Oscillator-based neuronal modeling for seizure progression investigation and seizure control strategy

The coupled oscillator model has previously been used for the simulation of neuronal activities in in vitro rat hippocampal slice seizure data and the evaluation of seizure suppression algorithms. Each model unit can be described as either an oscillator which can generate action potential spike trains without inputs, or a threshold-based unit. With the change of only one parameter, each unit can either be an oscillator or a threshold-based spiking unit. This would eliminate the need for a new set of equations for each type of unit. Previous analysis has suggested that long kernel duration and imbalance of inhibitory feedback can cause the system to intermittently transition into and out of ictal activities. The state transitions of seizure-like events were investigated here; specifically, how the system excitability may change when the system undergoes transitions in the preictal and postictal processes. Analysis showed that the area of the excitation kernel is positively correlated with the mean firing rate of the ictal activity. The kernel duration is also correlated to the amount of ictal activity. The transition into ictal activity involved the escape from the saddle point foci in the state space trajectory identified by using Newton\u27s method. The ability to accurately anticipate and suppress seizures is an important endeavor that has tremendous impact on improving the quality of lives for epileptic patients. The stimulation studies have suggested that an electrical stimulation strategy that uses the intrinsic high complexity dynamics of the biological system may be more effective in reducing the duration of seizure-like activities in the computer model. In this research, we evaluate this strategy on an in vitro rat hippocampal slice magnesium-free model. Simulated postictal field potential data generated by an oscillator-based hippocampal network model was applied to the CA1 region of the rat hippocampal slices through a multi-electrode array (MEA) system. It was found to suppress and delay the onset of future seizures temporarily. The average inter-seizure time was found to be significantly prolonged after postictal stimulation when compared to the negative control trials and bipolar square wave signals. The result suggests that neural signal-based stimulation related to resetting may be suitable for seizure control in the clinical environment

Stochastic neural network model for spontaneous bursting in hippocampal slices

A biologically plausible, stochastic, neural network model that exhibits spontaneous transitions between a low-activity ͑normal͒ state and a high-activity ͑epileptic͒ state is studied by computer simulation. Brief excursions of the network to the high-activity state lead to spontaneous population bursting similar to the behavior observed in hippocampal slices bathed in a high-potassium medium. Although the variability of interburst intervals in this model is due to stochasticity, first return maps of successive interburst intervals show trajectories that resemble the behavior expected near unstable periodic orbits ͑UPOs͒ of systems exhibiting deterministic chaos. Simulations of the effects of the application of chaos control, periodic pacing, and anticontrol to the network model yield results that are qualitatively similar to those obtained in experiments on hippocampal slices. Estimation of the statistical significance of UPOs through surrogate data analysis also leads to results that resemble those of similar analysis of data obtained from slice experiments and human epileptic activity. These results suggest that spontaneous population bursting in hippocampal slices may be a manifestation of stochastic bistable dynamics, rather than of deterministic chaos. Our results also question the reliability of some of the recently proposed, UPO-based, statistical methods for detecting determinism and chaos in experimental time-series data

Modeling focal epileptic activity in the Wilson-Cowan model with depolarization block

Measurements of neuronal signals during human seizure activity and evoked epileptic activity in experimental models suggest that, in these pathological states, the individual nerve cells experience an activity driven depolarization block, i.e. they saturate. We examined the effect of such a saturation in the Wilson–Cowan formalism by adapting the nonlinear activation function; we substituted the commonly applied sigmoid for a Gaussian function. We discuss experimental recordings during a seizure that support this substitution. Next we perform a bifurcation analysis on the Wilson–Cowan model with a Gaussian activation function. The main effect is an additional stable equilibrium with high excitatory and low inhibitory activity. Analysis of coupled local networks then shows that such high activity can stay localized or spread. Specifically, in a spatial continuum we show a wavefront with inhibition leading followed by excitatory activity. We relate our model simulations to observations of spreading activity during seizures

