The rapidtide package

Rapidtide is a suite of Python programs used to model, characterize, visualize, and remove time varying, physiological blood signals from fMRI and fNIRS datasets. The primary workhorses of the package are the rapidtide program, which characterizes bulk blood flow, and happy, which focusses on the cardiac band.

Full documentation is at: http://rapidtide.readthedocs.io/en/latest/

The rapidtide program

Rapidtide is also the name of the first program in the package, which is used to perform rapid time delay analysis on functional imaging data to find time lagged correlations between the voxelwise time series and other time series, primarily in the LFO band.

Why do I want to know about time lagged correlations?

This comes out of work by our group (The Opto-Magnetic group at McLean Hospital - http://www.nirs-fmri.net) looking at the correlations between neuroimaging data (fMRI) and NIRS data recorded simultaneously, either in the brain or the periphery. We found that a large fraction of the "noise" we found at low frequency in fMRI data was due to real, random[*] fluctuations of blood oxygenation and volume (both of which affect the intensity of BOLD fMRI images) in the blood passing through the brain. More interestingly, because these characteristics of blood move with the blood itself, this gives you a way to determine blood arrival time at any location in the brain. This is interesting in and of itself, but also, this gives you a method for optimally modelling (and removing) in band physiological noise from fMRI data (see references below).

After working with this for several years we've also found that you don't need to used simultaneous NIRS to find this blood borne signal - you can get it from blood rich BOLD voxels for example in the superior sagittal sinus, or bootstrap it out of the global mean signal in the BOLD data. You can also track exogenously applied waveforms, such as hypercarbic and/or hyperoxic gas challenges to really boost your signal to noise. So there are lots of times when you might want to do this type of correlation analysis.

As an aside, some of these tools are just generally useful for looking at correlations between timecourses from other sources – for example doing PPI, or even some seed based analyses.

[*] "random" in this context means "determined by something we don't have any information about" - maybe EtCO2 variation, or sympathetic nervous system activity - so not really random.

Correlation analysis is easy - why use this package?

The simple answer is "correlation analysis is easy, but using a prewritten package that handles file I/O, filtering, resampling, windowing, and the rest for you is even easier". A slightly more complex answer is that while correlation analysis is pretty easy to do, it's hard to do right; there are lots and lots of ways to do it incorrectly. Fortunately, I've made most of those mistakes for you over the last 8 years, and corrected my code accordingly. So rather than repeat my boring mistakes, why not make new, interesting mistakes? Explore your own, unique chunk of wrongspace…

Happy

More recently, inspired by Henning Voss' paper on hypersampling of cardiac signals in fMRI, we developed a method to extract and clean cardiac waveforms from fMRI data, even when the fMRI TR is far too long to properly sample cardiac waveforms. This cardiac waveform can then be to track the pulsatile cardiac pressure wave through the brain in somewhat the same way that we track the LFO signals. Among other things, this allows you to get cardiac waveforms during scans even when either 1) you didn't use a plethysmograph, or 2) you did, but the recording was of poor quality, which happens more than you might think.

What does "happy" have to do with any of this?

As to why happy is part of rapidtide, that's partially for practical reasons (the libraries in rapidtide have an awful lot of code that is reused in happy), and partially thematically - rapidtide has evolved from a "let's look at low frequency signals in fMRI data" package to a "let's look at everything in fMRI data EXCEPT neuronal activation", so happy fits right in.

Why are you releasing this package?

For a number of reasons.

I want people to use it! I think if it were easier for people to do time delay analysis, they'd be more likely to do it. I don't have enough time or people in my group to do every experiment that I think would be interesting, so I'm hoping other people will, so I can read their papers and learn interesting things.
It's the right way to do science – I can say lots of things, but if nobody can replicate my results, nobody will believe it (we've gotten that a lot, because some of the implications of what we've seen in resting state data can be a little uncomfortable). We've reached a stage in fMRI where getting from data to results involves a huge amount of processing, so part of confirming results involves being able to see how the data were processed. If you had to do everything from scratch, you'd never even try to confirm anybody's results.
In any complicated processing scheme, it's quite possible (or in my case, likely) to make dumb mistakes, either coding errors or conceptual errors, and I almost certainly have made some (although hopefully the worst ones have been dealt with at this point). More users and more eyes on the code make it more likely that they will be found. As much as I'm queasy about somebody potentially finding a mistake in my code, I'd rather that they did so, so I can fix it[‡].
It's giving back to the community. I benefit from the generosity of a lot of authors who have made the open source tools I use for work and play, so I figure I can pony up too.

