Relationship of topology, multiscale phase synchronization, and state transitions in human brain networks

How the brain reconstitutes consciousness and cognition after a major perturbation like general anesthesia is an important question with significant neuroscientific and clinical implications. Recent empirical studies in animals and humans suggest that the recovery of consciousness after anesthesia is not random but ordered. Emergence patterns have been classified as progressive and abrupt transitions from anesthesia to consciousness, with associated differences in duration and electroencephalogram(EEG) properties. We hypothesized that the progressive and abrupt emergence patterns from the unconscious state are associated with, respectively, continuous and discontinuous synchronization transitions in functional brain networks. The discontinuous transition is explainable with the concept of explosive synchronization, which has been studied almost exclusively in network science. We used the Kuramato model, a simple oscillatory network model, to simulate progressive and abrupt transitions in anatomical human brain networks acquired from diffusion tensor imaging (DTI) of 82 brain regions. To facilitate explosive synchronization, distinct frequencies for hub nodes with a large frequency disassortativity (i.e., higher frequency nodes linking with lower frequency nodes, or vice versa) were applied to the brain network. In this simulation study, we demonstrated that both progressive and abrupt transitions follow distinct synchronization processes at the individual node, cluster, and global network levels. The characteristic synchronization patterns of brain regions that are ��progressive and earlier�� or ��abrupt but delayed�� account for previously reported behavioral responses of gradual and abrupt emergence from the unconscious state. The characteristic network synchronization processes observed at different scales provide new insights into how regional brain functions are reconstituted during progressive and abrupt emergence from the unconscious state. This theoretical approach also offers a principled explanation of how the brain reconstitutes consciousness and cognitive functions after physiologic (sleep), pharmacologic (anesthesia), and pathologic (coma) perturbations. ? 2017 Kim, Kim, Mashour and Lee.115sciescopu

Structure-function clustering in weighted brain networks

Abstract: Functional networks, which typically describe patterns of activity taking place across the cerebral cortex, are widely studied in neuroscience. The dynamical features of these networks, and in particular their deviation from the relatively static structural network, are thought to be key to higher brain function. The interactions between such structural networks and emergent function, and the multimodal neuroimaging approaches and common analysis according to frequency band motivate a multilayer network approach. However, many such investigations rely on arbitrary threshold choices that convert dense, weighted networks to sparse, binary structures. Here, we generalise a measure of multiplex clustering to describe weighted multiplexes with arbitrarily-many layers. Moreover, we extend a recently-developed measure of structure-function clustering (that describes the disparity between anatomical connectivity and functional networks) to the weighted case. To demonstrate its utility we combine human connectome data with simulated neural activity and bifurcation analysis. Our results indicate that this new measure can extract neurologically relevant features not readily apparent in analogous single-layer analyses. In particular, we are able to deduce dynamical regimes under which multistable patterns of neural activity emerge. Importantly, these findings suggest a role for brain operation just beyond criticality to promote cognitive flexibility

