Stochastic neural network dynamics: synchronisation and control

Biological brains exhibit many interesting and complex behaviours. Understanding of the mechanisms behind brain behaviours is critical for continuing advancement in fields of research such as artificial intelligence and medicine. In particular, synchronisation of neuronal firing is associated with both improvements to and degeneration of the brain’s performance; increased synchronisation can lead to enhanced information-processing or neurological disorders such as epilepsy and Parkinson’s disease. As a result, it is desirable to research under which conditions synchronisation arises in neural networks and the possibility of controlling its prevalence. Stochastic ensembles of FitzHugh-Nagumo elements are used to model neural networks for numerical simulations and bifurcation analysis. The FitzHugh-Nagumo model is employed because of its realistic representation of the flow of sodium and potassium ions in addition to its advantageous property of allowing phase plane dynamics to be observed. Network characteristics such as connectivity, configuration and size are explored to determine their influences on global synchronisation generation in their respective systems. Oscillations in the mean-field are used to detect the presence of synchronisation over a range of coupling strength values. To ensure simulation efficiency, coupling strengths between neurons that are identical and fixed with time are investigated initially. Such networks where the interaction strengths are fixed are referred to as homogeneously coupled. The capacity of controlling and altering behaviours produced by homogeneously coupled networks is assessed through the application of weak and strong delayed feedback independently with various time delays. To imitate learning, the coupling strengths later deviate from one another and evolve with time in networks that are referred to as heterogeneously coupled. The intensity of coupling strength fluctuations and the rate at which coupling strengths converge to a desired mean value are studied to determine their impact upon synchronisation performance. The stochastic delay differential equations governing the numerically simulated networks are then converted into a finite set of deterministic cumulant equations by virtue of the Gaussian approximation method. Cumulant equations for maximal and sub-maximal connectivity are used to generate two-parameter bifurcation diagrams on the noise intensity and coupling strength plane, which provides qualitative agreement with numerical simulations. Analysis of artificial brain networks, in respect to biological brain networks, are discussed in light of recent research in sleep theor

Theta and gamma rhythmic coding through two spike output modes in the hippocampus during spatial navigation

Hippocampal CA1 neurons generate single spikes and stereotyped bursts of spikes. However, it is unclear how individual neurons dynamically switch between these output modes and whether these two spiking outputs relay distinct information. We performed extracellular recordings in spatially navigating rats and cellular voltage imaging and optogenetics in awake mice. We found that spike bursts are preferentially linked to cellular and network theta rhythms (3–12 Hz) and encode an animal's position via theta phase precession, particularly as animals are entering a place field. In contrast, single spikes exhibit additional coupling to gamma rhythms (30–100 Hz), particularly as animals leave a place field. Biophysical modeling suggests that intracellular properties alone are sufficient to explain the observed input frequency-dependent spike coding. Thus, hippocampal neurons regulate the generation of bursts and single spikes according to frequency-specific network and intracellular dynamics, suggesting that these spiking modes perform distinct computations to support spatial behavior.Fil: Lowet, Eric. Boston University; Estados UnidosFil: Sheehan, Daniel J.. Boston University; Estados UnidosFil: Chialva, Ulises. Universidad Nacional del Sur. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca; ArgentinaFil: De Oliveira Pena, Rodrigo. New Jersey Institute of Technology; Estados UnidosFil: Mount, Rebecca A.. Boston University; Estados UnidosFil: Xiao, Sheng. Boston University; Estados UnidosFil: Zhou, Samuel L.. Boston University; Estados UnidosFil: Tseng, Hua-an. Boston University; Estados UnidosFil: Gritton, Howard. University of Illinois. Urbana - Champaign; Estados UnidosFil: Shroff, Sanaya. Boston University; Estados UnidosFil: Kondabolu, Krishnakanth. Boston University; Estados UnidosFil: Cheung, Cyrus. Boston University; Estados UnidosFil: Wang, Yangyang. Boston University; Estados UnidosFil: Piatkevich, Kiryl D.. Westlake University; ChinaFil: Boyden, Edward S.. McGovern Institute for Brain Research; Estados Unidos. Massachusetts Institute of Technology; Estados UnidosFil: Mertz, Jerome. Boston University; Estados UnidosFil: Hasselmo, Michael E.. Boston University; Estados UnidosFil: Rotstein, Horacio. New Jersey Institute of Technology; Estados UnidosFil: Han, Xue. Boston University; Estados Unido

Influence of Focal Activity on Macroscale Brain Dynamics in Health and Disease

Macroscopic recordings of brain activity (e.g. fMRI, EEG) are a sensitive biomarker of the neural networks supporting neurocognitive function. However, it remains largely unclear what mechanisms mediate changes in macroscale networks after focal brain injuries like stroke, seizure, and TBI. Recently, optical neuroimaging in animal models has emerged as a powerful tool to begin addressing these questions. Using widefield imaging of cortical calcium dynamics in mice, this dissertation investigates the mechanisms by which focal disruptions in activity alter brain-wide functional dynamics. In two chapters, I demonstrate 1) that focal sensory stimulation elicits state-dependent, global slow waves propagating from primary somatosensory cortex (S1). Using a focal ischemic stroke model, I show that bilateral activation of somatosensory cortices is required for initiating global SWs, while spontaneous SWs are generated independent of S1. 2) That regional disruption of cortical excitability induces widespread changes across cortical networks, using chemogenetic manipulation of parvalbumin interneurons to model focal epileptiform activity in S1. We further show that local imbalances in excitability propagate differentially through intra- and interhemispheric connections, and can induce plasticity in large-scale networks. These studies begin to define the mechanisms of macro-scale network disruption after focal injuries, adding to our understanding of how local cortical circuits modulate global brain networks