[‡] or better yet, you, empowered user, can fix it, and push back a fix that benefits everybody…

Stability, etc.

This is an evolving code base. I'm constantly tinkering with it. That said, now that I've sent this off into to the world, I'm being somewhat more responsible about locking down stable release points. In between releases, however, I'll be messing with things, although for the most part this will be restricted to the dev branch. It's very possible that at any given time the dev branch will be very broken, so stay away from it unless you have a good reason to be using it. I've finally become a little more modern and started adding automated testing, so as time goes by hopefully the "in between" releases will be somewhat more reliable. That said, my tests routinely fail, even when things actually work. Probably should deal with that. Check back often for exciting new features and bug fixes!

Testing lanes

The test suite now supports marker-based lanes so you can run fast checks separately from heavier workflow tests.

unit: fast parser/math/small mocked tests
slow: heavier workflow-oriented tests

Using pytest directly:

pytest -m unit
pytest -m slow
pytest -m "not slow"

Using the local test helper script:

cd rapidtide/tests
./runlocaltest unit
./runlocaltest notslow (or ./runlocaltest pr)
./runlocaltest slow
./runlocaltest all

Recommended CI split:

Fast lane (default PR checks): pytest -m "not slow"
Slow lane (scheduled/nightly or dedicated job): pytest -m slow

Current CircleCI lane mapping:

Fast lane jobs (-m "not slow"): test_py310, test_py311_with_optional, test_py311_with_coverage, test_py312, test_py313, test_py314
Slow lane job (-m slow): test_py311_slow

Lane intent and expected runtime:

unit: parser/math/mocked checks intended for very fast local feedback. Typical runtime is usually a few minutes or less, depending on hardware.
not slow: primary PR lane. Covers unit tests plus non-heavy workflows while excluding long-running integration tests.
slow: heavy integration-style tests (fullrun/simroundtrip and other marked workflow tests). This lane is intended for dedicated CI jobs.

Suggested pre-push workflow:

Before most commits: pytest -m unit
Before opening a PR: pytest -m "not slow"
Before release or in scheduled CI: pytest -m slow

Python version compatibility

Since I depend on a number of packages that have dropped Python 2.x support, as of rapidtide 2.0, so did rapidtide. And given that I use fairly modern constructs, I don’t support anything prior to Python 3.9. The current UPPER limit is 3.12, because tensorflow (needed for happy) does not yet support 3.13 or later. In 2025, I don’t imagine anybody is running rapidtide on a system that can’t upgrade to a modern Python, but if you are, as of version 1.9.0 the package is also available in a docker container (fredericklab/rapidtide), which has everything nicely installed in a fully configured Python 3 environment, so there's really no need for me continue 2.x support. So now it’s f-strings all the way, kids!

Ok, I'm sold. What's in here?

rapidtide - This is the heart of the package - this is the workhorse program that will determine the time lagged correlations between all the voxels in a NIFTI file and a temporal "probe" regressor (which can come from a number of places, including the data itself) - it rapidly determines time delays… There are a truly bewildering array of options, and just about everything can be adjusted, however I've tried to pick a good set of default options for the most basic processing to get you going. At a minimum, it requires a 4D NIFTI file as input, and a root name for all of the output files. It generates a number of 3D NIFTI file maps of various parameters (lag time of maximum correlation, maximum correlation value, a mask of which voxels have valid fits, etc.) and some text files with useful information (significance thresholds, processing timing information, a list of values of configurable options).
happy - This is a companion to rapidtide that focusses on cardiac signals. happy does three things - it attempts to determine the cardiac waveform over the time course of an fMRI dataset using slice selective averaging of fully unprocessed fMRI data. It also cleans up this initial estimate using a deep learning filter to infer what the simultaneously recorded plethysmogram would be. Finally, it uses either the derived or a supplied plethysmogram signal to construct a cardiac pulsation map over a single cycle of the cardiac waveform, a la Voss.
showxcorrx - Like rapidtide, but for single time courses. Takes two text files as input, calculates and displays the time lagged cross correlation between them, fits the maximum time lag, and estimates the significance of the correlation. It has a range of filtering, windowing, and correlation options.
showxcorr_legacy - The older versions of the similarly named program. This uses the old calling conventions, for compatibility with older workflows. This will go away eventually, and it doesn’t really get updates or bugfixes, so if you’re using it, change to the new one, and if you’re not using it, don’t.
rapidtide2std - This is a utility for registering rapidtide output maps to standard coordinates. It's usually much faster to run rapidtide in native space then transform afterwards to MNI152 space. NB: this will only work if you have a working FSL installation.
happy2std - Guess.
showtc - A very simple command line utility that takes timecourses from text files and plots the data in it in a matplotlib window. That's it. A good tool for quickly seeing what's in a file. Has a number of options to make the plot prettier.
showxy - Another simple command line utility that displays the the data contained in text files containing whitespace separated x-y pairs.
showhist - Another simple command line utility that displays the histograms generated by rapidtide.
resamp1tc - takes an input text file at some sample rate and outputs a text file resampled to the specified sample rate.
resamplenifti - takes an input nifti file at some TR and outputs a nifti file resampled to the specified TR.
tidepool - This is a GUI tool for displaying all of the various maps and timecourses generated by rapidtide in one place, overlaid on an anatomic image. This makes it a bit easier to see how all the maps are related to one another, how the probe regressor evolves over the run, and the effect of the filtering parameters. To use it, launch tidepool from the command line, and then select a lag time map - tidepool will figure out the root name and pull in all of the other associated data. Works in native or standard space.

