Metabolite Concentration Calculation from Amplitudes

Hi MRSHub,

A newbie here trying to analyze some MRS using jMRUI for research purposes. I have some MRS data from thigh muscles; ultimately, I aim to quantify the metabolites and compare them between subjects.

I use the AMARES method for quantitation and get the amplitudes of the metabolites. When I read the literature, I see authors normally report the concentration of the metabolites (in mmol/L or mmol/kg). My question is how do I go from the amplitude to the concentration? Is there a fixed established formula that people use? If yes, what is that?

This might be a very baseline question but reading different papers made me more confused as I haven’t understood how people did it. Any help is appreciated! Thanks for your time.

Hi Droy,

I’ll try to give some background to answer your question, but you might be better off just skipping to the references at the end, finding them and giving them a good read.

To calculate metabolite concentrations from signal amplitudes, you need to consider a few things.
First approximation is that the size of the signal is determined by the amount of the substance present - so more of metabolite X, gives a bigger signal for metabolite X.
Caveats, or adjustments to this approximation are that

  1. signal is also determined by the number of nuclei present in metabolite X, such that if metabolite X has 3 x as many nuclei of interest in its molecualr structure, it will give 3 times as much signal. (this is really just an extension of the more of somehting there is, the more signal you get rule, but at the level of the nuclei of interest, 1h, 31P etc.). Some metabolites will give rise to more than one peak, and you will need to know how many nuclei are giving rise to the peak you are fitting.
  2. relaxation properties also affect signal (T1 and T2 relaxation)
  3. spectral pattern, and the effects of J-coupling, can also impact the size of peak amplitudes - this is something to especially consider when using AMARES which just gives you amplitude, or area under the peak for the peaks you chose. As mentioned above some metabolites have more than one peak in their spectral pattern, and you will need to know how many nuclei are giving rise to the peak you are fitting, and if there are any other factors that could affect it.
  4. Any specific effects of the pulse sequence you are using (e.g. - are you using and editing pulse sequence - then editing efficency should be considered) - this is not likely to be an issue for MRS in the muscle.

Usually, factors 1 and 2 above are what most people consider when using AMARES for fitting, and is likely a good first approximation for work in the muscle.

So, more amplitude for X means more of X present - but how much? To get to this you need a reference signal of some sort, where the signal height:concentration ratio is known (or assumed). Usually this is acheived by using the signal of some metabolite wihtin the acquired spectrum, which has an known/assumed concentration. In brain MRS, this is usually unsuppressed water collected either just before, or just after the metabolite signals are also collected, although people may also use the total creatine peak (and just express the result as the ratio to creatine).
From the first aproximation:
[Met] = [Ref]X(SigMet/SigRef)
adding in the adjustments above
[Met] = [Ref]X((SigMet/#NucMet)/(SigRef/#NucRef))X(Relaxation correction factors)*

So, basiclally if you have a reference signal of known concentration, you can now work out your metabolite concentrations.
The problem you will have with your data is deciding if you actually do have a reference of known conentration in the spectra. Are you doing proton, or phopshorous (or other X nuclei) MRS? If phosphorous, ATP is usually used, with an assumed concentration of 8.2 mM. If Proton - I’m not sure what reference you want to use, but I use an unsupressed water scan.

*I’m not very good at using the forum tools to express these equations fully, so the above are somewhat abbreviated, for a good reference with more detail on brain MRS see:
Near, J., Harris, A. D., Juchem, C., Kreis, R., Marjańska, M., Öz, G., Slotboom, J., Wilson, M., & Gasparovic, C. (2020). Preprocessing, analysis and quantification in single-voxel magnetic resonance spectroscopy: Experts’ consensus recommendations. NMR in Biomedicine, n/a(n/a), e4257.

and for 31P MRS in Muscle see:
Meyerspeer, M., Boesch, C., Cameron, D., Dezortova, M., Forbes, S. C., Heerschap, A., Jeneson, J. A. L., Kan, H. E., Kent, J., Layec, G., Prompers, J. J., Reyngoudt, H., Sleigh, A., Valkovic, L., Kemp, G. J., & Experts’ Working Group on, P. M. R. S. of S. M. (2020). 31P magnetic resonance spectroscopy in skeletal muscle: Experts’ consensus recommendations. NMR Biomed, e4246.

