Tools for performing correlation analysis on fMRI data.

## 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.

### 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!

## Python version compatibility

I switched over a while ago to using Python 3 as my daily driver, so I know that everything works there. However, I know that a lot of people can't or won't switch from Python 2x, so I kept Python 2.7 compatibility for quite some time.

That said, the writing is on the wall, and since I depend on a number of packages that have dropped Python 2.x support, as of 2.0, so has rapidtide. However, as of version 1.9.0 I'm also releasing the code 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.

• rapidtide2x_legacy, happy_legacy, showxcorr_legacy - The older versions of the similarly named programs. These use the old calling conventions, for compatibility with older workflows. These will go away eventually, and they don’t really get updates or bugfixes, so if you’re using them, change to the new ones, and if you’re not using them, 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 a grant from the US NIH (1R01 NS097512).

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

### numpy:

1. Stéfan van der Walt, S. Chris Colbert and Gaël Varoquaux. The NumPy Array: A Structure for Efficient Numerical Computation, Computing in Science & Engineering, 13, 22-30 (2011) | https://doi.org/10.1109/MCSE.2011.37

### scipy:

1. Pauli Virtanen, Ralf Gommers, Travis E. Oliphant, Matt Haberland, Tyler Reddy, David Cournapeau, Evgeni Burovski, Pearu Peterson, Warren Weckesser, Jonathan Bright, Stéfan J. van der Walt, Matthew Brett, Joshua Wilson, K. Jarrod Millman, Nikolay Mayorov, Andrew R. J. Nelson, Eric Jones, Robert Kern, Eric Larson, CJ Carey, İlhan Polat, Yu Feng, Eric W. Moore, Jake VanderPlas, Denis Laxalde, Josef Perktold, Robert Cimrman, Ian Henriksen, E.A. Quintero, Charles R Harris, Anne M. Archibald, Antônio H. Ribeiro, Fabian Pedregosa, Paul van Mulbregt, and SciPy 1.0 Contributors. (2020) SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods, 17, 261–272 (2020) | https://doi.org/10.1038/s41592-019-0686-2

### matplotlib:

1. John D. Hunter. Matplotlib: A 2D Graphics Environment, Computing in Science & Engineering, 9, 90-95 (2007) | https://doi.org/10.1109/MCSE.2007.55

### scikit-learn:

1. Pedregosa, F., Varoquaux, G., Gramfort, A., Michel, V., Thirion, B., Grisel, O., Blondel, M., Prettenhofer, P., Weiss, R., Dubourg, V., Vanderplas, J., Passos, A., Cournapeau, D., Brucher, M., Perrot, M., and Duchesnay, E., Scikit-learn: Machine Learning in Python. Journal of Machine Learning Research, 2011. 12: p. 2825-2830. | https://scikit-learn.org

### pandas:

1. McKinney, W., pandas: a foundational Python library for data analysis and statistics. Python for High Performance and Scientific Computing, 2011. 14.

## 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. Tong Y, Hocke LM, Frederick BB. (2019) Low Frequency Systemic Hemodynamic "Noise" in Resting State BOLD fMRI: Characteristics, Causes, Implications, Mitigation Strategies, and Applications. Front. Neurosci., 14 August 2019 | https://doi.org/10.3389/fnins.2019.00787

### Multimodal Cerebral Circulation Imaging

1. Tong Y, Frederick BD. (2010) 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.

2. Tong Y, Hocke L, Frederick BD. (2011) Isolating the sources of widespread physiological fluctuations in fNIRS signals. J Biomed Opt. 16(10), 106005.

3. Tong Y, Bergethon PR, Frederick BD. (2011c) 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.

4. Tong Y, Frederick BD. (2012) Concurrent fNIRS and fMRI processing allows independent visualization of the propagation of pressure waves and bulk blood flow in the cerebral vasculature. Neuroimage, Jul 16;61(4): 1419-27.

5. Tong Y, Hocke LM, Licata SC, Frederick BD. (2012) Low frequency oscillations measured in the periphery with near infrared spectroscopy (NIRS) are strongly correlated with blood oxygen level-dependent functional magnetic resonance imaging (BOLD fMRI) signals. J Biomed Opt, 2012;17(10):106004. doi: 10.1117/1.JBO.17.10.106004. PubMed PMID: 23224003; PMCID: 3461094.

