# The Basics of MRI

## BASIC IMAGING TECHNIQUES

### 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 initial presentation easier to understand. Some of these principles will be presented in a little more depth in this section. The principles of multislice imaging, volume or three dimensional (3D) imaging, and oblique imaging will be introduced. Two new imaging sequences called the spin-echo sequence and inversion recovery sequence will be introduced.

If the 90-FID imaging sequence presented in the previous chapter was used, we would record only half of k-space. We would like to produce the equivalent of an echo in the center of our acquisition window when the frequency encoding gradient is turned on. This would give us both the left and right halves of k-space. To achieve this we need to turn on a wind-up gradient, as it is called, in the frequency encoding direction. Here is its timing diagram. In this sequence a slice selective RF pulse is applied to the imaged object. This RF pulse typically produces a rotation angle of between 0 and 90o, although a 0o rotation is not of much use because it produces no signal. A slice selection gradient is applied with the RF pulse.

A phase encoding gradient is applied next. The phase encoding gradient is varied between Gm and -Gm 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. The reversal of the gradient is responsible for the echo. So as not to confuse this type of echo with one produced by a 180o pulse, this echo is called a gradient echo.

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 signal from a gradient-echo sequence is as follows. More on this sequence will be presented in the Fast Imaging Techniques chapter.

S = k ρ (1-exp(-TR/T1)) exp(-TE/T2*)

Imaging with a gradient-echo sequence is intrinsically more sensitive to magnetic field inhomogeneities because of the use of the refocusing gradient or wind-up gradient.

### Multislice Imaging

In the gradient-echo sequence introduced in the last section of this chapter, the time to acquire an image is equal to the product of the TR value and the number of phase encoding steps. If TR was 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 90o 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 ν1, ν2, and ν3. As a consequence the pulses affect different slices in the imaged object.

Multislice imaging is the default mode on a clinical scanner because it allows a volume of anatomy to be imaged in the shortest time.

There are several acquisition schemes for multislice sequences. There is interleaved, contiguous, and n skip m. The animation window compares each of these to a single slice. Consider a set of 3 mm slices placed one next to another so that 10 slices exactly span 30 mm. These are said to be contiguous slices. If we position 4 slices evenly spaced in the same 30 mm we are applying a 4 skip 2 acquisition. A set of contiguous or n skip m slices can be acquired sequentially in an interleaved fashion. Sequentially means we acquire the slices in order (1, 2, 3, ...) while interleaved means we do not acquire adjacent slices simultaneously (e.g. 1,5,10,…, 2,6,11,…, 3,7,12, ...). Interleaved acquisitions are preferable because RF pulses and hence slices are not perfect. An RF pulse can rotate spins adjacent to the desired slice location by a lesser amount. This changes the effective TR of a sequence and hence the contrast.

### Volume Imaging (3D Imaging)

Volume imaging is the acquisition of magnetic resonance data from a volume rather than a single tomographic slice. It can be thought of as collecting several contiguous slices through a region of imaged object. The number of contiguous slices will always be a multiple of 2.

The actual timing diagram for a volume imaging pulse sequence looks like this. There is a volume selection RF pulse and gradient which rotates only those spins in the imaged volume of the object. This combination of pulses is equivalent to a slice selection combination except the slice thickness can be 10 or 20 cm. The volume selection pulses are followed by a phase encoding gradient in dimension 1 and another one in dimension 2. Each is varied between a maximum and minimum value, just as all the phase encoding gradients have been. The two gradient pulses are applied at the same time and are cycled through all possible combinations. The frequency encoding gradient has its dephasing negative lobe to cause the spins to be in phase at the center of the acquisition window. The frequency encoding gradient is applied and a signal recorded, just as it has been in all the previous sequences.

The imaging time is equal to the product of the TR value times the number of phase encoding steps in dimension 1 times the number of steps in dimension 2. Because of this large value, a gradient recalled echo sequence is typically used for volume imaging. The resolution in the direction corresponding to the slice direction in a 2D sequence can be much less in a volume imaging sequence than in a tomographic sequence. Therefore, volume acquisition sequences are often used when the desired resolution in the corresponding slice direction is less than ~2 mm. It is also used when isotropic voxels are desired.

