Estimation of the depth of anaesthesia from interacting physiological oscillators

Nowadays, physiological monitoring is imperative for the safety of medical operations. However, systems which monitor the depth of anaesthesia are still far from reliable, such that still some patients may experience the trauma of remaining conscious under general anaesthesia during surgery. The long term goal of our interdisciplinary project "BRACCIA" was to develop a device to measure the depth of anaesthesia. And, in view of this important goal, the main objective of research was to establish how the couplings between the cardiac, respiratory and cortical oscillations change in anaesthesia. Under the framework of this project, our objectives were: 1) The detection of the deep-light change of anaesthesia from experimental recordings on rats, and furthermore, the investigation of the interdependencies among three physiological activities, namely, the cardiac activity (H), respiration (R) and cortical activities (B) from experimental recordings of rats and humans, for each state of the depth of anaesthesia. 2) The modelling of the slow brain waves, and to consider the effect of anaesthesia on this realized model. The analysis of the recordings were carried out with five methods. First method is the "S-estimator", which indirectly quantifies the amount of synchronization within a data set measuring the contraction of the embedding dimension of the state space. Second method is the "new S-estimator". In this new one, a linear transformation of the reconstructed state space trajectory orthonormalizes the state variables within each model such that global state space volume reduction becomes a measure of synchronization exclusively between the different models. Third method is the "embedding dimension analysis", which examines the time evolution of the embedding dimension obtained with false nearest neighbors method on each windowed time series. The last two methods consist in a more detailed analysis of the dependencies among three systems. Fourth method is the "coupling matrix". This calculates the coupling matrix, CM, which infers linear interactions between multivariate time series after constructing separately the self model of each signal from reconstructed states. The last method is the "nonparametric Granger causality". This method calculates the Granger causality, GC, which measures bivariate causal influence in frequency domain. Here, a nonparametric estimation approach was used to remove the difficulties such as uncertainty in model parameters. For this method, permutation tests are added to figure out the real causality. From the obtained results, in most of the groups of experimental recordings, a change in the synchronization inside of the whole system between deep and light anaesthesia or between resting state and anaesthesia was found. For the results on Ketamine-Xylazine (KX) anaesthetized rats, a decrease of this synchronization was so clear that we succeeded to detect the deep-light transition of the anaesthesia, and automatically in one group of the recordings. The changes in the synchronization exclusively between three sub-systems as measured with the "new S-estimator" was only found on the results on Pentobarbital anaesthetized rats. Interestingly, a change in the time evolution of the embedding dimension was found on B and H in most of the results of the recordings. Furthermore, some changes in the couplings were found according to the depth of anaesthesia. For KX anaesthetized rats and human, coupling direction change was also observed. The nonparametric GC agreed for some causality change obtained with coupling matrix, but still some disagreements remained. From our literature study about the rhythmic activity of the brain, we deduce that it is generally accepted in the neuroscience community that the rhythms of the EEG are created by the interaction between the cortex and the thalamus. Consequently, we chose one of the Hodgkin-Huxley based model which considers the thalamocortical assemblies, the model of Bazhenov et al. This model includes four layers of neurons where two of them are for the thalamus (RE: thalamic reticular neuron, TC: thalamic relay neuron) and the other two are for the cortex (PY: pyramidal neuron, IN: interneuron). Not without having difficulties to set parameters and equations, we succeeded to reproduce this model and simulated it. Furthermore, we performed simulations on this model varying the parameter of maximal conductance of Ca2+ channels or the closing/opening rate of GABAA receptors from one simulation to another, and determined how the collective behavior of PY neurons, which should be interpreted as a field potential analogous to the EEG can be modified according to these parameter changes. Finally, to understand the model itself, some studies on the reproduced model were carried out. As a results, from observing the collective spiking activity of the PY cells on the reproduced Bazhenov model, we confirmed the presence of slow oscillations, namely the δ-waves. The reaction of the model to changes of the parameters related to anesthetics showed that reinforcement of the inhibition that suppresses the spiking activities was effectively induced by all changes of the parameters, but the degree of this reaction was different in each case. From the studies of the size of the model, we found that the local synchrony and the mean field frequency is not influenced by the size of network, but the global synchrony is not preserved at larger sizes. In conclusion, our data analysis studies showed a clear possibility for the detection of the depth of anaesthesia and a clear change in the interdependency changes depending on the anaesthesia. Moreover, our modelling study took an essential step for the investigation of the effect of anaesthesia on a brain model. As future work, all the unsolved problems which appear in the analysis chapter of this thesis should be treated, but especially the embedding dimension analysis should be followed up in detail. For modelling, as we just made the first step, we should continue with the understanding of the model and the closing of the gap between the mathematical model and the reality.

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