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Table of contents
Chapter 1 Neuroscience of general anesthesia
1.1 General anesthesia
1.2 General anesthetics
1.3 Anesthetics effects on single neurons (microscopic level)
1.3.1 Molecular targets of general anesthetics
1.3.2 Neuroanatomical targets of general anesthetics
1.4 Anesthetics effects on EEG signals (macroscopic level)
1.5 Current theories of general anesthesia
1.6 Conclusion
Chapter 2 Studying neural population models of EEG activity
2.1 Damped harmonic oscillator
2.2 Linear delay differential equations
2.2.1 Stability of delay differential equations
2.2.2 Power spectrum of delay differential equations
2.3 Neural population models
2.3.1 Neural field models
2.3.2 Thalamo-cortical circuits
2.3.3 Robinson model
2.3.4 A thalamo-cortical model to reproduce the EEG rhythms
2.4 Conclusion
Chapter 3 Modeling the anesthetic action on synaptic and extra-synaptic receptors
3.1 Function of extra-synaptic receptors
3.2 Effect of propofol on cortical and thalamic neural populations
3.3 EEG acquisition and the experimental observations
3.4 Theoretical power spectrum
3.5 Reproducing the experimental observations
3.5.1 The role of synaptic inhibition
3.5.2 The role of extra-synaptic inhibition
3.6 Induction of delta activity in EEG rhythms
3.7 Discussion
3.8 Conclusion
Chapter 4 Modeling of EEG power spectrum over frontal and occipital regions during propofol sedation
4.1 GABAergic inhibition in thalamic cells
4.2 Theoretical power spectrum
4.3 Experimental power spectrum
4.4 Power spectrum of full thalamo-cortical model
4.5 Reduced thalamo-cortical model
4.5.1 The role of different populations and anatomical loops
4.5.2 Frontal spectrum
4.5.3 Occipital spectrum
4.6 Discussion
4.6.1 Origin of spectral peaks
4.6.2 Multiple resting states
4.6.3 Effective sub-circuits in the cortico-thalamic model
4.6.4 Model limitations
4.7 Conclusion
Chapter 5 Spectral power fitting using stochastic optimization algorithms
5.1 Parameter estimation (inverse problem)
5.2 Optimization problem
5.2.1 Formulating an optimization problem
5.2.2 Objective function
5.2.3 Types of optimization methods
5.3 Optimization algorithms
5.3.1 Levenberg-Marquardt algorithm (LM)
5.3.2 Particle Swarm Optimization (PSO)
5.3.3 Differential evolution (DE)
5.3.4 Metropolis-Hastings (MH)
5.3.5 Simulated Annealing (SA)
5.4 Precision of the estimates
5.4.1 Confidence regions
5.4.2 Correlation analysis
5.4.3 Sensitivity analysis
5.5 Case Studies
5.5.1 Case Study I: A stochastic damped harmonic oscillator
5.5.2 Case Study II: A stochastic linear delay differential equation
5.5.3 Case Study III: A thalamo-cortical model reproducing the EEG rhythms .
5.6 Results of the parameter estimation in Case Studies I, II, and III
5.7 Discussion
5.8 Conclusion
References
