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The magnetic resonance phenomenon
Magnetic resonance (MR) in all its forms (spectroscopy, imaging and relaxometry) is based on four simple facts:
(1) Many nuclides possess permanent magnetic moments and, when placed into an external magnetic field, tend to align themselves along the field. Due to thermal fluctuations, however, the orientation (polarization) is never complete and, besides, some kinds of nuclides prefer to orient themselves parallel to the field, while others prefer the anti-parallel arrangement. The magnetic moments of all nuclides present in a sample sum up to a macroscopic vector quantity called nuclear magnetization. In equilibrium, nuclear magnetization is aligned along the magnetic field and, being tiny and static, is almost impossible to detect against the main field background.
(2) Applying a suitable radiofrequency pulse, nuclear magnetization can be rotated by any desired angle and thus brought into a non-equilibrium state in which it is no longer aligned with the field. We call this process excitation. The excitation pulse is typically very powerful (0.1-10 kW) but short (of the order of 1-100 microseconds).
(3) The component of the excited nuclear magnetization vector which is transversal to the magnetic field precesses (rotates) around the field direction with a frequency f proportional to the field strength B, f = γB, where the proportionality constant γ is characteristic of the particular nuclide. This so-called Larmor frequency is usually in the radiofrequency (RF) range (which is why MR is said to be a radiofrequency technique). In this context, two more facts are important:
a) The excitation pulse, in order to be effective, must have a carrier frequency very close to the Larmor frequency (the resonance condition). Consequently, it can only excite, for example, 1H nuclides or 13C nuclides, but not both at the same time.
b) The precessing component of nuclear magnetization, though tiny, is easy to detect because it rotates and thus can induce RF signals in a nearby receiver coil (hence the term nuclear induction).
(4) After excitation, nuclear magnetization returns back to its equilibrium state. This process is called relaxation and the return paths (relaxation curves) can be quite complex. In the simplest and somewhat idealized case, it is characterized by two times:
T1, the exponential rate with which the longitudinal component of the magnetization returns to its equilibrium value, and
T2, the exponential rate with which the transversal component, while precessing around the field direction, decreases in magnitude towards zero.
The two relaxation times are subject to the condition T2 ≤ T1. Their numeric values are characteristics of the measured substance and of its thermodynamic state and can assume values ranging from a few microseconds to several days. This means that, after excitation, there is often a relatively long period during which the receiver coil picks up a decaying (transient) response signal, called free induction decay or FID.
What makes magnetic resonance interesting
If all nuclides in a sample perceived the same magnetic field, NMR would be a very limited technique.
Fortunately, the following facts act in synergy to make NMR infinitely more exciting:
(I) There are differences between the magnetic fields perceived by individual nuclides due to:
a) Local variations induced by the electronic shells of molecules which partially screen the nuclides from the external field and whose magnitudes depends upon the local molecular structure in the vicinity of the nucleus. These variations are called chemical shifts and are the basis of NMR spectroscopy and its many applications to chemistry. Being very small, they are measured in parts per million (ppm) with respect to the external field.
b) Local field variations at a nuclide's location due to interactions with close-by nuclides of the same or different kind. These may be either direct (dipolar; the fields of close-by magnetic dipoles) or indirect (scalar; mediated by chemical bond electrons). The magnitudes of these interactions are independent of the external field and range from tens of kHz (direct) to a few Hz or even a fraction of Hz (indirect).
c) Field variations between different areas of a heterogeneous sample due to internal susceptibility variations. Like chemical shifts, the magnitudes of these variations are proportional to the external field and are usually expressed in ppm.
d) Field variations produced on purpose by precisely controlled magnetic field gradients which vary the field perceived in each voxel of the sample according to its location in space. This is the technical basis of magnetic resonance imaging (MRI).
