Part I NMR: from quantum mechanics to bioimaging

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Part I

NMR: from quantum mechanics

to bioimaging

Chapter 2. Principles of Nuclear Magnetic Resonance Chapter 3. Magnetic Resonance Imaging

Overview

In this part of the thesis the fundamental principles of magnetic resonance imaging are described, in order to provide the reader with the theoretical background that is at the basis of the original work described later. In particular, chapter 2 introduces the physical principles of nuclear magnetic resonance, including both the quantum and classical description of the phenomenon. Chapter 3 gives instead details on the procedure of Magnetic Resonance Imaging, explaining how MR signal can be exploited and modified to generate radiological images.

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Chapter 2 Principles of Nuclear

Magnetic Resonance

2.1 Nuclear Magnetic Resonance (NMR)

The property of Nuclear Magnetic Resonance (NMR) was first described by Purcell [1] and Bloch [2] in 1946, work for which they received the Nobel prize in 1952. Since then NMR has become a powerful tool in the analysis of chemical composition and structure. In 1973 Lauterbur [3] and Mansfield [4] used the principles of NMR to describe a technique for determining physical structure. Since then Magnetic Resonance Imaging (MRI) has been used in many biomedical, chemical and engineering applications.

2.1.1 The quantum mechanical description of NMR

The quantum mechanical description of atomic nuclei, as described by Dirac in 1930, predicted the property of spin angular momentum. In fact the property of electron spin was observed six years earlier by Stern and Gerlach [5], who passed a beam of neutral atoms through a non-uniform magnetic field, and observed the effect of half-integral angular momentum, that could not be explained by the previously accepted Bohr’s model. This spin angular momentum is characterized by the spin

quantum number I. The value of I is an intrinsic property of the nucleus.

To exhibit the property of magnetic resonance the nucleus must have a non-zero value of I. In nature, several nuclei of atoms with odd atomic number have spin quantum number different from zero, like 1H, 13C, 19F and 31P; for all these nuclei the spin quantum number equals 1/2. As far as medical applications are concerned, the proton (1H) is the nucleus of most interest, because of its high natural abundance; other nuclei have been studied, however, most noticeably 13C whose low natural abundance relative to 12C makes it suitable for tracer studies.

The magnitude of the spin angular momentum P is related to the spin quantum number I through the formula

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Part I:NMR: from quantum mechanics to bioimaging

8

!

P = I(I + 1)

h

Likewise, nuclei are characterized by a magnetic momentum µ, which is proportional to the angular momentum through the gyromagnetic ratio according to the formula

!

µ

=

"

P

Each nucleus has its particular gyromagnetic ratio; for the hydrogen proton it equals 2.675 x 108 rad/s/T.

Though the magnitude of the magnetic momentum is constant, its direction is completely random in absence of an external magnetic field. In condition of thermal equilibrium, there exists therefore no net magnetization. To obtain a net magnetization it is necessary to apply a strong external magnetic field, in order to orient the magnetic spins along its direction.

When the nucleus is immersed in a magnetic field, applied along a generic z-axis, the possible values of the z-components of the magnetic momentum are given by:

!

µ

z

= m

I

"

h

with mI=I,I-1…,-I

For a hydrogen nucleus, possible values of µz are therefore either

-1/2γ

!

h

or +1/2γ

!

h

.

Fig. 2-1. Nuclear spins in absence (left) and presence (right) of an external magnetic field.

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Principles of Nuclear Magnetic Resonance E=-µ•B that is

!

E = " m

I

#

hB

z

So for a proton, passing from one state to another an increase in energy is required and equals

∆E= γ !

hBz

This phenomenon is known as Zeeman splitting. The two possible states are commonly referred to as “spin-down” and “spin-up”, with spin-down indicating the higher energy configuration.

Since according to quantum mechanics an electromagnetic wave is made up of energy quantum with energy equal to

E=hν

a transition between the two states is accompanied by the emission or absorption of a photon of frequency

ν=γB,

relation known with the name of Larmor law. 2.1.2 The classical description of NMR

When dealing with macroscopic sample made up of large number of protons, the laws of classical mechanics predict the correct behaviour of a magnetized sample.

When a spin is placed in a magnetic field it will experience a torque

!

d

P

r

dt

=

r

µ

"

B

r

In a static magnetic field B0 this will result in a motion of nuclear precession. The precession frequency will be equal to the Larmor

frequency ω0=γB0

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Fig. 2-2. Spin precession and magnetic dipole moment components.

