Sampling and Super-resolution of Sparse Signals Beyond the Fourier Domain

Recovering a sparse signal from its low-pass projections in the Fourier domain is a problem of broad interest in science and engineering and is commonly referred to as super-resolution. In many cases, however, Fourier domain may not be the natural choice. For example, in holography, low-pass projections of sparse signals are obtained in the Fresnel domain. Similarly, time-varying system identification relies on low-pass projections on the space of linear frequency modulated signals. In this paper, we study the recovery of sparse signals from low-pass projections in the Special Affine Fourier Transform domain (SAFT). The SAFT parametrically generalizes a number of well known unitary transformations that are used in signal processing and optics. In analogy to the Shannon's sampling framework, we specify sampling theorems for recovery of sparse signals considering three specific cases: (1) sampling with arbitrary, bandlimited kernels, (2) sampling with smooth, time-limited kernels and, (3) recovery from Gabor transform measurements linked with the SAFT domain. Our work offers a unifying perspective on the sparse sampling problem which is compatible with the Fourier, Fresnel and Fractional Fourier domain based results. In deriving our results, we introduce the SAFT series (analogous to the Fourier series) and the short time SAFT, and study convolution theorems that establish a convolution--multiplication property in the SAFT domain.Comment: 42 pages, 3 figures, manuscript under revie

Model-free reconstruction of neuronal network connectivity from calcium imaging signals

A systematic assessment of global neural network connectivity through direct electrophysiological assays has remained technically unfeasible even in dissociated neuronal cultures. We introduce an improved algorithmic approach based on Transfer Entropy to reconstruct approximations to network structural connectivities from network activity monitored through calcium fluorescence imaging. Based on information theory, our method requires no prior assumptions on the statistics of neuronal firing and neuronal connections. The performance of our algorithm is benchmarked on surrogate time-series of calcium fluorescence generated by the simulated dynamics of a network with known ground-truth topology. We find that the effective network topology revealed by Transfer Entropy depends qualitatively on the time-dependent dynamic state of the network (e.g., bursting or non-bursting). We thus demonstrate how conditioning with respect to the global mean activity improves the performance of our method. [...] Compared to other reconstruction strategies such as cross-correlation or Granger Causality methods, our method based on improved Transfer Entropy is remarkably more accurate. In particular, it provides a good reconstruction of the network clustering coefficient, allowing to discriminate between weakly or strongly clustered topologies, whereas on the other hand an approach based on cross-correlations would invariantly detect artificially high levels of clustering. Finally, we present the applicability of our method to real recordings of in vitro cortical cultures. We demonstrate that these networks are characterized by an elevated level of clustering compared to a random graph (although not extreme) and by a markedly non-local connectivity.Comment: 54 pages, 8 figures (+9 supplementary figures), 1 table; submitted for publicatio

Automated detection and analysis of fluorescence changes evoked by molecular signalling

