Improving Quantification of Aperiodic (1/f) Dynamics: Bayesian Model Selection in SPRiNT

1845 

Abstract Submission 

Benjamin Lévesque Kinder¹, Luc Wilson¹, Jason da Silva Castanheira¹, Sylvain Baillet²

¹McGill University, Montreal, Quebec, ²Montreal Neurological Institute, Montreal, Quebec

Benjamin Lévesque Kinder  
McGill University
Montreal, Quebec

Luc Wilson  
McGill University
Montreal, Quebec

Jason da Silva Castanheira  
McGill University
Montreal, Quebec

Sylvain Baillet  
Montreal Neurological Institute
Montreal, Quebec

Neural oscillations are central to the study of neurophysiology (Buzsáki, 2006). These oscillatory dynamics are composed of rhythmic and arrhythmic components. Although the rhythmic components of these signals have been studied extensively, the arrhythmic components have largely been disregarded as noise despite being behaviourally (Albouy et al., 2017) and pathologically (Molina et al., 2020) meaningful. SPRiNT (Spectral Parametrization Resolved in Time; Wilson et al., 2021) characterizes the rhythmic and arrhythmic dynamics of neural oscillations by sequentially applying specparam (Donoghue et al., 2020) to the average of the time series bounded within a sliding window. This method allows users to quantify the evolution of the spectral parameters through time. But, because of its extension into the time-domain, SPRiNT is prone to fitting far more spurious peaks than regular specparam. To remedy this shortcoming, SPRiNT came outfitted with an optional peak post-processing step which uses a heuristic to prune spurious peaks. Although this peak post-processing is moderately effective, it makes the method more obtuse by adding an additional level of user tuning on top of specparam hyperparameter tuning. To improve the method, we implemented Bayesian model selection into SPRiNT (ms-SPRiNT).

At each time-point, the model selection algorithm initially fits the aperiodic component of the spectra and then creates an additional model for each peak it fits, up to the limit set by the user. Then, it selects the best model by weighting the additional goodness-of-fit provided by fitting the new peak against the loss of parsimony caused by the additional parameters. To accomplish this, the model selection algorithm selects the model with the lowest Bayesian information criterion.

To validate the use of model selection in SPRiNT, we ran SPRiNT and ms-SPRiNT with and without post-processing on 10'000 time series (60s duration each) with temporal dynamics in both the periodic and aperiodic components of the spectra. We used liberal hyperparameters.

We found that peak post-processing had a significant impact on SPRiNT's positive predictive value with relatively small loss in sensitivity; confirming that the amount of post-processing applied has a considerable impact on fit quality. We found that when we applied ms-SPRiNT to the same data ms-SPRiNT provided fits significantly better than SPRiNT without post-processing and provided similar fits to SPRiNT with post-processing. The highest quality fits came from the combination of ms-SPRiNT with post-processing where we saw a 37.5 percentage point increase to PPV as compared to SPRiNT without model selection.

Independent of processing applied, the absolute error of the aperiodic exponent and absolute error of the aperiodic offset did not vary. This shows that additional processing does not affect the error in the aperiodic component of the signal. Also, we found that irrespective of processing, SPRiNT does not tend to fit spectra with more than 3 peaks, so it shows root-like trends on simulation-detection matrices.

We improved upon the original SPRiNT algorithm by implementing Bayesian model selection, and proposed improved hyperparameter and post-processing parameter recommendations. Because SPRiNT is based on specparam, it tends to overfit peaks before post-processing. This issue is compounded by the decrease in signal-to-noise ratio intrinsic to averaging across contiguous time windows. In the original version of SPRiNT judicious selection of hyperparameters and post-processing parameters was crucial to the quality of the fit. This makes analysis and data sharing more difficult. To address this issue, we implemented model selection which allows for far more liberal hyperparameters and rivals optimal post-processing in its performance. This significantly lowers the barrier of entry to using SPRiNT.

Bayesian Modeling

EEG/MEG Modeling and Analysis ²

Methods Development ¹

Neurophysiology of Imaging Signals

Data analysis

ELECTROPHYSIOLOGY

MEG

Modeling

Open-Source Code

Statistical Methods