Causal Measures of Structure and Plasticity in Simulated and Living Neural Networks

A major goal of neuroscience is to understand the relationship between neural structures and their function. Recording of neural activity with arrays of electrodes is a primary tool employed toward this goal. However, the relationships among the neural activity recorded by these arrays are often highly complex making it problematic to accurately quantify a network's structural information and then relate that structure to its function. Current statistical methods including cross correlation and coherence have achieved only modest success in characterizing the structural connectivity. Over the last decade an alternative technique known as Granger causality is emerging within neuroscience. This technique, borrowed from the field of economics, provides a strong mathematical foundation based on linear auto-regression to detect and quantify “causal” relationships among different time series. This paper presents a combination of three Granger based analytical methods that can quickly provide a relatively complete representation of the causal structure within a neural network. These are a simple pairwise Granger causality metric, a conditional metric, and a little known computationally inexpensive subtractive conditional method. Each causal metric is first described and evaluated in a series of biologically plausible neural simulations. We then demonstrate how Granger causality can detect and quantify changes in the strength of those relationships during plasticity using 60 channel spike train data from an in vitro cortical network measured on a microelectrode array. We show that these metrics can not only detect the presence of causal relationships, they also provide crucial information about the strength and direction of that relationship, particularly when that relationship maybe changing during plasticity. Although we focus on the analysis of multichannel spike train data the metrics we describe are applicable to any stationary time series in which causal relationships among multiple measures is desired. These techniques can be especially useful when the interactions among those measures are highly complex, difficult to untangle, and maybe changing over time

Modelling and analysis of cortico-hippocampal interactions and dynamics during sleep and anaesthesia

The standard memory consolidation model assumes that new memories are temporarily stored in the hippocampus and later transferred to the neocortex, during deep sleep, for long-term storage, signifying the importance of studying functional and structural cortico-hippocampal interactions. Our work offers a thorough analysis on such interactions between neocortex and hippocampus, along with a detailed study of their intrinsic dynamics, from two complementary perspectives: statistical data analysis and computational modelling. The first part of this study reviews mathematical tools for assessing directional interactions in multivariate time series. We focus on the notion of Granger Causality and the related measure of generalised Partial Directed Coherence (gPDC) which we then apply, through a custom built numerical package, to electrophysiological data from the medial prefrontal cortex (mPFC) and hippocampus of anaesthetized rats. Our gPDC analysis reveals a clear lateral-to-medial hippocampus connectivity and suggests a reciprocal information flow between mPFC and hippocampus, altered during cortical activity. The second part deals with modelling sleep-related intrinsic rhythmic dynamics of the two areas, and examining their coupling. We first reproduce a computational model of the cortical slow oscillation, a periodic alteration between activated (UP) states and neuronal silence. We then develop a new spiking network model of hippocampal areas CA3 and CA1, reproducing many of their intrinsic dynamics and exhibiting sharp wave-ripple complexes, suggesting a novel mechanism for their generation based on CA1 interneuronal activity and recurrent inhibition. We finally couple the two models to study interactions between the slow oscillation and hippocampal activity. Our simulations propose a dependence of the correlation between UP states and hippocampal spiking on the excitation-to-inhibition ratio induced by the mossy fibre input to CA3 and by a combination of the Schaffer collateral and temporoammonic input to CA1. These inputs are shown to affect reported correlations between UP states and ripples

Modelling and analysis of cortico-hippocampal interactions and dynamics during sleep and anaesthesia

