Common methods to decompose the power spectra of neural voltage recordings suffer from model misspecification, leading to misinterpretations
Patrick F. Bloniasz1, Emily P. Stephen*2
1Graduate Program for Neuroscience, Boston University, Boston, USA 2Department of Mathematics and Statistics, Boston University, Boston, USA
*Email: estephen@bu.edu
Introduction The power spectra of neural voltage recordings (e.g. local field potentials, LFPs) show robust changes during a wide variety of brain states, showing both narrowband (i.e. rhythmic) and broadband (i.e. spanning a large frequency range) effects. Broadband effects have gained recent interest, and are interpreted in terms of asynchronous population activity [1] and the relative dominance of dynamic processes with different timescales (e.g. excitatory/inhibitory synaptic activity) [2,3]. Many decomposition approaches have been developed to algorithmically decompose power spectra into rhythmic and broadband components [4-9], leading to a large body of empirical results [10]. Nevertheless, many decomposition approaches have critical model misspecifications which can lead to systematic errors in the interpretation of power spectral effects.
Methods Here we use statistical theory and simulation to demonstrate how two kinds of model misspecification can lead to inaccuracies and misinterpretations of neural power spectra, and we present solutions. First, under the well-accepted standard model [11], LFPs are well-modeled by a linear-additive superposition of biophysical processes. In contrast, several decomposition methods implicitly assume a multiplicative superposition [6, 9]. Second, time-domain LFPs are typically modeled by Gaussian processes, so the empirical power spectra should be Gamma distributed, with variance scaling with power. However, many decomposition methods use a Gaussian model for neural power spectra [6,12] and assume homoscedasticity in variance.
Results Modeling LFPs as linear-additive superpositions of time-domain Gaussian processes, we demonstrate that: (1) the sampling distribution of the power spectrum is Gamma distributed, not homoscedastic Gaussian (2) using a misspecified model to decompose the power spectrum leads to systematic errors in both narrowband and broadband feature estimates (3) using a Gamma-Generalized Linear Model (GLM) with identity link function yields more accurate decompositions
We also present a more biophysically grounded simulation of LFPs using Filtered Point Processes [13], and show that: (1) it is consistent with the Gamma-GLM model (2) the decompositions can be directly interpreted as the population firing rate and the rhythmic power of the rate process of each modeled biophysical process (3) it accounts for cross-frequency coupling at short timescales
Discussion Based on these results, we recommend that researchers take caution in interpreting the results of existing spectral decomposition techniques, particularly with regard to the presence/height of rhythmic components and the height/slope of broadband components. Interpreting the power spectrum of neural voltage recordings in biophysical terms requires biophysically grounded statistical models with empirical validation. Our group aims to build and validate such models across brain states.
We would like to thank our funders: (Stephen) the Boston University Department for Mathematics and Statistics and the Boston University Center for Systems Neuroscience, (Bloniasz) NIH NINDS JSTPN T32NS131178, the NSF GRFP (2234657), and the Graduate Program for Neuroscience (GPN). We would also like to thank the following individuals for valuable feedback: Mark Kramer, Uri Eden, Thomas Donoghue.
