Optimal Model Parameter Estimation from EEG Power Spectrum Features Observed during General Anesthesia

Abstract

Mathematical modeling is a powerful tool that enables researchers to describe the experimentally observed dynamics of complex systems. Starting with a robust model including model parameters, it is necessary to choose an appropriate set of model parameters to reproduce experimental data. However, estimating an optimal solution of the inverse problem, i.e., finding a set of model parameters that yields the best possible fit to the experimental data, is a very challenging problem. In the present work, we use different optimization algorithms based on a frequentist approach, as well as Monte Carlo Markov Chain methods based on Bayesian inference techniques to solve the considered inverse problems. We first probe two case studies with synthetic data and study models described by a stochastic non-delayed linear second-order differential equation and a stochastic linear delay differential equation. In a third case study, a thalamo-cortical neural mass model is fitted to the EEG spectral power measured during general anesthesia induced by anesthetics propofol and desflurane. We show that the proposed neural mass model fits very well to the observed EEG power spectra, particularly to the power spectral peaks within δ - (0 - 4 Hz) and α - (8 - 13 Hz) frequency ranges. Furthermore, for each case study, we perform a practical identifiability analysis by estimating the confidence regions of the parameter estimates and interpret the corresponding correlation and sensitivity matrices. Our results indicate that estimating the model parameters from analytically computed spectral power, we are able to accurately estimate the unknown parameters while avoiding the computational costs due to numerical integration of the model equations.

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

“…Since the computational demands of fitting our model directly to EEG time series data are prohibitive, we fit the EEG spectrum instead. This approach is in accordance with earlier fits of neural population models [50, 61, 62], which involved fewer unknown parameters than we have here, and generally only fit a single EEG spectrum. We are thus assuming stationarity of the system over the one-minute EEG signal, where stationarity here means that it is the parameters that are constant; the states are allowed to vary about a stable fixed point.…”

“…Unlike in systems biology modeling, in neurophysical modeling there has been little recognition of the problem of unidentifiability, beyond select examples in neural code models [49], a thalamo-cortical neural population model [50], and dynamic causal models [51]. This has been cited in [52] as an example of how approaches used in systems biology can help address problems in computational neuroscience [53].…”

On the influence of prior information evaluated by fully Bayesian criteria in a personalized whole-brain model of epilepsy spread

“…The parameter estimation within a Bayesian framework is treated as the quantification and propagation of uncertainty, defined via a probability, in the light of observations [4]. The uncertainty over the range of possible parameter values is also estimated, rather than a single point estimate (e.g., the maximum likelihood estimate) in the frequentist approach [3].…”

“…However, the intrinsic uncertainty associated with parameters of dynamical models translates into uncertainty in model predictions, thereby, in the model selection among a set of candidates having best balance between complexity and accuracy. In practice, the nonlinearity and complexity of most dynamical models render the model calibration and hypothesis testing nontrivial [1][2][3][4]. Bayesian framework offers a powerful approach to deal with model uncertainty in parameter estimation, and a principled method for model prediction with a broad range of applications [5][6][7][8][9][10][11][12][13].…”

Inference of brain networks with approximate Bayesian computation – assessing face validity with an example application in Parkinsonism

“…This approach can be formalized, using algorithmic schemes for parameter estimation ( Rowe et al., 2004 ; Wendling et al., 2009 ). More recently, Bayesian optimization schemes provide a principled way of including prior knowledge of a system when computing an inverse model ( Moran et al., 2009 ; Hadida et al., 2018 ; Hashemi et al., 2018 ). These approaches can estimate the posterior distribution over model parameters (i.e.…”