The standard memory consolidation model assumes that new memories are temporarily stored in the hippocampus and later transferred to the neocortex, during deep sleep, for long-term storage, signifying the importance of studying functional and structural cortico-hippocampal interactions. Our work offers a thorough analysis on such interactions between neocortex and hippocampus, along with a detailed study of their intrinsic dynamics, from two complementary perspectives: statistical data analysis and computational modelling. The first part of this study reviews mathematical tools for assessing directional interactions in multivariate time series. We focus on the notion of Granger Causality and the related measure of generalised Partial Directed Coherence (gPDC) which we then apply, through a custom built numerical package, to electrophysiological data from the medial prefrontal cortex (mPFC) and hippocampus of anaesthetized rats. Our gPDC analysis reveals a clear lateral-to-medial hippocampus connectivity and suggests a reciprocal information flow between mPFC and hippocampus, altered during cortical activity. The second part deals with modelling sleep-related intrinsic rhythmic dynamics of the two areas, and examining their coupling. We first reproduce a computational model of the cortical slow oscillation, a periodic alteration between activated (UP) states and neuronal silence. We then develop a new spiking network model of hippocampal areas CA3 and CA1, reproducing many of their intrinsic dynamics and exhibiting sharp wave-ripple complexes, suggesting a novel mechanism for their generation based on CA1 interneuronal activity and recurrent inhibition. We finally couple the two models to study interactions between the slow oscillation and hippocampal activity. Our simulations propose a dependence of the correlation between UP states and hippocampal spiking on the excitation-to-inhibition ratio induced by the mossy fibre input to CA3 and by a combination of the Schaffer collateral and temporoammonic input to CA1. These inputs are shown to affect reported correlations between UP states and ripples

Connectivity Measures for In Vitro Neuronal Cell Networks

In this thesis, different connectivity measures are reviewed in detail in order to investigate what kind of information they provide, what are the advantages and limitations of them. Based on the literature review comparison, we selected three methods; Phase Lock Value (PLV), generalized Partial Directed Coherence (gPDC) and Transfer Entropy (TE). The selected methods were tested and evaluated with the data from human embryonic stem cell derived neuronal cell (hESC) networks which are cultured on MEAs. The analysis is divided into two parts: simulated connectivity signal studies and real MEA data analysis.The simulation study indicates that PLV method correctly recognized the connections, while gPDC provided unreliable results. TE provided the most detailed results only with few inaccuracies. Based on the simulation results, TE and PLV seem potential for further research on MEA signals. However, incoherent results were obtained in real MEA data analysis. For example, PLV claimed connections between signals measured from different wells. Based on the results, further research is needed in order to assess whether the incoherencies are influenced by the measurement environment, the methods themselves, or by the quality problem of signals in 6-well MEA

Olfactory bulb drives respiration-coupled beta oscillations in the rat hippocampus

The synchronization of neuronal oscillations has been suggested as a mechanism to coordinate information flow between distant brain regions. In particular, the olfactory bulb (OB) and the hippocampus (HPC) have been shown to exhibit oscillations in the beta frequency range (10-20 Hz) that are likely to support communication between these structures. Here we further characterize features of beta oscillations in OB and HPC of rats anesthetized with urethane. We find that beta oscillations simultaneously appear in HPC and OB and phase-lock across structures. Moreover, Granger causality analysis reveals that OB beta activity drives HPC beta. The laminar voltage profile of beta in HPC shows the maximum amplitude in the dentate gyrus, spatially coinciding with olfactory inputs to this region. Finally, we also find that the respiratory cycle and respiration-coupled field potential rhythms (1-2 Hz) - but not theta oscillations (3-5 Hz) - modulate beta amplitude in OB and HPC. In all, our results support the hypothesis that beta activity mediates the communication between olfactory and hippocampal circuits in the rodent brain. This article is protected by copyright. All rights reserved.2018-09-2

Linear and nonlinear approaches to unravel dynamics and connectivity in neuronal cultures

