4D image bias field correction for quantitative MRI

[nolog2025]

Hello everyone,

I am trying to perform a bias field correction on 4D magnitude data, which is then used for quantitative brain maps. Unfortunately, especially the later echoes are visibly affected by what i assume are B0 inhomogeneities, as for example posterior parts of the brain are consistently brighter than anterior parts, which is in turn visible in the quantitative data. These artifacts are more apparent as TE increases, so calculating a bias field from a single echo (or from a mean of all echoes) and applying to all didnt work out.

I was able to reduce the artifacts in the magnitude data via echo-wise 3D N4 correction in SimpleITK, however, this understandably destroys the signal evolution and subsequently calculated quantitative maps show nonsensical values. Since i read that the N4 filter in AntsPy in theory supports 4D images, i tried it, hoping that it would preserve the signal evolution. This was the case, however, it had barely any effect on the bias field, that the 3D N4 was previously able to correct.

With the ants.N4, I already tried spline_param between 200 and 50 (which produced between 4 and 6 control points in all dimensions, which was similar to my sitk settings), as well as different shrink factors, convergence limits and turning the rescale_intensities on, which all had only a minor effect on the output image.

I was wondering if anyone here had any experience with the usage of the N4 filter on 4D data, and might be willing to share parameters that worked. I am also thankful for any other ideas regarding this.

[ntustison]

It is true that N4 is dimensionality-agnostic like many filters in ITK. And I did play around with some 4-D data when I first wrote it but it doesn't work because the temporal and spatial dimensions should be treated differently. If I were to approach this problem de novo, I would try wrapping a temporal smoothing around the 3D-series correction (and perhaps iterating over the different scales with that temporal smoothing).

[nolog2025]

Hi, thank you very much for the reply! I'll definitely try the temporal smoothing after 3D correction, if anything ends up working, I'll report back here.

I also tried applying the sitk PatchBasedDenoising filter to each previously 3D N4 corrected echo and then stitching the 4D image back together, which interestingly somehow "fixed" the change in signal evolution and gave me reasonable quantitative values again. I might use this as a fall-back if I can figure out why this happens, if you know why this occurs, any insight would be greatly appreciated.

Thanks!

[ntustison]

I should ask first --- are you using Simple ITK's version of N4 or the one in ANTsPy?

[nolog2025]

Ah, sorry, for the 3D N4 correction as well as the PatchBasedDenoising I used the SimpleITK version, I only tried the ANTsPy version for the 4D input. I understand if my follow-up question is misplaced on this page, I can repost on the ITK forum if you'd prefer.

As for my question regarding the denoising filter, I now have some idea of what might be going on: I tried k-means clustering voxels over signal decay values after the 3D N4, and then set each cluster intensity to its median value for each echo separately, and it had a similar effect to the PatchBasedDenoising. I assume the N4 introduces some local error that is averaged out over the cluster, thus somewhat restoring the original signal evolution, and that the patchbaseddenoising has a similar effect. I would still be thankful for any thoughts you have on this.

[ntustison]

Yeah, you should really post your questions on the forum specific to the implementation that you're using---N4 is a perfect example. Even though both implementations use the base class itkN4BiasFieldCorrectionImageFilter, there are some external preprocessing choices that might not be shared between the two implementations. Specifically related to your observation about the intensity values --- that's actually a known phenomenon associated with the core N3 algorithm from which N4 is derived. Over the course of optimization, the global intensity of the corrected image can drift up or down. That's why we have a "rescale intensity" option as part of our implementation. I don't know if that's a part of SiTK. Another possible difference is that the ANTs user can specify a "spline distance" in addition to a mesh size which requires some image padding as part of preprocessing. I wouldn't expect SiTK to also have that option.

Regarding denoising with this specific filter, you'll have to ask over at the forum. I'm not very familiar with its current state. I just remember the execution time being particularly long when it first came out. In ANTs, we use an algorithmically related filter that's also part of ITK but I don't know if it's made it's way into SiTK.

[nolog2025]

Alright, I see. I thought the N4 implementions were somewhat interchangeable, I'll try out the ANTsPy version as well then, perhaps the "rescale intensity" option helps with my problem with the 3D N4 correction. As for the SimpleITK denoising, I'll ask my question on the ITK page.
Thank you very much for your help on this!