Parameter estimation and identifiability in a neural population model for electro-cortical activity

Abstract

Electroencephalography (EEG) provides a non-invasive measure of brain electrical activity. Neural population models, where large numbers of interacting neurons are considered collectively as a macroscopic system, have long been used to understand features in EEG signals. By tuning dozens of input parameters describing the excitatory and inhibitory neuron populations, these models can reproduce prominent features of the EEG such as the alpha-rhythm. However, the inverse problem, of directly estimating the parameters from fits to EEG data, remains unsolved. Solving this multi-parameter non-linear fitting problem will potentially provide a real-time method for characterizing average neuronal properties in human subjects. Here we perform unbiased fits of a 22-parameter neural population model to EEG data from 82 individuals, using both particle swarm optimization and Markov chain Monte Carlo sampling. We estimate how much is learned about individual parameters by computing Kullback-Leibler divergences between posterior and prior distributions for each parameter. Results indicate that only a single parameter, that determining the dynamics of inhibition, is directly identifiable, while other parameters have large, though correlated, uncertainties. We show that the eigenvalues of the Fisher information matrix are roughly uniformly spaced over a log scale, indicating that the model is sloppy, like many of the regulatory network models in systems biology. These eigenvalues indicate that the system can be modeled with a low effective dimensionality, with inhibition being prominent in driving system behavior. Author summaryElectroencephalography (EEG), where electrodes are used to measure electric potential on the outside of the scalp, provides a simple, non-invasive way to study brain activity. Physiological interpretation of features in EEG signals has often involved use of collective models of neural populations. These neural population models have dozens of input parameters to describe the properties of inhibitory and excitatory neurons. Being able to estimate these parameters by direct fits to EEG data holds the promise of providing a real-time non-invasive method of inferring neuronal properties in different December 5, 2018 1/27 individuals. However, it has long been impossible to fit these nonlinear, multi-parameter models effectively. Here we describe fits of a 22-parameter neural population model to EEG spectra from 82 different subjects, all exhibiting alpha-oscillations. We show how only one parameter, that describing inhibitory dynamics, is constrained by the data, although all parameters are correlated. These results indicate that inhibition plays a central role in the generation and modulation of the alpha-rhythm in humans. Introduction1 The classical alpha rhythm is one of the most remarkable features observed in 2 electroencephalogram (EEG) recordings from humans [1, 2]. First discovered by Berger 3 in the 1920s [3, 4] these waxing and waning oscillations of 8 -13 Hz, that are prominent 4 during eyes-closed...

Inferring a simple mechanism for alpha-blocking by fitting a neural population model to EEG spectra

“…The EEG data used in this study is provided in the online repository [38] 72 (https://www.physionet.org/pn4/eegmmidb/). We use data from the occipital electrode 73 from 82 individuals, as in our previous study [33], although this time we use eyes-open 74 as well as eyes-closed data. We apply Welch's method [39] to estimate the 2 × 82 power 75 spectra.…”

“…Here we use the Jensen-Shannon divergence, D JS , which provides a 90 scalar measure of the difference in shape between (normalized) eyes-closed (EC) and The model used in this paper is the local variant of the mean-field model originally 102 described in Refs [22,26]. As described in our previous study [33], this model consists of 103 10 coupled non-linear ODEs parameterized by 22 physiologically-motivated parameters 104 (see Table 1). Local equations are linearized around a fixed point and the power 105 spectral density (PSD) is derived assuming a stochastic driving signal of the excitatory 106 population that represents thalamo-cortical and long range cortico-cortical inputs, 107 assumed to be Gaussian white noise.…”

“…For example, 26 alpha attenuation has been attributed to coincident changes in several thalamo-cortical 27 parameters controlling the feedforward, cortico-thalamo-cortical, and intra-cortical 28 circuits [32]. 29 A fundamental challenge in using neural population models is the difficulty in 30 estimating parameter values directly from fits to EEG data [33]. Although forward 31 calculations have provided plausible explanations for spontaneous alpha generation, 32 solving the inverse problem to determine the many unknown model parameters is 33 crucial if we want to relate the subject-to-subject variability observed in EEG signals to 34 an associated variability in certain microscopic parameters.…”

“…29 A fundamental challenge in using neural population models is the difficulty in 30 estimating parameter values directly from fits to EEG data [33]. Although forward 31 calculations have provided plausible explanations for spontaneous alpha generation, 32 solving the inverse problem to determine the many unknown model parameters is 33 crucial if we want to relate the subject-to-subject variability observed in EEG signals to 34 an associated variability in certain microscopic parameters. This will help identify (and 35 potentially control) the underlying microscopic drivers of the EEG response, and fitting to EEG spectra exhibiting alpha oscillations from subjects with their eyes closed.…”

“…We refer to this as the 2-state fitting problem since this will involve fitting two 54 spectra (eyes closed and eyes open) from a single individual. Thus our previous 55 study [33], where we only fit to the eyes-closed spectra in each individual, was a 1-state 56 fitting problem. 57 Naively, it would seem that the unidentifiability we found for the 1-state problem 58 would doom the 2-state fitting problem since one seemingly needs to perform separate 59 fits to each state.…”