Now, as well as the static B0 field applied along z, consider a time

varying field B1, applied perpendicularly to B0 and oscillating at a

frequency equal to ω0. If only the circularly polarised component of B1

rotating in the same direction as the precessing magnetization vector is considered, the net result will be that the magnetization simultaneously precesses about B0 at ω0 and about B1 at ω1, where

ω0=γB0

The most common way to carry out an NMR experiment is to apply a short burst of resonant radiofrequency (RF) field. If the duration of this r.f. pulse is t, then the magnetization will rotate by an angle α = γ B1 t (Flip Angle). If that angle is 90 degrees then the pulse is referred to as a 90° pulse. In a typical NMR experiment a 90° pulse is applied, which tips the magnetization vector from the longitudinal plane (parallel to B0)

to the transverse plane (perpendicular to B0). Once in the transverse

plane the magnetization can be detected as it precesses about the z-axis, and this is what gives rise to the NMR signal, which is discussed in the next section.

2.1.3 Longitudinal and transverse relaxation

Since the application of a resonant r.f. pulse disturbs the spin system, there must subsequently be a process of coming back to equilibrium. This involves exchange of energy among the spins and between the spin system and its surroundings.

The process thanks to which after an RF pulse the longitudinal magnetization is recreated is called longitudinal relaxation. The temporal evolution of this phenomenon is described by a characteristic time indicated as longitudinal relaxation time, indicated as T1.

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Principles of Nuclear Magnetic Resonance

The longitudinal relaxation time is an indication of the time needed by protons of a tissue to return to the equilibrium longitudinal magnetization. At a given magnetic field this parameter is a characteristic property of each tissue, and depends on the efficiency with which tissue protons can transfer their energy to the surrounding structures. The energy transfer involved in the T1 relaxation is referred to as spin-lattice interaction.

The law that describes the temporal evolution of the longitudinal magnetization after an RF pulse is

!

dM_z dt =

M₀" Mz

T1

If at t=0 the longitudinal magnetization is null (Mz (0) = 0), the

longitudinal magnetization increases with time with an exponential law

! M_z(t) = M01" exp " t T1 # $ % & ' ( ) * + , - .

In this way, the longitudinal relaxation time can be defined as the time at which after a 90° RF pulse the longitudinal magnetization recovers 63% of its original value at the equilibrium.

Fig. 2-3. Longitudinal relaxation.

The upper limit for the T1 of biological tissues is represented by pure water, and it is about 3 seconds. In pure water, like in other viscous liquids, molecules move rapidly and the energy transfer is inefficient,

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12

making relaxation times longer. The movement of tissues such as the fat acids is instead limited, and this improves the efficiency of the T1 relaxation, so that fat tissues have the shortest longitudinal relaxation times.

The spins, however, do not exchange energy only with the surrounding lattice, but also among themselves. This is generally a faster process than spin-lattice relaxation, and is called spin-spin or transverse

relaxation. Similarly to the longitudinal relaxation, transverse relaxation

is characterized by the transverse relaxation time or T2. The law that govern transverse relaxation is

, ,

2

x y x y

dM M

dt = ! T

which produces an exponential decay of the transverse magnetization according to the formula

2 , , (0) t T x y x y M =M e! .

Transverse relaxation time can be defined as the time after which transverse magnetization drops at 37% of the original value.

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Fig. 2-5. Transverse relaxation

The relaxation times T1 and T2 are very important in imaging, as they have the greatest effect in determining contrast. The overall evolution in time of the magnetization is depicted in Fig. 2-6.

Fig. 2-6. Magnetization recovery after a 90° pulse.

To detect the NMR signal it is necessary to have an r.f. coil which is in the transverse plane, that is perpendicular to the B0 field, in which an

electromagnetic force (e.m.f.) is induced which is proportional to the transverse magnetization Mx. Since the signal is modulated on a sinusoidal oscillation with frequency equal to ω0, the signal from the coil

is first transformed as if it was acquired in a rotating frame at ω0; this

procedure is done by phase sensitive detection. Normally, this involves separately mixing the e.m.f. with two reference signals, both oscillating at the Larmor frequency, but 90 degrees out of phase with each other. Thus the signal detected in the coil has the form:

S = S0e

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which after phase sensitive detection has 'real' and 'imaginary' components ! S_R = S0e "t /T 2_cos#t ! S_I = S0e "t /T 2_cos#t

here ∆= ω-ω0. If ∆=0 then the signal is just an exponential decay,

however if ∆ is different than zero then the signal will oscillate at a frequency. The signal after phase sensitive detection is known as the Free Induction Decay (FID). Fourier transformation of the FID gives the value of ∆ as shown in Fig. 2-7.