Financial Support

This code base is being developed and supported by grants from the US NIH (1R01 NS097512, RF1 MH130637-01)

Additional packages used

Rapidtide would not be possible without many additional open source packages. These include:

numpy:

[1]

Charles R. Harris, K. Jarrod Millman, Stéfan J. van der Walt, Ralf Gommers, Pauli Virtanen, David Cournapeau, Eric Wieser, Julian Taylor, Sebastian Berg, Nathaniel J. Smith, Robert Kern, Matti Picus, Stephan Hoyer, Marten H. van Kerkwijk, Matthew Brett, Allan Haldane, Jaime Fernández del Río, Mark Wiebe, Pearu Peterson, Pierre Gérard-Marchant, Kevin Sheppard, Tyler Reddy, Warren Weckesser, Hameer Abbasi, Christoph Gohlke, and Travis E. Oliphant. Array programming with NumPy. Nature, 585(7825):357–362, September 2020. URL: https://doi.org/10.1038/s41586-020-2649-2, doi:10.1038/s41586-020-2649-2.

scipy:

[1]

Ralf Gommers, Pauli Virtanen, Matt Haberland, Evgeni Burovski, Warren Weckesser, Tyler Reddy, Travis E. Oliphant, David Cournapeau, Andrew Nelson, alexbrc, Pamphile Roy, Pearu Peterson, Ilhan Polat, Josh Wilson, endolith, Nikolay Mayorov, Stefan van der Walt, Matthew Brett, Denis Laxalde, Eric Larson, Atsushi Sakai, Jarrod Millman, Lucas Colley, Lars, peterbell10, CJ Carey, Paul van Mulbregt, Jake Bowhay, eric-jones, and Kai Striega. Scipy/scipy: scipy 1.14.1. August 2024. URL: https://doi.org/10.5281/zenodo.13352243, doi:10.5281/zenodo.13352243.

matplotlib:

[1]

John D. Hunter. Matplotlib: a 2d graphics environment. Computing in Science & Engineering, 9(3):90–95, 2007. doi:10.1109/MCSE.2007.55.

nibabel:

[1]

