Dynamics and precursor signs for phase transitions in neural systems

This thesis investigates neural state transitions associated with sleep, seizure and anaesthesia. The aim is to address the question: How does a brain traverse the critical threshold between distinct cortical states, both healthy and pathological? Specifically we are interested in sub-threshold neural behaviour immediately prior to state transition. We use theoretical neural modelling (single spiking neurons, a network of these, and a mean-field continuum limit) and in vitro experiments to address this question. Dynamically realistic equations of motion for thalamic relay neuron, reticular nuclei, cortical pyramidal and cortical interneuron in different vigilance states are developed, based on the Izhikevich spiking neuron model. A network of cortical neurons is assembled to examine the behaviour of the gamma-producing cortical network and its transition to lower frequencies due to effect of anaesthesia. Then a three-neuron model for the thalamocortical loop for sleep spindles is presented. Numerical simulations of these networks confirms spiking consistent with reported in vivo measurement results, and provides supporting evidence for precursor indicators of imminent phase transition due to occurrence of individual spindles. To complement the spiking neuron networks, we study the Wilson–Cowan neural mass equations describing homogeneous cortical columns and a 1D spatial cluster of such columns. The abstract representation of cortical tissue by a pair of coupled integro-differential equations permits thorough linear stability, phase plane and bifurcation analyses. This model shows a rich set of spatial and temporal bifurcations marking the boundary to state transitions: saddle-node, Hopf, Turing, and mixed Hopf–Turing. Close to state transition, white-noise-induced subthreshold fluctuations show clear signs of critical slowing down with prolongation and strengthening of autocorrelations, both in time and space, irrespective of bifurcation type. Attempts at in vitro capture of these predicted leading indicators form the last part of the thesis. We recorded local field potentials (LFPs) from cortical and hippocampal slices of mouse brain. State transition is marked by the emergence and cessation of spontaneous seizure-like events (SLEs) induced by bathing the slices in an artificial cerebral spinal fluid containing no magnesium ions. Phase-plane analysis of the LFP time-series suggests that distinct bifurcation classes can be responsible for state change to seizure. Increased variance and growth of spectral power at low frequencies (f < 15 Hz) was observed in LFP recordings prior to initiation of some SLEs. In addition we demonstrated prolongation of electrically evoked potentials in cortical tissue, while forwarding the slice to a seizing regime. The results offer the possibility of capturing leading temporal indicators prior to seizure generation, with potential consequences for understanding epileptogenesis. Guided by dynamical systems theory this thesis captures evidence for precursor signs of phase transitions in neural systems using mathematical and computer-based modelling as well as in vitro experiments

Electroencephalogram fractal dimension as a measure of depth of anesthesia

This paper proposes a combined method including adaptive segmentation and Higuchi fractal dimension (HFD) of electroencephalograms (EEG) to monitor depth of anesthesia (DOA). The EEG data was captured in both ICU and operating room and different anesthetic drugs, including propofol and isoflurane were used. Due to the nonstationary nature of EEG signal, adaptive segmentation methods seem to have better results. The HFD of a single channel EEG was computed through adaptive windowing methods consist of adaptive variance and auto correlation function (ACF) based methods. We have compared the results of fixed and adaptive windowing in different methods of calculating HFD in order to estimate DOA. Prediction probability (Pk) was used as a measure of correlation between the predictors and BIS index to evaluate our proposed methods. The results show that HFD increases with increasing BIS index. In ICU, all of the methods reveal better performance than in other groups. In both ICU and operating room, the results indicate no obvious superiority in calculating HFD through adaptive segmentation

Extraction of BIS™ index sub-parameters in different anesthetic and sedative levels

Monitoring the depth of anesthesia is important to prevent undesirable events during surgery. According to direct effect of anesthetic drugs on synaptic activity of neurons and after presentation of anesthesia depth monitor (BIS) in 1996, there was a great interest on electroencephalogram analysis to investigate depth of anesthesia. Now there are large numbers of methods and algorithms in this field and every new method is compared with BIS index. BIS algorithm is based on three sub-parameters including time, frequency and higher order statistics domain parameters but the detailed algorithm is not in the public domain. In this paper, proper methods are presented for calculating three sub-parameters. Results of applying these methods to collected clinical data are presented. Efficiency of these methods will be evaluated based on appropriate statistical analysis

Which System Variables Carry Robust Early Signs of Upcoming Phase Transition? An Ecological Example.

