Coupling and stochasticity in mesoscopic brain dynamics

The brain is known to operate under the constant influence of noise arising from a variety of sources. It also organises its activity into rhythms spanning multiple frequency bands. These rhythms originate from neuronal oscillations which can be detected via measurements such as electroen-cephalography (EEG) and functional magnetic resonance (fMRI). Experimental evidence suggests that interactions between rhythms from distinct frequency bands play a key role in brain processing, but the dynamical mechanisms underlying this cross-frequency interactions are still under investigation. Some rhythms are pathological and harmful to brain function. Such is the case of epileptiform rhythms characterising epileptic seizures. Much has been learnt about the dynamics of the brain from computational modelling. Particularly relevant is mesoscopic scale modelling, which is concerned with spatial scales exceeding those of individual neurons and corresponding to processes and structures underlying the generation of signals registered in the EEG and fMRI recordings. Such modelling usually involves assumptions regarding the characteristics of the background noise, which represents afferents from remote, non-modelled brain areas. To this end, Gaussian white noise, characterised by a flat power spectrum, is often used. In contrast, macroscopic fluctuations in the brain typically follow a `1/f b ¿ spectrum, which is a characteristic feature of temporally correlated, coloured noise. In Chapters 3-5 of this Thesis we address by means of a stochastically driven mesoscopic neuronal model, the three following questions. First, in Chapter 3 we ask about the significance of deviations from the assumption of white noise in the context of brain dynamics, and in particular we study the role that temporally correlated noise plays in eliciting aberrant rhythms in the model of an epileptic brain. We find that the generation of epileptiform dynamics in the model depends non-monotonically on the noise correlation time. We show that this is due to the maximisation of the spectral content of epileptogenic rhythms in the noise. These rhythms fall into frequency bands that indeed were experimentally shown to increase in power prior to epileptic seizures. We explain these effects in terms of the interplay between specific driving frequencies and bifurcation structure of the model. Second, in Chapter 4 we show how coupling between cortical modules leads to complex activity patterns and to the emergence of a phenomenon that we term collective excitability. Temporal patterns generated by this model bear resemblance to clinically observed characteristics of epileptic seizures. In that chapter we also introduce a fast method of tracking a loss of stability caused by excessive inter-modular coupling in a neuronal network. Third, in Chapter 5 we focus on cross-frequency interactions occurring in a network of cortical modules, in the presence of coloured noise. We suggest a mechanism that underlies the increase of power in a fast rhythm due to driving with a slow rhythm, and we find the noise parameters that best recapitulate experimental power spectra. Finally, in Chapter 6, we examine models of haemodynamic and metabolic brain processes, we test them on experimental data, and we consider the consequences of coupling them with mesoscopic neuronal models. Taken together, our results show the combined influence of noise and coupling in computational models of neuronal activity. Moreover, they demonstrate the relevance of dynamical properties of neuronal systems to specific physiological phenomena, in particular related to cross-frequency interactions and epilepsy. Insights from this Thesis could in the future empower studies of epilepsy as a dynamic disease, and could contribute to the development of treatment methods applicable to drug-resistant epileptic patients.El cervell opera sota la influència de sorolls amb diversos orígens. També organitza la seva activitat en una sèrie de ritmes que s'expandeixen en diverses bandes de freqüència. Aquests ritmes tenen el seu origen en les osci∙lacions neuronals i poden detectar-se via mesures com les electroencefalogràfiques (EEG) o la ressonància magnètica funcional (fMRI). Les evidències experimentals suggereixen que les interaccions entre ritmes operant en bandes de freqüència diferents juguen un paper central en el processat cerebral però els mecanismes dinàmics subjacents a les interaccions inter-freqüència encara estan investigant-se. Alguns ritmes són patològics i fan malbé el funcionament cerebral. És el cas dels ritmes epileptiformes que caracteritzen les convulsions epilèptiques. Fent servir el modelatge computacional s'ha après molt sobre la dinàmica del cervell. Especialment rellevant és el modelatge a l’escala mesoscòpica, que té a veure amb les escales espacials superiors a les de les neurones individuals i que correspon als processos que generen EEG i fMRI. Tal modelatge, en general, implica supòsits relatius a les característiques del soroll de fons que representa zones remotes del cervell no modelades. Amb aquesta finalitat s'utilitza sovint el soroll blanc gaussià, que es caracteritza per un espectre de potència pla. Les fluctuacions macroscòpiques en el cervell, però, normalment segueixen un espectre '1/fb', que és un tret característic de les correlacions temporals i el soroll de color. Als Capítols 3-5 d'aquesta tesi abordem mitjançant un model neuronal mesoscòpic forçat estocàsticament, les tres preguntes següents. En primer lloc, en el Capítol 3 ens preguntem sobre la importància de les desviacions de l'assumpció de soroll blanc en el context de la dinàmica del cervell i, en particular, estudiem el paper que juga el soroll amb correlació temporal en l'obtenció de ritmes aberrants d'un cervell epilèptic. Trobem que la generació de les dinàmiques epileptiformes depèn de forma monòtona del temps de correlació del soroll. Aquests ritmes es divideixen en bandes de freqüència que, segons, s'ha mostrat experimentalment, augmenten la seva potència espectral abans de les crisis epilèptiques. Expliquem aquests efectes en termes de la interacció entre les freqüències específiques del forçament i l'estructura de bifurcació del model. En segon lloc, en el Capítol 4 es mostra com l'acoblament entre mòduls corticals condueix a patrons d'activitat complexes i a l'aparició d'un fenomen que anomenem excitabilitat col∙lectiva. Els patrons temporals generats per aquest model s'assemblen a les observacions clíniques de les convulsions epilèptiques. En aquest capítol també introduïm un mètode d'anàlisi de la pèrdua d'estabilitat causada per l'acoblament inter-modular excessiu en les xarxes neuronals. En tercer lloc, en el Capítol 5 ens centrem en les interaccions inter-freqüència que es produeixen en una xarxa de mòduls corticals en presència de soroll de color. Suggerim un mecanisme subjacent a l'augment de la potència spectral de ritmes ràpids a causa del forçament amb un ritme lent, i veiem quins paràmetres del soroll descriuen millor els espectres de potència experimental. Finalment, en el Capítol 6, estudiem models dels processos hemodinàmics i metabòlics del cervell, els comparem amb dades experimentals i considerem les conseqüències del seu acoblament amb models neuronals mesoscopics. En conjunt, els nostres resultats mostren la influència combinada del soroll i l'acoblament en models computacionals de l'activitat neuronal. D'altra banda, també demostren la importància de les propietats dinàmiques dels sistemes neuronals en fenòmens fisiològics específics com les interaccions inter-frequència i l'epilèpsia. Els resultats d'aquesta Tesi contribueixen a potenciar l’estudi de l'epilèpsia com una malaltia dinàmica, i el desenvolupament de mètodes de tractament aplicables a pacients epilèptics resistents als fàrmacs.Postprint (published version