6. Tong Y, Hocke LM, Frederick BD. (2013) Short repetition time multiband EPI with simultaneous pulse recording allows dynamic imaging of the cardiac pulsation signal. Magn Reson Med 2014;72(5):1268-76. Epub Nov 22, 2013. doi: 10.1002/mrm.25041. PubMed PMID: 24272768.

7. Tong Y, Frederick B. (2014) Studying the Spatial Distribution of Physiological Effects on BOLD Signals using Ultrafast fMRI. Front Hum Neurosci 2014;5(196). doi: doi: 10.3389/fnhum.2014.00196.

8. Tong Y, Frederick B. (2014) Tracking cerebral blood flow in BOLD fMRI using recursively generated regressors. Hum Brain Mapp. 2014;35(11):5471-85. doi: 10.1002/hbm.22564. PubMed PMID: 24954380; PMCID: PMC4206590.

9. Donahue M, Strother M, Lindsey K, Hocke L, Tong Y, Frederick B. (2015) Time delay processing of hypercapnic fMRI allows quantitative parameterization of cerebrovascular reactivity and blood flow delays. Journal of Cerebral Blood Flow & Metabolism. 2015. PubMed PMID: 26661192. Epub October 19, 2015. doi: 10.1177/0271678X15608643.

10. Hocke L, Cayetano K, Tong Y, Frederick B. (2015) An optimized multimodal fMRI/NIRS probe for ultra-high resolution mapping. Neurophotonics. 2(4), 045004 (Oct-Dec 2015). doi: 10.1117/1.NPh.2.4.0450004.

11. Tong Y, Hocke LM, Fan X, Janes AC, Frederick B (2015). Can apparent resting state connectivity arise from systemic fluctuations? Frontiers in human neuroscience. 2015;9. doi: 10.3389/fnhum.2015.00285.

12. Tong Y, Lindsey KP, Hocke LM, Vitaliano G, Mintzopoulos D, Frederick B. (2016) Perfusion information extracted from resting state functional magnetic resonance imaging. Journal of cerebral blood flow and metabolism : official journal of the International Society of Cerebral Blood Flow and Metabolism. 2016. doi: 10.1177/0271678X16631755. PubMed PMID: 26873885.

### Cardiac waveform extraction and refinement

1. Aslan S, Hocke L, Schwarz N, Frederick B. (2019) Extraction of the cardiac waveform from simultaneous multislice fMRI data using slice sorted averaging and a deep learning reconstruction filter. NeuroImage 198, 303–316 (2019).

### Physiological noise identification and removal using time delay methods

1. Tong Y, Lindsey KP, Frederick BD. (2011b) Partitioning of physiological noise signals in the brain with concurrent near-infrared spectroscopy (NIRS) and fMRI. J Cereb Blood Flow Metab. 31(12), 2352-62.

2. Frederick BD, Nickerson LD, Tong Y. (2012) Physiological denoising of BOLD fMRI data using Regressor Interpolation at Progressive Time Delays (RIPTiDe) processing of concurrent fMRI and near-infrared spectroscopy (NIRS). Neuroimage, Apr 15;60(3): 1419-27.

3. Tong Y, Hocke LM, Nickerson LD, Licata SC, Lindsey KP, Frederick BB (2013) Evaluating the effects of systemic low frequency oscillations measured in the periphery on the independent component analysis results of resting state networks. NeuroImage. 2013;76C:202-15. doi: 10.1016/j.neuroimage.2013.03.019. PubMed PMID: 23523805; PMCID: PMC3652630.

4. Hocke LM, Tong Y, Lindsey KP, Frederick BB (2016). 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 : official journal of the Society of Magnetic Resonance in Medicine / Society of Magnetic Resonance in Medicine. 2016. | http://dx.doi.org/10.1002/mrm.26038. PubMed PMID: 26854203.

5. Erdoğan S, Tong Y, Hocke L, Lindsey K, Frederick B (2016). Correcting resting state fMRI-BOLD signals for blood arrival time enhances functional connectivity analysis. Front. Hum. Neurosci., 28 June 2016 | http://dx.doi.org/10.3389/fnhum.2016.00311

6. Tong, Y, Hocke, LM, and Frederick, BB, Low Frequency Systemic Hemodynamic "Noise" in Resting State BOLD fMRI: Characteristics, Causes, Implications, Mitigation Strategies, and Applications. Front Neurosci, 2019. 13: p. 787. | http://dx.doi.org/10.3389/fnins.2019.00787

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