(II) All local field variations translate into corresponding variations of the Larmor frequency of the nuclides. The observed signal is therefore a sum of superposed signals with many different frequencies. Fortunately, there are various ways of mathematically decomposing such a composite signal (interferogram) into its harmonic components. The best known and most widely used of these methods is the Fourier transform. There is nothing mysterious about this procedure: in acoustics we are continuously faced with the same problem and most of us solve it without even noticing, thanks to the fact that we are all equipped with such a marvelous build-in analog Fourier transform device as the inner-ear cochlea.
(III) Frequency measurements are those we know how to carry out with incredible precision. In principle, electronic instruments permit us to estimate frequencies of periodic signals to over 16 decimal digits (provided the signal itself is that stable).
Combining the above facts in various ways, one opens the doors to such exciting applications as NMR Spectroscopy, MR Imaging, self-diffusion measurements, MR diffusion imaging, etc.
Why must the external magnetic field be stable and homogeneous
Common to all such techniques is the necessity to dispose of an external magnetic field which is sufficiently stable in time and homogeneous across the sample volume.
Suppose, for example, that we measure the NMR spectrum of a molecule, trying to distinguish between protons A and B present at two locations in the molecule and that the respective chemical shifts differ by 0.01 ppm. If our spectrometer operates around 600 MHz, this difference amounts to easily measurable 6 Hz. But what if the main magnetic field of the magnet were subject to random variations of the same order of magnitude. How could we ever make sure that the frequency of a spectral line is what it is because of a chemical shift and not because of a temporary, random excursion of the main field. It is necessary that the external magnetic field be at least as stable (in terms of maximum excursions from its mean value) as the frequency differences we want to measure!
The same applies to magnetic field homogeneity across the sample volume. Since the signals from all sample voxels add up, differences between main field values at different voxels might get mis-interpreted as false chemical shifts. In practice, the effect of magnetic field inhomogeneity on NMR spectra is a broadening of spectral lines (when excessive, it can reduce an intricate spectrum with hundreds of sharp lines to a broad, featureless hump). In MRI, where frequency differencies correspond to different voxel locations, main field inhomogeneity causes distorsions of the images and other image artifacts.
The requirements on stability and homogeneity of the main magnetic field, being dictated by the magnitude of the phenomena we want to observe, are different for different application areas. NMR Spectroscopy has by far the most stringent requirements (tolerances down to 0.0001 ppm), followed by MR Imaging (1-10 ppm) and some time-domain techniques (known also as low-resolution NMR) of systems with inherently very broad spectral lines which may be practicable even at the 1000 ppm level.
Since NMR Relaxometry is not concerned with Larmor frequencies, relaxation measurements can be carried out in quite inhomogeneous and unstable fields (1000 ppm or even still worse) but, nevertheless, their precision and reproducibility improves considerably with improving field quality.
A few after-thoughts:
(a) Much of the above holds also for magnetic resonance of electrons, known under the equivalent names Electron Spin Resonance (ESR), Electron Paramagnetic Resonance (EPR) and Electron Magnetic Resonance (EMR). At this introductory level, the only difference is that the proportionality constant γ between field strength and Larmor frequency is about 658 times larger for electrons than for protons so that ESR is typically carried out in the microwave frequency region. The requirements on field stability and homogeneity are milder than in NMR (100 ppm is good, 1000 ppm so-so).
(b) Three more general reasons for the amazing success of nuclear magnetic resonance in so many disparate areas:
--- Nuclides present in molecules interact among themselves and with their environment, but do not do so too strongly. As the values of relaxation times indicate, it takes relatively long time before their state is significantly altered due to the interactions, making it easy for us to follow what's going on.
--- The interaction between radio waves and matter, with the exception of bulk metals, is weak enough to permit ample sample penetration but, when it comes to magnetic nuclides, strong enough to be observable. If any of these two conditions were not satisfied, NMR and MRI as we know them today could not exist.
--- Nuclides with large magnetic moments (1H, 13C, 31P, ...) are abundant in exactly those substances which interest us most.
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