On the methodological unification in electroencephalography

BACKGROUND: This paper presents results of a pursuit of a repeatable and objective methodology of analysis of the electroencephalographic (EEG) time series. METHODS: Adaptive time-frequency approximations of EEG are discussed in the light of the available experimental and theoretical evidence, and applicability in various experimental and clinical setups. RESULTS: Four lemmas and three conjectures support the following conclusion. CONCLUSION: Adaptive time-frequency approximations of signals unify most of the univariate computational approaches to EEG analysis, and offer compatibility with its traditional (visual) analysis, used in clinical applications

Global dynamics of neural mass models

Neural mass models are used to simulate cortical dynamics and to explain the electrical and magnetic fields measured using electro- and magnetoencephalography. Simulations evince a complex phase-space structure for these kinds of models; including stationary points and limit cycles and the possibility for bifurcations and transitions among different modes of activity. This complexity allows neural mass models to describe the itinerant features of brain dynamics. However, expressive, nonlinear neural mass models are often difficult to fit to empirical data without additional simplifying assumptions: e.g., that the system can be modelled as linear perturbations around a fixed point. In this study we offer a mathematical analysis of neural mass models, specifically the canonical microcircuit model, providing analytical solutions describing slow changes in the type of cortical activity, i.e. dynamical itinerancy. We derive a perturbation analysis up to second order of the phase flow, together with adiabatic approximations. This allows us to describe amplitude modulations in a relatively simple mathematical format providing analytic proof-of-principle for the existence of semi-stable states of cortical dynamics at the scale of a cortical column. This work allows for model inversion of neural mass models, not only around fixed points, but over regions of phase space that encompass transitions among semi or multi-stable states of oscillatory activity. Crucially, these theoretical results speak to model inversion in the context of multiple semi-stable brain states, such as the transition between interictal, pre-ictal and ictal activity in epilepsy

A unifying explanation of primary generalized seizures through nonlinear brain modeling and bifurcation analysis

The aim of this paper is to explain critical features of the human primary generalized epilepsies by investigating the dynamical bifurcations of a nonlinear model of the brain’s mean field dynamics. The model treats the cortex as a medium for the propagation of waves of electrical activity, incorporating key physiological processes such as propagation delays, membrane physiology and corticothalamic feedback. Previous analyses have demonstrated its descriptive validity in a wide range of healthy states and yielded specific predictions with regards to seizure phenomena. We show that mapping the structure of the nonlinear bifurcation set predicts a number of crucial dynamic processes, including the onset of periodic and chaotic dynamics as well as multistability. Quantitative study of electrophysiological data supports the validity of these predictions and reveals processes unique to the global bifurcation set. Specifically, we argue that the core electrophysiological and cognitive differences between tonic-clonic and absence seizures are predicted by the global bifurcation diagram of the model’s dynamics. The present study is the first to present a unifying explanation of these generalized seizures using the bifurcation analysis of a dynamical model of the brain

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

Modeling Brain Resonance Phenomena Using a Neural Mass Model

Stimulation with rhythmic light flicker (photic driving) plays an important role in the diagnosis of schizophrenia, mood disorder, migraine, and epilepsy. In particular, the adjustment of spontaneous brain rhythms to the stimulus frequency (entrainment) is used to assess the functional flexibility of the brain. We aim to gain deeper understanding of the mechanisms underlying this technique and to predict the effects of stimulus frequency and intensity. For this purpose, a modified Jansen and Rit neural mass model (NMM) of a cortical circuit is used. This mean field model has been designed to strike a balance between mathematical simplicity and biological plausibility. We reproduced the entrainment phenomenon observed in EEG during a photic driving experiment. More generally, we demonstrate that such a single area model can already yield very complex dynamics, including chaos, for biologically plausible parameter ranges. We chart the entire parameter space by means of characteristic Lyapunov spectra and Kaplan-Yorke dimension as well as time series and power spectra. Rhythmic and chaotic brain states were found virtually next to each other, such that small parameter changes can give rise to switching from one to another. Strikingly, this characteristic pattern of unpredictability generated by the model was matched to the experimental data with reasonable accuracy. These findings confirm that the NMM is a useful model of brain dynamics during photic driving. In this context, it can be used to study the mechanisms of, for example, perception and epileptic seizure generation. In particular, it enabled us to make predictions regarding the stimulus amplitude in further experiments for improving the entrainment effect

