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

Cognitive manipulation of brain electric microstates

EEG studies of wakeful rest have shown that there are brief periods in which global electrical brain activity on the scalp remains semi-stable (so-called microstates). Topographical analyses of this activity have revealed that much of the variance is explained by four distinct microstates that occur in a repetitive sequence. A recent fMRI study showed that these four microstates correlated with four known functional systems, each of which is activated by specific cognitive functions and sensory inputs. The present study used high density EEG to examine the degree to which spatial and temporal properties of microstates may be altered by manipulating cognitive task (a serial subtraction task vs. wakeful rest) and the availability of visual information (eyes open vs. eyes closed conditions). The hypothesis was that parameters of microstate D would be altered during the serial subtraction task because it is correlated with regions that are part of the dorsal attention functional system. It was also expected that the sequence of microstates would preferentially transition from all other microstates to microstate D during the task as compared to rest. Finally, it was hypothesized that the eyes open condition would significantly increase one or more microstate parameters associated with microstate B, which is associated with the visual system. Topographical analyses indicated that the duration, coverage, and occurrence of microstate D were significantly higher during the cognitive task compared to wakeful rest; in addition, microstate C, which is associated with regions that are part of the default mode and cognitive control systems, was very sensitive to the task manipulation, showing significantly decreased duration, coverage, and occurrence during the task condition compared to rest. Moreover, microstate B was altered by manipulations of visual input, with increased occurrence and coverage in the eyes open condition. In addition, during the eyes open condition microstates A and D had significantly shorter durations, while C had increased occurrence. Microstate D had decreased coverage in the eyes open condition. Finally, at least 15 microstates (identified via k-means clustering) were required to explain a similar amount of variance of EEG activity as previously published values. These results support important aspects of our hypotheses and demonstrate that cognitive manipulation of microstates is possible, but the relationships between microstates and their corresponding functional systems are complex. Moreover, there may be more than four primary microstates

Mental states as macrostates emerging from brain electrical dynamics

Psychophysiological correlations form the basis for different medical and scientific disciplines, but the nature of this relation has not yet been fully understood. One conceptual option is to understand the mental as “emerging” from neural processes in the specific sense that psychology and physiology provide two different descriptions of the same system. Stating these descriptions in terms of coarser- and finer-grained system states (macro- and microstates), the two descriptions may be equally adequate if the coarse-graining preserves the possibility to obtain a dynamical rule for the system. To test the empirical viability of our approach, we describe an algorithm to obtain a specific form of such a coarse-graining from data, and illustrate its operation using a simulated dynamical system. We then apply the method to an electroencephalographic recording, where we are able to identify macrostates from the physiological data that correspond to mental states of the subject

MEG cortical microstates: Spatiotemporal characteristics, dynamic functional connectivity and stimulus-evoked responses

EEG microstate analysis is an approach to study brain states and their fast transitions in healthy cognition and disease. A key limitation of conventional microstate analysis is that it must be performed at the sensor level, and therefore gives limited anatomical insight. Here, we generalise the microstate methodology to be applicable to source-reconstructed electrophysiological data. Using simulations of a neural-mass network model, we first established the validity and robustness of the proposed method. Using MEG resting-state data, we uncovered ten microstates with distinct spatial distributions of cortical activation. Multivariate pattern analysis demonstrated that source-level microstates were associated with distinct functional connectivity patterns. We further demonstrated that the occurrence probability of MEG microstates were altered by auditory stimuli, exhibiting a hyperactivity of the microstate including the auditory cortex. Our results support the use of source-level microstates as a method for investigating brain dynamic activity and connectivity at the millisecond scale

Detecting event-related recurrences by symbolic analysis: Applications to human language processing

Quasistationarity is ubiquitous in complex dynamical systems. In brain dynamics there is ample evidence that event-related potentials reflect such quasistationary states. In order to detect them from time series, several segmentation techniques have been proposed. In this study we elaborate a recent approach for detecting quasistationary states as recurrence domains by means of recurrence analysis and subsequent symbolisation methods. As a result, recurrence domains are obtained as partition cells that can be further aligned and unified for different realisations. We address two pertinent problems of contemporary recurrence analysis and present possible solutions for them.Comment: 24 pages, 6 figures. Draft version to appear in Proc Royal Soc

Hidden Markov Models for dimensionality reduction of neural activity

Recentemente, gli Hidden Markov Models (HMM) sono stati usati per ridurre le dimensioni di dati complessi e ad alta dimensionalità. In particolare, è noto che l'attività neurale registrata tramite elettroencefalogramma (EEG) presenta pattern globali di attività coordinate a bassa dimensionalità, chiamati "microstati". In questa tesi esamineremo prima il framework degli HMM per poi applicarlo ai dati EEG registrati in soggetti sani su 64 canali a riposo (e durante lo svolgimento di un compito). Infine, caratterizzeremo la statistica dello spazio a bassa dimensionalità, come la durata media, la frequenza di occorrenza e le probabilità di transizione.Recently, Hidden Markov Models (HMM) have been used to reduce the dimensionality of complex and high-dimensional data. In particular, it is known that neural activity recorded through electroencephalogram (EEG) displays low-dimensional global patterns of coordinated activity, termed "microstates". In this thesis we will first review the framework of HMM to then apply it on EEG data recorded from healthy subjects on 64 channels at rest (and during task). Finally, we will characterize the statistics on the low dimensional space, such as the average duration, the frequency of occurrence and the transition probabilities

