
Nuclear Magnetic Resonance and Fourier Transform (2017) - aroman_ro
https://compphys.go.ro/nuclear-magnetic-resonance-and-fourier-transform/
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kurthr
This is a nice overview, however, the images seem to be for NMR imaging (NMRI)
while the equations are for 1D NMR. As other posts comment the NMR only
portion can be relatively simple, but it's usually used to characterize
chemical samples by their resonances. Imaging is very different.

I'd note that for 3D NMRI the challenge of tomography (extracting the 3D data
from a bunch of interfering resonant torus regions) is actually more difficult
in practice (I haven't heard of ML/DL techniques, but I'd expect they are now
used) though the concept of NMR (without imaging) is more physically
interesting. Furthermore, when chemistry is important the fitting algorithms
to extract weak NMR signals overlapping strong signals is actually also
moderately complex and over looked here for the sake of clarity and brevity.

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aroman_ro
The Fourier Transform in 2D or 3D is not really a much bigger deal, that's why
I handled only the 1D one there in equations (I was too lazy to type in latex,
I guess). NMR spectroscopy is indeed quite different than NMR imaging, I might
have something about that on the blog sometime, it would be an interesting
topic...

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4258HzG
I find how the Fourier Transform works so simply in multiple dimensions as
long as you have cartesian sampling is where the transform starts to shine.
Just apply along one dimension then the others and because it's a linear
unitary operator they are incredibly robust and it makes no difference which
order you apply them. Then you can combine them with other measurement types
in higher dimensional measurements (e.g. a relaxation period) and still just
mindlessly apply the Fourier Transform along the frequency dimensions (first
since it's so robust) and get the desired result.

There isn't any difference in the Fourier analysis between spectroscopy and
imaging. In imaging you're just encoding position as a frequency and if you
enforce Cartesian sampling the analysis remains the same, including combining
extra dimensions. Spectroscopy and flow imaging experiments can get pretty
crazy with 5-6 encoding dimensions limited only by your patience and
instrument drift over longer periods (weeks).

The differences between spectroscopy and MRI are primarily application driven
and then because it is tricker to apply precise magnetic field gradient pulses
vs precisely timing RF pulses. Combined with the fact people are a lot bigger,
more impatient and more delicate than test tubes while imaging can also be far
less quantitative drives the design of very different NMR/MRI pulse sequences.
In imaging, the speed gains and human placed limits on gradient slew rates
(Audio frequency dB/dt induces currents in neurons) often justify the trouble
of non-Cartesian and/or incomplete sampling.

If you want a next step for MRI signal processing, look into multiple-coil
reconstruction techniques and how they not only combine the spacial
sensitivity profiles of the coils with gradient imaging, without knowing the
actual sensitivity profiles a-priori. Pretty much every medical MRI machine
uses multiple receive coils to reduce imaging times.

Note: My user name is proton gamma though I left the field mid-career to do sw
development. (A far better career though not as exciting if you love physics
like I do.)

(edits: grammar, probably still missed a few typos)

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aroman_ro
Of course there isn't any difference in the Fourier analysis, but there is a
difference between spectroscopy and MRI, enough to warrant a different post on
the blog. In the MRI case you have a human with macroscopic inhomogeneities,
while in the spectroscopic case you are not interested in those macroscopic
inhomogeneities, but in the local differences in molecules, that the active
nuclei 'feel'. It's quite a difference in scale and also you have one human in
the 'sample' in the case of MRI, but many molecules in case of spectroscopy :)

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vondur
The software we had to run in O-Chem lab would take the raw files from the NMR
machine, run the FFT on it, then integrate the results. I was able to "borrow"
a copy of the software myself so I could run the analysis on my NMR specs
outside of lab.

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dnautics
Could have just taken the FID data and computed it in Julia in five lines of
code!! (but you might not get that fancy tool that makes your integration
shoulders nice and even.) Still though bruker charges an arm and a leg for the
postprocessing of 1ds

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fabian2k
Topspin is free for academic users for a while now, so that has changed at
some point.

And while it's certainly possible to process 1D NMR spectra with a bit of
code, it's certainly more than 5 lines. There's stuff like removing the
digital filter that is an implementation detail of Bruker spectrometers you
have to deal with. The FFT is the smallest parts, you also need window
functions and phasing to make something useful. And for 2D NMR you
additionally need to handle the various methods of quadrature detection in the
indirect dimension.

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carbocation
This is one of the most accessible explanations of the mechanics of magnetic
resonance imaging that I've come across. Thanks for sharing.