How to build a functional connectomic biomarker for mild cognitive impairment from source reconstructed MEG resting-state activity: the combination of ROI representation and connectivity estimator matters

Our work aimed to demonstrate the combination of machine learning and graph theory for the designing of a connectomic biomarker for mild cognitive impairment (MCI) subjects using eyes-closed neuromagnetic recordings. The whole analysis based on source-reconstructed neuromagnetic activity. As ROI representation, we employed the principal component analysis (PCA) and centroid approaches. As representative bi-variate connectivity estimators for the estimation of intra and cross-frequency interactions, we adopted the phase locking value (PLV), the imaginary part (iPLV) and the correlation of the envelope (CorrEnv). Both intra and cross-frequency interactions (CFC) have been estimated with the three connectivity estimators within the seven frequency bands (intra-frequency) and in pairs (CFC), correspondingly. We demonstrated how different versions of functional connectivity graphs single-layer (SL-FCG) and multi-layer (ML-FCG) can give us a different view of the functional interactions across the brain areas. Finally, we applied machine learning techniques with main scope to build a reliable connectomic biomarker by analyzing both SL-FCG and ML-FCG in two different options: as a whole unit using a tensorial extraction algorithm and as single pair-wise coupling estimations. We concluded that edge-weighed feature selection strategy outperformed the tensorial treatment of SL-FCG and ML-FCG. The highest classification performance was obtained with the centroid ROI representation and edge-weighted analysis of the SL-FCG reaching the 98% for the CorrEnv in α1:α2 and 94% for the iPLV in α2. Classification performance based on the multi-layer participation coefficient, a multiplexity index reached 52% for iPLV and 52% for CorrEnv. Selected functional connections that build the multivariate connectomic biomarker in the edge-weighted scenario are located in default-mode, fronto-parietal and cingulo-opercular network. Our analysis supports the notion of analysing FCG simultaneously in intra and cross-frequency whole brain interactions with various connectivity estimators in beamformed recordings