Fluorescent dyes and genetically encoded fluorescence indicators (GEFI) are common tools for visualizing concentration changes of specific ions and messenger molecules during intra- as well as intercellular communication. While fluorescent dyes have to be directly loaded into target cells and function only transiently, the expression of GEFIs can be controlled in a cell and time-specific fashion, even allowing long-term analysis in living organisms. Dye and GEFI based fluorescence fluctuations, recorded using advanced imaging technologies, are the foundation for the analysis of physiological molecular signaling. Analyzing the plethora of complex fluorescence signals is a laborious and time-consuming task. An automated analysis of fluorescent signals circumvents user bias and time constraints. However, it requires to overcome several challenges, including correct estimation of fluorescence fluctuations at basal concentrations of messenger molecules, detection and extraction of events themselves, proper segmentation of neighboring events as well as tracking of propagating events. Moreover, event detection algorithms need to be sensitive enough to accurately capture localized and low amplitude events exhibiting a limited spatial extent. This thesis presents three novel algorithms, PBasE, CoRoDe and KalEve, for the automated analysis of fluorescence events, developed to overcome the aforementioned challenges. The algorithms are integrated into a graphical application called MSparkles, specifically designed for the analysis of fluorescence signals, developed in MATLAB. The capabilities of the algorithms are demonstrated by analyzing astroglial Ca2+ events, recorded in anesthetized and awake mice, visualized using genetically encoded Ca2+ indicators (GECIs) GCaMP3 as well as GCaMP5. The results were compared to those obtained by other software packages. In addition, the analysis of neuronal Na+ events recorded in acute brain slices using SBFI-AM serve to indicate the putatively broad application range of the presented algorithms. Finally, due to increasing evidence of the pivotal role of astrocytes in neurodegenerative diseases such as epilepsy, a metric to assess the synchronous occurrence of fluorescence events is introduced. In a proof-of-principle analysis, this metric is used to correlate astroglial Ca2+ events with EEG measurementsFluoreszenzfarbstoffe und genetisch kodierte Fluoreszenzindikatoren (GEFI) sind gängige Werkzeuge zur Visualisierung von Konzentrationsänderungen bestimmter Ionen und Botenmoleküle der intra- sowie interzellulären Kommunikation. Während Fluoreszenzfarbstoffe direkt in die Zielzellen eingebracht werden müssen und nur über einen begrenzten Zeitraum funktionieren, kann die Expression von GEFIs zell- und zeitspezifisch gesteuert werden, was darüber hinaus Langzeitanalysen in lebenden Organismen ermöglicht. Farbstoff- und GEFI-basierte Fluoreszenzfluktuationen, die mit Hilfe moderner bildgebender Verfahren aufgezeichnet werden, bilden die Grundlage für die Analyse physiologischer molekularer Kommunikation. Die Analyse einer großen Zahl komplexer Fluoreszenzsignale ist jedoch eine schwierige und zeitaufwändige Aufgabe. Eine automatisierte Analyse ist dagegen weniger zeitaufwändig und unabhängig von der Voreingenommenheit des Anwenders. Allerdings müssen hierzu mehrere Herausforderungen bewältigt werden. Unter anderem die korrekte Schätzung von Fluoreszenzschwankungen bei Basalkonzentrationen von Botenmolekülen, die Detektion und Extraktion von Signalen selbst, die korrekte Segmentierung benachbarter Signale sowie die Verfolgung sich ausbreitender Signale. Darüber hinaus müssen die Algorithmen zur Signalerkennung empfindlich genug sein, um lokalisierte Signale mit geringer Amplitude sowie begrenzter räumlicher Ausdehnung genau zu erfassen. In dieser Arbeit werden drei neue Algorithmen, PBasE, CoRoDe und KalEve, für die automatische Extraktion und Analyse von Fluoreszenzsignalen vorgestellt, die entwickelt wurden, um die oben genannten Herausforderungen zu bewältigen. Die Algorithmen sind in eine grafische Anwendung namens MSparkles integriert, die speziell für die Analyse von Fluoreszenzsignalen entwickelt und in MATLAB implementiert wurde. Die Fähigkeiten der Algorithmen werden anhand der Analyse astroglialer Ca2+-Signale demonstriert, die in narkotisierten sowie wachen Mäusen aufgezeichnet und mit den genetisch kodierten Ca2+-Indikatoren (GECIs) GCaMP3 und GCaMP5 visualisiert wurden. Erlangte Ergebnisse werden anschließend mit denen anderer Softwarepakete verglichen. Darüber hinaus dient die Analyse neuronaler Na+-Signale, die in akuten Hirnschnitten mit SBFI-AM aufgezeichnet wurden, dazu, den breiten Anwendungsbereich der Algorithmen aufzuzeigen. Zu guter Letzt wird aufgrund der zunehmenden Indizien auf die zentrale Rolle von Astrozyten bei neurodegenerativen Erkrankungen wie Epilepsie eine Metrik zur Bewertung des synchronen Auftretens fluoreszenter Signale eingeführt. In einer Proof-of-Principle-Analyse wird diese Metrik verwendet, um astrogliale Ca2+-Signale mit EEG-Messungen zu korrelieren

Analysis of resting-state neurovascular coupling and locomotion-associated neural dynamics using wide-field optical mapping

