Analysis of pattern dynamics for a nonlinear model of the human cortex via bifurcation theories

This thesis examines the bifurcations, i.e., the emergent behaviours, for the Waikato cortical model under the influence of the gap-junction inhibitory diffusion D₂ (identified as the Turing bifurcation parameter) and the time-to-peak for hyperpolarising GABA response γi (i.e., inhibitory rate-constant, identified as the Hopf bifurcation parameter). The cortical model simplifies the entire cortex to a cylindrical macrocolumn (∼ 1 mm³) containing ∼ 10⁵ neurons (85% excitatory, 15% inhibitory) communicating via both chemical and electrical (gap-junction) synapses. The linear stability analysis of the model equations predict the emergence of a Turing instability (in which separated areas of the cortex become activated) when gap-junction diffusivity is increased above a critical level. In addition, a Hopf bifurcation (oscillation) occurs when the inhibitory rate-constant is sufficiently small. Nonlinear interaction between these instabilities leads to spontaneous cortical patterns of neuronal activities evolving in space and time. Such model dynamics of delicately balanced interplay between Turing and Hopf instabilities may be of direct relevance to clinically observed brain dynamics such as epileptic seizure EEG spikes, deep-sleep slow-wave oscillations and cognitive gamma-waves. The relationship between the modelled brain patterns and model equations can normally be inferred from the eigenvalue dispersion curve, i.e., linear stability analysis. Sometimes we experienced mismatches between the linear stability analysis and the formed cortical patterns, which hampers us in identifying the type of instability corresponding to the emergent patterns. In this thesis, I investigate the pattern-forming mechanism of the Waikato cortical model to better understand the model nonlinearities. I first study the pattern dynamics via analysis of a simple pattern-forming system, the Brusselator model, which has a similar model structure and bifurcation phenomena as the cortical model. I apply both linear and nonlinear perturbation methods to analyse the near-bifurcation behaviour of the Brusselator in order to precisely capture the dominant mode that contributes the most to the final formed-patterns. My nonlinear analysis of the Brusselator model yields Ginzburg-Landau type amplitude equations that describe the dynamics of the most unstable mode, i.e., the dominant mode, in the vicinity of a bifurcation point. The amplitude equations at a Turing point unfold three characteristic spatial structures: honeycomb Hπ, stripes, and reentrant honeycomb H₀. A codimension-2 Turing–Hopf point (CTHP) predicts three mixed instabilities: stable Turing–Hopf (TH), chaotic TH, and bistable TH. The amplitude equations precisely determine the bifurcation conditions for these instabilities and explain the pattern-competition mechanism once the bifurcation parameters cross the thresholds, whilst driving the system into a nonlinear region where the linear stability analysis may not be applicable. Then, I apply the bifurcation theories to the cortical model for its pattern predictions. Analogous to the Brusselator model, I find cortical Turing pattens in Hπ, stripes and H₀ spatial structures. Moreover, I develop the amplitude equations for the cortical model, with which I derive the envelope frequency for the beating-waves of a stable TH mode; and propose ideas regarding emergence of the cortical chaotic mode. Apart from these pattern dynamics that the cortical model shares with the Brusselator system, the cortical model also exhibits “eye-blinking” TH patterns latticed in hexagons with localised oscillations. Although we have not found biological significance of these model pattens, the developed bifurcation theories and investigated pattern-forming mechanism may enrich our modelling strategies and help us to further improve model performance. In the last chapter of this thesis, I introduce a Turing–Hopf mechanism for the anaesthetic slow-waves, and predict a coherence drop of such slow-waves with the induction of propofol anaesthesia. To test this hypothesis, I developed an EEG coherence analysing algorithm, EEG coherence, to automatically examine the clinical EEG recordings across multiple subjects. The result shows significantly decreased coherence along the fronto-occipital axis, and increased coherence along the left- and right-temporal axis. As the Waikato cortical model is spatially homogenous, i.e., there are no explicit front-to-back or right-to-left directions, it is unable to produce different coherence changes for different regions. It appears that the Waikato cortical model best represents the cortical dynamics in the frontal region. The theory of pattern dynamics suggests that a mode transition from wave–Turing–wave to Turing–wave–Turing introduces pattern coherence changes in both positive and negative directions. Thus, a further modelling improvement may be the introduction of a cortical bistable mode where Turing and wave coexist

