Essential Concepts in MRI. Yang Xia

axis (Figure 1.2), that is, B₀ = B₀k, where k in this expression is the usual unit vector along the z direction in a 3-dimensional (3D) Cartesian coordinate system. The direction of this z axis in Cartesian coordinates, however, can be either in the vertical direction (for vertical-bore superconducting magnets, which are common in research labs, or “open” MRI scanners, which reduce claustrophobia for some patients) or in the horizontal direction (for the electromagnets in research labs, the “vertical donut” magnet MRI, or the horizontal-bore superconducting magnets in common clinical MRI scanners).

      Figure 1.2 The B0 direction in NMR and MRI. (a) Vertical-bore superconducting magnet, which is common for NMR spectrometers in science and industry laboratories. (b) “Horizontal double-donut” magnet for “open” MRI. (c) Electromagnet or magnet in “vertical double-donut” MRI. (d) Horizontal-bore superconducting magnet, which is common for whole-body imagers for humans or animals.

In addition, this book adapts the convention that the clockwise rotation is positive when one looks into the arrowhead of any axis, shown in Figure 1.3. Among the NMR and MRI literature, this convention for rotation is not consistently adapted (i.e., some authors use the counterclockwise rotation as the positive rotation). This inconsistency can lead to either a + or – sign in some equations that describe the motion of the macroscopic magnetization. The notation used in this book is consistent with many books; for example, those by Fukushima and Roeder [1], Callaghan [2], Canet [3], and Haacke et al. [4]. We will comment on this issue at several places in Chapter 2.

      Figure 1.3 The positive directions of rotations in a 3D Cartesian coordinate system, (a) when one looks into the +z axis, and (b) when one looks into the +x axis.

      1.3 MAJOR MILESTONES IN THE HISTORY OF NMR AND MRI

The physics of NMR started in 1924 when Wolfgang Pauli suggested that hydrogen nuclei might possess a magnetic moment. Pauli made this suggestion based on the observation of optical spectroscopy hyperfine splitting. The first observation of a nuclear magnetic moment was made in 1938 by Isidor I. Rabi, who used molecular-beam magnetic resonance to measure the signs of nuclear magnetic moments in individual atoms and molecules. In 1946, the phenomenon of NMR in liquids and solids was first reported simultaneously by two groups of scientists: Purcell, Torrey, and Pound at Harvard using paraffin as the specimen [5]; and Bloch, Hansen, and Packard at Stanford using water as the specimen [6]. The practical usefulness of NMR was noticed in 1950 by Proctor and Yu [7] and by Dickinson [8], who found that in ammonium nitrate and a variety of fluorine compounds, some kind of chemical effect caused the compounds to have multiple resonant lines. With the publication of the first ethanol spectrum where the three groups of protons in the same ethanol molecules resonated at three different frequencies (Figure 1.4) [9], the power of the NMR technique, being able to measure different chemical environments inside the same molecule (later termed “chemical shift”), initiated the widespread application of NMR in chemistry.

      Figure 1.4 The first NMR spectrum of ethanol (CH₃CH₂OH), which demonstrated the huge potential of NMR spectroscopy by identifying three sets of non-equivalent ¹H nuclei in the same molecule. Three separate peaks corresponded to the resonant frequencies of the ¹H nuclei in the OH, CH₂, and CH₃ groups, respectively. Furthermore, the relative areas under the three peaks corresponded to the number of protons in each different chemical environment. Source: Reproduced with permission from Arnold et al. [9].

In 1950, Erwin L. Hahn developed a practical way to form a spin echo by using two radio-frequency (rf) pulses [10], which has had a long-lasting influence on NMR experiments, both spectroscopy and imaging. This was significant since once you knew how to use two (or more) pulses to manipulate the spin system, you could truly control the motion of the nuclear spins in the sample to gain insight into the molecular environment. In 1957, Irving Lowe and Richard Norberg demonstrated that the NMR spectrum in the frequency domain is mathematically equivalent to the Fourier transform (FT) of the NMR signal (called the free induction decay, FID) obtained in the time domain [11]. In 1966, Richard R. Ernst and Weston A. Anderson demonstrated the concept of FT NMR [12], which offers several orders of magnitude improvement in the signal-to-noise ratio (SNR) per unit time for a typical proton NMR spectroscopy experiment. Coupled with the then-new development of personal computers and the fast Fourier transform (FFT) algorithm in the 1960s, FT NMR permits the practical use of NMR for non-experts. In 1975, Ernst demonstrated a new class of multidimensional NMR spectroscopy, now termed as 2-dimensional (2D) NMR spectroscopy (e.g., COSY, NOESY, etc.), which permits the study of specimens with a complex molecular environment or large macromolecules.

The first application of NMR to study biological samples was done in 1955 by two Swedish researchers, Erik Odeblad and Gunnar Lindström [13]. Using a primitive NMR instrument that Lindström built for his graduate research at the Nobel Institute for Physics (Stockholm, Sweden), Odeblad and Lindström studied the characteristics of NMR signals in a number of biological tissues and speculated that the signal differences between water and biological tissues could be attributed to the absorption and organization of the water molecules to the proteins in the tissue, which was remarkably accurate. A 2016 paper recounts some fascinating facts about this first biological application of NMR [14].

In 1973, Paul C. Lauterbur demonstrated the construction of 2D images using the NMR technique, which opened a completely new direction in the application of NMR (Figure 1.5) [15]. Several key developments in NMR imaging (i.e., MRI), in particular the use of a pulsed gradient approach for the slice selection by Peter Mansfield in 1974, stimulated the building of NMR scanners for humans since the late 1970s. Today, whole-body human NMR imagers, which are called whole-body MRI scanners, are the indisputable diagnostic choice for soft tissue diseases in all hospitals and clinics since MRI is completely non-invasive and totally non-destructive.

      Figure 1.5 The first proton NMR image of two tubes of H₂O, which was produced by P.C. Lauterbur by combining four projections taken from different angles from his setup on a Varian A-60 spectrometer, which is currently on display at the State University of New York at Stony Brook. Source: Reproduced with permission from Lauterbur [15].

While most of the imaging community was geared toward the optimization of NMR scanners for humans, several research groups started to push the resolution of NMR imaging to the other extreme – the microscopic scale. This effort resulted in the 1986 publication of NMR images with structural features smaller than what can be recognized by the human eye (~100 microns) [16, 17]. This high-resolution imaging field has been termed as NMR microscopy (microscopic MRI, µMRI).

      The latest “history” of this fascinating field is still being written as of today in the twenty-first century. NMR and MRI are very active and still evolving, with diverse applications in biology and medicine and various industries. There are many new and exciting developments in recent years, such as the optical pumping in NMR and MRI that improves SNR by more than 1000 times, compressed sensing that can shorten the experimental time tremendously, and exotic pulse sequences that fascinate our imagination. So far, a number of Nobel prizes have been awarded for discoveries related to NMR and MRI, including Rabi (1944) in physics, Bloch and Purcell (1952) in physics, Ernst (1991) in chemistry, Wüthrich