Understanding the relationship between neural activity and cortical hemodynamics, or neurovascular coupling is the foundation to interpret neuroimaging signals such as functional magnetic resonance imaging (fMRI) which measure local changes in hemodynamics as a proxy for underlying neural activity. Even though the stereotypical stimulus-evoked hemodynamic response pattern with increased concentration of oxy- and total-hemoglobin and decrease in concentration of deoxy-hemoglobin has been well-recognized, the linearity of neurovascular coupling and its variances depending on brain state and tasks haven’t been thoroughly evaluated. To directly assess the cortical neurovascular coupling, simultaneous recordings of neural and hemodynamic activity were imaged by wide-field optical mapping (WFOM) over the bilateral dorsal surface of the mouse brain through a bilateral thinned-skull cranial window. Neural imaging is achieved through wide-field fluorescence imaging in animals expressing genetically encoded calcium sensor (Thy1-GCaMP). Hemodynamics are recorded via simultaneous imaging of multi-spectral reflectance. Significant hemodynamic crosstalk was found in the detected fluorescence signal and the physical model of the contamination, methods of correction as well as electrophysiological verification are presented. A linear model between neural and hemodynamic signals was used to fit spatiotemporal hemodynamics can be predicted by convolving local fluorescence changes with hemodynamic response functions derived through both deconvolution and gamma-variate fitting. Beyond confirming that the resting-state hemodynamics in the awake and anesthetized brain are coupled to underlying neural activity, the patterns of bilaterally symmetric spontaneous neural activity observed by WFOM emulate the functionally connected networks detected by fMRI. This result provides reassurance that resting-state functional connectivity has neural origins. With the access to cortical neural activity at mesoscopic level, we further explore the cortical neural representations preceding and during spontaneous locomotion

Whole Brain Network Dynamics of Epileptic Seizures at Single Cell Resolution

Epileptic seizures are characterised by abnormal brain dynamics at multiple scales, engaging single neurons, neuronal ensembles and coarse brain regions. Key to understanding the cause of such emergent population dynamics, is capturing the collective behaviour of neuronal activity at multiple brain scales. In this thesis I make use of the larval zebrafish to capture single cell neuronal activity across the whole brain during epileptic seizures. Firstly, I make use of statistical physics methods to quantify the collective behaviour of single neuron dynamics during epileptic seizures. Here, I demonstrate a population mechanism through which single neuron dynamics organise into seizures: brain dynamics deviate from a phase transition. Secondly, I make use of single neuron network models to identify the synaptic mechanisms that actually cause this shift to occur. Here, I show that the density of neuronal connections in the network is key for driving generalised seizure dynamics. Interestingly, such changes also disrupt network response properties and flexible dynamics in brain networks, thus linking microscale neuronal changes with emergent brain dysfunction during seizures. Thirdly, I make use of non-linear causal inference methods to study the nature of the underlying neuronal interactions that enable seizures to occur. Here I show that seizures are driven by high synchrony but also by highly non-linear interactions between neurons. Interestingly, these non-linear signatures are filtered out at the macroscale, and therefore may represent a neuronal signature that could be used for microscale interventional strategies. This thesis demonstrates the utility of studying multi-scale dynamics in the larval zebrafish, to link neuronal activity at the microscale with emergent properties during seizures

The spatiotemporal dynamics of human focal seizures

Spontaneous human focal seizures can present with a plethora of behavioral manifestations that vary according to the affected cortical regions; however, several key features have been consistently observed. During my doctoral studies, I applied both theoretical and experimental methods to study mechanisms underpinning these consistently seen dynamics. I first analyzed human intracranial EEG recordings, describing statistical methods for measuring their electrophysiological signatures. I next proposed several neurophysiological hypotheses that could explain seizure dynamics and verified them in rodent seizure models. Finally, a computational model was developed, successfully explaining how the complex spatiotemporal evolution of focal seizures emerges from simple neurophysiological principles. In Chapter 1, the long-standing behavioral manifestations and the most up-to-date electrophysiology findings are reviewed. This section details the inspiration for the studies reported in the subsequent chapters. In Chapter 2, I describe several statistical methods for estimating traveling wave velocities. I show most ictal discharges can be described as traveling waves whose velocities contain rich information about the stages of seizure evolution. I compare performance of various statistical methods and propose a robust approach to boost the quality of each method’s estimation results. In Chapter 3, I show how inhibition modulates seizure propagation patterns. Surround inhibition spatially restrains focal seizures and masks excitatory projections of ictal activities. When compromised, two patterns of seizure propagation emerge according to the position of inhibition defects relative to the ictal focus. I show that two distant ictal foci can communicate via physiological connectivity without any chronic rewiring processes – confirming the existence of long-range propagation pathways that could lead to epileptic network formation. In Chapter 4, I show that thalamic inputs might be necessary for interictal epileptiform discharges (IEDs). The relative positions between IEDs and ictal foci indicate that surround inhibition, shown in the previous chapter, can be exhausted by repetitive exposure to ictal projections. In Chapter 5, I propose a neural network model that can explain both long-standing behavioral observations of seizures and account for the most up-to-date electrophysiological recordings of spontaneous human focal seizures. The model relies on few assumptions, all of which are proved or supported in earlier chapters of this thesis. The model explains phasic evolution of seizure dynamics – how the commonly observed patterns arise from simple neurophysiological principles, as well as seizure onset subtypes, traveling wave directions and speeds. The model also predicts how spontaneous seizures might arise from synaptic plasticity. The chapter ends with a discussion of the model’s implications and future work. The thesis is organized in a way that each chapter can be read independently, with Chapter 5 summarizing the central theory spanning the whole study. Each chapter is also tightly linked to a clinically relevant question. In sum, the dissertation’s goal is to provide an in-principle understanding of focal seizure dynamics. With rapid advancement of clinical and experimental tools, I believe this work provides a roadmap for future therapies for epilepsy patients