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

Oscillations in microvascular flow:their relationship to tissue oxygenation, cellular metabolic function and their diagnostic potential for detecting skin melanoma - clinical, experimental and theoretical investigations

Tumour vasculature is known to be inefficient and abnormal due to poorly regulated angiogenesis during tumour growth. This leads to irregular patterns of blood flow which are spatially and temporally heterogeneous. Many investigations into the characteristics of tumours are invasive and performed on animal models. However, continuous technological and theoretical advancement is leading to the use of non-invasive imaging techniques, providing in vivo information on humans. Here, data recorded using laser Doppler flowmetry (LDF) in malignant melanoma and control lesions are analysed using techniques designed for application to non-stationary, time-varying data. Many studies utilising LDF have previously revealed increased blood flow in malignant lesions, but very little attention has been paid to the dynamics of this blood flow, or how it changes over time. As it has been demonstrated previously that the oscillations observed within blood flow data are physiologically significant, failure to extract these characteristics loses information about the underlying dynamical system from which the blood flow data were recorded. Significant differences in blood flow dynamics are revealed and used in the development of a diagnostic test for melanoma. In addition to the characterization of the blood flow dynamics in melanoma, possible causes for the observed changes are investigated and related to two widely observed characteristics of cancer, intermittent hypoxia and altered cellular energy metabolism. The former is explored through the analysis of blood flow and oxygenation data recorded during dry static apnoea, whilst the latter is modelled using coupled phase oscillators

Optogenetic Interrogation and Manipulation of Vascular Blood Flow in Cortex

Understanding blood flow regulatory mechanisms that correlate the regional blood flow with the level of local neuronal activity in brain is an ongoing research. Discerning different aspects of this coupling is of substantial importance in interpretation of functional imaging results, such as functional magnetic resonance imaging (fMRI), that rely on hemodynamic recordings to detect and image brain neuronal activity. Moreover, this understanding can provide insight into blood flow disorders under different pathophysiological conditions and possible treatments for such disorders. The blood regulatory mechanisms can be studied at two different; however, complementary levels: at the cellular level or at the vascular level. To fully understand the regulatory mechanisms in brain, it is essential to discern details of the coupling mechanism in each level. While, the cellular pathways of the coupling mechanism has been studied extensively in the past few decades, our understanding of the vascular response to brain activity is fairly basic. The main objective of this dissertation is to develop proper methods and instrumentation to interrogate regional cortical vasodynamics in response to local brain stimulation. For this purpose we offer the design of a custom-made OCT scanner and the necessary lens mechanisms to integrate the OCT system, fluorescence imaging, and optogenetic stimulation technologies in a single system. The design uses off-the-shelf components for a cost-effective design. The modular design of the device allows scientists to modify it in accordance with their research needs. With this multi-modal system we are able to monitor blood flow, blood velocity, and lumen diameter of pial vessels, simultaneously. Additionally, the system design provides the possibility of generating arbitrary spatial stimulation light pattern on brain. These abilities enables researchers to capture more diverse datasets and, eventually, obtain a more comprehensive picture of the vasodynamics in the brain. Along with the device we also proposed new biological experiments that are tailored to investigate the spatio-temporal properties of the vascular response to optical neurostimulation of the excitatory neurons. We demonstrate the ability of the proposed methods to investigate the effect of length and amplitude of stimulation on the temporal pattern of response in the blood flow, blood velocity, and diameter of the pial vessels. Moreover, we offer systemic approaches to investigate the spatial characteristics of the response in a vascular network. In these methods we apply arbitrary spatial patterns of optical stimulation to the cortex of transgenic mice and monitor the attributes of surrounding vessels. With this flexibility we were able to image the brain region that is influenced by a pial artery. After characterizing the spatio-temporal properties of the vascular blood flow response to optical neuro-modulation, we demonstrate the design and application of an optogenetic-based closed-loop controller mechanism in the brain. This controller, uses a proportional–integral–derivative (PID) compensator to engineer temporal optogenetic stimulation light pulses and maintain the flow of blood at various user defined levels in a set of selected arteries. Upon tuning the gain values of the PID controller we obtained a near to critically-damped response in the blood flow of selected arterial vessels

Formation of feedforward networks and frequency synchrony by spike-timing-dependent plasticity

Spike-timing-dependent plasticity (STDP) with asymmetric learning windows is commonly found in the brain and useful for a variety of spike-based computations such as input filtering and associative memory. A natural consequence of STDP is establishment of causality in the sense that a neuron learns to fire with a lag after specific presynaptic neurons have fired. The effect of STDP on synchrony is elusive because spike synchrony implies unitary spike events of different neurons rather than a causal delayed relationship between neurons. We explore how synchrony can be facilitated by STDP in oscillator networks with a pacemaker. We show that STDP with asymmetric learning windows leads to self-organization of feedforward networks starting from the pacemaker. As a result, STDP drastically facilitates frequency synchrony. Even though differences in spike times are lessened as a result of synaptic plasticity, the finite time lag remains so that perfect spike synchrony is not realized. In contrast to traditional mechanisms of large-scale synchrony based on mutual interaction of coupled neurons, the route to synchrony discovered here is enslavement of downstream neurons by upstream ones. Facilitation of such feedforward synchrony does not occur for STDP with symmetric learning windows.Comment: 9 figure