Control of chaos in nonlinear circuits and systems

Nonlinear circuits and systems, such as electronic circuits (Chapter 5), power converters (Chapter 6), human brains (Chapter 7), phase lock loops (Chapter 8), sigma delta modulators (Chapter 9), etc, are found almost everywhere. Understanding nonlinear behaviours as well as control of these circuits and systems are important for real practical engineering applications. Control theories for linear circuits and systems are well developed and almost complete. However, different nonlinear circuits and systems could exhibit very different behaviours. Hence, it is difficult to unify a general control theory for general nonlinear circuits and systems. Up to now, control theories for nonlinear circuits and systems are still very limited. The objective of this book is to review the state of the art chaos control methods for some common nonlinear circuits and systems, such as those listed in the above, and stimulate further research and development in chaos control for nonlinear circuits and systems. This book consists of three parts. The first part of the book consists of reviews on general chaos control methods. In particular, a time-delayed approach written by H. Huang and G. Feng is reviewed in Chapter 1. A master slave synchronization problem for chaotic Lur’e systems is considered. A delay independent and delay dependent synchronization criteria are derived based on the H performance. The design of the time delayed feedback controller can be accomplished by means of the feasibility of linear matrix inequalities. In Chapter 2, a fuzzy model based approach written by H.K. Lam and F.H.F. Leung is reviewed. The synchronization of chaotic systems subject to parameter uncertainties is considered. A chaotic system is first represented by the fuzzy model. A switching controller is then employed to synchronize the systems. The stability conditions in terms of linear matrix inequalities are derived based on the Lyapunov stability theory. The tracking performance and parameter design of the controller are formulated as a generalized eigenvalue minimization problem which is solved numerically via some convex programming techniques. In Chapter 3, a sliding mode control approach written by Y. Feng and X. Yu is reviewed. Three kinds of sliding mode control methods, traditional sliding mode control, terminal sliding mode control and non-singular terminal sliding mode control, are employed for the control of a chaotic system to realize two different control objectives, namely to force the system states to converge to zero or to track desired trajectories. Observer based chaos synchronizations for chaotic systems with single nonlinearity and multi-nonlinearities are also presented. In Chapter 4, an optimal control approach written by C.Z. Wu, C.M. Liu, K.L. Teo and Q.X. Shao is reviewed. Systems with nonparametric regression with jump points are considered. The rough locations of all the possible jump points are identified using existing kernel methods. A smooth spline function is used to approximate each segment of the regression function. A time scaling transformation is derived so as to map the undecided jump points to fixed points. The approximation problem is formulated as an optimization problem and solved via existing optimization tools. The second part of the book consists of reviews on general chaos controls for continuous-time systems. In particular, chaos controls for Chua’s circuits written by L.A.B. Tôrres, L.A. Aguirre, R.M. Palhares and E.M.A.M. Mendes are discussed in Chapter 5. An inductorless Chua’s circuit realization is presented, as well as some practical issues, such as data analysis, mathematical modelling and dynamical characterization, are discussed. The tradeoff among the control objective, the control energy and the model complexity is derived. In Chapter 6, chaos controls for pulse width modulation current mode single phase H-bridge inverters written by B. Robert, M. Feki and H.H.C. Iu are discussed. A time delayed feedback controller is used in conjunction with the proportional controller in its simple form as well as in its extended form to stabilize the desired periodic orbit for larger values of the proportional controller gain. This method is very robust and easy to implement. In Chapter 7, chaos controls for epileptiform bursting in the brain written by M.W. Slutzky, P. Cvitanovic and D.J. Mogul are discussed. Chaos analysis and chaos control algorithms for manipulating the seizure like behaviour in a brain slice model are discussed. The techniques provide a nonlinear control pathway for terminating or potentially preventing epileptic seizures in the whole brain. The third part of the book consists of reviews on general chaos controls for discrete-time systems. In particular, chaos controls for phase lock loops written by A.M. Harb and B.A. Harb are discussed in Chapter 8. A nonlinear controller based on the theory of backstepping is designed so that the phase lock loops will not be out of lock. Also, the phase lock loops will not exhibit Hopf bifurcation and chaotic behaviours. In Chapter 9, chaos controls for sigma delta modulators written by B.W.K. Ling, C.Y.F. Ho and J.D. Reiss are discussed. A fuzzy impulsive control approach is employed for the control of the sigma delta modulators. The local stability criterion and the condition for the occurrence of limit cycle behaviours are derived. Based on the derived conditions, a fuzzy impulsive control law is formulated so that the occurrence of the limit cycle behaviours, the effect of the audio clicks and the distance between the state vectors and an invariant set are minimized supposing that the invariant set is nonempty. The state vectors can be bounded within any arbitrary nonempty region no matter what the input step size, the initial condition and the filter parameters are. The editors are much indebted to the editor of the World Scientific Series on Nonlinear Science, Prof. Leon Chua, and to Senior Editor Miss Lakshmi Narayan for their help and congenial processing of the edition

Simulation of Abnormal/Normal Brain States Using the KIV Model

Recent studies have focused on the phenomena of abnormal electrical brain activity which may transition into a debilitating seizure state through the entrainment of large populations of neurons.Starting from the initial epileptogenisis of a small population of abnormally firing neurons, to the mobilization of mesoscopic neuron populations behaving in a synchronous manner, a model has been formulated that captures the initial epileptogenisis to the semi-periodic entrainment of distant neuron populations.The normal non-linear dynamic signal captured through EEG, moves into a semi-periodic state, which can be quantified as the seizure state.Capturing the asynchronous/synchronous behavior of the normal/pathological brain state will be discussed.This model will also demonstrate how electrical stimulation applied to the limbic system restores the seizure state of the brain back to its original normal condition.Human brain states are modeled using a biologically inspired neural network, the KIV model.The KIV model exhibits the noisy, chaotic attributes found in the limbic system of brains of higher forms of organisms, and in its normal basal state, represents the homogeneous activity of millions of neuron activations.The KIV can exhibit the ’unbalanced state’ of neural activity, whereas when a small cluster of abnormal firing neurons starts to exhibit periodic neural firings that eventually entrain all the neurons within the limbic system, the network has moved into the ‘seizure’ state.These attributes have been found in human EEG recordings and have been duplicated in this model of the brain.The discussion in this dissertation covers the attributes found in human EEG data and models these attributes.Additionally, this model proposes a methodology to restore the modeled ‘seizure’ state, and by doing so, proposes a manner for external electrical titration to restore the abnormal seizure state back to a normal chaotic EEG signal state.Quantification measurements of normal, abnormal, and restoration to normal brain states will be exhibited using the following approaches:Analysis of human EEG dataQuantification measurements of brain states.Development of models of the different brain states, i.e. fit parameters of the model on individual personal data/history.Implementation of quantitative measurements on “restored” simulated seizure state