Sincronização induzida por forças externas em redes modulares

Orientador: Marcus Aloizio Martinez de AguiarTese (doutorado) - Universidade Estadual de Campinas, Instituto de Física Gleb WataghinResumo: Neste trabalho estudamos a sincronização de osciladores de Kuramoto sujeitos a forças externas em redes modulares complexas. A motivação está na dinâmica neuronal que ocorre durante o processamento de informação no córtex cerebral que parece estar relacionada ao disparo síncrono de grupos de neurônios. A organização dos neurônios é modular, com agrupamentos associados a diferentes funções e estruturas cerebrais, e precisa responder constantemente a estímulos externos. Anormalidades no processo de sincronização, como a ativação de múltiplos módulos têm sido associadas à doenças como epilepsia e Alzheimer. Nesse contexto, estudamos o comportamento de osciladores de Kuramoto forçados, onde apenas uma fração deles é submetida a uma força externa periódica. Quando todos os osciladores recebem o estímulo externo o sistema sempre sincroniza com a força externa se a sua intensidade for suficientemente grande. Mostramos que as condições para a sincronização global dependem da fração de nós forçada e da topologia da rede e das intensidades do acoplamento interno e da força externa. Desenvolvemos cálculos numéricos e analíticos para a força crítica que leva a rede à sincronização global em função da fração de osciladores forçados. Como uma aplicação estudamos a resposta da rede de junções elétricas do \textit{C. elegans} ao estímulo externo usando o modelo de Kuramoto parcialmente forçado, aplicando a força a grupos específicos de neurônios. Os estímulos foram aplicados a três módulos topológicos, dois gânglios, especificados por sua localização anatômica, e aos grupos funcionais compostos por todos os neurônios sensoriais e motores. Encontramos que os módulos topológicos não contêm grupos puramente anatômicos ou classes funcionais e que estimular diferentes classes neuronais leva a respostas muito diferentes, medidas em termos de sincronização e correlações de velocidade de fase. Em todos os casos a estrutura modular impede a sincronização global, protegendo o sistema de falhas. As respostas aos estímulos aplicados aos módulos topológicos e funcionais mostram padrões pronunciados de correlação ou anti-correlação com outros módulos que não foram observados quando o estímulo foi aplicado a um gânglio com neurônios funcionais mistos. Todos os códigos e dados utilizados nesta tese estão disponível em [1]Abstract: In this work we study the synchronization of Kuramoto oscillators driven by external forces in complex modular networks. The motivation is the neuronal dynamics that takes place during information processing in the neural cortex, which seems to be related to the synchronous firing of groups of neurons. The neuron organization is modular, with clusters associated to different functions and brain structures, and need to constantly respond to external stimuli. Abnormalities in the process of synchronization, such as the activation of multiple modules, have been associated with epilepsy and Alzheimer's disease. In this context, we study the behavior of forced Kuramoto oscillators where only a fraction of them is subjected to a periodic external force. When all oscillators receive the external drive the system always synchronize with the periodic force if its intensity is sufficiently large. We show that the conditions for global synchronization depend on the fraction of nodes being forced and on network topology, strength of internal couplings and intensity of external forcing. We develop numerical and analytical calculations for the critical force for global synchronization as a function of the fraction of forced oscillators. As an application we study the response of the electric junction \textit{C. elegans} network to external stimuli using the partially forced Kuramoto model and applying the force to specific groups of neurons. Stimuli were applied to three topological modules, two ganglia, specified by their anatomical localization, and to the functional groups composed of all sensory and motoneurons. We found that topological modules do not contain purely anamotical groups or functional classes, and that stimulating different classes of neurons lead to very different responses, measured in terms of synchronization and phase velocity correlations. In all cases the modular structure hindered full synchronization, protecting the system from seizures. The responses to stimuli applied to topological and functional modules showed pronounced patterns of correlation or anti-correlation with other modules that were not observed when the stimulus was applied to a ganglion with mixed functional neurons. All codes and data used in this thesis are available in [1]DoutoradoFísicaDoutora em Ciências141021/2017-9CNP