Matthew Brett, Christopher J. Markiewicz, Michael Hanke, Marc-Alexandre Côté, Ben Cipollini, Dimitri Papadopoulos Orfanos, Paul McCarthy, Dorota Jarecka, Christopher P. Cheng, Eric Larson, Yaroslav O. Halchenko, Michiel Cottaar, Satrajit Ghosh, Demian Wassermann, Stephan Gerhard, Gregory R. Lee, Zvi Baratz, Brendan Moloney, Hao-Ting Wang, Erik Kastman, Jakub Kaczmarzyk, Roberto Guidotti, Jonathan Daniel, Or Duek, Ariel Rokem, Mathieu Scheltienne, Cindee Madison, Anibal Sólon, Félix C. Morency, Mathias Goncalves, Ross Markello, Cameron Riddell, Christopher Burns, Jarrod Millman, Alexandre Gramfort, Jaakko Leppäkangas, Jasper J.F. van den Bosch, Robert D. Vincent, Henry Braun, Krish Subramaniam, Andrew Van, Jon Haitz Legarreta, Krzysztof J. Gorgolewski, Pradeep Reddy Raamana, Julian Klug, Reinder Vos de Wael, B. Nolan Nichols, Eric M. Baker, Serge Koudoro, Soichi Hayashi, Basile Pinsard, Christian Haselgrove, Mark Hymers, Oscar Esteban, Fernando Pérez-García, Guillaume Becq, Jérôme Dockès, Nikolaas N. Oosterhof, Bago Amirbekian, Horea Christian, Ian Nimmo-Smith, Ly Nguyen, Peter Suter, Samir Reddigari, Samuel St-Jean, Egor Panfilov, Eleftherios Garyfallidis, Gael Varoquaux, Joshua Newton, Kevin S. Hahn, Lea Waller, Oliver P. Hinds, Sandro, Bennet Fauber, Blake Dewey, Fabian Perez, Jacob Roberts, Jean-Baptiste Poline, Jon Stutters, Kesshi Jordan, Matthew Cieslak, Miguel Estevan Moreno, Tomáš Hrnčiar, Valentin Haenel, Yannick Schwartz, Benjamin C Darwin, Bertrand Thirion, Carl Gauthier, Igor Solovey, Ivan Gonzalez, Jath Palasubramaniam, Justin Lecher, Katrin Leinweber, Konstantinos Raktivan, Markéta Calábková, Peter Fischer, Philippe Gervais, Syam Gadde, Thomas Ballinger, Thomas Roos, Venkateswara Reddy Reddam, and freec84. Nipy/nibabel: 5.3.1. October 2024. URL: https://doi.org/10.5281/zenodo.13936989, doi:10.5281/zenodo.13936989.

scikit-image:

[1]

Stefan Van der Walt, Johannes L Schönberger, Juan Nunez-Iglesias, François Boulogne, Joshua D Warner, Neil Yager, Emmanuelle Gouillart, and Tony Yu. Scikit-image: image processing in python. PeerJ, 2:e453, 2014.

scikit-learn:

[1]

The scikit-learn developers. Scikit-learn. September 2024. URL: https://doi.org/10.5281/zenodo.13749328, doi:10.5281/zenodo.13749328.

statsmodels:

[1]

Skipper Seabold and Josef Perktold. Statsmodels: econometric and statistical modeling with python. In 9th Python in Science Conference. 2010.

pandas:

[1]

The pandas development team. Pandas-dev/pandas: pandas. February 2020. URL: https://doi.org/10.5281/zenodo.3509134, doi:10.5281/zenodo.3509134.

nilearn:

[1]

Nilearn contributors. nilearn. URL: https://github.com/nilearn/nilearn, doi:https://doi.org/10.5281/zenodo.8397156.

pyqtgraph:

[1]

The pyqtgraph developers. Pyqtgraph. URL: https://www.pyqtgraph.org.

References

Links to PDFs of all papers mentioned here can be found on the OMG website: https://www.nirs-fmri.net/home/publications

General overview of systemic low frequency oscillations in fMRI data

[1]

Yunjie Tong, Lia M Hocke, and Blaise B Frederick. Low frequency systemic hemodynamic “noise” in resting state bold fmri: characteristics, causes, implications, mitigation strategies, and applications. Frontiers in neuroscience, 13:787, 2019. URL: https://doi.org/10.3389/fnins.2019.00787, doi:10.3389/fnins.2019.00787.

Multimodal Cerebral Circulation Imaging

[1]

Y. Tong and B. D. Frederick. Time lag dependent multimodal processing of concurrent fmri and near-infrared spectroscopy (nirs) data suggests a global circulatory origin for low-frequency oscillation signals in human brain. Neuroimage, 53(2):553–64, 2010. Tong, Yunjie Frederick, Blaise Deb eng R21 DA021817/DA/NIDA NIH HHS/ R21 DA027877/DA/NIDA NIH HHS/ R21-DA021817/DA/NIDA NIH HHS/ Research Support, N.I.H., Extramural Neuroimage. 2010 Nov 1;53(2):553-64. doi: 10.1016/j.neuroimage.2010.06.049. Epub 2010 Jun 28. URL: https://www.ncbi.nlm.nih.gov/pubmed/20600975, doi:10.1016/j.neuroimage.2010.06.049.