### 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 30o with respect to the Y axis and 60o 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. Please also note that a positive gradient will achieve the same thing as a negative gradient, and Cos(θ) = Sin(90-&theta) and Cos(90-θ) = Sin(&theta). The timing diagram for the sequence looks as follows.

Oblique imaging has become very common in MRI because the most diagnostically useful imaging planes are are not always perpendicular to the X, Y, or Z axes, or parallel to each other. The orientation of the imaging plane is set graphically by the operator after obtaining a set of initial scans through the anatomy. The scanner's operating system calculates the exact Gz, Gy, and Gx values to use to create the Gs, G, and Gf needed to produce the oblique slice.

Please see the additional detail for information on using the rotation matrices to calculate the linear combinations of Gx, Gy, and Gz.

### 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 90o RF pulse is applied in conjunction with a slice selection gradient. A period of time equal to TE/2 elapses and a 180o slice selective 180o pulse is applied in conjunction with the slice selection gradient.

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

The frequency encoding gradient is applied after the 180o pulse during the time that echo is collected. The recorded signal is the echo. The FID, which is found after every 90o pulse, is not used. One additional gradient is applied between the 90o and 180o 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. The signal from a spin echo sequence is as follows.

S = k ρ (1-exp(-TR/T1)) exp(-TE/T2)

### 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.

An inversion recovery sequence which uses a spin-echo sequence to detect the magnetization will be presented. The RF pulses are 180-90-180. An inversion recovery sequence which uses a gradient-echo signal detection is similar, with the exception that a gradient-echo sequence is substituted for the spin-echo part of the sequence.

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 180o 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 180o pulse. (A gradient-echo 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 90o and 180o pulses a phase encoding gradient is applied. The phase encoding gradient is varied in 128 or 256 steps between Gm and -Gm.

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

The recorded signal is the echo. The FID after the 90o pulse is not used. The dephasing gradient between the 90o and 180o 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. The signal from a repeated inversion recovery sequence which uses a gradient echo to record the signal is

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

and for the sequence using a spin-echo sequence the signal is as follows.

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

### Chemical Contrast Agents

A chemical contrast agent (CA) is a substance which is introduced into the body to change the contrast between the tissues. Contrast agents are predominantly paramagnetic materials, but some are ferromagnetic. The contrast mechanism is different for these two classes of materials.

Contrast Mechanism
Ferromagnetic contrast agents change the contrast by distorting the Bo magnetic field around ferromagnetic material in the contrast agent. This changes T2* of the water molecules around the ferromagnetic contrast agent. Ferromagnetic contrast agents are typically iron nanoparticles attached to an organic substrate.

Paramagnetic contrast agents change the contrast by creating time varying magnetic fields which promote spin-lattice and spin-spin relaxation of the water molecules. The time varying magnetic fields come from both rotational motion of the contrast agent and electron spin flips associated with the unpaired electrons in the paramagnetic material in the contrast agent. Recall time-varying magnetic fields at ν and 2ν promote T1 and time-varying magnetic fields < 2ν promote T2. A typical paramagnetic contrast media is a complex of a paramagnetic metal ion such as manganese (Mn+2), iron (Fe+3), or gadolinium (Gd+3). Gd is the most common metal ion used in paramagnetic contrast agents. It has an electron spin of 7/2 and hence seven unpaired electrons promoting spin relaxation due to flipping spins and rotational motion.

The relaxivity (r1 or r2) of a contrast agent in water is the change in 1/T1 or 1/T2 of water per concentration of contrast agent. To appreciate this concept, consider the following diagram of 1/T1 in units of s-1 versus the concentration of gadolinium [Gd+3] at 273 K. The 1/T1 intercept of the line at zero concentration is the 1/T1 value of water. The slope is the relaxivity r1. The relationship between T1, r1, and the concentration of the paramagnetic material is given by the following equation.