Synchronization in Complex Networks Under Uncertainty

La sincronització en xarxes és la música dels sistemes complexes. Els ritmes col·lectius que emergeixen de molts oscil·ladors acoblats expliquen el batec constant del cor, els patrons recurrents d'activitat neuronal i la sincronia descentralitzada a les xarxes elèctriques. Els models matemàtics són sòlids i han avançat significativament, especialment en el problema del camp mitjà, on tots els oscil·ladors estan connectats mútuament. Tanmateix, les xarxes reals tenen interaccions complexes que dificulten el tractament analític. Falta un marc general i les soluciones existents en caixes negres numèriques i espectrals dificulten la interpretació. A més, la informació obtinguda en mesures empíriques sol ser incompleta. Motivats per aquestes limitacions, en aquesta tesi proposem un estudi teòric dels oscil·ladors acoblats en xarxes sota incertesa. Apliquem propagació d'errors per predir com una estructura complexa amplifica el soroll des dels pesos microscòpics fins al punt crític de sincronització, estudiem l'efecte d'equilibrar les interaccions de parelles i d'ordre superior en l'optimització de la sincronia i derivem esquemes d'ajust de pesos per mapejar el comportament de sincronització en xarxes diferents. A més, un desplegament geomètric rigorós de l'estat sincronitzat ens permet abordar escenaris descentralitzats i descobrir regles locals òptimes que indueixen transicions globals abruptes. Finalment, suggerim dreceres espectrals per predir punts crítics amb àlgebra lineal i representacions aproximades de xarxa. En general, proporcionem eines analítiques per tractar les xarxes d'oscil·ladors en condicions sorolloses i demostrem que darrere els supòsits predominants d'informació completa s'amaguen explicacions mecanicistes clares. Troballes rellevants inclouen xarxes particulars que maximitzen el ventall de comportaments i el desplegament exitós del binomi estructura-dinàmica des d'una perspectiva local. Aquesta tesi avança la recerca d'una teoria general de la sincronització en xarxes a partir de principis mecanicistes i geomètrics, una peça clau que manca en l'anàlisi, disseny i control de xarxes neuronals biològiques i artificials i sistemes d'enginyeria complexos.La sincronización en redes es la música de los sistemas complejos. Los ritmos colectivos que emergen de muchos osciladores acoplados explican el latido constante del corazón, los patrones recurrentes de actividad neuronal y la sincronía descentralizada de las redes eléctricas. Los modelos matemáticos son sólidos y han avanzado significativamente, especialmente en el problema del campo medio, donde todos los osciladores están conectados entre sí. Sin embargo, las redes reales tienen interacciones complejas que dificultan el tratamiento analítico. Falta un marco general y las soluciones en cajas negras numéricas y espectrales dificultan la interpretación. Además, las mediciones empíricas suelen ser incompletas. Motivados por estas limitaciones, en esta tesis proponemos un estudio teórico de osciladores acoplados en redes bajo incertidumbre. Aplicamos propagación de errores para predecir cómo una estructura compleja amplifica el ruido desde las conexiones microscópicas hasta puntos críticos macroscópicos, estudiamos el efecto de equilibrar interacciones por pares y de orden superior en la optimización de la sincronía y derivamos esquemas de ajuste de pesos para mapear el comportamiento en estructuras distintas. Una expansión geométrica del estado sincronizado nos permite abordar escenarios descentralizados y descubrir reglas locales que inducen transiciones abruptas globales. Por último, sugerimos atajos espectrales para predecir puntos críticos usando álgebra lineal y representaciones aproximadas de red. En general, proporcionamos herramientas analíticas para manejar redes de osciladores en condiciones ruidosas y demostramos que detrás de las suposiciones predominantes de información completa se ocultaban claras explicaciones mecanicistas. Hallazgos relevantes incluyen redes particulares que maximizan el rango de comportamientos y la explicación del binomio estructura-dinámica desde una perspectiva local. Esta tesis avanza en la búsqueda de una teoría general de sincronización en redes desde principios mecánicos y geométricos, una pieza clave que falta en el análisis, diseño y control de redes neuronales biológicas y artificiales y sistemas de ingeniería complejos.Synchronization in networks is the music of complex systems. Collective rhythms emerging from many interacting oscillators appear across all scales of nature, from the steady heartbeat and the recurrent patterns in neuronal activity to the decentralized synchrony in power-grids. The mathematics behind these processes are solid and have significantly advanced lately, especially in the mean-field problem, where oscillators are all mutually connected. However, real networks have complex interactions that difficult the analytical treatment. A general framework is missing and most existing results rely on numerical and spectral black-boxes that hinder interpretation. Also, the information obtained from measurements is usually incomplete. Motivated by these limitations, in this thesis we propose a theoretical study of network-coupled oscillators under uncertainty. We apply error propagation to predict how a complex structure amplifies noise from the link weights to the synchronization onset, study the effect of balancing pair-wise and higher-order interactions in synchrony optimization, and derive weight-tuning schemes to map the synchronization behavior of different structures. Also, we develop a rigorous geometric unfolding of the synchronized state to tackle decentralized scenarios and to discover optimal local rules that induce global abrupt transitions. Last, we suggest spectral shortcuts to predict critical points using linear algebra and network representations with limited information. Overall, we provide analytical tools to deal with oscillator networks under noisy conditions and prove that mechanistic explanations were hidden behind the prevalent assumptions of complete information. Relevant finding include particular networks that maximize the range of behaviors and the successful unfolding of the structure-dynamics interplay from a local perspective. This thesis advances the quest of a general theory of network synchronization built from mechanistic and geometric principles, a key missing piece in the analysis, design and control of biological and artificial neural networks and complex engineering systems