[eng] In the present thesis, we propose to explore neuronal circuits at the mesoscale, an approach in which one monitors small populations of few thousand neurons and concentrates in the emergence of collective behavior. In our case, we carried out such an exploration both experimentally and numerically, and by adopting an analysis perspective centered on time series analysis and dynamical systems. Experimentally, we used neuronal cultures and prepared more than 200 of them, which were monitored using fluorescence calcium imaging. By adjusting the experimental conditions, we could set two basic arrangements of neurons, namely homogeneous and aggregated. In the experiments, we carried out two major explorations, namely development and disintegration. In the former we investigated changes in network behavior as it matured; in the latter we applied a drug that reduced neuronal interconnectivity. All the subsequent analyses and modeling along the thesis are based on these experimental data. Numerically, the thesis comprised two aspects. The first one was oriented towards a simulation of neuronal connectivity and dynamics. The second one was oriented towards the development of linear and nonlinear analysis tools to unravel dynamic and connectivity aspects of the measured experimental networks. For the first aspect, we developed a sophisticated software package to simulate single neuronal dynamics using a quadratic integrate–and–fire model with adaptation and depression. This model was plug into a synthetic graph in which the nodes of the network are neurons, and the edges connections. The graph was created using spatial embedding and realistic biology. We carried out hundreds of simulations in which we tuned the density of neurons, their spatial arrangement and the characteristics of the fluorescence signal. As a key result, we observed that homogeneous networks required a substantial number of neurons to fire and exhibit collective dynamics, and that the presence of aggregation significantly reduced the number of required neurons. For the second aspect, data analysis, we analyzed experiments and simulations to tackle three major aspects: network dynamics reconstruction using linear descriptions, dynamics reconstruction using nonlinear descriptors, and the assessment of neuronal connectivity from solely activity data. For the linear study, we analyzed all experiments using the power spectrum density (PSD), and observed that it was sufficiently good to describe the development of the network or its disintegration. PSD also allowed us to distinguish between healthy and unhealthy networks, and revealed dynamical heterogeneities across the network. For the nonlinear study, we used techniques in the context of recurrence plots. We first characterized the embedding dimension m and the time delay δ for each experiment, built the respective recurrence plots, and extracted key information of the dynamics of the system through different descriptors. Experimental results were contrasted with numerical simulations. After analyzing about 400 time series, we concluded that the degree of dynamical complexity in neuronal cultures changes both during development and disintegration. We also observed that the healthier the culture, the higher its dynamic complexity. Finally, for the reconstruction study, we first used numerical simulations to determine the best measure of ‘statistical interdependence’ among any two neurons, and took Generalized Transfer Entropy. We then analyzed the experimental data. We concluded that young cultures have a weak connectivity that increases along maturation. Aggregation increases average connectivity, and more interesting, also the assortativity, i.e. the tendency of highly connected nodes to connect with other highly connected node. In turn, this assortativity may delineates important aspects of the dynamics of the network. Overall, the results show that spatial arrangement and neuronal dynamics are able to shape a very rich repertoire of dynamical states of varying complexity.[cat] L’habilitat dels teixits neuronals de processar i transmetre informació de forma eficient depèn de les propietats dinàmiques intrínseques de les neurones i de la connectivitat entre elles. La present tesi proposa explorar diferents tècniques experimentals i de simulació per analitzar la dinàmica i connectivitat de xarxes neuronals corticals de rata embrionària. Experimentalment, la gravació de l’activitat espontània d’una població de neurones en cultiu, mitjançant una càmera ràpida i tècniques de fluorescència, possibilita el seguiment de forma controlada de l’activitat individual de cada neurona, així com la modificació de la seva connectivitat. En conjunt, aquestes eines permeten estudiar el comportament col.lectiu emergent de la població neuronal. Amb l’objectiu de simular els patrons observats en el laboratori, hem implementat un model mètric aleatori de creixement neuronal per simular la xarxa física de connexions entre neurones, i un model quadràtic d’integració i dispar amb adaptació i depressió per modelar l’ampli espectre de dinàmiques neuronals amb un cost computacional reduït. Hem caracteritzat la dinàmica global i individual de les neurones i l’hem correlacionat amb la seva estructura subjacent mitjançant tècniques lineals i no–lineals de series temporals. L’anàlisi espectral ens ha possibilitat la descripció del desenvolupament i els canvis en connectivitat en els cultius, així com la diferenciació entre cultius sans dels patològics. La reconstrucció de la dinàmica subjacent mitjançant mètodes d’incrustació i l’ús de gràfics de recurrència ens ha permès detectar diferents transicions dinàmiques amb el corresponent guany o pèrdua de la complexitat i riquesa dinàmica del cultiu durant els diferents estudis experimentals. Finalment, a fi de reconstruir la connectivitat interna hem testejat, mitjançant simulacions, diferents quantificadors per mesurar la dependència estadística entre neurona i neurona, seleccionant finalment el mètode de transferència d’entropia gereralitzada. Seguidament, hem procedit a caracteritzar les xarxes amb diferents paràmetres. Malgrat presentar certs tres de xarxes tipus ‘petit món’, els nostres cultius mostren una distribució de grau ‘exponencial’ o ‘esbiaixada’ per, respectivament, cultius joves i madurs. Addicionalment, hem observat que les xarxes homogènies presenten la propietat de disassortativitat, mentre que xarxes amb un creixent nivell d’agregació espaial presenten assortativitat. Aquesta propietat impacta fortament en la transmissió, resistència i sincronització de la xarxa

