, Volume 16, Issue 2, pp 231–251 | Cite as

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

  • Meysam Hashemi
  • Axel Hutt
  • Laure Buhry
  • Jamie Sleigh
Original Article


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 Optimization Stochastic differential equation Spectral power General anesthesia 



The authors acknowledge funding from the European Research Council for support under the European Union’s Seventh Framework Programme (FP7/2007-2013)/ERC grant agreement no. 257253.

Supplementary material

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12021_2018_9369_MOESM2_ESM.pdf (190 kb)
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Authors and Affiliations

  • Meysam Hashemi
    • 1
  • Axel Hutt
    • 2
    • 3
  • Laure Buhry
    • 4
    • 5
    • 6
  • Jamie Sleigh
    • 7
  1. 1.INSERM, INS, Institut de Neurosciences des SystèmesAix Marseille UniversitéMarseilleFrance
  2. 2.German Meteorology ServiceOffenbach am MainGermany
  3. 3.Department of Mathematics and StatisticsUniversity of ReadingReadingUK
  4. 4.INRIA Grand Est - Nancy, Team NEUROSYS, 615 rue du Jardin BotaniqueVillers-lès-NancyFrance
  5. 5.CNRS, Loria, UMR nō 7503Vandoeuvre-lès-NancyFrance
  6. 6.Université de Lorraine, Loria, UMR nō 7503Vandoeuvre-lès-NancyFrance
  7. 7.University of AucklandHamiltonNew Zealand

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