Modeling the effects of anesthesia on the electroencephalogram

Abstract

Changes to the electroencephalogram (EEG) observed during general anesthesia are modeled with a physiological mean field theory of electrocortical activity. To this end a parametrization of the postsynaptic impulse response is introduced which takes into account pharmacological effects of anesthetic agents on neuronal ligand-gated ionic channels. Parameter sets for this improved theory are then identified which respect known anatomical constraints and predict mean firing rates and power spectra typically encountered in human subjects. Through parallelized simulations of the eight nonlinear, two-dimensional partial differential equations on a grid representing an entire human cortex, it is demonstrated that linear approximations are sufficient for the prediction of a range of quantitative EEG variables. More than 70,000 plausible parameter sets are finally selected and subjected to a simulated induction with the stereotypical inhaled general anesthetic isoflurane. Thereby 86 parameter sets are identified that exhibit a strong "biphasic" rise in total power, a feature often observed in experiments. A sensitivity study suggests that this "biphasic" behavior is distinguishable even at low agent concentrations. Finally, our results are briefly compared with previous work by other groups and an outlook on future fits to experimental data is provided.

Effects of the anesthetic agent propofol on neural populations

“…$ X K E,I (x)dx = 1. This nonlocal approach generalizes previous diffusive models ( Steyn-Ross et al 2001a;Rennie et al 2002;Bojak and Liley 2005) by considering higher spatial derivatives Coombes et al 2007).…”

“…The function f(p) quantifies the action of the propofol concentration on the inhibitory synapses and will be specified in section ''The weighting factor p''. A similar model approach has been taken in previous studies to study the transitions in general anesthesia (Steyn-Ross et al 2001a;Bojak and Liley 2005). Further a e and a i denote the synaptic gain or level excitation and inhibition, respectively.…”

“…Since this activity spread may be viewed as increases of the rise and decay time of the activity, essentially the activity propagation increases the rise and decay time of the synaptic impulse response function h e and thus decreases the rate constants a 1 , a 2 . To handle this parameter problem, previous neuron ensemble studies have either taken into account explicitly estimates of the physiological structure (Wright and Kydd 1992;Liley 2001, 1995) or have chosen suitable model parameters to fit optimally experimental encephalographic activity (Robinson et al 2001(Robinson et al , 2004Bojak and Liley 2005). The present work takes a slightly different approach and aims to classify the ensemble dynamics as general as possible while ruling out totally unphysiological parameter regimes.…”

“…The latter theoretical studies (Steyn-Ross and SteynRoss 1999; Bojak and Liley 2005;Molaee-Ardekani et al 2007) are based on the model of Liley et al (1999), whose basic elements we discuss briefly in the following. The model considers a continuous spatial mean-field of neurons in one or two spatial dimensions, synapses and axonal connections; the synapses and neurons may be excitatory and inhibitory.…”

An analysis of the transitions between down and up states of the cortical slow oscillation under urethane anaesthesia

“…Indeed, our range of time constants is typical of that used in neural modelling. For example, Bojak and Liley allowed the somatic time constants to range from 5 to 150 ms [30] and Steyn-Ross et al have used 50 ms [31]. We find that the time constants are correlated with the membrane potential of the down state (R = −0.47, with a probability of obtaining such a correlation assuming uncorrelated variables as p = 0.0047), presumably because of changes in potassium channel conductance in the down state.…”