Fig. 2-7. Frequency representation of in-resonance and off-resonance MR signal.

A summary of the theory of NMR as presented so far under a classical description is that, a static magnetic field, B0, polarizes the sample such

that it has a bulk magnetization aligned with the direction of the field. An oscillating magnetic field at the Larmor frequency applied for a short time orthogonally to B0 will cause the longitudinal magnetization to be

tipped into the transverse plane. This makes the Larmor precession of the magnetization under B0 detectable, and Fourier transformation of the

phase sensitively detected signal yields its offset from the expected value. It is this offset from expected value that is most useful in magnetic resonance, as the B0 field experienced by the different spins in

the system is sensitive to nature of the chemical environment and can be manipulated by the application of external magnetic field gradients. While the former has a great importance in Magnetic Resonance Spectroscopy (MRS) application, the latter is at the basis of Magnetic Resonance Imaging.

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2.2 References

1 Purcell, E. M., Torrey, H. C. and Pound, R. V. Resonance Absorption

by Nuclear Magnetic Moments in a Solid. Phys. Rev. 1946;69,37-38 2 Bloch, F., Hansen, W. W. and Packard, M. Nuclear Induction. Phys.

Rev.1946; 69,127

3 Lauterbur, P. C. Image Formation by Induced Local Interactions: Examples Employing Nuclear Magnetic Resonance. Nature 1973; 242,190-191.

4 Mansfield, P. and Grannell, P. K. NMR `diffraction' in solids? J. Phys. 1973 C 6, L422-L426.

5 Stern, O. and Gerlach, W. Uber die Richtungsquantelung im Magnetfeld. Ann. Phys. Leipzig. 1924; 74,673

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Chapter 3 Magnetic Resonance Imaging

3.1 Localization of the MR signal

As shown in chapter 2, the MR signal measured in a NMR experiment is the sum of all the signals originating from the whole volume of the sample. The main task to perform to achieve Magnetic Resonance Imaging is to separate the signal coming from all these “voxels” in order to use the signal intensity produced by a single point to draw a grey-scale image.

The fundamental equation of magnetic resonance is the Larmor equation, ω=γB0. In an NMR experiment a measurement of the

frequency of precession of the magnetization gives information on the field experienced by that group of spins. By manipulating the spatial variation of the field in a known way, this frequency information now yields spatial information.

3.1.1 Slice selection

Consider a linear field gradient in B which increases along the z axis, such that:

B= B0 + Gzz

where G is the gradient strength. This makes the Larmor equation

ω = γ (B0 + Gzz)

Under a linear field gradient along the z-axis, all the spins that lie at a particular value of z will precess at the same frequency. The FID from such a sample will contain components from each of the z values represented by the sample, and the frequency spectrum will therefore represent the number of spins that lie along that plane.

This feature can be exploited to select a particular volume to image, through a procedure called slice selection. Slice selection is a technique used to isolate a single imaging plane, limiting the effect of the RF pulse to a single thin slice. To do that, it is necessary to apply a magnetic field

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Part I. NMR: from quantum mechanics to bioimaging

18

gradient along the slice selection axis while the RF pulse is applied. The RF pulse is designed in order to contain only a limited frequency range, centred on the desired resonance frequency with the scope to excite uniquely a thin slice of the specimen.

Fig. 3-1. Slice selection in a sample aligned along the z-axis through application of a magnetic field gradient

With this procedure it is possible to delimit the volume of interest by exciting only the desired portion of the sample; the acquired signal however, is still the sum of all the signals coming from the whole plane. 3.1.2 Frequency encoding

To map the MR signal frequency encoding is used. This kind of signal encoding makes the oscillation frequency of the MR signal linearly depending on its spatial position. Let us consider for instance a one-dimensional object with spin density function ρ(x).

If the action of the magnetic field on the object is given by the static external field B0 plus that produced by the field gradient Gxx, the

Larmor frequency at position x is ω(x)=ω0+ γGxx

Likewise, the FID signal generated locally by the spins in the infinitesimal interval dx at distance x is (neglecting transverse relaxation)

!

dS(x,t) = " e#i$ (B0+Gxx )dx

This signal is said to be frequency encoded because its oscillation frequency

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Magnetic Resonance Imaging

ω(x)=ω0+ γGxx

depends linearly on its spatial position, while Gx is called frequency

encoding gradient.

