"Ill conditioned matrix" while trying to run kineticmodel SRTM

[cepa995]

Hi,

I have successfully managed to clone and install your package, and I tried out SRTM method on my own data where as a reference mask I've used whole brain mask (for testing purposes).

Problem I am running into is that during the computation of DVR, while trying to fit Linear Regression model, it always seems to hit the LinAlgException where the b cannot be solved due to Ill-conditioned matrix, specifically at lines 254:

as well as line 311:

Although this may be "just a warning", could you help me understand the root of this issue and how can I address it? Why, and what matrix exactly is ill-conditioned?

Thanks!

[bilgelm]

Hi @cepa995, thanks for your question!

Both of these computations are performed per voxel. I'm imaging that the warnings you're seeing are being generated at a small number of voxels relative to the number of voxels in the brain mask – perhaps some background voxels that got included in the mask you're using, or a voxel in or near the ventricles, or some other voxel where there isn't a clear time activity curve. The ill-conditioned matrix warning could also be stemming from voxels (especially voxels in the reference region) where the time activity curve (TAC) is very close to the mean TAC in the reference region. This would mean that the 2nd and 3rd columns of the matrix x are almost collinear, making it difficult to solve the linear system.

[cepa995]

Thanks @bilgelm, that makes sense!

[cepa995]

Sorry, but I have a question. What is the target region in SRTM model? How do I define it? For exmaple, I want to use Whole Cerebellum as reference, and Hippocampus as target @bilgelm

[bilgelm]

Hi @cepa995,

An SRTM is fitted per voxel (if a 4-D PET image is supplied as input to kineticmodel) or per ROI (if a TAC tsv file is supplied). That is, each voxel/ROI is considered as target in separate SRTMs. After model fitting, you'll need to extract the results for the hippocampus (by using a hippocampus mask if you used a 4-D PET image as input to kineticmodel, or by getting the corresponding hippocampus entry from the output tsv file if you used a TAC tsv as input).

If you want to estimate SRTM kinetic parameters only in the hippocampus, you can speed up the computation by ignoring non-hippocampus:

• if you're using a 4-D PET image as input, supply a binary mask of the hippocampus as the petmask argument to kineticmodel. This will result in kinetic parameter estimation to be skipped for voxels that are not in petmask.
• if you're using a TAC tsv file as input, include only the TACs for your reference region (whole cerebellum) and the hippocampus as columns in the input TAC tsv file.

[cepa995]

I think I get it. So in summary, I can use typical reference region, such as Cerebellum or White Matter, and 4D PET image, estimate DVR, and then mask out hippocampus?

Regarding the 2nd option, I already tried that but I get an error that reference mask (e.g. white matter) does not fit into pet mask (hippocampus). So I guess I would need to supply entire brain mask, and later extraxt results per specific regions, like FDG stats, etc. Correct?

[bilgelm]

Yes, that's right.

My bad re: the 2nd option -- the way it is currently implemented, you need to include the reference region in the petmask in addition to the hippocampus. From a user perspective, it makes more sense to use petmask to designate target voxels only. Leave this issue open and I'll make that update.