Dynamics of biologically informed neural mass models of the brain

This book contributes to the development and analysis of computational models that help brain function to be understood. The mean activity of a brain area is mathematically modeled in such a way as to strike a balance between tractability and biological plausibility. Neural mass models (NMM) are used to describe switching between qualitatively different regimes (such as those due to pharmacological interventions, epilepsy, sleep, or context-induced state changes), and to explain resonance phenomena in a photic driving experiment. The description of varying states in an ordered sequence gives a principle scheme for the modeling of complex phenomena on multiple time scales. The NMM is matched to the photic driving experiment routinely applied in the diagnosis of such diseases as epilepsy, migraine, schizophrenia and depression. The model reproduces the clinically relevant entrainment effect and predictions are made for improving the experimental setting.Die vorliegende Arbeit stellt einen Beitrag zur Entwicklung und Analyse von Computermodellen zum Verständnis von Hirnfunktionen dar. Es wird die mittlere Aktivität eines Hirnareals analytisch einfach und dabei biologisch plausibel modelliert. Auf Grundlage eines Neuronalen Massenmodells (NMM) werden die Wechsel zwischen Oszillationsregimen (z.B. durch pharmakologisch, epilepsie-, schlaf- oder kontextbedingte Zustandsänderungen) als geordnete Folge beschrieben und Resonanzphänomene in einem Photic-Driving-Experiment erklärt. Dieses NMM kann sehr komplexe Dynamiken (z.B. Chaos) innerhalb biologisch plausibler Parameterbereiche hervorbringen. Um das Verhalten abzuschätzen, wird das NMM als Funktion konstanter Eingangsgrößen und charakteristischer Zeitenkonstanten vollständig auf Bifurkationen untersucht und klassifiziert. Dies ermöglicht die Beschreibung wechselnder Regime als geordnete Folge durch spezifische Eingangstrajektorien. Es wird ein Prinzip vorgestellt, um komplexe Phänomene durch Prozesse verschiedener Zeitskalen darzustellen. Da aufgrund rhythmischer Stimuli und der intrinsischen Rhythmen von Neuronenverbänden die Eingangsgrößen häufig periodisch sind, wird das Verhalten des NMM als Funktion der Intensität und Frequenz einer periodischen Stimulation mittels der zugehörigen Lyapunov-Spektren und der Zeitreihen charakterisiert. Auf der Basis der größten Lyapunov-Exponenten wird das NMM mit dem Photic-Driving-Experiment überein gebracht. Dieses Experiment findet routinemäßige Anwendung in der Diagnostik verschiedener Erkrankungen wie Epilepsie, Migräne, Schizophrenie und Depression. Durch die Anwendung des vorgestellten NMM wird der für die Diagnostik entscheidende Mitnahmeeffekt reproduziert und es werden Vorhersagen für eine Verbesserung der Indikation getroffen

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

Imaging the spatial-temporal neuronal dynamics using dynamic causal modelling

Oscillatory brain activity is a ubiquitous feature of neuronal dynamics and the synchronous discharge of neurons is believed to facilitate integration both within functionally segregated brain areas and between areas engaged by the same task. There is growing interest in investigating the neural oscillatory networks in vivo. The aims of this thesis are to (1) develop an advanced method, Dynamic Causal Modelling for Induced Responses (DCM for IR), for modelling the brain network functions and (2) apply it to exploit the nonlinear coupling in the motor system during hand grips and the functional asymmetries during face perception. DCM for IR models the time-varying power over a range of frequencies of coupled electromagnetic sources. The model parameters encode coupling strength among areas and allows the differentiations between linear (within frequency) and nonlinear (between-frequency) coupling. I applied DCM for IR to show that, during hand grips, the nonlinear interactions among neuronal sources in motor system are essential while intrinsic coupling (within source) is very likely to be linear. Furthermore, the normal aging process alters both the network architecture and the frequency contents in the motor network. I then use the bilinear form of DCM for IR to model the experimental manipulations as the modulatory effects. I use MEG data to demonstrate functional asymmetries between forward and backward connections during face perception: Specifically, high (gamma) frequencies in higher cortical areas suppressed low (alpha) frequencies in lower areas. This finding provides direct evidence for functional asymmetries that is consistent with anatomical and physiological evidence from animal studies. Lastly, I generalize the bilinear form of DCM for IR to dissociate the induced responses from evoked ones in terms of their functional role. The backward modulatory effect is expressed as induced, but not evoked responses