The total signal produced by the whole sample in the presence of this gradient is ! S(t) = dS(x,t) sample

"

= #(x)e$i% (B0 + +Gx)tdx $& &

"

= #(x)e$i%Gxtdx $& &

"

' ( ) * + , e$i-0t

After demodulation, i.e. after removing the leading signal e-iω0t_{, it}

results ! S(t) = "(x)e#i$Gxxtdx #% %

&

Generalizing, the frequency-encoding gradient is better represented by a vector

Gfe=(Gx,Gy,Gz)

since the gradient direction may vary in time and direction. Under this assumption the measured signal is

!

S(t) = "(r)e#i$Gfer_dx

sample

%

where r is the vector indicating the generic position in the sample. If we look closer at the last expression, we notice that the acquired signal is simply the Fourier Transform of the sample to image. In other words, the acquired signal represents a sampling of the spatial frequencies of the image, called K-space.

3.1.3 k-space

The k-space is a matrix of complex numbers, whose inverse discrete Fourier transform represents the desired image. The k-space represent the raw data acquired which needs to be processed in order to reconstruct the image.

The centre of k-space include slow frequencies, i.e. the data which determine most of the contrast and total intensity of the image, but provide low spatial resolution. The periphery of the k-space includes

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high spatial frequencies and determines the boundaries and the smaller details of the image.

If we recall the expression for the signal, it can be written as

2 ( ) ( ) i oggetto S e ! d " # $ =

_%

k r k r r by simply substituting ! k = " 2#Gfet .

It is clear that the role of the gradient Gfe is to map a signal in the time

domain and a signal in k-space. Since S(k) is a sampled signal, this is available only for a limited amount of points in the k-space, and their coordinates define the sampling trajectory of the k-space. In the more general case in which Gfe is a time function, the mapping relation

between time and k-space becomes

0

( )

2

t fe

t

!

" "

d

#

=

_$

k

G

_,

so that the k-space can be crossed linearly or not according to the temporal evolution of the frequency encoding gradient.

3.2 Image contrast

Unlike many other medical imaging modalities, the contrast in an MR image is strongly dependent upon the way the image is acquired. By adding r.f. or gradient pulses, and by careful choice of timings, it is possible to highlight different components in the object being imaged. The basis of contrast is the spin density throughout the object. If there are no spins present in a region it is not possible to get an NMR signal at all. Proton spin densities depend on water content, typical values of which are given in for various human tissues [1]. The low proton spin density of bone makes MRI a less suitable choice for skeletal imaging than X-ray shadowgraphs or X-ray CT. Since there is such a small difference in proton spin density between most other tissues in the body, other suitable contrast mechanisms must be employed. These are generally based on the variation in the values of T1 and T2 for different tissues.

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When describing the effect of the two relaxation times on image contrast, it is important to distinguish between relaxation time maps, and relaxation time weighted images. In the former the pixel intensities in the image have a direct correspondence to the value of the relaxation time, whilst in the latter the image is a proton density image that has been weighted by the action of the relaxation.

3.2.1 T1 contrast

The spin-lattice relaxation time T1 is a measure of the time for the longitudinal magnetization to recover. A proton density image can be weighted by applying an r.f. pulse that saturates the longitudinal magnetization prior to imaging. Spins that have recovered quickly will have greater available z-magnetization prior to imaging than those which recover slowly. This effect is apparent if the same slice, or set of slices, is imaged rapidly, because the excitation pulse of the previously imaged slice affects the magnetization available for the current slice. More commonly however, if T1 maps, or T1 weighted images are required then the imaging module is preceded by a 180-degree pulse (Fig. 3-2). The 180-degree pulse will invert the longitudinal magnetization, whilst not producing any transverse magnetization. The recovery of the longitudinal magnetization is governed by the Bloch equation for Mz, which has the solution:

Mz= M0 [1- 2 exp(-t/T1)]

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The magnetization is allowed to recover for a time TI, after which it is imaged using a 90-degree pulse, and usual imaging gradients. The amount of signal available will depend on the rate of recovery of Mz. If the sample has spins with several different relaxation times, it is possible to choose TI such that the signal from spins with one recovery curve is nulled completely, whilst giving a good contrast between spins with other recovery curves. In order to calculate the values of T1, to create a T1 map, it is necessary to obtain a number of points along the magnetization recovery curve, and then fit the points to the equation.