EEG Microstate Sequences From Different Clustering Algorithms Are Information-Theoretically Invariant

We analyse statistical and information-theoretical properties of EEG microstate sequences, as seen through the lens of five different clustering algorithms. Microstate sequences are computed for n = 20 resting state EEG recordings during wakeful rest. The input for all clustering algorithms is the set of EEG topographic maps obtained at local maxima of the spatial variance. This data set is processed by two classical microstate clustering algorithms (1) atomize and agglomerate hierarchical clustering (AAHC) and (2) a modified K-means algorithm, as well as by (3) K-medoids, (4) principal component analysis (PCA) and (5) fast independent component analysis (Fast-ICA). Using this technique, EEG topographies can be substituted with microstate labels by competitive fitting based on spatial correlation, resulting in a symbolic, non-metric time series, the microstate sequence. Microstate topographies and symbolic time series are further analyzed statistically, including static and dynamic properties. Static properties, which do not contain information about temporal dependencies of the microstate sequence include the maximum similarity of microstate maps within and between the tested clustering algorithms, the global explained variance and the Shannon entropy of the microstate sequences. Dynamic properties are sensitive to temporal correlations between the symbols and include the mixing time of the microstate transition matrix, the entropy rate of the microstate sequences and the location of the first local maximum of the autoinformation function. We also test the Markov property of microstate sequences, the time stationarity of the transition matrix and detect periodicities by means of time-lagged mutual information. Finally, possible long-range correlations of microstate sequences are assessed via Hurst exponent estimation. We find that while static properties partially reflect properties of the clustering algorithms, information-theoretical quantities are largely invariant with respect to the clustering method used. As each clustering algorithm has its own profile of computational speed, ease of implementation, determinism vs. stochasticity and theoretical underpinnings, our results convey a positive message concerning the free choice of method and the comparability of results obtained from different algorithms. The invariance of these quantities implies that the tested properties are algorithm-independent, inherent features of resting state EEG derived microstate sequences

MULTIVARIATE MODELING OF COGNITIVE PERFORMANCE AND CATEGORICAL PERCEPTION FROM NEUROIMAGING DATA

State-of-the-art cognitive-neuroscience mainly uses hypothesis-driven statistical testing to characterize and model neural disorders and diseases. While such techniques have proven to be powerful in understanding diseases and disorders, they are inadequate in explaining causal relationships as well as individuality and variations. In this study, we proposed multivariate data-driven approaches for predictive modeling of cognitive events and disorders. We developed network descriptions of both structural and functional connectivities that are critical in multivariate modeling of cognitive performance (i.e., fluency, attention, and working memory) and categorical perceptions (i.e., emotion, speech perception). We also performed dynamic network analysis on brain connectivity measures to determine the role of different functional areas in relation to categorical perceptions and cognitive events. Our empirical studies of structural connectivity were performed using Diffusion Tensor Imaging (DTI). The main objective was to discover the role of structural connectivity in selecting clinically interpretable features that are consistent over a large range of model parameters in classifying cognitive performances in relation to Acute Lymphoblastic Leukemia (ALL). The proposed approach substantially improved accuracy (13% - 26%) over existing models and also selected a relevant, small subset of features that were verified by domain experts. In summary, the proposed approach produced interpretable models with better generalization.Functional connectivity is related to similar patterns of activation in different brain regions regardless of the apparent physical connectedness of the regions. The proposed data-driven approach to the source localized electroencephalogram (EEG) data includes an array of tools such as graph mining, feature selection, and multivariate analysis to determine the functional connectivity in categorical perceptions. We used the network description to correctly classify listeners behavioral responses with an accuracy over 92% on 35 participants. State-of-the-art network description of human brain assumes static connectivities. However, brain networks in relation to perception and cognition are complex and dynamic. Analysis of transient functional networks with spatiotemporal variations to understand cognitive functions remains challenging. One of the critical missing links is the lack of sophisticated methodologies in understanding dynamics neural activity patterns. We proposed a clustering-based complex dynamic network analysis on source localized EEG data to understand the commonality and differences in gender-specific emotion processing. Besides, we also adopted Bayesian nonparametric framework for segmentation neural activity with a finite number of microstates. This approach enabled us to find the default network and transient pattern of the underlying neural mechanism in relation to categorical perception. In summary, multivariate and dynamic network analysis methods developed in this dissertation to analyze structural and functional connectivities will have a far-reaching impact on computational neuroscience to identify meaningful changes in spatiotemporal brain activities