Proceedings of the 3rd International Mobile Brain/Body Imaging Conference : Berlin, July 12th to July 14th 2018

The 3rd International Mobile Brain/Body Imaging (MoBI) conference in Berlin 2018 brought together researchers from various disciplines interested in understanding the human brain in its natural environment and during active behavior. MoBI is a new imaging modality, employing mobile brain imaging methods like the electroencephalogram (EEG) or near infrared spectroscopy (NIRS) synchronized to motion capture and other data streams to investigate brain activity while participants actively move in and interact with their environment. Mobile Brain / Body Imaging allows to investigate brain dynamics accompanying more natural cognitive and affective processes as it allows the human to interact with the environment without restriction regarding physical movement. Overcoming the movement restrictions of established imaging modalities like functional magnetic resonance tomography (MRI), MoBI can provide new insights into the human brain function in mobile participants. This imaging approach will lead to new insights into the brain functions underlying active behavior and the impact of behavior on brain dynamics and vice versa, it can be used for the development of more robust human-machine interfaces as well as state assessment in mobile humans.DFG, GR2627/10-1, 3rd International MoBI Conference 201

Parameter identification in networks of dynamical systems

Mathematical models of real systems allow to simulate their behavior in conditions that are not easily or affordably reproducible in real life. Defining accurate models, however, is far from trivial and there is no one-size-fits-all solution. This thesis focuses on parameter identification in models of networks of dynamical systems, considering three case studies that fall under this umbrella: two of them are related to neural networks and one to power grids. The first case study is concerned with central pattern generators, i.e. small neural networks involved in animal locomotion. In this case, a design strategy for optimal tuning of biologically-plausible model parameters is developed, resulting in network models able to reproduce key characteristics of animal locomotion. The second case study is in the context of brain networks. In this case, a method to derive the weights of the connections between brain areas is proposed, utilizing both imaging data and nonlinear dynamics principles. The third and last case study deals with a method for the estimation of the inertia constant, a key parameter in determining the frequency stability in power grids. In this case, the method is customized to different challenging scenarios involving renewable energy sources, resulting in accurate estimations of this parameter

Implantable Asynchronous Epilectic Seizure Detector

RÉSUMÉ Plusieurs algorithmes de détection à faible consommation ont été proposés pour le traitement de l'épilepsie focale. La gestion de l'énergie dans ces microsystèmes est une question importante qui dépend principalement de la charge et de la décharge des capacités parasites des transistors et des courants de court-circuit pendant les commutations. Dans ce mémoire, un détecteur asynchrone de crise pour le traitement de l'épilepsie focale est présenté. Ce système fait partie d'un dispositif implantable intégré pour stopper la propagation de la crise. L'objectif de ce travail est de réduire la dissipation de puissance en évitant les transitions inutiles de signaux grâce à la technique du « clock tree » ; en conséquence, les transistors ne changent pas d'état transitoire dans ce mode d'économie d'énergie (période de surveillance des EEG intracrâniens), sauf si un événement anormal est détecté. Le dispositif intégré proposé comporte un bio-amplificateur en amont (front-end) à faible bruit, un processeur de signal numérique et un détecteur. Un délai variable et quatre détecteurs de fenêtres de tensions variables en parallèles sont utilisés pour extraire de l’information sur le déclenchement des crises. La sensibilité du détecteur est améliorée en optimisant les paramètres variables en fonction des activités de foyers épileptiques de chaque patient lors du début des crises. Le détecteur de crises asynchrone proposé a été implémenté premièrement en tant que prototype sur un circuit imprimé circulaire, ensuite nous l’avons intégré sur une seule puce dans la technologie standard CMOS 0.13μm. La puce fabriquée a été validée in vitro en utilisant un total de 34 enregistrements EEG intracrâniens avec la durée moyenne de chaque enregistrement de 1 min. Parmi ces jeux de données, 15 d’entre eux correspondaient à des enregistrements de crises, tandis que les 19 autres provenaient d’enregistrements variables de patients tels que de brèves crises électriques, des mouvements du corps et des variations durant le sommeil. Le système proposé a réalisé une performance de détection précise avec une sensibilité de 100% et 100% de spécificité pour ces 34 signaux icEEG enregistrés. Le délai de détection moyen était de 13,7 s après le début de la crise, bien avant l'apparition des manifestations cliniques, et une consommation d'énergie de 9 µW a été obtenue à partir d'essais expérimentaux.----------ABSTRACT Several power efficient detection algorithms have been proposed for treatment of focal epilepsy. Power management in these microsystems is an important issue which is mainly dependent on charging and discharging of the parasitic capacitances in transistors and short-circuit currents during switching. In this thesis, an asynchronous seizure detector for treatment of the focal epilepsy is presented. This system is part of an implantable integrated device to block the seizure progression. The objective of this work is reducing the power dissipation by avoiding the unnecessary signal transition and clock tree; as a result, transistors do not change their transient state in power saving mode (icEEG monitoring period) unless an abnormal event detected. The proposed integrated device contains a low noise front-end bioamplifier, a digital signal processor and a detector. A variable time frame and four concurrent variable voltage window detectors are used to extract seizure onset information. The sensitivity of the detector is enhanced by optimizing the variable parameters based on specific electrographic seizure onset activities of each patient. The proposed asynchronous seizure detector was first implemented as a prototype on a PCB and then integrated in standard 0.13 μm CMOS process. The fabricated chip was validated offline using a total of 34 intracranial EEG recordings with the average time duration of 1 min. 15 of these datasets corresponded to seizure activities while the remaining 19 signals were related to variable patient activities such as brief electrical seizures, body movement, and sleep patterns. The proposed system achieved an accurate detection performance with 100% sensitivity and 100 % specificity for these 34 recorded icEEG signals. The average detection delay was 13.7 s after seizure onset, well before the onset of the clinical manifestations. Finally, power consumption of the chip is 9 µW obtained from experimental tests