T1-weighted images can be obtained by reducing the pulse repetition time. An MR image is usually obtained using an RF pulse sequence separated by a time called repetition time (TR). If TR is much larger than the T1 of the tissue taken into consideration, the longitudinal magnetization will recover completely between two following excitations, and contrast will derive completely from proton density. If TR is instead shorter than tissue T1, longitudinal magnetization does not have enough time to recover completely its original value, and the signal intensity will be weighted by a factor depending on the TR/T1 ratio.

In choosing the TR it is to be kept in mind that a large signal-to-noise ratio is highly desired. The Ernst angle is the flip angle at which a particular signal maximizes its SNR and equals

1 cos TR T E e ! = " .

Tissues with long T1 recover slowly after the excitation, thus their Ernst angles are small than those of tissues with shorter T1.

3.2.2 T2 contrast

The spin-spin relaxation time T2 is a measure of the time for the transversal magnetization to be lost due to the spin-spin energy exchange, which creates local field inhomogeneities. It is possible to obtain the real value of T2 by refocusing the effect of field inhomogeneity on the transverse magnetization using a spin-echo. A spin-echo is formed by applying a 180-degree pulse at a time t after the excitation pulse. This has the effect of refocusing the signal at time 2τ (Fig. 3-3).

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T2-weighted images can be obtained by increasing the echo time (TE). For short TE, two tissues with different T2 but similar proton density show little contrast. For longer TE the tissue with shorter T2 (i.e. faster transverse relaxation) will lose its entire signal. This condition is exploited to obtain a good T2 image contrast. It must be avoided, however, to use excessively long TE in order to suppress completely the tissue signal, preventing the signal detection itself.

Fig. 3-4 shows the different mechanisms to achieve T1 or T2 contrast.

Fig. 3-4. Mechanisms for T1 and T2 contrast creation.

3.2.3 T2* contrast

Due to the field inhomogeneities caused by the field magnet and the magnetic susceptivity difference at the tissues interface, the spins in a single voxel cannot experience exactly the same field. The coherence of their magnetization will be reduced, an effect which increases with time. The combined effect of spin-spin relaxation and an inhomogeneous field on transverse magnetization is characterised by another time constant T2*. In fact T2* weighted images are desirable for functional MRI applications, as is explained in the next chapter. To change the T2* weighting of an image, it is only necessary to change the time between the excitation pulse and the imaging gradients. The longer the delay, the greater the T2* weighting.

3.2.4 Flow and diffusion contrast

One of the usual assumptions about imaging using magnetic resonance is that the spins are stationary throughout the imaging process. This of course may not be true, for example if blood vessels are in the region being imaged. Take for example the situation of imaging a plane through which a number of blood vessels flow. A slice is selected and all the spins in that slice are excited, however in the time before imaging, spins

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in the blood have flown out of the slice and unexcited spins have flown in. This means that there may be no signal from the blood vessels. In order to measure the rate of flow, some kind of phase encoding that is flow sensitive can be applied. This is done by applying a magnetic field gradient along the direction in which flow is to be measured. A large gradient dephases the spins depending on their position along the gradient. This gradient is then reversed, which will completely rephase any stationary spins. Spins that have moved however will not be completely rephased (Fig. 3-5). If the flow is coherent within a voxel, when the spins are imaged the phase difference can be calculated, and by varying the time between the forward and reverse gradients the flow can be calculated. Diffusion is measured in a similar way, but since the motion of the spins within the voxel is not coherent, the effect of diffusion is simply to diminish the signal.

Fig. 3-5. Bipolar gradients and their effect on stationary and moving spins.

3.3 MR imaging sequences

As it has been shown in the previous sections a preselected set of RF (and/or gradient) magnetic field pulses and time spacing between these pulses used in conjunction with magnetic field gradients and MR signal reception produce MR images. The tuning of these components determines the contrast in the images and defines a so-called MR sequence. For each sequence three acquisition parameters are defined:

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• TR • FA

TE is the echo time (the time between the RF excitation and the refocusing of the spins) and TR is the repetition time of the MR imaging sequence (time between two excitations of the same ensemble of spins). FA is the flip angle and it is used to define the angle of excitation for a field echo pulse sequence. It is the angle to which the net magnetization is rotated or tipped relative to the main magnetic field direction via the application of a RF excitation pulse at the Larmor frequency. It is also referred to as the tip angle or nutation angle.

