and a frequency encoding gradient which is along the remaining edge of the image. For example, if we wanted to image a slice lying along the X axis but passing between the Z and Y axes such that it made an angle of 30^o with respect to the Y axis and 60^o with the Z axis, the following combination of gradients would be needed.

Slice Selection Gradient	Gz = Gs Sin 60o
	Gy = -Gs Cos 60o
Phase Encoding Gradient	Gz = G Sin 30o
	Gy = G Cos 30o
Frequency Encoding Gradient	Gx = Gf

The frequency and phase encoding gradients are interchangeable. The timing diagram for the sequence looks as follows.

Spin-Echo Imaging

In Chapter 4 we saw that signal could be produced by a spin-echo sequence. An advantage of using a spin-echo sequence is that it introduces T₂ dependence to the signal. Since some tissues and pathologies have similar T₁ values but different T₂ values it is advantageous to have an imaging sequence which produces images with a T₂ dependence. The spin-echo imaging sequence will be presented in the form of a timing diagram only, since the evolution of the magnetization vectors from the application of slice selection, phase encoding, and frequency encoding gradients are similar to that presented in Chapter 7.

The timing diagram for a spin-echo imaging sequence has entries for the RF pulses, the gradients in the magnetic field, and the signal. A slice selective 90^o RF pulse is applied in conjunction with a slice selection gradient. A period of time equal to TE/2 elapses and a 180^o slice selective 180^o pulse is applied in conjunction with the slice selection gradient.

A phase encoding gradient is applied between the 90^o and 180^o pulses. As in the previous imaging sequences, the phase encoding gradient is varied in 128 or 256 steps between G_m and -G_m. The phase encoding gradient could be applied after the 180^o pulse, however if we want to minimize the TE period the pulse is applied between the 90^o and 180^o RF pulses.

The frequency encoding gradient is applied after the 180^o pulse during the time that echo is collected. The recorded signal is the echo. The FID, which is found after every 90^o pulse, is not used. One additional gradient is applied between the 90^o and 180^o pulses. This gradient is along the same direction as the frequency encoding gradient. It dephases the spins so that they will rephase by the center of the echo. This gradient in effect prepares the signal to be at the edge of k-space by the start of the acquisition of the echo.

The entire sequence is repeated every TR seconds until all the phase encoding steps have been recorded.

Inversion Recovery Imaging

In Chapter 4 we saw that a magnetic resonance signal could be produced by an inversion recovery sequence. An advantage of using an inversion recovery sequence is that it allows nulling of the signal from one component due to its T₁. Recall from Chapter 4 that the signal intensity is zero when TI = T₁ ln2. Once again, this sequence will be presented in the form of a timing diagram only, since the evolution of the magnetization vectors from the application of slice selection, phase encoding, and frequency encoding gradients are similar to that presented in Chapter 7.

The timing diagram for an inversion recovery imaging sequence has entries for the RF pulses, the gradients in the magnetic field, and the signal. A slice selective 180^o RF pulse is applied in conjunction with a slice selection gradient. A period of time equal to TI elapses and a spin-echo sequence is applied.

The remainder of the sequence is equivalent to a spin-echo sequence. This spin-echo part recorded the magnetization present at a time TI after the first 180^o pulse. (A 90-FID sequence could be used instead of the spin-echo.) All the RF pulses in the spin-echo sequence are slice selective. The RF pulses are applied in conjunction with the slice selection gradients. Between the 90^o and 180^o pulses a phase encoding gradient is applied. The phase encoding gradient is varied in 128 or 256 steps between G_m and -G_m.

The phase encoding gradient could not be applied after the first 180^o pulse because there is no transverse magnetization to phase encode at this point. The frequency encoding gradient is applied after the second 180^o pulse during the time that echo is collected.

The recorded signal is the echo. The FID after the 90^o pulse is not used. The dephasing gradient between the 90^o and 180^o pulses to position the start of the signal acquisition at the edge of k-space, as was described in the section on spin-echo imaging. The entire sequence is repeated every TR seconds.

Gradient Recalled Echo Imaging

The imaging sequences mentioned thus far have one major disadvantage. For maximum signal, they all require the transverse magnetization to recover to its equilibrium position along the Z axis before the sequence is repeated. When the T₁ is long, this can significantly lengthen the imaging sequence. If the magnetization does not fully recover to equilibrium the signal is less than if full recovery occurs. If the magnetization is rotated by an angle q less than 90^o its M_z component will recover to equilibrium much more rapidly, but there will be less signal since the signal will be proportional to the Sinq. So we trade off signal for imaging time. In some instances, several images can be collected and averaged together and make up for the lost signal.

The gradient recalled echo imaging sequence is the application of these principles. Here is its timing diagram. In the gradient recalled echo imaging sequence a slice selective RF pulse is applied to the imaged object. This RF pulse typically produces a rotation angle of between 10^o and 90^o. A slice selection gradient is applied with the RF pulse.

A phase encoding gradient is applied next. The phase encoding gradient is varied between G_m and -G_m in 128 or 256 equal steps as was done in all the other sequences.

A dephasing frequency encoding gradient is applied at the same time as the phase encoding gradient so as to cause the spins to be in phase at the center of the acquisition period. This gradient is negative in sign from that of the frequency encoding gradient turned on during the acquisition of the signal. An echo is produced when the frequency encoding gradient is turned on because this gradient refocuses the dephasing which occurred from the dephasing gradient.

