(This section is a modified excerpt from doi:10.1016/j.ejpb.2008.08.012)

In nuclear magnetic resonance (NMR) the magnetic moments of certain nuclei in the sample, which is placed in an external magnetic field B₀, align with this field and then can be excited with a pulse of radiation. The excitation of the nuclei leads to absorption of photons and subsequent re-emission which is measured as the NMR signal.

In the presence of B0 the nuclear spin energies of all nuclei in the sample with a non-zero nuclear spin quantum number (such as ¹H, ¹³C, ¹⁹F, ...) become non-degenerate, which means that they split into different energy states. This phenomenon, called the Zeemann effect, forms the basis for NMR experiments. For a nucleus such as hydrogen, which exhibits only two different spin energy states (+1/2 and -1/2), the nuclear spin can either align to precess with the field or opposite to the field. The energy state that corresponds to an alignment parallel with the field has a slightly lower energy compared to the spin aligned opposite (or anti-parallel) to the field. The distribution of spins between the two states follows the Boltzman distribution and as a consequence of the very small energy difference between the spin states at room temperature compared to kT only a small excess in the number of spins are in the ground state, aligned with the field, at equilibrium. This makes spectroscopic observations difficult, as a difference in populations between ground state and excited state is required to measure the transition between the states. However, with increasing field strength of B₀ the energy gap between the states increases linearly and with it the excess population of the lower energy level - which explains the advantage of performing NMR experiments with stronger magnetic fields B₀. The alignment of the nuclear spins in the static magnetic field leads to the formation of a net magnetisations vector M₀ along the field B₀. The magnitude of M₀ is directly proportional to the number of resonant spins in the sample.

The equilibrium magnetisation vector associated with the nuclear spin system can be perturbed by pulses of electromagnetic radiation that are generated in coils within the static magnetic field. When the photon energy of an excitation pulse exactly the energy difference between the states, photons are absorbed from the lower energy state (spins precessing parallel to B₀) to the higher energy state (spins precessing anti-parallel to B₀).

For hydrogen the gyromagnetic ratio, a nucleus specific constant which describes the ratio of the magnetic dipole moment over the angular momentum, is highest, which is the reason for the particular attraction to study hydrogen nuclei in NMR studies. The excitation photon energy falls in the radio frequency (r.f.) range of the electromagnetic spectrum. After a finite time photons are re-emitted by transition of the nuclear spin system to the lower energy state. When the aligned nuclei are perturbed by a pulse of r.f. radiation, they are subject to a torque on their magnetic moment and start to precess about the direction of B₀ in the xy plane at a frequency called the Larmor frequency. During the return to equilibrium conditions, the precession of the nuclei leads to the induction of a voltage in the receiver, an additional coil around the sample, which is measured as the NMR signal.

Beyond the mere discrimination of different isotopes by their Larmor frequency, NMR has very high chemical sensitivity. The precise splitting of the energy levels for the different nuclei of the same isotope in a molecule is influenced by its electronic environment. Rather than a single energy, and hence resonance frequency, the energies of the different nuclei in the sample exhibit a subtle shift relative to the nominal level depending on the molecular structure or chemical environment. This variation is called the chemical shift and forms the basis of NMR spectroscopy. Further information on the physico-chemical properties of the sample can be extracted from NMR experiments by quantifying the time it takes for the bulk magnetisation in the sample to return to equilibrium after excitation, a process called relaxation in NMR terminology. Two different relaxation processes are commonly used to characterise a sample: the time it takes the net magnetisation to build up along the field B₀ in the z direction (called T₁, spin-lattice or better longitudinal relaxation time) and the time it takes for the magnetisation in the x and y directions to decay to zero (referred to as T₂, spin-spin or transversal relaxation time). Again, the exact details of these processes and the underlying quantum mechanics would be far beyond the scope of this review and the reader is referred to introductory texts on the topic such as the excellent texts by Levitt and Keeler.

From a technical perspective, NMR experiments are usually carried out by placing the sample in the static magnetic field of a superconducting magnet. Commercial equipment is available with magnetic field strengths up to 22.31 T (this is equivalent to an resonance frequency of 950 MHz in the case of the hydrogen nucleus). The sample is positioned at the centre of the homogenous magnetic field inside the bore that runs through the magnet. For the perturbation from equilibrium r.f. pulses are applied using oscillating currents in one or more coils around the sample inside the magnet. After excitation, the induced NMR signal is typically measured by the same coil which then acts as a receiver. The NMR signal, which is measured in the time-domain and is also referred to as the free induction decay (FID), is then separated into its frequency components by Fast Fourier transformation.

A good overview of applications of NMR spectroscopy in a pharmaceutical context is provided by the reviews by Holzgrabe et al., Harris and Geppi et al.

The concept of generating a spatially resolved NMR signal for tomographic experiments was first demonstrated by Lauterbur by imaging two test tubes of water surrounded by D₂O. At the same time Mansfield and Grannell published their findings of NMR 'diffraction' in solids which made use of the same concept. Lauterbur referred to this technique as zeugmatography but despite the impact of his paper, he was awarded the Nobel Prize for this work in 2003 together with Sir Peter Mansfield, this term did not prevail. In magnetic resonance imaging (MRI), as the technique is now commonly refereed to, spatial resolution is introduced to the NMR experiment by applying one or multiple magnetic field gradients G in addition to B₀.

The additional gradient has the effect that it slightly shifts the resonance frequency of the sample nuclei within the magnetic field depending on their position. The resonant frequency becomes a function of the sample position in real space and by applying gradients in the x, y and z directions three dimensional tomographic images can be acquired. Further details on the background of MRI are beyond the scope of this review and the reader is referred to the literature introducing MRI in a chemical engineering context (Gladden 1994, Gladden 2005) and more detailed textbooks on the technique itself, e.g. by Callaghan or Kimmich.

MRI images of solids are typically acquired indirectly by measuring the signal of liquids interacting with the dosage form rather than imaging the solid phase directly. On standard imaging setups it is not possible to readily acquire images with sufficient spatial resolution from solid materials. This is due to line broadening and extremely short T₂ times in solids which leads to a very low NMR signal. However, new imaging sequences, such as SPRITE, have been successfully applied to image rigid polymers and it is quite possible that, along with future developments in MRI technology, MR imaging of solids will become more attractive in the future.

In order to acquire the information that is required to reconstruct MR images a number of different so-called pulse sequences are used. The pulse sequence describes the timing, strength and sequence of the r.f. pulses and gradient pulses that are applied, and usually repeated for a large number of cycles, for the MRI experiment. The pulse sequence is usually described in an abstract schematic as it needs to be adapted to the specific conditions of different magnets, coils, amplifiers and software on each MRI instrument.

A large number of pulse sequences have been developed which allow MR images to be acquired under a variety of conditions and acquisition speeds and which also allow us to measure a number of different properties, such as the spatial distribution of velocity of flowing liquids in a sample. The pulse sequences also enable the operator to enhance the contrast within MR images depending on the physico-chemical properties of the samples, e.g. the T₁ or T₂. The sequences are distinguished by a tremendous number of acronyms such as RARE, GERVAIS or SPRITE and whole books have been dedicated to the topic. Most often basic pulse sequences such as the spin echo sequence have been used for pharmaceutical MRI applications so far and the reader is referred to the literature for further details of specific pulse sequences.

So far, MRI has been widely applied for quantitative analysis of chemical products and processes and in chemical processes and reaction engineering. Melia et al. and Richardson et al. provided first overviews of different applications for MRI to characterise controlled release pharmaceutical dosage forms.