The diagram in Fig. 3-6 shows, in general, how just tuning these parameters T1, T2 or Proton Density different weighted images can be obtained:

Fig. 3-6. Choice of TR and TE to achieve different kinds of contrast.

The most common MR imaging sequences are Spin Echo, Gradient Echo and Echo Planar Imaging (EPI).

3.3.1 Spin Echo

The most common pulse sequence used in MR imaging is based on the detection of a spin echo. It uses 90° radiofrequency pulses to excite the magnetization and one or more 180° pulses to refocus the spins to generate signal echoes named spin echoes (SE). In the pulse sequence timing diagram, the simplest form of a spin echo sequence is illustrated (Fig. 3-7). The 90° excitation pulse rotates the longitudinal magnetization (Mz) into the xy-plane and the dephasing of the transverse magnetization (Mxy) starts. The following application of a 180°

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refocusing pulse (rotates the magnetization in the x-plane) generates signal echoes. The purpose of the 180° pulse is to rephase the spins, causing them to regain coherence and thereby to recover transverse magnetization, producing a spin echo. In the simplest form of SE imaging, the pulse sequence has to be repeated as many times as the image has lines. The recovery of the z-magnetization occurs with the T1 relaxation time and typically at a much slower rate than the T2-decay, because in general T1 is greater than T2 for living tissues and is in the range of 100–2000 ms.

Fig. 3-7. Scheme of Spin Echo pulse sequence

Below the typical contrast values for a spin-echo sequence: − PD weighted: Short TE (20 ms) and long TR.

− T1 weighted: Short TE (10-20 ms) and short TR (300-600 ms) − T2 weighted: Long TE (greater than 60 ms) and long TR

(greater than 1600 ms).

With spin echo imaging no T2* occurs, caused by the 180° refocusing pulse. For this reason, spin echo sequences are more robust against e.g., susceptibility artefacts than gradient echo sequences.

3.3.2 Gradient Echo

Gradient echo sequences represent an evolution of the spin echo sequence in terms of scan time reduction and clinical utility. Spin echo sequences, in fact, have a great disadvantage: to get the maximum signal it requires that the transverse magnetization recovers its equilibrium position along the z-axis. If the T1 is long, this can make significantly long the imaging sequence, or the magnetization does not recover completely and the signal is minor than that obtained with a complete recovery (Fig. 3-8).

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Fig. 3-8. Effect of using a short TR in comparison to tissue T1

The time diagram of a generic gradient echo sequence is in Fig. 3-9

Fig. 3-9. Scheme of a Gradient Echo pulse sequence.

In a gradient echo sequence a slice selection gradients is applied during an RF pulse. A dephasing gradient for frequency encoding is used along with the phase encoding gradient in order to place the in phase at the centre of the acquisition time. This gradient is negative since the frequency-encoding gradient is active throughout the acquisition window. An echo is produced during the frequency encoding since it recovers the dephasing occurred during the dephasing gradient.

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The sequence is repeated with a time period TR, where TR is typically of the order of milliseconds. This method to create signal echo does not allow eliminating possible magnetic field inhomogeneities; this makes gradient echo techniques more sensitive to imaging artefacts.

Gradient echo sequences are considered fast sequences: in fact, the application of an inverted polarity gradient results faster than a RF signal. Besides, it is not necessary to wait for the spin rephasing after the 180° pulse as in Spin Echo sequences. All this allows shortening significantly TR and consequently scan time.

Contrast and image weighting through Gradient Echo sequences depends on TE, TR and flip angle. A strong T1-weighting is obtained with large flip angles (>60°) and short TE (<10 ms); using longer TE and smaller flip angles (<20°) the signal dependence on T1 decreases and the images result more T2*-weighted.

Gradient Echo sequences are also capable to visualize vascular structures with high signal: this relies on the fact that for small TR stationary tissues are hypointense since they do not recover completely longitudinal magnetization, while flowing blood introduces in the imaging plane blood with complete longitudinal magnetization.

