The lecture provides a basic understanding of the mechanisms essential to in vivo MR spectroscopy, i.e. those that influence the time and frequency representations of the MR signal in the absence of imaging gradients. Topics include nuclear interactions, the free induction decay (FID), data representations,and signal characteristics in the time and frequency domains. An effort will be made to give intuitive insight and fresh perspectives on the very basics, including interpretations of math frequently appearing in MRS literature.
The audience will be left with a basic understanding of the mechanisms essential to in vivo MR spectroscopy, i.e. those that influence the time and frequency representations of the MR signal in the absence of imaging gradients [1]. Topics include nuclear interactions, the free induction decay (FID), data representations,and signal characteristics in the time and frequency domains. An effort will be made to give intuitive insight and fresh perspectives on the very basics, including interpretations of math frequently appearing in MRS literature. In particular, the following aspects are covered:
Classical analogies will be used to improve the understanding of nuclear interactions and spectral features.
Essentially all MR techniques are spectroscopic, meaning that they rely on the frequency content of the signal. Imaging is an example, but is not a direct focus of the lecture addressing mostly mechanisms that influence in vivo MR spectroscopy. Most aspects discussed also have general relevance, however, not least because normal imaging is an example of multi-dimensional spectroscopy.
The MR signal reflects interactions between the various magnetic fields applied during MR, e.g. B0, B1, but also unwanted field contributions such as background field inhomogeneity (imperfect shimming) and fields related to hardware imperfections. These fields are approximately locally homogeneous, and therefore preserve the relative orientations between nuclei on a sub-micrometer scale.
There are also fields fluctuating on atomic time and length scales, defined by molecular motion and dimensions [1]: Nuclei interact magnetically with the shielding electrons, which causes the chemical shift. They also interact directly with each other due to magnetic dipolar coupling causing relaxation (both T1 and T2). Finally, they interact indirectly via the electronic cloud surrounding molecules (J-coupling), which causes broadening and peak splitting.
In addition to the macroscopic fields generated by MR hardware, each individual nucleus experience more or less random field fluctuations caused by interactions with the ever-changing environment of other magnetic particles, most notably other nuclei. The effects of these interactions depend strongly on the nature of interactions, and particularly the expected interval between changes of magnetic environment. This is the correlation time that is of major importance for relaxation properties.
These effects are largely expected classically, and are correspondingly intuitive, although there are surprising aspects which originate in quantum mechanics [3]. An example of the latter is that so-called spin-1/2 particles (e.g. the proton in hydrogen) are magnetic, and largely behave as rotating, charged particles (magnetic dipoles with angular momentum). Also the strength of J-coupling is governed by quantum mechanics, whereas its effect on spectra is less surprising.
[1] Malcolm H. Levitt, Spin dynamics, John Wiley & Sons, 2nd edition, 2008.
[2] MR basics math supplement, http://drcmr.dk/Docs/mathappendix.pdf
[3] Lars G. Hanson, Is quantum mechanics necessary for understanding magnetic resonance?, Concepts of Magn Reson part A, 32A(5), 329, 2008. https://doi.org/10.1002/cmr.a.20123