Negative beta values?

[kendrickkay]

(Moved from a previous discussion):

Hi Dr Kay,

My colleague Torben Ellegaard Lund and I are working on a setup for 3T L-fMRI, and in that context we have been very impressed with TDM, which seems to minimize the impact of draining veins dramatically in our activation maps obtained with GE-BOLD. It seems like the collinearity between the regressors sometimes leads to negative beta values even in voxels with large negative t-scores. It happens for instance for the late beta when the response in that voxel has shorter latency than the early HRF.
In our situation, the latencies for the early and late HRFs were very similar, and we found that changing some parameters in the TDM algorithm (e.g. selecting the points on the arc corresponding to +/- 2 STD instead of +/- 1) helped, but I noticed you used the same (default) parameters for all subjects.

I wonder if you experienced something similar in your datasets from the Nature Methods paper and how you handled it?

Best regards,
Lasse Knudsen

[kendrickkay]

Hi Lasse,

Thanks for your message. I am in general very curious to hear about yours (or anyone else's) experience with TDM and veins more broadly. I know what we have observed in our own paradigms and datasets, but am fully aware of the many different ways to think about data and many different acquisition schemes out there, so I think we have potentially much more to learn.

I indeed noticed that there is some propensity to find negative beta values on either the Early or Late temporal regressor, and if i remember correctly it did generally happen near "venous" regions. It is likely that there is a potentially simple statistical reason for this. First, let's assume the Early and Late are "correct" (assuming there is a sense in which we can describe the fMRI responses as literally a mixture of two fundamental timecourses). Then even in that case, due to random measurement noise, we will of course potentially see negative beta weights for incidental reasons (even if the true BOLD responses are non-negative). Second, the assumption of correctness might be wrong. If the Early and Late timecourses are too "close together" on the unit sphere, then in order to compensate for this inaccuracy, the loading (weights) on the Early and Late will indeed be negative. (Hopefully that's clear.)

I think that explanation is consistent with what you were saying: e.g.

It happens for instance for the late beta when the response in that voxel has shorter latency than the early HRF.

Regarding the following:

we found that changing some parameters in the TDM algorithm (e.g. selecting the points on the arc corresponding to +/- 2 STD instead of +/- 1) helped, but I noticed you used the same (default) parameters for all subjects.

Yes, that sounds reasonable. In low-res (and/or 3T data), the full expectation is that the diversity of timecourses will be decreased. (We show some 3T data in the Supplemental materials, if i remember correctly.)

I agree that the idea of +/- 1 is arbitrary and I struggled to find a better solution than this heuristic. That being said, if choosing a different dynamic range might produce better results (according to some criterion that you see in your data), that seems reasonable.

It does seem that the choice of +/- N will directly influence the prevalence and existence of the negative betas that you were referring to. So it does seem that it would be nice if we could come up with some additional principles to guide that parameter selection.

In the datasets demonstrated in the paper, I did not explore other parameter choices --- this was deliberate as it becomes a finicky situation if one has to hand tune parameters on every single dataset. It did seem that a default choice of +/- 1 STD seems to generally work well across the board in our data. But of course, that might be just a first-pass observation.

In general, I think further observations and insights into how this all works would be useful and could lead to productive follow-up research for the field.

Kendrick

[kendrickkay]

(Copied from a different thread):

Thank you very much for the swift and elaborate answer.

I fully agree with your take on the negative betas, after changing the parameters and thereby increasing the latency differences between early and late HRFs, only a few voxels has negative values and these are usually associated with small t-scores, so I guess these fall into the “negative due to noise” category as you described. It is indeed most convenient when default settings does the trick, but I really like the way you implemented easy adjustment of the parameters and a clear and informative documentation, it makes it much easier to handle troubling datasets and get a feel for how different adjustments changes the output.

Would you expect 3 T datasets to have less diverse timecourses than 7 T datasets even at similar resolutions? I am not quite sure, but perhaps the larger weighting towards the macrovasculature could result in less voxels with a “clean” microvascular response and the response of every voxel might thus look more macrovascular-like?

Best regards
Lasse

[kendrickkay]

I fully agree with your take on the negative betas, after changing the parameters and thereby increasing the latency differences between early and late HRFs, only a few voxels has negative values and these are usually associated with small t-scores, so I guess these fall into the “negative due to noise” category as you described. It is indeed most convenient when default settings does the trick, but I really like the way you implemented easy adjustment of the parameters and a clear and informative documentation, it makes it much easier to handle troubling datasets and get a feel for how different adjustments changes the output.

That sounds good. I debated whether to make the "+/- N" parameter part of the function versus the user having write some lines of code. It was a difficult design decision, but hopefully it's not too painful.

Would you expect 3 T datasets to have less diverse timecourses than 7 T datasets even at similar resolutions? I am not quite sure, but perhaps the larger weighting towards the macrovasculature could result in less voxels with a “clean” microvascular response and the response of every voxel might thus look more macrovascular-like?

Hmm, that is an interesting question. It certainly gets into the whole field-strength dependence of the relative contribution of intravascular vs. extravascular components of the micro- and macro-vasculature, which has been talked a lot about in the literature. I guess my reasoning would go as follows: If spatial resolution is fixed, then certainly we can assume that from an imaging and anatomical point of view, 3T and 7T should be similar. However, I think you are right that at lower field strengths, we generally expect the relative contribution from the macrovasculature should be larger than the microvasculature. This would mean that the timecourse of the response of a single voxel to a single experimental condition would, on average, be more likely to "look like" a late-peaking macrovasculature response. I guess this gets into difficult issues that are directly related to the +/- N issue. That is, we don't really have a principle or a priori expectation for how to extract the underlying manifold. This is because how the manifold will "look" on the unit sphere will be affected by spatial resolution and the relative contribution of macro- and microvasculature and measurement noise, which is complicated and I don't think we have a good handle on. Thus, I agree that the fact that +/- 1 STD seemed to work for the datasets we presented in the paper might be "incidental" and that it would be cool to derive some new principles or techniques for figuring out (perhaps in a data-driven manner) how to set the separation. I think Supplementary Figure 5 in the TDM paper might be interesting to you on this matter.