1/T1 (Measured) = 1/T1 (Water) + r1 [Gd]

The relaxivity is dependent on the magnetic field and temperature, so it is usually reported along with a Bo of proton resonance frequency and temperature.

Chemical Structures
Unfortunately, many paramagnetic metal ions (M) are toxic. To lessen their toxicity, these metal ions are typically complexed with other molecules or ions called ligands (L) to prevent them from complexing with molecules in the body. The stability of the metal-ligand complex (ML) is given by the formation constant (K) for the reaction

M + L ML

where

K = [ML] / [M] [L] .

Ideally, it would be nice to have K under physiological conditions, for example pH=7.4. Unfortunately some buffers that are used to achieve the desired pH can precipitate Gd and alter the equilibrium. For this reason, only K values at pH=7 are reported below.

K is not the only quantity that determines toxicity. A large K can still result in the release of a toxic metal ions if another ligand molecule or ion (L') or another metal ion (M') can compete with M and L. For example ligand exchange,

ML + L' ML' + L ,

releases ML' which may be more toxic than ML.

Transmetallation is the exchange of the metal in the contrast agent with a metal ion in solution.

ML + M' M'L + M

In transmetallation with a gadolinium based contrast agent, toxic Gd is released. Some contrast agents undergo transmetallation and ligand exchange more easily than others. For example, contrast agents containing cyclic ligands tend to undergo less transmetallation than contrast agents with linear ligands.

Although you should always be concerned when an external material is injected, most MRI contrast agents are safe unless given in large quantities and to individuals with compromized kidney function. The administration of certain contrast agents in large doses to patients with compromized kidney function is thought to be the cause of nephrogenic systemic fibrosis (NSF).

The following table contains a list of some common MRI contrast agents and their structures, trade names, applications, equilibrium constants, and relaxivities.

MRI Paramagnetic Contrast Agents
(mfr.)
Name,
(Abbreviation),
& Structure
Application   Structure
Relaxivities
K
Ablavar
(Lantheus),
Vasovist
(Bayer Schering)
trisodium
MRA
Dotarem
(Guerbet)
meglumine
(Gd-DOTA)
CNS, Vas
Eovist
(Bayer Schering),
Primovist
(Bayer Schering)
disodium salt
Liver
(Bayer Schering)
(Gd-DO3A-butrol)
MRA
Magnevist
(Bayer Schering)
dimeglumine
(Gd-DTPA)
CNS, Vas
MultiHance
(Bracco)
dimeglumine
(Gd-BOPTA)
CNS
Liver
MRA
Omniscan
(GE)
(Gd-DTPA-BMA)
CNS, Vas
OptiMARK
(Covidien)
CNS, Liver
ProHance
(Bracco)
(Gd-HP-DO3A)
CNS, Vas
FerriSeltz
(Otsuka),
Geritol
(GlaxoSmithKline)
feric ammonium
citrate
Stomach and
upper small intestine
Teslascan
(GE)
Mangafodipir
Trisodium
Liver

Functionality
Except for contrast agents which are intended for imaging the digestive system, contrast agents are administered intravenously. After the injection of a contrast agent, the circulatory system carries it throughout the body. At this point, contrast agents take a different course depending on their intended functionality: intravascular (IV), extracellular (EC), or intracellular (IC).

An intravascular contrast agent by design stays in the circulatory system until it is removed by the kidneys. These contrast agnets are used for contrast enhnaced magnetic resonance angiography (MRA).

Extracellular contrast agents travel through the circulatory system and pass into the extracellular fluid, but do not enter into the cells. These contrast agents relax the extracellular water so quickly and exchangeable H+ ions diffuse so quickly across a cell membrane that even water within the cells gets relaxed. Tumors have a higher vasculature then healthy tissues and hence receive more contrast agent than healthy tissues. Therefore, the greater the vasculature the greater the change in T1 and the greater the contrast.

