Stability and dynamics of a spectral graph model of brain oscillations

Abstract

We explore the stability and dynamic properties of a hierarchical, linearized, and analytic spectral graph model for neural oscillations that integrates the structuring wiring of the brain. Previously we have shown that this model can accurately capture the frequency spectra and the spatial patterns of the alpha and beta frequency bands obtained from magnetoencephalography recordings without regionally varying parameters. Here, we show that this macroscopic model based on long-range excitatory connections exhibits dynamic oscillations with a frequency in the alpha band even without any oscillations implemented at the mesoscopic level. We show that depending on the parameters, the model can exhibit combinations of damped oscillations, limit cycles, or unstable oscillations. We determined bounds on model parameters that ensure stability of the oscillations simulated by the model. Finally, we estimated time-varying model parameters to capture the temporal fluctuations in magnetoencephalography activity. We show that a dynamic spectral graph modeling framework with a parsimonious set of biophysically interpretable model parameters can thereby be employed to capture oscillatory fluctuations observed in electrophysiological data in various brain states and diseases.

Bayesian Inference of a Spectral Graph Model for Brain Oscillations

“…We compare the performance of SBI-SGM with the performance of the annealing SGM approach [39][40][41],…”

Spectral graph modeling reveals global slowing of neurophysiological network transmission in Alzheimer's disease

“…The model used here is similar to the SGM developed previously [25,26,66,67], and is described in detail in the supplementary document. Briefly, it is characterized by the following model parameters at the mesoscopic level: excitatory time constant (τ e ), inhibitory time constant (τ i ), excitatory gain (g ee , assumed to be 1 for parameter identifiability), inhibitory gain (g ii ), coupled population gain (g ei ); and the following model parameters at the macroscopic level: coupling constant (α), speed (v), graph excitatory time constant (τ G ).…”

“…Parameter initial guesses and bounds for estimating the static spectra are specified in Table 1. We defined three different bounds on the neural gain terms to ensure that the model is stable, based on prior work on model stability [66]. First, we supplied a larger bound on the neural gains for optimization.…”

Structure-function models of temporal, spatial, and spectral characteristics of non-invasive whole brain functional imaging

“…The structure of SGM is similar to that of Jansen-Rit model (Jansen and Rit, 1995 ; Sanz-Leon et al, 2015 ). Further methodological comparisons can be found elsewhere (Verma et al, 2022b ).…”

“…Since the development of the SGM, there have been various extensions as well. We recently improved SGM by enhancing the biophysical interpretability of the mesoscopic model (Verma et al, 2022a ), and subsequently demonstrated various stability properties of this improved model (Verma et al, 2022b ). In the latter, we also outlined a strategy to capture temporal fluctuations in MEG by fitting the SGM parameters to MEG frequency spectra at various time points.…”