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

Chimera states in a multi-weighted neuronal network

There are multiple types of interactions among neurons, each of which has a remarkable effect on the neurons' behavior. Due to the significance of chimeras in neural processes, in this paper, we study the impact of different electrical, chemical, and ephaptic couplings on the emergence of chimera. Consequently, a multi-weighted small-world network of neurons is considered. The simultaneous effects of two and three couplings are explored on the chimera and complete synchronization. The results represent that the synchronization is achieved in very small coupling strengths in the absence of chemical synapses. In contrast, without electrical synapses, the neurons only exhibit chimera behavior. In the three-weighted network, the synchronization is enhanced for special chemical coupling strengths. The network with directed links is also examined. The general behaviors of the directed and undirected networks are the same; however, the directed links lead to lower synchronization error

Memristors for the Curious Outsiders

We present both an overview and a perspective of recent experimental advances and proposed new approaches to performing computation using memristors. A memristor is a 2-terminal passive component with a dynamic resistance depending on an internal parameter. We provide an brief historical introduction, as well as an overview over the physical mechanism that lead to memristive behavior. This review is meant to guide nonpractitioners in the field of memristive circuits and their connection to machine learning and neural computation.Comment: Perpective paper for MDPI Technologies; 43 page

Dynamic models of brain imaging data and their Bayesian inversion

This work is about understanding the dynamics of neuronal systems, in particular with respect to brain connectivity. It addresses complex neuronal systems by looking at neuronal interactions and their causal relations. These systems are characterized using a generic approach to dynamical system analysis of brain signals - dynamic causal modelling (DCM). DCM is a technique for inferring directed connectivity among brain regions, which distinguishes between a neuronal and an observation level. DCM is a natural extension of the convolution models used in the standard analysis of neuroimaging data. This thesis develops biologically constrained and plausible models, informed by anatomic and physiological principles. Within this framework, it uses mathematical formalisms of neural mass, mean-field and ensemble dynamic causal models as generative models for observed neuronal activity. These models allow for the evaluation of intrinsic neuronal connections and high-order statistics of neuronal states, using Bayesian estimation and inference. Critically it employs Bayesian model selection (BMS) to discover the best among several equally plausible models. In the first part of this thesis, a two-state DCM for functional magnetic resonance imaging (fMRI) is described, where each region can model selective changes in both extrinsic and intrinsic connectivity. The second part is concerned with how the sigmoid activation function of neural-mass models (NMM) can be understood in terms of the variance or dispersion of neuronal states. The third part presents a mean-field model (MFM) for neuronal dynamics as observed with magneto- and electroencephalographic data (M/EEG). In the final part, the MFM is used as a generative model in a DCM for M/EEG and compared to the NMM using Bayesian model selection

Whole Brain Network Dynamics of Epileptic Seizures at Single Cell Resolution

Epileptic seizures are characterised by abnormal brain dynamics at multiple scales, engaging single neurons, neuronal ensembles and coarse brain regions. Key to understanding the cause of such emergent population dynamics, is capturing the collective behaviour of neuronal activity at multiple brain scales. In this thesis I make use of the larval zebrafish to capture single cell neuronal activity across the whole brain during epileptic seizures. Firstly, I make use of statistical physics methods to quantify the collective behaviour of single neuron dynamics during epileptic seizures. Here, I demonstrate a population mechanism through which single neuron dynamics organise into seizures: brain dynamics deviate from a phase transition. Secondly, I make use of single neuron network models to identify the synaptic mechanisms that actually cause this shift to occur. Here, I show that the density of neuronal connections in the network is key for driving generalised seizure dynamics. Interestingly, such changes also disrupt network response properties and flexible dynamics in brain networks, thus linking microscale neuronal changes with emergent brain dysfunction during seizures. Thirdly, I make use of non-linear causal inference methods to study the nature of the underlying neuronal interactions that enable seizures to occur. Here I show that seizures are driven by high synchrony but also by highly non-linear interactions between neurons. Interestingly, these non-linear signatures are filtered out at the macroscale, and therefore may represent a neuronal signature that could be used for microscale interventional strategies. This thesis demonstrates the utility of studying multi-scale dynamics in the larval zebrafish, to link neuronal activity at the microscale with emergent properties during seizures

Summaries of FY 1996 engineering research

This report documents the Basic Energy Sciences (BES) Engineering Research Program for fiscal year 1996; it provides a summary for each of the program projects in addition to a brief program overview. The report is intended to provide staff of Congressional committees, other executive departments, and other DOE offices with substantive program information so as to facilitate governmental overview and coordination of Federal research programs. Of equal importance, its availability facilitates communication of program information to interested research engineers and scientists. Each BES Division administers basic, mission oriented research programs in the area indicated by its title. The BES Engineering Research Program is one such program; it is administered by the Engineering and Geosciences Division of BES. In preparing this report the principal investigators were asked to submit summaries for their projects that were specifically applicable to fiscal year 1996. The summaries received have been edited if necessary, but the press for timely publication made it impractical to have the investigators review and approve the revised summaries prior to publication. For more information about a given project, it is suggested that the investigators be contacted directly

Applicable Solutions in Non-Linear Dynamical Systems

From Preface: The 15th International Conference „Dynamical Systems - Theory and Applications” (DSTA 2019, 2-5 December, 2019, Lodz, Poland) gathered a numerous group of outstanding scientists and engineers who deal with widely understood problems of theoretical and applied dynamics. Organization of the conference would not have been possible without great effort of the staff of the Department of Automation, Biomechanics and Mechatronics of the Lodz University of Technology. The patronage over the conference has been taken by the Committee of Mechanics of the Polish Academy of Sciences and Ministry of Science and Higher Education of Poland. It is a great pleasure that our event was attended by over 180 researchers from 35 countries all over the world, who decided to share the results of their research and experience in different fields related to dynamical systems. This year, the DSTA Conference Proceedings were split into two volumes entitled „Theoretical Approaches in Non-Linear Dynamical Systems” and „Applicable Solutions in Non-Linear Dynamical Systems”. In addition, DSTA 2019 resulted in three volumes of Springer Proceedings in Mathematics and Statistics entitled „Control and Stability of Dynamical Systems”, „Mathematical and Numerical Approaches in Dynamical Systems” and „Dynamical Systems in Mechatronics and Life Sciences”. Also, many outstanding papers will be recommended to special issues of renowned scientific journals.Cover design: Kaźmierczak, MarekTechnical editor: Kaźmierczak, Mare