[2]

Y. Tong, L. M. Hocke, and Bd Frederick. Isolating the sources of widespread physiological fluctuations in functional near-infrared spectroscopy signals. J Biomed Opt, 16(10):106005, 2011. Tong, Yunjie Hocke, Lia Maria Frederick, Blaise deB eng R21 DA027877/DA/NIDA NIH HHS/ R21DA027877/DA/NIDA NIH HHS/ Research Support, N.I.H., Extramural J Biomed Opt. 2011 Oct;16(10):106005. doi: 10.1117/1.3638128. URL: https://www.ncbi.nlm.nih.gov/pubmed/22029352, doi:10.1117/1.3638128.

[3]

Y. J. Tong, P. R. Bergethon, and B. D. Frederick. An improved method for mapping cerebrovascular reserve using concurrent fmri and near-infrared spectroscopy with regressor interpolation at progressive time delays (riptide). Neuroimage, 56(4):2047–2057, 2011. Tong, Yunjie Bergethon, Peter R. Frederick, Blaise deB. doi:10.1016/j.neuroimage.2011.03.071.

[4]

Y. J. Tong and B. D. Frederick. Concurrent fnirs and fmri processing allows independent visualization of the propagation of pressure waves and bulk blood flow in the cerebral vasculature. Neuroimage, 61(4):1419–1427, 2012. Tong, Yunjie Frederick, Blaise deB. URL: <Go to ISI>://WOS:000305920600065, doi:10.1016/j.neuroimage.2012.03.009.

[5]

Yunjie Tong, Lia Maria Hocke, Stephanie C Licata, and Blaise deB Frederick. Low-frequency oscillations measured in the periphery with near-infrared spectroscopy are strongly correlated with blood oxygen level-dependent functional magnetic resonance imaging signals. Journal of biomedical optics, 17(10):106004–1–106004–10, 2012. doi:10.1117/1.JBO.17.10.106004.

[6]

Y. Tong, L. M. Hocke, and Bd Frederick. Short repetition time multiband echo-planar imaging with simultaneous pulse recording allows dynamic imaging of the cardiac pulsation signal. Magn Reson Med, 72(5):1268–76, 2014. Tong, Yunjie Hocke, Lia M Frederick, Blaise deB eng K25DA031769/DA/NIDA NIH HHS/ R21 DA027877/DA/NIDA NIH HHS/ K25 DA031769/DA/NIDA NIH HHS/ T32 DA015036/DA/NIDA NIH HHS/ R21 DA032746/DA/NIDA NIH HHS/ R21 DA034766/DA/NIDA NIH HHS/ Research Support, N.I.H., Extramural Magn Reson Med. 2014 Nov;72(5):1268-76. doi: 10.1002/mrm.25041. Epub 2013 Nov 22. URL: https://www.ncbi.nlm.nih.gov/pubmed/24272768, doi:10.1002/mrm.25041.

[7]

Y. Tong and B. D. Frederick. Studying the spatial distribution of physiological effects on bold signals using ultrafast fmri. Front Hum Neurosci, 8(196):196, 2014. Tong, Yunjie Frederick, Blaise Deb eng K25 DA031769/DA/NIDA NIH HHS/ R21 DA027877/DA/NIDA NIH HHS/ R21 DA032746/DA/NIDA NIH HHS/ Switzerland Front Hum Neurosci. 2014 Apr 1;8:196. doi: 10.3389/fnhum.2014.00196. eCollection 2014. URL: https://www.ncbi.nlm.nih.gov/pubmed/24744722, doi:10.3389/fnhum.2014.00196.

[8]

Y. Tong and BD Frederick. Tracking cerebral blood flow in bold fmri using recursively generated regressors. Hum Brain Mapp, 35(11):5471–85, 2014. Tong, Yunjie Frederick, Blaise deB eng K25 DA031769/DA/NIDA NIH HHS/ R21 DA032746/DA/NIDA NIH HHS/ Research Support, N.I.H., Extramural Hum Brain Mapp. 2014 Nov;35(11):5471-85. doi: 10.1002/hbm.22564. Epub 2014 Jun 23. URL: https://www.ncbi.nlm.nih.gov/pubmed/24954380, doi:10.1002/hbm.22564.

[9]

Manus J Donahue, Megan K Strother, Kimberly P Lindsey, Lia M Hocke, Yunjie Tong, and Blaise deB Frederick. Time delay processing of hypercapnic fmri allows quantitative parameterization of cerebrovascular reactivity and blood flow delays. Journal of Cerebral Blood Flow & Metabolism, 36(10):1767–1779, 2016. URL: https://doi.org/10.1177/0271678X15608643, doi:10.1177/0271678X15608643.

