What is the definition of linewidth in apodization?

Hi!

I’m reading a book on in vivo MRS processing, it says that apodization can be done by multiplying FID with exp(-t/T). In jMRUI, however, we input a value in Hz to do apodization. Then my question is, what is the definition of that value in Hz?

I guess it’s FWHM, or maybe also called linewidth. But if F(v) is the Fourier transform of exp(-t/T)u(t), then F(v) has different FWHM when we are measuring its magnitude or real part.

Here u(t)=0 for t<=0, u(t)=1 for t>0

I thought about this question because I was wondering whether B0 will affect the parameter. For example, if we do the same experiment with a 3T scanner and 9.4T scanner (suppose other conditions are identical), we find that 5Hz apodization works very well on 3T data. Will 5Hz work as well for 9.4T data?

I didn’t find the definition in the book. So I’m hoping someone in the forum would know and tell me.

Thanks!

Though I still don’t know the relation between T in exp(-t/T) and the Hz value in apodization, I think I’ve got the answer to my original curious question.

The Hz value, denoted as FWHM, must be in the form of A/T, where A is a constant.

If 5Hz works well with 3T data, then with 9.4T data, the peaks are farther away from each other, so 9.4T data can tolerate more severe line broadening. That means we can use at least 9.4/3*5=15.67 Hz for 9.4T, it will achieve the same spectral resolution while suppressing noise more heavily, provided that all other conditions are identical. That indicates that, for higher B0, it’s normal to use higher apodization Hz value than for lower B0.

Correct me if I’m wrong. Thanks

Oh I see. The definition must be the real part. Because the magnitude is not Lorentzian line shape. Only the real part is Lorentzian.

Therefore, the relation is FWHM=1/T/pi

Thanks.

Hi @zui,

I think you answered your own question re the width of the apodization (broadening) function, but a few comments on your apodization approach in general. This depends a bit on what sequence you’re using, which metabolites you’re hoping to isolate, and what model you’re using to fit the data, but:

  • If you are fitting the data with a linear combination of basis sets, many implementations strongly discourage linebroadening/smoothing/apodization since this invalidates the statistical modelling and may limit the seperability of metabolites with similar spectral patterns
  • Some simple curve-fitting algorithms may be more stable with moderate apodisation, particularly in otherwise low SNR scenarios.
  • The quoted values (5Hz for 3T, 15Hz for 9.4T) sound very high for most applications.
  • One of the great advantages of higher field is the better separation between peaks, as you note – allowing us to more accurately discriminate between certain substances. If you apply heavy apodization, then you lose this benefit

Basically, a visually “clean”, smooth spectrum won’t necessarily give better results than a sharp spectrum with a bit of noise.

If you’re looking at sparse, non-proton spectra this might be okay, but if you are working with standard proton MR it may be worth re-considering whether this much apodization is desirable.

Hi @alex,

I’m more than glad to receive your comments! And, your guess is right, I’m working with 13C hyperpolairzed data, which has only two peaks (KIC and Leucine).

I’m trying with AMARES implemented in jMRUI and OXSA. Based on my understanding, AMARES doesn’t use a basis sets. (Not quite sure, I think in this way just because I didn’t see any pop up window asking for a basis set. But maybe AMARES sometimes also works with a basis set?)

Thanks agin for your insights!

Hi Zui,

You are right, AMARES does not work with a basis set. It parameterizes individual metabolite signals (e.g., amplitude, frequency, phase, linewidth, lineshape) and fits them to the raw FID. You can fix or constrain some or all of the parameters with your prior knowledge.

Mathematically, apodization corresponds to increased damping that AMARES can fit, and thus you can still get the correct amplitude with broader linewidth from apodized MRS data. However, since apodization alters the noise distribution (e.g., heavily suppresses the noise in the FID tail), the SNR estimation and CRLB estimation can be skewed (over-estimated). I agree with Alex that a sparse, non-proton spectrum can be more tolerant of apodization. However, preferably you would just use apodization for visualization, not for quantification.

Btw, jMRUI and OXSA are great tools that provide AMARES algorithms via Java and MATLAB. Recently, we developed a Python-based pyAMARES that may interest you. Here you can find examples of fitting X-nuclei data using AMARES: Examples of In Vivo X-Nuclei (\(^{129}\)Xe and \(^{2}\)H) MRS Fitting — pyAMARES 0.3.21dev documentation. Following the tutorial, you can try fitting hyperpolarized 129Xe data in a browser using Google Colab. Glad to discuss with you more about AMARES.

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