Stochastic and complex dynamics in mesoscopic brain networks

The aim of this thesis is to deepen into the understanding of the mechanisms responsible for the generation of complex and stochastic dynamics, as well as emerging phenomena, in the human brain. We study typical features from the mesoscopic scale, i.e., the scale in which the dynamics is given by the activity of thousands or even millions of neurons. At this scale the synchronous activity of large neuronal populations gives rise to collective oscillations of the average voltage potential. These oscillations can easily be recorded using electroencephalography devices (EEG) or measuring the Local Field Potentials (LFPs). In Chapter 5 we show how the communication between two cortical columns (mesoscopic structures) can be mediated efficiently by a microscopic neural network. We use the synchronization of both cortical columns as a probe to ensure that an effective communication is established between the three neural structures. Our results indicate that there are certain dynamical regimes from the microscopic neural network that favor the correct communication between the cortical columns: therefore, if the LFP frequency of the neural network is of around 40Hz, the synchronization between the cortical columns is more robust compared to the situation in which the neural network oscillates at a lower frequency (10Hz). However, microscopic topological characteristics of the network also influence communication, being a small-world structure the one that best promotes the synchronization of the cortical columns. Finally, this Chapter shows how the mediation exerted by the neural network cannot be substituted by the average of its activity, that is, the dynamic properties of the microscopic neural network are essential for the proper transmission of information between all neural structures. The oscillatory brain electrical activity is largely dependent on the interplay between excitation and inhibition. In Chapter 6 we study how groups of cortical columns show complex patterns of cortical excitation and inhibition taking into account their topological features and the strength of their couplings. These cortical columns segregate between those dominated by excitation and those dominated by inhibition, affecting the synchronization properties of networks of cortical columns. In Chapter 7 we study a dynamic regime by which complex patterns of synchronization between chaotic oscillators appear spontaneously in a network. We show what conditions must a set of coupled dynamical systems fulfill in order to display heterogeneity in synchronization. Therefore, our results are related to the complex phenomenon of synchronization in the brain, which is a focus of study nowadays. Finally, in Chapter 8 we study the ability of the brain to compute and process information. The novelty here is our use of complex synchronization in the brain in order to implement basic elements of Boolean computation. In this way, we show that the partial synchronization of the oscillations in the brain establishes a code in terms of synchronization / non-synchronization (1/0, respectively), and thus all simple Boolean functions can be implemented (AND, OR, XOR, etc.). We also show that complex Boolean functions, such as a flip-flop memory, can be constructed in terms of states of dynamic synchronization of brain oscillations.L'objectiu d'aquesta Tesi és aprofundir en la comprensió dels mecanismes responsables de la generació de dinàmica complexa i estocàstica, així com de fenòmens emergents, en el cervell humà. Estudiem la fenomenologia característica de l'escala mesoscòpica, és a dir, aquella en la que la dinàmica característica ve donada per l'activitat de milers de neurones. En aquesta escala l'activitat síncrona de grans poblacions neuronals dóna lloc a un fenomen col·lectiu pel qual es produeixen oscil·lacions del seu potencial mitjà. Aquestes oscil·lacions poden ser fàcilment enregistrades mitjançant aparells d'electroencefalograma (EEG) o enregistradors de Potencials de Camp Local (LFP). En el Capítol 5 mostrem com la comunicació entre dos columnes corticals (estructures mesoscòpiques) pot ser conduïda de forma eficient per una xarxa neuronal microscòpica. De fet, emprem la sincronització de les dues columnes corticals per comprovar que s'ha establert una comunicació efectiva entre les tres estructures neuronals. Els resultats indiquen que hi ha règims dinàmics de la xarxa neuronal microscòpica que afavoreixen la correcta comunicació entre les columnes corticals: si la freqüència típica de LFP a la xarxa neuronal està al voltant dels 40Hz la sincronització entre les columnes corticals és més robusta que a una menor freqüència (10Hz). La topologia de la xarxa microscòpica també influeix en la comunicació, essent una estructura de tipus món petit (small-world) la que més afavoreix la sincronització. Finalment, la mediació de xarxa neuronal no pot ser substituïda per la mitjana de la seva activitat, és a dir, les propietats dinàmiques microscòpiques són imprescindibles per a la correcta transmissió d'informació entre totes les escales cerebrals. L'activitat elèctrica oscil·latòria cerebral ve donada en gran mesura per la interacció entre excitació i inhibició neuronal. En el Capítol 6 estudiem com grups de columnes corticals mostren patrons complexos d'excitació i inhibició segons quina sigui la seva topologia i d'acoblament. D'aquesta manera les columnes corticals se segreguen entre aquelles dominades per l'excitació i aquelles dominades per la inhibició, influint en les capacitats de sincronització de xarxes de columnes corticals. En el Capítol 7 estudiem un règim dinàmic segons el qual patrons complexos de sincronització apareixen espontàniament en xarxes d'oscil·ladors caòtics. Mostrem quines condicions s'han de donar en un conjunt de sistemes dinàmics acoblats per tal de mostrar heterogeneïtat en la sincronització, és a dir, coexistència de sincronitzacions. D'aquesta manera relacionem els nostres resultats amb el fenomen de sincronització complexa en el cervell. Finalment, en el Capítol 8 estudiem com el cervell computa i processa informació. La novetat aquí és l'ús que fem de la sincronització complexa de columnes corticals per tal d'implementar elements bàsics de computació Booleana. Mostrem com la sincronització parcial de les oscil·lacions cerebrals estableix un codi neuronal en termes de sincronització/no sincronització (1/0, respectivament) amb el qual totes les funcions Booleanes simples poden ésser implementades (AND, OR, XOR, etc). Mostrem, també, com emprant xarxes mesoscòpiques extenses les capacitats de computació creixen proporcionalment. Així funcions Booleanes complexes, com una memòria del tipus flip-flop, pot ésser construïda en termes d'estats de sincronització dinàmica d'oscil·lacions cerebrals.Postprint (published version