Computational Approaches to Biological Network Inference and Modeling in Systems Biology

Living systems, which are composed of biological components such as molecules, cells, organisms or entire species, are dynamic and complex. Their behaviors are difficult to study with respect to the properties of individual elements. To study their behaviors, we use quantitative techniques in the "omic" fields such as genomics, bioinformatics and proteomics to measure the behavior of groups of interacting components, and we use mathematical and computational modeling to describe and predict their dynamical behavior. The first step in the understanding of a biological system is to investigate how its individual elements interact with each other. This step consist of drawing a static wiring diagram that connects the individual parts. Experimental techniques that are used - are designed to observe interactions among the biological components in the laboratory while computational approaches are designed to predict interactions among the individual elements based on their properties. In the first part of this thesis, we present techniques for network inference that are particularly targeted at protein-protein interaction networks. These techniques include comparative genomics, structure-based, biological context methods and integrated frameworks. We evaluate and compare the prediction methods that have been most often used for domain-domain interactions and we discuss the limitations of the methods and data resources. We introduce the concept of the Enhanced Phylogenetic Tree, which is a new graphical presentation of the evolutionary history of protein families; then, we propose a novel method for assigning functional linkages to proteins. This method was applied to predicting both human and yeast protein functional linkages. The next step is to obtain insights into the dynamical aspects of the biological systems. One of the outreaching goals of systems biology is to understand the emergent properties of living systems, i.e., to understand how the individual components of a system come together to form distinct, collective and interactive properties and functions. The emergent properties of a system are neither to be found in nor are directly deducible from the lower-level properties of that system. An example of the emergent properties is synchronization, a dynamical state of complex network systems in which the individual components of the systems behave coherently, almost in unison. In the second part of the thesis, we apply computational modeling to mimic and simplify real-life complex systems. We focus on clarifying how the network topology determines the initiation and propagation of synchronization. A simple but efficient method is proposed to reconstruct network structures from functional behaviors for oscillatory systems such as brain. We study the feasibility of network reconstruction systematically for different regimes of coupling and for different network topologies. We utilize the Kuramoto model, an interacting system of oscillators, which is simple but relevant enough to address our