[10]

L. M. Hocke, K. Cayetano, Y. Tong, and B. Frederick. An optimized multimodal functional magnetic resonance imaging/near-infrared spectroscopy probe for ultrahigh-resolution mapping. Neurophotonics, 2(4):045004, 2015. URL: https://www.ncbi.nlm.nih.gov/pubmed/26668816, doi:10.1117/1.NPh.2.4.045004.

[11]

Y. Tong, L. M. Hocke, X. Fan, A. C. Janes, and Bd Frederick. Can apparent resting state connectivity arise from systemic fluctuations? Front Hum Neurosci, 9(63):285, 2015. Tong, Yunjie Hocke, Lia M Fan, Xiaoying Janes, Amy C Frederick, Blaise deB eng K01 DA029645/DA/NIDA NIH HHS/ K25 DA031769/DA/NIDA NIH HHS/ R21 DA032746/DA/NIDA NIH HHS/ Switzerland Front Hum Neurosci. 2015 May 15;9:285. doi: 10.3389/fnhum.2015.00285. eCollection 2015. URL: https://www.ncbi.nlm.nih.gov/pubmed/26029095, doi:10.3389/fnhum.2015.00285.

[12]

Y. Tong, K. P. Lindsey, L. M. Hocke, G. Vitaliano, D. Mintzopoulos, and B. D. Frederick. Perfusion information extracted from resting state functional magnetic resonance imaging. J Cereb Blood Flow Metab, 37(2):564–576, 2017. Tong, Yunjie Lindsey, Kimberly P Hocke, Lia M Vitaliano, Gordana Mintzopoulos, Dionyssios Frederick, Blaise deB eng K08 DA037465/DA/NIDA NIH HHS/ K25 DA031769/DA/NIDA NIH HHS/ R21 DA032746/DA/NIDA NIH HHS/ J Cereb Blood Flow Metab. 2017 Feb;37(2):564-576. doi: 10.1177/0271678X16631755. Epub 2016 Jul 20. URL: https://www.ncbi.nlm.nih.gov/pubmed/26873885, doi:10.1177/0271678X16631755.

Physiological noise identification and removal using time delay methods

[1]

BB Frederick, L. D. Nickerson, and Y. Tong. Physiological denoising of bold fmri data using regressor interpolation at progressive time delays (riptide) processing of concurrent fmri and near-infrared spectroscopy (nirs). Neuroimage, 60(3):1913–23, 2012. URL: https://www.ncbi.nlm.nih.gov/pubmed/22342801, doi:10.1016/j.neuroimage.2012.01.140.

[2]

Y. J. Tong, K. P. Lindsey, and B. D. Frederick. Partitioning of physiological noise signals in the brain with concurrent near-infrared spectroscopy and fmri. Journal of Cerebral Blood Flow and Metabolism, 31(12):2352–2362, 2011. Tong, Yunjie Lindsey, Kimberly P. Frederick, Blaise deB. URL: https://journals.sagepub.com/doi/10.1038/jcbfm.2011.100, doi:10.1038/jcbfm.2011.100.

[3]

Y. Tong, L. M. Hocke, L. D. Nickerson, S. C. Licata, K. P. Lindsey, and B. D. Frederick. Evaluating the effects of systemic low frequency oscillations measured in the periphery on the independent component analysis results of resting state networks. Neuroimage, 76:202–15, 2013. URL: http://www.ncbi.nlm.nih.gov/pubmed/23523805, doi:10.1016/j.neuroimage.2013.03.019.

[4]

Lia M Hocke, Yunjie Tong, Kimberly P Lindsey, and Blaise de B. Frederick. Comparison of peripheral near-infrared spectroscopy low-frequency oscillations to other denoising methods in resting state functional mri with ultrahigh temporal resolution. Magnetic resonance in medicine, 76(6):1697–1707, 2016. URL: https://doi.org/10.1002/mrm.26038, doi:10.1002/mrm.26038.

[5]

SB Erdoğan, Y Tong, LM Hocke, KP Lindsey, and B deB Frederick. Correcting resting state fmri-bold signals for blood arrival time enhances functional connectivity analysis. Frontiers in Human Neuroscience, 10(June):311, 2016. URL: https://doi.org/10.3389/fnhum.2016.00311, doi:10.3389/fnhum.2016.00311.

[6]