3.3.3 Echo Planar Imaging (EPI)

Echo planar imaging is one of the early magnetic resonance imaging sequences (also known as Intascan), used in applications like diffusion, perfusion, and functional magnetic resonance imaging. Other sequences acquire one k-space line at each phase encoding step. When the echo planar imaging acquisition strategy is used, the complete image is formed from a single data sample (all k-space lines are measured in one repetition time), of a gradient echo or spin echo sequence with an acquisition time of about 20 to 100 ms. EPI requires higher performance from the MRI scanner like much larger gradient amplitudes. The scan time is dependent on the spatial resolution required, the strength of the applied gradient fields and the time the machine needs to ramp the gradients. On a typical EPI sequence, there is virtually no time at all for the flat top of the gradient waveform. The problem is solved by "ramp sampling" through most of the rise and fall time to improve image resolution. The benefits of the fast imaging time are not without cost. EPI is relatively demanding on the scanner hardware, in particular on gradient strengths, gradient switching times, and receiver bandwidth. In addition, EPI is extremely sensitive to image artefacts and distortions.

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Fig. 3-10. Scheme of EPI pulse sequence.

Fig. 3-11. k-space covering during an EPI sequence

3.4 Imaging artefacts

As with any imaging modality, magnetic resonance images suffer from a number of artefacts. In this section, a number of the common artefacts are described.

3.4.1 Field artefacts

The basic assumption of MRI is that the frequency of precession of a spin is only dependent on the magnitude of the applied magnetic field gradient at that point. There are two reasons why this may not be true. Firstly, there is the chemical shift. This has the effect of shifting the

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apparent position in the image of one set of spins relative to another, even if they originate from the same part of the sample. The chemical shift artefact is commonly noticed where fat and other tissues border, as in the image of the kidneys in Fig. 3-12, where the fat around the kidney forms a dark 'halo'. The artefact can be removed by spin suppression, such that a selective pulse excites only the protons in the fat [2]. When the image excitation pulse is subsequently applied, the fat spins are already saturated, and so do not contribute to the image.

Fig. 3-12. Chemical shift artefact around the kidneys resulting in a lower intensity border (black arrows).

Secondly, the static magnetic field B0 may not be perfectly

homogeneous. Even if the magnet is very well built, the differences in magnetic susceptibility between bone, tissue and air in the body, means that the local field is unlikely to be homogeneous. If the susceptibility differences are large, such that the local magnetic field across one voxel varies by a large amount, then the value of T2* is short and there is little or no signal from such voxels. This effect is particularly evident if any metal object is present as shown in Fig. 3-13.

Fig. 3-13. Susceptibility artefact caused by a metal object resulting in a signal loss (dark large area).

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If the differences are smaller, and the field is affected over a few voxels, then the effect is a smearing out of the image, as shown in Fig. 3-14 as the altered field is interpreted as a difference in position. To reduce the artefact it is possible to locally correct the field using a set of shim coils. These apply shaped fields across the sample and in combination increase homogeneity. Susceptibility artefact is more apparent in the rapid imaging methods such as EPI and FLASH, and is difficult to reduce without losing the fast imaging rates. One way to reduce the distortion is to acquire two images with the phase encoding applied in opposite directions.

Fig. 3-14. This pictures shows on the left the shape of the brain acquired with susceptibility artefacts, and on the right the correct brain shape after removing of

susceptibility artefacts.

3.4.2 Sampling artefacts

When using any digital technique, the question of sampling occurs. One of the most important theories in digital sampling is the Nyquist sampling theorem, which states that the highest frequency that can be sampled accurately is given by:

!

fmax =

1 2Ts

where Ts is the interval between sampling points. If the FID contains a

frequency component fmax+∆ then it will appear to have a frequency

fmax-∆. This manifests itself as 'wrap-around' of the image onto itself. It

is possible to reduce this problem in the readout, or switched, direction by using a band-pass filter to cut out any frequencies that could alias. An alternative is to suppress the signal from outside the field of view, using selective r.f. excitation [3]. There are three further artefacts due to sampling. Firstly, subject motion during the scan causes localized banding. Depending on the source of the movement, there are a number of solutions. Cardiac or respiratory gating, where the scanning is locked to a particular phase of the respective cycles, is often employed to image

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the heart. These cycles can be monitored directly, for example using the ECG, or by sampling the phase of the NMR signal just prior to gradient application, known as a navigator echo [4]. Echo planar imaging suffers from a different type of sampling artefact, known as the Nyquist, or N/2 ghost. This is because, in EPI adjacent lines in k-space are sampled under opposite read gradients. If there is any misalignment in sampling, or differences in positive and negative gradients, then there is an alternate line modulation in k-space, which leads to a 'ghosting' of the image, as shown in Fig. 3-15. If the aliased image and the actual image overlap, then banding or fringes appear.

Fig. 3-15. N/2 or Nyquist ghost artefacts in an image of patient knees.