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

Exact neural mass model for synaptic-based working memory

A synaptic theory of Working Memory (WM) has been developed in the last decade as a possible alternative to the persistent spiking paradigm. In this context, we have developed a neural mass model able to reproduce exactly the dynamics of heterogeneous spiking neural networks encompassing realistic cellular mechanisms for short-term synaptic plasticity. This population model reproduces the macroscopic dynamics of the network in terms of the firing rate and the mean membrane potential. The latter quantity allows us to get insight on Local Field Potential and electroencephalographic signals measured during WM tasks to characterize the brain activity. More specifically synaptic facilitation and depression integrate each other to efficiently mimic WM operations via either synaptic reactivation or persistent activity. Memory access and loading are associated to stimulus-locked transient oscillations followed by a steady-state activity in the $\beta-\gamma$ band, thus resembling what observed in the cortex during vibrotactile stimuli in humans and object recognition in monkeys. Memory juggling and competition emerge already by loading only two items. However more items can be stored in WM by considering neural architectures composed of multiple excitatory populations and a common inhibitory pool. Memory capacity depends strongly on the presentation rate of the items and it maximizes for an optimal frequency range. In particular we provide an analytic expression for the maximal memory capacity. Furthermore, the mean membrane potential turns out to be a suitable proxy to measure the memory load, analogously to event driven potentials in experiments on humans. Finally we show that the $\gamma$ power increases with the number of loaded items, as reported in many experiments, while $\theta$ and $\beta$ power reveal non monotonic behaviours.Comment: 47 pages, 14 figure

Computational Study of the Mechanisms Underlying Oscillation in Neuronal Locomotor Circuits

In this thesis we model two very different movement-related neuronal circuits, both of which produce oscillatory patterns of activity. In one case we study oscillatory activity in the basal ganglia under both normal and Parkinsonian conditions. First, we used a detailed Hodgkin-Huxley type spiking model to investigate the activity patterns that arise when oscillatory cortical input is transmitted to the globus pallidus via the subthalamic nucleus. Our model reproduced a result from rodent studies which shows that two anti-phase oscillatory groups of pallidal neurons appear under Parkinsonian conditions. Secondly, we used a population model of the basal ganglia to study whether oscillations could be locally generated. The basal ganglia are thought to be organised into multiple parallel channels. In our model, isolated channels could not generate oscillations, but if the lateral inhibition between channels is sufficiently strong then the network can act as a rhythm-generating ``pacemaker'' circuit. This was particularly true when we used a set of connection strength parameters that represent the basal ganglia under Parkinsonian conditions. Since many things are not known about the anatomy and electrophysiology of the basal ganglia, we also studied oscillatory activity in another, much simpler, movement-related neuronal system: the spinal cord of the Xenopus tadpole. We built a computational model of the spinal cord containing approximately 1,500 biologically realistic Hodgkin-Huxley neurons, with synaptic connectivity derived from a computational model of axon growth. The model produced physiological swimming behaviour and was used to investigate which aspects of axon growth and neuron dynamics are behaviourally important. We found that the oscillatory attractor associated with swimming was remarkably stable, which suggests that, surprisingly, many features of axonal growth and synapse formation are not necessary for swimming to emerge. We also studied how the same spinal cord network can generate a different oscillatory pattern in which neurons on both sides of the body fire synchronously. Our results here suggest that under normal conditions the synchronous state is unstable or weakly stable, but that even small increases in spike transmission delays act to stabilise it. Finally, we found that although the basal ganglia and the tadpole spinal cord are very different systems, the underlying mechanism by which they can produce oscillations may be remarkably similar. Insights from the tadpole model allow us to predict how the basal ganglia model may be capable of producing multiple patterns of oscillatory activity