Nuclear magnetic resonance (NMR) is a physical phenomenon that gives rise to emergence of magnetic resonance spectroscopy (MRS) and magnetic resonance imaging (MRI) tools that we are all using today. As the name indicates, NMR is all about interactions, or resonance, between atomic nuclei and magnetic fields.
An atomic nucleus is positively charged, and has an intrinsic angular momentum that makes it a ‘spin’. When a sample, test tube alike or human body as a whole, is placed into a magnet, spins in the sample interact with the static magnetic field of the magnet (B₀). This interaction aligns magnetic moment of the affected spins along the direction of B₀, and puts the spin ensemble into a new thermal equilibrium state. By applying radiofrequency (RF) radiations, or pulses, at a proper frequency via a transmission coil, equilibrium alignment of selected spins can be perturbed transiently, or in other words, the selected spins are excited. The perturbed spin alignment, or excited spins, are not stable, and will transit back to the thermal equilibrium state, upon the termination of RF radiations, via processes known as relaxation. Energy released during the returning of excited spins to the equilibrium state is picked up by a receiver coil, and gives rise to raw NMR signals that can then be transformed into spectra or images that we are familiar with.
The frequency at which the NMR signals are excited and acquired (ω) is known as Larmor frequency, named after French physicist Joseph Larmor. The Larmor frequency is proportional to gyromagnetic ratio (γ) of the nucleus under concern, and increases linearly with B₀ (i.e., ω= γB₀). Atomic nuclei are surrounded by electron clouds. The shielding effect of electron cloud can shift nuclear resonance frequencies slightly away from the theoretical Larmor frequency, in a manner that is characteristic to the chemical environment the nuclei are in. Thus, nuclei that are not chemically equivalent, whether in the same molecule or in different molecules, may have different resonance frequencies, or chemical shifts. The amplitude of chemical shift is usually in the range from few to hundreds ppm.
The excited spins return to the thermal equilibrium state via spin-spin (or transverse) relaxation and spin-lattice (or longitudinal) relaxation. As the names suggest, transverse relaxation is mainly mediated by interactions among the nuclei (or spins), and longitudinal relaxation by interactions between the nuclei and environment (or lattice). Transverse relaxation time (T₂) and longitudinal relaxation time (T₁) are two time constants that are commonly used to characterize how fast the two relaxation processes occur, respectively. In general, T₂ determines how fast the NMR signals dissipate, and T₁ determines how fast the NMR signals can be excited again next time.
The most commonly used features of NMR signals include frequency, amplitude and relaxation times, each of which, or in combination, provides rich information about the sample. For instance, the amplitudes of NMR signals tell not only abundance of the nuclei of interest, but also how homogenous the nuclei are within the sampling volume, as the signals from different nuclei in the test tube or a voxel can either add to or cancel each other. Under many circumstances, resonance frequency and relaxation times are sensitive to the chemical/biological environments the nuclei are in, and thus they are often measured as surrogates for a variety of environmental parameters, ranging from temperature to tissue microstructure.

Acknowledgements

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