Growth of critical fluctuations prior to catastrophic state transition is generally regarded as a universal phenomenon, providing a valuable early warning signal in dynamical systems. Using an ecological fisheries model of three populations (juvenile prey J, adult prey A and predator P), a recent study has reported silent early warning signals obtained from P and A populations prior to saddle-node (SN) bifurcation, and thus concluded that early warning signals are not universal. By performing a full eigenvalue analysis of the same system we demonstrate that while J and P populations undergo SN bifurcation, A does not jump to a new state, so it is not expected to carry early warning signs. In contrast with the previous study, we capture a significant increase in the noise-induced fluctuations in the P population, but only on close approach to the bifurcation point; it is not clear why the P variance initially shows a decaying trend. Here we resolve this puzzle using observability measures from control theory. By computing the observability coefficient for the system from the recordings of each population considered one at a time, we are able to quantify their ability to describe changing internal dynamics. We demonstrate that precursor fluctuations are best observed using only the J variable, and also P variable if close to transition. Using observability analysis we are able to describe why a poorly observable variable (P) has poor forecasting capabilities although a full eigenvalue analysis shows that this variable undergoes a bifurcation. We conclude that observability analysis provides complementary information to identify the variables carrying early-warning signs about impending state transition

Relationship between consciousness and electrical activity of brain neurons in patients undergoing aortic valve replacement surgery

Background & Objective: Monitoring the depth of anesthesia is very important to prevent undesirable events during surgery, such as intra operative awareness and overdosing. It is shown that anesthetic agents have direct effects on synaptic activity of brain neurons. So there is a great interest on electroencephalogram analysis as a depth of anesthesia estimator. Due to difficulties in visual explanation of EEG, automatic and computer based signal processing methods have been used to assess the depth of anesthesia. Investigating the relationship between conscious level of patients and electrical activity of brain neurons was the main aim of this study. Materials & Methods: In this study, EEG signals of six patients undergoing aortic valve replacement surgery have been acquired and recorded in a computer. After applying signal processing methods to these data, 3 different measures included temporal, spectral and bispectral parameters have been extracted. Mean values of mentioned parameters in different anesthetic regimens and levels have been analyzed by ANOVA in SPSS software. Results: Extracted temporal parameter is correlated with depth of anesthesia in deep anesthetic levels and spectral one is correlated with depth of anesthesia in moderate and light levels (P<0.05). Bispectral parameter is correlated with the depth of anesthesia only in ICU (P<0.05). Conclusion: Findings of this study confirm the relationship between consciousness and electrical activity of brain neurons and recommend the use of EEG processing techniques to monitor, control and estimate the depth of anesthesia in operating room and ICU ward

Numerically obtained fluctuation variance of model variables prior to saddle-node bifurcation.

<p>(a–d) For each value of <i>μ</i>_<i>P</i>, starting with <i>μ</i>_<i>P</i> = 0.4, the model is simulated for 60,000 time units with resolution of 0.01 time units, from which the population variances are computed. <i>μ</i>_<i>P</i> is incremented geometrically towards the catastrophic collapse at <i>μ</i>_<i>P</i> = <i>μ</i>_<i>B</i>₂. Death rates are perturbed every time unit using white noise with standard deviation of <i>σ</i>_noise = 2 × 10⁻⁶. (a) Noise added to the juvenile population (b) Noise added to the adult population (c). Independent noise added to all three populations. (d) Identical, fully correlated, noise added to all three populations. (e) An extra experiment where noise is added to <i>P</i> only population.</p