A neural population model of the bi-phasic EEG-power spectrum during general anaesthesia

International audienceThe neuronal mechanisms of general anaesthesia are still poorly understood, though the induction of analgesia, amnesia, immobility and loss of consciousness by anaesthetic agents is well-established in hospital practice. To shed some light onto these mysterious effects, the chapter analyzes mathematically a neural field model describing the neural population dynamics by an integro-differential equation. The power spectrum is derived and compared to experimental results

Effects of the anesthetic agent propofol on neural populations

The neuronal mechanisms of general anesthesia are still poorly understood. Besides several characteristic features of anesthesia observed in experiments, a prominent effect is the bi-phasic change of power in the observed electroencephalogram (EEG), i.e. the initial increase and subsequent decrease of the EEG-power in several frequency bands while increasing the concentration of the anaesthetic agent. The present work aims to derive analytical conditions for this bi-phasic spectral behavior by the study of a neural population model. This model describes mathematically the effective membrane potential and involves excitatory and inhibitory synapses, excitatory and inhibitory cells, nonlocal spatial interactions and a finite axonal conduction speed. The work derives conditions for synaptic time constants based on experimental results and gives conditions on the resting state stability. Further the power spectrum of Local Field Potentials and EEG generated by the neural activity is derived analytically and allow for the detailed study of bi-spectral power changes. We find bi-phasic power changes both in monostable and bistable system regime, affirming the omnipresence of bi-spectral power changes in anesthesia. Further the work gives conditions for the strong increase of power in the δ-frequency band for large propofol concentrations as observed in experiments

Mathematical optimization in intensity modulated radiation therapy

The design of an intensity modulated radiotherapy treatment includes the selection of beam angles (geometry problem), the computation of an intensity map for each selected beam angle (intensity problem), and finding a sequence of configurations of a multileaf collimator to deliver the treatment (realization problem). Until the end of the last century research on radiotherapy treatment design has been published almost exclusively in the medical physics literature. However, since then, the attention of researchers in mathematical optimization has been drawn to the area and important progress has been made. In this paper we survey the use of optimization models, methods, and theories in intensity modulated radiotherapy treatment design

Mathematical optimization in intensity modulated radiation therapy

The design of an intensity modulated radiotherapy treatment includes the selection of beam angles (geometry problem), the computation of an intensity map for each selected beam angle (intensity problem), and finding a sequence of configurations of a multileaf collimator to deliver the treatment (realization problem). Until the end of the last century research on radiotherapy treatment design has been published almost exclusively in the medical physics literature. However, since then, the attention of researchers in mathematical optimization has been drawn to the area and important progress has been made. In this paper we survey the use of optimization models, methods, and theories in intensity modulated radiotherapy treatment design