The Nyquist ghost can be corrected to a certain extent by applying various phase corrections to the data. Finally, since in EPI to switch the sign of the gradients so rapidly is difficult, the waveform of the switched gradient will not be square. In fact it is common to use a sinusoidal gradient waveform. If simple linear sampling of the signal is used with a sinusoidal gradient a complex ripple artefact in the switched direction is formed. To correct for this, the signal is usually over-sampled and then the points re-gridded to account for the sinusoidal nature of the gradients.

3.5 Hardware

The imaging hardware for MRI includes one or more computers, a radiofrequency transmitter and receiver, transmitting and receiving coils, field gradient coils and the main magnet. Timing and intensity of the magnetic field gradients are controlled by a computer that uses the parameters chosen by the operator; the commands given by the computer are transmitted to the gradient and radiofrequency amplifiers, which, in

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turn, produce field gradients and radio pulses. These are transmitted by an antenna or coil to excite water protons.

The signals coming from the different part of the body are examined and sent from the receiving coil to pre-amplifiers which prepare the signal to the digital conversion. At first the signal is made up by many analogical radio waves which make up a composite wave, containing numerous frequencies, phases and amplitudes. MR signals undergo analogical-digital conversion (ADC) producing digital data, represented in the k-space matrix; these data are filtered, loaded in memory and processed by a computer. The k-space data are then processed through Fourier analysis generating the final grey-scale image.

The main components of an MR scanner are shown in Fig. 3-16.

Fig. 3-16. Hardware of an MR scanner.

3.5.1 Magnet

The core instrument for Magnetic Resonance is the magnetic itself, which has the task to establish a net magnetization of the sample protons. Some systems use permanent magnets, creating directly a magnetic field oriented along the axis between the magnet poles, i.e. perpendicularly to the bore and the patient bed; resistive magnets generate instead magnetic fields perpendicular to an electrical current flowing in a cylindrical coil.

The magnetic field intensity created by permanent and resistive magnets is limited to about 0.5 Tesla, while higher magnetic fields can be created by superconductor magnets, in which the resistance to

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electrical current flow can be almost completely eliminated using suitable materials and a low enough temperature.

3.5.2 RF coils

RF coils are needed to transmit and/or receive the MR signal. In order to optimise signal-to-noise ratio (SNR), the RF coil should cover only the volume of interest. This is because the coil is sensitive to noise from the whole volume while the signal comes from the slice of interest. To this end there are many types of RF coil with trade-offs in terms of coverage and sensitivity. The most homogenous coils are of a 'birdcage' design. Examples of these include the head and body coils. Both these coils act as transceivers i.e. they transmit and receive. The body coil is integrated into the scanner bore and cannot be seen by the patient. The head coil, being smaller in size provides better SNR. Surface coils, as the name suggests, are used for imaging anatomy near to the coil. They are simple loop designs and have excellent SNR close to the coil but the sensitivity drops off rapidly with distance from the coil. These are only used as receivers, the body coil acting as the transmitter. Multiple loops can be connected into a phased array design, combining the excellent SNR with greater volume coverage. Quadrature or circularly-polarised coils comprise two coils 90° apart to improve SNR by a factor of 21⁄2. 3.5.3 Gradient coils

Gradient coils generate magnetic field gradient variable in space and time which add to the static magnetic field. These coils are placed along the three spatial directions around the magnet, and allow the spatial identification of the signal and the image reconstruction (Fig. 3-17).

Gradient specifications are stated in terms of a slew rate which is equal to the maximum achievable amplitude divided by the rise time. Typical modern slew rates are 150 mT/ms. The gradient coils are shielded in a similar manner to the main windings. This is to reduce eddy currents induced in the cryogen which would degrade image quality.

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3.6 References

1 Mansfield, P. Imaging by Nuclear Magnetic Resonance. J. Phys. E:

Sci. Instrum. 1988; 21,18-30.

2 Haase, A., Frahm, J., Hänicke, W. and Matthaei, D. 1H NMR Chemical Shift Selective (CHESS) Imaging. Phys. Med. Biol. 1985; 30,341-344.

3 Mansfield, P., Ordidge, R. J. and Coxon, R. Zonally magnified EPI in real time by NMR. J. Phys. E: Sci. Instrum. 1988; 21,275-280. 4 Ehman, R. L. and Felmlee, J. P. Adaptive Technique for

High-Definition MR Imaging of Moving Structures. Radiology 1989; 173,255-263.

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