The Impact of Mild Traumatic Brain injury on Neuronal Networks and Neurobehavior

Despite its enormous incidence, mild traumatic brain injury is not well understood. One aspect that needs more definition is how the mechanical energy during injury affects neural circuit function. Recent developments in cellular imaging probes provide an opportunity to assess the dynamic state of neural networks with single-cell resolution. In this dissertation, we developed imaging methods to assess the state of dissociated cortical networks exposed to mild injury. We probed the microarchitecture of an injured cortical circuit subject to two different injury levels, mild stretch (10% peak) and mild/moderate (35%). We found that mild injury produced a transient increase in calcium activity that dissipated within 1 h after injury. Alternatively, mild/moderate mechanical injury produced immediate disruption in network synchrony, loss in excitatory tone, and increased modular topology, suggesting a threshold for repair and degradation. The more significant changes in network behavior at moderate stretch are influenced by NMDA receptor activation and subsequent proteolytic changes in the neuronal populations. With the ability to analyze individual neurons in a circuit before and after injury, we identified several biomarkers that confer increased risk or protection from mechanical injury. We found that pre-injury connectivity and NMDA receptor subtype composition (NR2A and NR2B content) are important predictors of node loss and remodeling. Mechanistically, stretch injury caused a reduction in voltage-dependent Mg2+ block of the NR2B-cotaning NMDA receptors, resulting in increased uncorrelated activity both at the single channel and network level. The reduced coincidence detection of the NMDA receptor and overactivation of these receptors further impaired network function and plasticity. Given the demonstrated link between NR2B-NMDARs and mitochondrial dysfunction, we discovered that neuronal de-integration from the network is mediated through mitochondrial signaling. Finally, we bridged these network level studies with an investigation of changes in neurobehavior following blast-induced traumatic brain injury (bTBI), a form of mild TBI. We first developed and validated an open-source toolbox for automating the scoring of several common behavior tasks to study the deficits that occur following bTBI. We then specifically evaluated the role of neuronal transcription factor Elk-1 in mediating deficits following blast by exposing Elk-1 knockout mouse to equivalent blast pressure loading. Our systems-level behavior analysis showed that bTBI creates a complex change in behavior, with an increase in anxiety and loss of habituation in object recognition. Moreover, we found these behavioral deficits were eliminated in Elk-1 knockout animals exposed to blast loading. Together, we merged information from different perspectives (in silico, in vitro, and in vivo) and length scales (single channels, single-cells, networks, and animals) to study the impact of mild traumatic brain injury on neuronal networks and neurobehavior