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CHAPTER 1
Introduction to Magnetic Resonance Imaging
W. A. Worthoff*a, S. D. Yuna and N. J. Shaha, b, c
a Forschungszentrum Jülich, Institute of Neuroscience and Medicine – 4, Wilhelm-Johnen-Straße 1, 52428 Jülich, Germany
b JARA-BRAIN – Translational Medicine, Aachen, Germany
c Department of Neurology, RWTH Aachen University, Pauwelsstr. 30, 52074 Aachen, Germany
*E-mail:
[email protected] Nuclear magnetic resonance (NMR) is the technique that underpins magnetic resonance imaging (MRI) in its application in diagnostic medical imaging. Spin dynamics in NMR are described using a semi-classical model resulting in a net magnetisation, which is amenable to manipulation using radiofrequency pulses. The introduction of a spatially varying magnetic field, the magnetic field gradient, in the three orthogonal directions is introduced and it is shown how the application of gradients enables the selection of a physical slice and encoding of the two remaining in-plane dimensions. The concept of image encoding is then extended to 3D imaging. Beginning with a simple classical spin model, it is shown how the phenomenological Bloch equations can be derived and solved under the influence of particular field configurations. Eventually, the Bloch equations lead to the so-called signal equation and the introduction of the concept of a reciprocal space, the k-space, which is linked to real space by the Fourier transform (FT). Image reconstruction techniques going beyond the FT are also briefly touched upon to give the reader a fuller appreciation of modern, state-of-the-art MRI. In-plane acceleration methods operating both in k-space and in real space are described, as are multi-band acceleration techniques, which enable the acquisition of multiple slices simultaneously. Finally, a classification scheme, albeit a simple and incomplete one, is presented to enable the novice reader to gain an understanding of how order can be brought into the world of MRI pulse sequences.
1.1 Introduction
Nuclear magnetic resonance (NMR) has expanded rapidly from its initial discovery in 1946 into one of the most important analytical techniques in modern science, with applications in both physics and chemistry. It is NMR that forms the basis of magnetic resonance imaging (MRI), which has revolutionised diagnostic medicine since the late seventies. Indeed, even today the NMR techniques invented decades ago are finding application in MRI as new imaging sequences.
The introduction of linear magnetic field gradients to impose spatial information on the measured signal, in combination with the ubiquitous Fourier transform, led to an enormous research effort in the field of medical diagnostic imaging. In the early 1980s, there was already a growing feeling within the research community that NMR imaging would be used in other applications, and not solely for the study of the morphology of the body. Their prediction has indeed come to pass with the advent of functional MRI (fMRI), non-proton MRI to investigate metabolism and so on. In fact, it has been anecdotally reported that even the early NMR pioneers self-experimented. Edward Purcell placed his head in an NMR spectrometer to investigate differences in NMR signal shape dependent upon when he either concentrated hard on a specific task or freed his mind. Although no differences were measured at that time, it is apparent that these pioneers were already convinced about the possibility of applying NMR to study biological systems. A few decades later, MRI came of age.
In this chapter, even though some reference to quantum mechanics is briefly touched upon, the basics of MRI are described using a classical model, which suffices to explain standard proton-based imaging. Following on from the description of spin dynamics and the acquisition of the signal, image reconstruction methods are described, including up-to-date techniques for the acceleration of image acquisition employing parallel receive and multi-band excitation. The final section of this chapter concludes with a brief description of how sequences can be classified and, conceptually, understood.
1.2 Physics of the Dynamics of Spin
1.2.1 Spin
Nuclei, composed of protons and neutrons, possess a basic property referred to as spin angular momentum,
I⃑, which originates from the intrinsic spin of the nucleons. Nucleons are fermions and have a spin of ½ in units of
ħ, where
ħ is the reduced Planck's constant
. Thus, a given nucleus has a net spin, which depends on its mass number
Z (number of nucleons), atomic number
A (number of protons) and neutron number
N. In particular, a nucleus has a half-integer spin when the mass number
Z is odd and an integer spin when the mass number
Z is even and
A is odd. In the case that
Z and
A are even, a nucleus has a zero nuclear spin. From here on, it is assumed that the nucleus under discussion has non-zero nuclear spin. In most cases, MRI is concerned with a spin ½ nucleus, namely the proton of hydrogen nuclei. Nevertheless, other MR-active nuclei, such as sodium, possess a non-integer spin and are also of interest to imaging. These will be discussed in later chapters.
Spin value determines the magnetic dipole moment
=
γI⃑, with gyromagnetic ratio
1 given by
γ =
ge/2
mp. The gyromagnetic ratio depends on the nuclear
g factor, the elementary charge,
e, and the mass of a nucleon,
mp.
1 For reasons imposed by the uncertainty principle, the magnetic moment cannot be well defined in all spatial directions simultaneously and thus it is common to choose one axis along which the component of magnetic dipole moment is to be considered. Ordinarily, in NMR and MRI, one is interested in the component
of the magnetic dipole moment along the axis of an externally applied magnetic field, which is normally labelled
z. Nevertheless, this is based solely on convention, and in principle, the choice of this axis is arbitrary.
2 The dipole moment is a quantised variable, with quantification defined through the magnetic number
ml (eqn (1.1))
1.1 µ = γħml, with ml = {−I, −I + 1,…,I}
The macroscopic manifestation of spin is referred to as magnetisation, M⃑. The magnetisation is the vector sum of the individual magnetic dipole moments of the nuclear spin ensemble in the volume of interest. In the absence of a magnetic field, the nuclear spins are oriented randomly in all directions of s...