questions.Molekyylit, solut, eliöt ja eliölajit muodostavat monimutkaisia dynaamisia järjestelmiä, joiden käyttäytymistä on vaikea johtaa niiden yksittäisten osasten ominaisuuksista. omiikka -tekniikat, joihin kuuluvat esimerkiksi genomiikka, bioinformatiikka ja proteomiikka, mahdollistavat vuorovaikutuksessa olevien komponenttien käyttäytymisen kvantitatiivisen mittaamisen. Tässä työssä käytän matemaattista ja laskennallista mallinnusta kompleksisten systeemien kuvaamiseen ja niiden dynamiikan ennustamiseen. Biologisen systeemin ymmärtämisen ensimmäinen vaihe on yksittäisten elementtien vuorovaikutusten tutkiminen. Tuloksena on staattinen kytkentäkaavio yksittäisten komponenttien yhteyksistä. Kokeelliset menetelmät havainnoivat biologisten komponenttien välisiä vuorovaikutuksia laboratorio-oloissa, kun taas laskennalliset lähestymistavat pyrkivät ennustamaan vuorovaikutuksia yksittäisten komponenttien ominaisuuksien perusteella. Työn ensimmäisessä osassa esittelen proteiini-proteiini-interaktioiden ennustamiseen tarkoitettuja menetelmiä. Näihin menetelmiin kuuluvat vertaileva genomiikka, rakennepohjaiset ja biologiseen kontekstiin pohjautuvat sekä integroidut menetelmät. Arvioin ja vertailen domeeni-domeeni-interaktioiden ennustamiseen yleisimmin käytettyjä menetelmiä. Erityisesti pohdin menetelmien ja tietovarantojen rajoituksia. Otan käyttöön uuden käsitteen, Laajennetun Fylogeneettisen Puun, joka kuvaa graafisesti proteiiniperheiden kehityshistoriaa ja jonka pohjalta ehdotan uutta menetelmää proteiinien välisten toiminnallisten yhteyksien osoittamiseen. Sovelsin menetelmää proteiinien toiminnallisten yhteyksien ennustamiseen ihmisellä ja hiivalla. Biologisen systeemin ymmärtämisen seuraava vaihe on luoda käsitys sen dynamiikasta. Systeemibiologiassa pyritään ymmärtämään emergenttejä ominaisuuksia eli miten erillisten komponenttien yhteisvaikutuksesta syntyy erityisiä kollektiivisia ominaisuuksia ja toimintoja. Kompleksisen systeemin emergenttit ominaisuudet eivät ole näkyvissä eivätkä suoraan pääteltävissä systeemin alemman tason ominaisuuksista. Synkronointi on esimerkki emergentistä ominaisuudesta. Synkronoinnissa kompleksisen vuorovaikutusverkon yksittäiset komponentit tahdistuvat ja käyttäyvät lähes yhtenäisesti. Työn toisessa osassa käytän laskennallista mallinnusta jäljittelemään yksinkertaistettuja kompleksisia systeemejä. Keskityn selvittämään, kuinka vuorovaikutusverkon topologia vaikuttaa synkronoinnin viriämiseen ja leviämiseen. Esitän yksinkertaisen mutta tehokkaan menetelmän verkon rakenteen rekonstruointiin värähtelevän systeemin, kuten aivojen, toiminnallisen käyttäytymisen perusteella. Tutkin järjestelmällisesti verkon rekonstruoinnin onnistumista eri kytkentälujuuksilla ja erilaisilla verkon topologioilla. Hyödynnän Kuramoton mallia vuorovaikuttavista värähtelijöistä, joka on yksinkertainen mutta riittävä vastaamaan kysymyksiimme

Aerospace Medicine and Biology: A continuing bibliography with indexes (supplement 272)

This bibliography lists 360 reports, articles, and other documents introduced into the NASA scientific and technical information system in May 1985

