MATHANA: Mathematical Analysis of Anaesthesia (funded by an ERC Starting Grant (20112015)) Description: General anaesthesia is an important method in today's hospital practice and especially in surgery. To supervise the depth of anaesthesia during surgery, the anaesthesist applies electroencephalography (EEG) and monitors the brain activity of the subject on the scalp. The applied monitoring machine calculates the change of the power spectrum of the brain signals to indicate the anaesthetic depth. This procedure is based on the finding that the concentration increase of the anaesthetic drug changes the EEGpower spectrum in a significant way. Although this procedure is applied worldwide, the underlying neural mechanism of the spectrum change is still unknown. The project aims to elucidate the underlying neural mechanism by a detailed investigating a mathematical model of neural populations. The investigation is based on analytical calculations in a neural population model of the cortex involving intrinsic neural properties of brain areas and feedback loops to other areas, such as the loop between the cortex and the thalamus. Currently, there are two proposed mechanisms for the charactertisic change of the power spectrum: a highly nonlinear jump in the activation (socalled phase transition) and a linear behaviour. The project mainly focusses on the nonlinear jump to finally rule it out or support it. A subsequent comparison to previous experimenta results aims to fit the physiological parameters. Since the cortex population is embedded into a network of other cortical areas and the thalamus, the corresponding analytical investigations takes into account external stochastic (from other brain areas) and timeperiodic (thalamic) forces. To this end it is necessary to develop several novel nonlinear analysis technique of neural populations to derive the power spectrum close to the phase transition and conditions for physiological parameters. Researchers:
Principal Investigator 



Postdoctoral Researcher 



Software Engineer 



Meysam Hashemi PhDstudent 

Press publications :
Interview with Republicain Lorraine, March 2011
Scientific publications :
A. Hutt and L. Buhry, Study of GABAergic extrasynaptic tonic inhibition in single neurons and neural populations by traversing neural scales: application to propofolinduced anaesthesia, Journal of Computational Neuroscience, in press (2014)
K. K. Sellers, D. V. Bennett, A. Hutt and F. Frohlich, Anesthesia Differentially Modulates Spontaneous Network Dynamics by Cortical Area and Layer, Journal of Neurophysiology 110, 27392751 (2013)
J. Lefebvre and A. Hutt, Additive noise quenches delayinduced oscillations, Europhysics Letters 102 60003 (2013)
A. Hutt and L. Zhang, Distributed nonlocal feedback delays may destabilize fronts in neural fields, distributed transmission delays do not, accepted by Journal Mathematical Neuroscience (2013)
P. beim Graben and A. Hutt, Detecting metastable states of dynamical systems by recurrencebased symbolic dynamics, Physical Review Letters 110, 154101 (2013)
A. Hutt, The anaesthetic propofol shifts the frequency of maximum spectral power in EEG during general anaesthesia: analytical insights from a linear model, Frontiers in Computational Neuroscience 7, 2 (2013)
J. Lefebvre, A. Hutt, V.G. LeBlanc and A. Longtin, Reduced dynamics for delayed systems with harmonic or stochastic forcing, Chaos 22, 043121 (2012)
A. Hutt, J. Lefebvre, A. Hutt, A. Longtin, Delay stabilizes stochastic systems near an nonoscillatory instability, Europhysics Letters 98, 20004 (2012)
A. Hutt, The population firing rate in the presence of GABAergic tonic inhibition in single neurons and application to general anaesthesia, Cognitive Neurodynamics 6, 227237 (2012)
A.Hutt, A neural population model of the biphasic EEGpower spectrum during general anaesthesia, in A. Hutt (Ed.), Sleep and Anesthesia: Neural correlates in theory and experiments, Springer (2011)
A.Hutt (Editor), Sleep and Anesthesia: Neural correlated in theory and experiments, SpringerVerlag (2011)
Software :
The Neural Field Simulator allows to integrate numerically an integraldifferential equation involving finite transmission speed in two spatial dimensions.
It is planned to add a GUI to visualize the solution in space and time.
Updated : August 2014