Proceedings of Abstracts Engineering and Computer Science Research Conference 2019

© 2019 The Author(s). This is an open-access work distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. For further details please see https://creativecommons.org/licenses/by/4.0/. Note: Keynote: Fluorescence visualisation to evaluate effectiveness of personal protective equipment for infection control is © 2019 Crown copyright and so is licensed under the Open Government Licence v3.0. Under this licence users are permitted to copy, publish, distribute and transmit the Information; adapt the Information; exploit the Information commercially and non-commercially for example, by combining it with other Information, or by including it in your own product or application. Where you do any of the above you must acknowledge the source of the Information in your product or application by including or linking to any attribution statement specified by the Information Provider(s) and, where possible, provide a link to this licence: http://www.nationalarchives.gov.uk/doc/open-government-licence/version/3/This book is the record of abstracts submitted and accepted for presentation at the Inaugural Engineering and Computer Science Research Conference held 17th April 2019 at the University of Hertfordshire, Hatfield, UK. This conference is a local event aiming at bringing together the research students, staff and eminent external guests to celebrate Engineering and Computer Science Research at the University of Hertfordshire. The ECS Research Conference aims to showcase the broad landscape of research taking place in the School of Engineering and Computer Science. The 2019 conference was articulated around three topical cross-disciplinary themes: Make and Preserve the Future; Connect the People and Cities; and Protect and Care

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

Inhibitory neurons exhibit high controlling ability in the cortical microconnectome

脳が安定して活動を続けられるメカニズムの一端を解明 --新皮質で、抑制性細胞は他細胞を制御しやすいトポロジカルな位置取りをする--. 京都大学プレスリリース. 2021-04-09.The brain is a network system in which excitatory and inhibitory neurons keep activity balanced in the highly non-random connectivity pattern of the microconnectome. It is well known that the relative percentage of inhibitory neurons is much smaller than excitatory neurons in the cortex. So, in general, how inhibitory neurons can keep the balance with the surrounding excitatory neurons is an important question. There is much accumulated knowledge about this fundamental question. This study quantitatively evaluated the relatively higher functional contribution of inhibitory neurons in terms of not only properties of individual neurons, such as firing rate, but also in terms of topological mechanisms and controlling ability on other excitatory neurons. We combined simultaneous electrical recording (~2.5 hours) of ~1000 neurons in vitro, and quantitative evaluation of neuronal interactions including excitatory-inhibitory categorization. This study accurately defined recording brain anatomical targets, such as brain regions and cortical layers, by inter-referring MRI and immunostaining recordings. The interaction networks enabled us to quantify topological influence of individual neurons, in terms of controlling ability to other neurons. Especially, the result indicated that highly influential inhibitory neurons show higher controlling ability of other neurons than excitatory neurons, and are relatively often distributed in deeper layers of the cortex. Furthermore, the neurons having high controlling ability are more effectively limited in number than central nodes of k-cores, and these neurons also participate in more clustered motifs. In summary, this study suggested that the high controlling ability of inhibitory neurons is a key mechanism to keep balance with a large number of other excitatory neurons beyond simple higher firing rate. Application of the selection method of limited important neurons would be also applicable for the ability to effectively and selectively stimulate E/I imbalanced disease states