Multi-Scale Mathematical Modelling of Brain Networks in Alzheimer's Disease

Perturbations to brain network dynamics on a range of spatial and temporal scales are believed to underpin neurological disorders such as Alzheimer’s disease (AD). This thesis combines quantitative data analysis with tools such as dynamical systems and graph theory to understand how the network dynamics of the brain are altered in AD and experimental models of related pathologies. Firstly, we use a biophysical neuron model to elucidate ionic mechanisms underpinning alterations to the dynamics of principal neurons in the brain’s spatial navigation systems in an animal model of tauopathy. To uncover how synaptic deficits result in alterations to brain dynamics, we subsequently study an animal model featuring local and long-range synaptic degeneration. Synchronous activity (functional connectivity; FC) between neurons within a region of the cortex is analysed using two-photon calcium imaging data. Long-range FC between regions of the brain is analysed using EEG data. Furthermore, a computational model is used to study relationships between networks on these different spatial scales. The latter half of this thesis studies EEG to characterize alterations to macro-scale brain dynamics in clinical AD. Spectral and FC measures are correlated with cognitive test scores to study the hypothesis that impaired integration of the brain’s processing systems underpin cognitive impairment in AD. Whole brain computational modelling is used to gain insight into the role of spectral slowing on FC, and elucidate potential synaptic mechanisms of FC differences in AD. On a finer temporal scale, microstate analyses are used to identify changes to the rapid transitioning behaviour of the brain’s resting state in AD. Finally, the electrophysiological signatures of AD identified throughout the thesis are combined into a predictive model which can accurately separate people with AD and healthy controls based on their EEG, results which are validated on an independent patient cohort. Furthermore, we demonstrate in a small preliminary cohort that this model is a promising tool for predicting future conversion to AD in patients with mild cognitive impairment

Mechanisms of the Coregulation of Multiple Ionic Currents for the Control of Neuronal Activity

An open question in contemporary neuroscience is how neuromodulators coregulate multiple conductances to maintain functional neuronal activity. Neuromodulators enact changes to properties of biophysical characteristics, such as the maximal conductance or voltage of half-activation of an ionic current, which determine the type and properties of neuronal activity. We apply dynamical systems theory to study the changes to neuronal activity that arise from neuromodulation. Neuromulators can act on multiple targets within a cell. The coregulation of mulitple ionic currents extends the scope of dynamic control on neuronal activity. Different aspects of neuronal activity can be independently controlled by different currents. The coregulation of multiple ionic currents provides precise control over the temporal characteristics of neuronal activity. Compensatory changes in multiple ionic currents could be used to avoid dangerous dynamics or maintain some aspect of neuronal activity. The coregulation of multiple ionic currents can be used as bifurcation control to ensure robust dynamics or expand the range of coexisting regimes. Multiple ionic currents could be involved in increasing the range of dynamic control over neuronal activity. The coregulation of multiple ionic currents in neuromodulation expands the range over which biophysical parameters support functional activity

Modeling of ATP-mediated signal transduction and wave propagation in astrocytic cellular networks

Astrocytes, a special type of glial cells, were considered to have supporting role in information processing in the brain. However, several recent studies have shown that they can be chemically stimulated by neurotransmitters and use a form of signaling, in which ATP acts as an extracellular messenger. Pathological conditions, such as spreading depression, have been linked to abnormal range of wave propagation in astrocytic cellular networks. Nevertheless, the underlying intra- and inter-cellular signaling mechanisms remain unclear. Motivated by the above, we constructed a model to understand the relationship between single-cell signal transduction mechanisms and wave propagation and blocking in astrocytic networks. The model incorporates ATP-mediated IP production, the subsequent Ca release from the ER through IPR channels and ATP release into the extracellular space. For the latter, two hypotheses were tested: Ca- or IP-dependent ATP release. In the first case, single astrocytes can exhibit excitable behavior and frequency-encoded oscillations. Homogeneous, one-dimensional astrocytic networks can propagate waves with infinite range, while in two dimensions, spiral waves can be generated. However, in the IP-dependent ATP release case, the specific coupling of the driver ATP-IP system with the driven Ca subsystem leads to one- and two-dimensional wave patterns with finite range of propagation. © 2006 Elsevier Ltd. All rights reserved