Intracellular contrast agents go one step further than extracellular contrast agents. They can enter into a cell. Targeted contrast agents accumulate in a specific tissue. The cause of the accumulation is an affinity for a specific tissue. These contrast agents have a group designated as P in the drawing which could be transferin, other proteins, antibodies, DNA snipits, or oligonucleotides. The P group is attached to a protected Gd or some other paramagntic ion, or a ferromagnetic particle.

Some extracellular contrast agents are physiology activated. These contrast agents experience a change structure in the presence of an activator. The change in structure causes a change in access to the Gd by water molecules and hence r1 and r2 The activator could be pH or a concentration of another substance. The animation window displays a contrast agent that is sensitivie to calcium ions. The -COO- groups have a higher selectivity for Ca2+ than Gd3+. As the calcium ion concentration increases, the -COO- groups preferentially bind to Ca2+ and expose more water molecules to the Gd3+ and their fluctuating magnetic fields.

### Fat Suppression

Fat suppression imaging is the production of an image from just the water in the body. For example if the object being imaged is composed of water and fat hydrogens, a chemical shift image would be an image of just the water hydrogen NMR signal in the object. There are several methods of performing chemical shift imaging, the two which are covered here the inversion recovery method and the saturation method. Although both of these sequences are most often used to suppress the fat signal, they can also be used to suppress the water signal. Fat suppression imaging is sometimes called chemical shift imaging.

In the inversion recovery method an inversion recovery imaging sequence is used and the TI time is set to T1ln2 where T1 is the spin-lattice relaxation time of the component one wishes to suppress. For fat suppression that component is fat, for water suppression it is water. This technique only works when the T1 values for the two components are different.

In the saturation method a frequency selective saturation pulse is applied before the standard imaging pulses of a sequence, for example a spin-echo sequence. The saturation pulse sets to zero the magnetization from the component we wish to suppress. When the standard imaging sequence follows it detects no signal from the suppressed component. The accompanying animation shows an RF timing diagram for the sequence. The saturation pulse consists of the frequency selective pulse which causes the Z magnetization for a specific chemical shift to be zero. In the case of a fat saturation sequence, this chemical shift compound is fat. This pulse is followed by a dephasing gradient to force the transverse magnetization from this chemical shift component to zero. The saturation pulse is followed by, in this example, a spin-echo sequence. This technique works best when the T1 for the suppressed tissue is long compared to the time between the saturation pulse and the spin-echo sequence.

### Problems

1. How many slices could you image with a gradient-echo 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 gradient-echo sequence rather than a spin-echo sequence to detect the signal present TI after the inversion (180 degree) pulse.

3. You wish to image an oblique slice located at an angle of 45o to the +Z-axis and 45o 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?

4. How many slices could you image with a Gradient-echo sequence that uses a 20 ms slice selection gradient, 10 ms phase encoding gradient, 10 ms dephasing frequency gradient, 100 ms frequency encoding gradient, and TR = 1 s?

5. Assuming the standard magnetic coordinate system, what components of the gradients Gx, Gy, and Gz should be applied to create the gradients Gslice, Gphase, and Gfrequency for the following slice selection? A slice located 30o away from the Z-axis and forming equal angles with the +X and +Y axes.

6. What are the T1 values of the following: a) a 1 mM aqueous solution Gd+3 at 7 T and 293 K, and b) a 1 mM aqueous solution of Omniscan at 0.43 T and 313 K ?

7. There are two adjacent tissues in an object image with T1a = 300 ms, T2a* = 20 ms, ρa = 50 ASDU, and T1b = 150 ms, T2b* = 20 ms, ρb = 50 ASDU. (ASDU = arbitrary spin density units.) You wish to produce a 90° gradient echo image of the tissues such that the contrast between the tissues is maximized. What TR should be used?

8. Calculate and plot the relative signal from muscle at 1.5T from a gradient echo sequence as a function of θ for TR=50 ms and TE=5 ms.

9. The MRI contrast agent Omniscan® (gadodiamide) has a relaxivity (r1) at 0.235 T of 4.5 mM-1s-1. What concentration of Omniscan is needed to change the R1 of water from 0.34 s-1 to 1.0 s-1? What change in T1 does this represent?