Shape Representation in Primate Visual Area 4 and Inferotemporal Cortex

The representation of contour shape is an essential component of object recognition, but the cortical mechanisms underlying it are incompletely understood, leaving it a fundamental open question in neuroscience. Such an understanding would be useful theoretically as well as in developing computer vision and Brain-Computer Interface applications. We ask two fundamental questions: “How is contour shape represented in cortex and how can neural models and computer vision algorithms more closely approximate this?” We begin by analyzing the statistics of contour curvature variation and develop a measure of salience based upon the arc length over which it remains within a constrained range. We create a population of V4-like cells – responsive to a particular local contour conformation located at a specific position on an object’s boundary – and demonstrate high recognition accuracies classifying handwritten digits in the MNIST database and objects in the MPEG-7 Shape Silhouette database. We compare the performance of the cells to the “shape-context” representation (Belongie et al., 2002) and achieve roughly comparable recognition accuracies using a small test set. We analyze the relative contributions of various feature sensitivities to recognition accuracy and robustness to noise. Local curvature appears to be the most informative for shape recognition. We create a population of IT-like cells, which integrate specific information about the 2-D boundary shapes of multiple contour fragments, and evaluate its performance on a set of real images as a function of the V4 cell inputs. We determine the sub-population of cells that are most effective at identifying a particular category. We classify based upon cell population response and obtain very good results. We use the Morris-Lecar neuronal model to more realistically illustrate the previously explored shape representation pathway in V4 – IT. We demonstrate recognition using spatiotemporal patterns within a winnerless competition network with FitzHugh-Nagumo model neurons. Finally, we use the Izhikevich neuronal model to produce an enhanced response in IT, correlated with recognition, via gamma synchronization in V4. Our results support the hypothesis that the response properties of V4 and IT cells, as well as our computer models of them, function as robust shape descriptors in the object recognition process

The neuroscience of musical creativity using complexity tools

This project is heavily experimental and draws on a wide variety of disciplines from musicology and music psychology to cognitive neuroscience and (neuro)philosophy. The objective is to explore and characterise brain activity during the process of creativity and corroborating this with self-assessments from participants and external assessments from professional “judges”. This three-way experimental design bypasses the semantically difficult task of defining and assessing creativity by asking both participants and judges to rate ‘How creative did you think that was?’. Characterising creativity is pertinent to complexity as it is an opportunity to comprehensively investigate a neural and cognitive system from multiple experimental and analytical facets. This thesis explores the anatomical and functional system underlying the creative cognitive state by analysing the concurrent time series recorded from the brain and furthermore, investigates a model in the stages of creativity using a behavioural experiment, in more detail than hitherto done in this domain. Experimentally, the investigation is done in the domain of music and the time series is the recorded Electroencephalogram (EEG) of a pianist’s whilst performing the two creative musical tasks of ‘Interpretation’ and ‘Improvisation’ manipulations of musical extracts. An initial pilot study consisted of 5 participants being shown 30 musical extracts spanning the Classical soundworld across different rhythms, keys and tonalities. The study was then refined to only 20 extracts and modified to include 10 Jazz extracts and 8 participants from a roughly equal spread of Classical and Jazz backgrounds and gender. 5 external assessors had a roughly even spread of expertise in Jazz and Classical music. Source localisation was performed on the experimental EEG data collected using a software called sLORETA that allows a linear inverse mapping of the electrical activity recorded at the scalp surface onto deeper cortical structures as the source of the recorded activity. Broadman Area (BA) 37 which has previously been linked to semantic processing, was robustly related to participants from a Classical background and BA 7 which has previously been linked to altered states of consciousness such as hypnagogia and sleep, was robustly related to participants from a Jazz background whilst Improvising. Analyses exploring the spread, agreement and biases of ratings across the different judges and self-ratings revealed a judge and participant inter-rater reliability at participant level. There was also an equal agreement between judges when rating the different genres Jazz or Classical, across the different tasks of ‘Improvisation’ and ‘Interpretation’, increasing confidence in inter-genre rating reliability for further analyses on the EEG of the extracts themselves. Furthermore, based on the ratings alone, it was possible to partition participants into either Jazz or Classical, which agreed with phenomenological interview information taken from the participants themselves. With the added conditions of extracts that were deemed creative by objective judge assessment, source localisation analyses pinpointed BA 32 as a robust indicator of Creativity within the participants’ brain. It is an area that is particularly well connected and allows an integration of motoric and emotional communication with a maintenance of executive control. Network analysis was performed using the PLV index (Phase Locking Value) between the 64 electrodes, as the strength of the links in an adjacency matrix of a complex network. This revealed the brain network is significantly more efficient and more strongly synchronised and clustered when participants’ are playing Classical extracts compared to Jazz extracts, in the fronto-central region with a clear right hemispheric lateralization. A behavioural study explored the role of distraction in the ‘Incubation’ period for both interpretation and improvisation using a 2-back number exercise occupying working memory, as the distractor. Analysis shows that a distractor has no significant effect on ‘Improvisation’ but significantly impairs ‘Interpretation’ based on the self-assessments by the participants.Open Acces