A period called the echo time (TE) is defined as the time between the start of the RF pulse and the maximum in the signal. The sequence is repeated every TR seconds. The TR period could be as short as tens of milliseconds.

Image Contrast

In order for pathology or any tissue for that matter to be visible in a magnetic resonance image there must be contrast or a difference in signal intensity between it and the adjacent tissue. The signal intensity, S, is determined by the signal equation for the specific pulse sequence used. Some of the intrinsic variables are the:

The spin density is the concentration of signal bearing spins. The instrumental variables are the:

T₂* falls on both lists because it contains a component dependent on the homogeneity of the magnetic field and the the molecular motions. The signal equations for the pulse sequences presented thus far are:

Spin-Echo

S = k r (1-exp(-TR/T₁)) exp(-TE/T₂)

Inversion Recovery (180-90)

S = k r (1-2exp(-TI/T₁)+exp(-TR/T₁))

Inversion Recovery (180-90-180)

S = k r (1-2exp(-TI/T₁)+exp(-TR/T₁)) exp(-TE/T₂)

Gradient Recalled Echo

S = k r (1-exp(-TR/T₁)) Sinq exp(-TE/T₂*) / (1 -Cosq exp(-TR/T₁))

In each of these equations, S represents the amplitude of the signal in the frequency domain spectrum. The quantity k is a proportionality constant which depends on the sensitivity of the signal detection circuitry on the imager. The values of T₁, T₂, and r are specific to a tissue or pathology. The following table lists the range of T₁, T₂, and r values at 1.5T for tissues found in a magnetic resonance image of the human head.

The contrast, C, between two tissues A and B will be equal to the difference between the signal for tissue A, S_A, and that for tissue B, S_B.

S_A and S_B are determined by the signal equations given above. For any two tissues there will be a set of instrumental paramenters which yield a maximum contrast. For example in a spin-echo sequence the contrast between two tissues as a function of TR is graphically presented in the accompanying curve.

A contrast curve for tissues A and B as a function of TE is presented in the accompanying curve.

To assure that signals from all phase encoding steps possess the same signal properties a few equilibrating cycles through the sequence are added to the beginning of every image acquisition. The necessity of this can be seen by examining the M_Z and M_XY components as a function of time in a 90-FID type sequence. Note that the amount of transverse magnetization from a 90^o pulse reaches an equilibrium value after a few TR cycles. This practice lengthens the imaging time by a few TR periods.

The magnetic resonance community has adopted nomenclature to signify the predominant contrast mechanism in an image. Images whose contrast is predominantly caused by differences in T₁ of the tissues is called a T₁-weighted image. Similarly for T₂ and r, the images are called T₂-weighted and spin density weighted images. The following table contains the set of conditions necessary to produce weighted images.

It is impressive to see how the choice of the instrumental parameters TR, TE, TI, and q affect the contrast between the various tissues of the brain. In the accompanying set of graphics you can select an imaging sequence and the imaging parameters, the resultant image will be displayed in the graphics window. The spin-echo images are actual magnetic resonance images of the human brain. The remaining images are calculated images based on the signal equations above and a set of measured overall T₁, T₂, and r images of the human brain. The two bright circles to the bottom right and left sides of each calculated image are spin density standards, or phantoms, placed next to the head.

	TE (ms)
TR (ms)	20	40	60	80
250
500
750
1000
2000

Inversion Recovery Images (180-90)

	TR (ms)
TI (ms)	1000	2000
50
100
250
500
750

Gradient Recalled Echo Images ( TE=5 ms )

	TR (ms)
q ( o )	25	50	100	200
15
30
45
60
90

Signal Averaging

The signal-to-noise ratio (SNR) of a tissue in an image is the ratio of the average signal for the tissue to the standard deviation of the noise in the background of the image. The signal-to-noise ratio may be improved by performing signal averaging. Signal averaging is the collection and averaging together of several images. The signals are present in each of the averaged images so their contribution to the resultant image add. Noise is random so it does not add, but begins to cancel as the number of spectra averaged increases. The signal-to-noise improvement from signal averaging is proportional to the square root of the number of images averaged (Nex). Nex is more commonly referred to as the number of excitations.

SNR Nex^1/2

Compare the results of averaging together the following number of images of a bottle of water.

Nex	Nex1/2	Image
1	1.00
2	1.41
4	2.00
16	4.00

Problems

1. How many slices could you image with a 90-FID sequence which uses a 20 ms slice selection gradient, 10 ms phase encoding gradient, 100 ms frequency encoding gradient, and TR of 1 second?

2. Draw a timing diagram for an inversion recovery imaging sequence which uses a 90-FID sequence rather than a spin-echo sequence to detect the signal present TI after the inversion (180 degree) pulse.

3. There are two adjacent tissues in an image with a T₂ of 30 and 50 ms. You wish to produce a spin-echo image of the tissues wuch that the contrast between the tissues is maximized. What TE should be used?

4. You wish to image an oblique slice located at an angle of 45^o to the +Z-axis and 45^o to the +Y-axis. Since gradients can only be produced with the three gradient coil systems located around the x, y, and z-axes, what combination of the three gradients should be applied to produce a slice selection, phase encoding, and frequency encoding gradient?

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