Filtered Point Processes Tractably Capture Rhythmic And Broadband Power Spectral Structure in Neural Electrophysiological Recordings

Neural electrophysiological recordings arise from interacting rhythmic (oscillatory) and broadband (aperiodic) biological subprocesses. Both rhythmic and broadband processes contribute to the neural power spectrum, which decomposes the variance of a neural recording across frequencies. Although an extensive body of literature has successfully studied rhythms in various diseases and brain states, researchers only recently have systematically studied the characteristics of broadband effects in the power spectrum. Broadband effects can generally be categorized as 1) shifts in power across all frequencies, which correlate with changes in local firing rates and 2) changes in the overall shape of the power spectrum, such as the spectral slope or power law exponent. Shape changes are evident in various conditions and brain states, influenced by factors such as excitation to inhibition balance, age, and various diseases. It is increasingly recognized that broadband and rhythmic effects can interact on a sub-second timescale. For example, broadband power is time-locked to the phase of < 1 Hz rhythms in propofol induced unconsciousness. Modeling tools that explicitly deal with both rhythmic and broadband contributors to the power spectrum and that capture their interactions are essential to help improve the interpretability of power spectral effects. Here, we introduce a tractable stochastic forward modeling framework designed to capture both narrowband and broadband spectral effects when prior knowledge or theory about the primary biophysical processes involved is available. Population-level neural recordings are modeled as the sum of filtered point processes (FPPs), each representing the contribution of a different biophysical process such as action potentials or postsynaptic potentials of different types. Our approach builds on prior neuroscience FPP work by allowing multiple interacting processes and time-varying firing rates and by deriving theoretical power spectra and cross-spectra. We demonstrate several properties of the models, including that they divide the power spectrum into frequency ranges dominated by rhythmic and broadband effects, and that they can capture spectral effects across multiple timescales, including sub-second cross-frequency coupling. The framework can be used to interpret empirically observed power spectra and cross-frequency coupling effects in biophysical terms, which bridges the gap between theoretical models and experimental results.