tl;dr: This repository contains MATLAB code for combining BOSC and FOOOF

Tutorial script HERE

Scripts to validate fBOSC versus other methods can be found at: https://github.com/neurofractal/fBOSC_validation

• fBOSC
  • BOSC
  • FOOOF (Donoghue et al., 2020)
  • So why use FOOOF in combination with BOSC?
  • Does this really help?
  • What are the consequences of a poor 1/f fit?
  • Using fBOSC
  • Test scripts
  • Code and Citations
  • Acknowledgments:

The Better oscillation detection (BOSC) method has been widely used to characterise oscillatory activity in continuous data and/or at the single trial level. In brief, the method first computes a "power threshold" and a "duration threshold (DT)" for transient oscillatory burst detection.

The power threshold is determined by first modelling the background aperiodic (1/f) neural spectrum. For each frequency of interest a probability distribution function is fitted to the (linear) aperiodic fit (using a χ2 distribution). The power threshold is then typically set on the 95th percentile of the χ2(2) distribution. This ensures only quantitativly large increases in neural power (above and beyond the aperiodic signal) are classed as potential 'oscillations'.

The duration threshold is usually set at 2-3 oscillatory cycles.

In the time domain, if both power and duration thresholds are passed an oscillation is said to be "detected".

FOOOF is a fast, efficient, and physiologically-informed tool to parameterize neural power spectra. FOOOF conceives of a model of the power spectrum as a combination of two distinct functional processes:

• An aperiodic component, reflecting 1/f like characteristics, with
• A variable number of periodic components (putative oscillations), as peaks rising above the aperiodic component

In short, it provides more robust and flexible way of parametising the aperiodic 1/f component of neural data.

As noted by Kosciessa et al., (2020), the standard BOSC analysis applies "a linear fit in log-log space to define the background power, which may overestimate the background at the frequencies of interest in the case of data with large rhythmic peaks."

The extended BOSC (eBOSC) toolbox uses MATLAB's robustfit function and allows the user to define peaks in the power spectrum, and these frequencies will not be used during the linear fit in log-log space.

However two problems remain:

This is an example where eBOSC hasn't worked very well. A linear fit is unsuitable for this dataset.

The parametisation tools from FOOOF can address these issues. Firstly, FOOOF performs a sequential decomposition of the power spectrum into aperiodic and periodic components, optimizing the modelled spectrum using a least-squared-error approach. Secondly, FOOOF can (optionally) fit a "knee" parameter during the aperiodic fit when the aperiodic features of the spectrum plotted in log-log space are not linear.

fBOSC seems to fit the 1/f aperiodic signal much better and therefore sets a more sensible power threshold for subsequent oscillation detection

YES!

In this example, I have simulated data with a nonlinear aperiodic frequency spectrum, alongside two oscillatory signals at 4Hz and 10Hz. The frequency spectrum is plotted in the thick black line.

The coloured dotted lines are the 1/f fits computed using BOSC (orange, no frequencies excluded) and eBOSC (pink, robustfit and frequencies around the theta and alpha peaks excluded), and fBOSC (blue).

Because we know apriori, the exact characteristics of the original aperiodic data, we can compute the root mean squared error (RMSE) from the 1/f fits estimated using BOSC, eBOSC and fBOSC:

The RMSE is consistently lower for fBOSC compared with the other two methods in this example.

In the worst circumstances, at a particular fixed threshold used in the chi-squared function (e.g. 0.99) your sensitivity for detecting oscillations will vary between different frequency bands.

THIS IS NOT IDEAL.

In our non-linear 1/f simulations, we can get drastically different hit-rates for theta and alpha oscillations when using both BOSC and eBOSC. However fBOSC has very similar hit-rates between theta and alpha at a given fixed threshold.

This is the same for false alarm rate:

From https://github.com/neurofractal/fBOSC

FOOOF was originally implemented in Python. The FOOOF documentation has clear + simple instructions for installing the package. You will also need to install scipy and numpy. When using fBOSC specify:

cfg.fBOSC.fooof.version           = 'python';

Getting MATLAB and python to talk properly is tricker. Please refer to this blog-post if you are having issues.

N.B. On my mac I had to rename /Applications/MATLAB_R2016b.app/sys/os/maci64/libgfortran.3.dylib to libgfortran.3.dylib.old to let Matlab search for the gcc gfortran

Using the python version of FOOOF is recommended, as the code has been robustly tested in a wide range of scenerios.

We have also implemented a MATLAB-only version of FOOOF, based on code from Brainstorm. To use this simply specify:

cfg.fBOSC.fooof.version           = 'matlab';

This code works, but has not been thoroughly tested within fBOSC. Use at your own risk.

cd(path_to_fBOSC);
start_fBOSC

Please note, this code is built upon the original BOSC and extended (eBOSC) implementations. These can be found in the /eBOSC folder and eBOSC/external/BOSC folder. Any new code (written by Robert A Seymour) is within /custom /experimental /media /simulation folders.

The license is GNU General Public License v3.0.

If you use this code please cite the following:

Kosciessa, J. Q., Grandy, T. H., Garrett, D. D., & Werkle-Bergner, M. (2020). Single-trial characterization of neural rhythms: Potential and challenges. Neuroimage, 206, 116331.

Citation for fBOSC coming soon

In addition, please think about citing the original authors of the FOOOF algorithm:

Donoghue, T., Haller, M., Peterson, E. J., Varma, P., Sebastian, P., Gao, R., ... & Voytek, B. (2020). Parameterizing neural power spectra into periodic and aperiodic components. Nature Neuroscience, 23(12), 1655-1665.

I would like to thank Kosciessa and colleagues; and Donoghue and colleagues for making their code openly available and freely editable.