Hopefully this is helpful, and not too confusing. (and don’t get too worried if it is confusing right now - it’s not you, it’s just a little complicated).



I can emphasize enough how much I appreciate you for the explanation you provided! Your explanation totally makes sense. I have been trying to understand the equations of getting metabolite concentrations from amplitudes for the past few months from different papers but couldn’t get a good hold of it. I was also seeking help from authors who have published in this field but couldn’t get a simple answer. Perhaps my question was too elementary!!

Can’t ask for a better, simple explanation than this! Thank you so much.

I am doing proton MRS and yes I have a reference unsuppressed water signal that was calculated just before getting the metabolite information. I can get that unsuppressed water amplitude from jMRUI and use that in the equation.

My muscle region of interest is the vastus lateralis of the quadriceps. I haven’t searched the literature yet, but is the concentration of water in this muscle group known? I am guessing different muscle groups would have different water concentrations.

Finally, how do I know the numbers for NucRef and NucMet? Can you kindly provide an example of that?

Thanks again for your time. I really appreciate it.

Hi Droy,

I do not know much about assumed water concentrations in muscle - I tend to work only in the brain these days.
#NucRef and #NucMEt refers to the number of nuclei of interest in the molecule. So for proton MRS in water, #NucRef is 2, and then it depends on the metabolite of interest for #NucMet. You would get that information from the chemical structure of the molecule though.

This reference suggests water makes up 76% of lean muscle mass.
Lorenzo I, Serra-Prat M, YĂ©benes JC. The Role of Water Homeostasis in Muscle Function and Frailty: A Review. Nutrients. 2019 Aug 9;11(8):1857. doi: 10.3390/nu11081857. PMID: 31405072; PMCID: PMC6723611.
And this one suggests the same (~ 76 ml/100 gms)

Best of luck with your work.


Really appreciate the information. Thank you!

While it’s helpful to know 76% of a muscle mass is water, I am wondering how to use that to calculate water concentration in that muscle. As with MRI Scans, I can calculate the area of a certain muscle group in a scan from software like ImageJ, How do I go to mass from it? I am curious how you do it for the brain when you need to know the water concentration in a region that has not been found before.

One paper I was reading calculated choline concentration in muscle and they used a formula like this:

[Cho] = (Signal of Cho/Signal of water) * (nH20/ nCho) * (T1 correction factor) *(T2 correction factor) * (CFH20/ MWH20) * CFlipid

CFlipid is the lipid correction factor that accounts for the chemical shift artifact but the interesting thing is for reference water concentration in their specific muscle group, they divided CFH20, which is 0.76 (76% water in muscle) by the molecular weight of water, which is a known number (18.0153 x 10^-6 kg/mmol).

Based on what I understand, this does normalize the reference water signal amplitude by the amount of water in the muscle and gives a value in the unit of absolute concentration (mmol/kg). Would be great if you let me know what you think about this.

Another thing I am curious about is the number of nuclei of interest in the molecule. nH20 of water is 2, which makes sense but what about a more complex structure? I am particularly interested in the intra and extra-myocellular lipids of the muscles. For choline, it’s 9, which is visible from its structure here:

For muscle MRS, different hydrogens of the lipids resonate at different frequencies, but the two main detectable ones are IMCL (-CH2) and IMCL (-CH3), the same for EMCL.

So when I plug in numbers for nIMCL or nEMCL in the equation, do I write 2 when doing calculations for IMCL(-CH2) and 3 for IMCL(-CH3)? Here’s a reference MRS from the muscle of interest I am working on:

Sorry for all the questions. Would be a great help for me to have some insights on this. Thanks for your time again.

Hi Divya,
you are on the right track here, and this equaltion looks sensible. It also has the benifit of being used by another group, so should give you data to compare your results against.

Hi Again - yes, again, you are on the right track. The -CH2 peak would mean a 2 for the no of protons and the -CH3 would need a 3.