Recent multielectrode array recordings in ganglionated plexi of canine atria have opened the way to the study of population dynamics of intrinsic cardiac neurons. These data provide critical insights into the role of local processing that these ganglia play in the regulation of cardiac function. Low firing rates, marked non-stationarity, interplay with the cardiovascular and pulmonary systems and artifacts generated by myocardial activity create new constraints not present in brain recordings for which almost all neuronal analysis techniques have been developed. We adapted and extended the jitter-based synchrony index (SI) to (1) provide a robust and computationally efficient tool for assessing the level and statistical significance of SI between cardiac neurons, (2) estimate the bias on SI resulting from neuronal activity possibly hidden in myocardial artifacts, (3) quantify the synchrony or anti-synchrony between neuronal activity and the phase in the cardiac and respiratory cycles. The method was validated on firing time series from a total of 98 individual neurons identified in 8 dog experiments. SI ranged from -0.14 to 0.66, with 23 pairs of neurons with SI > 0.1. The estimated bias due to artifacts was typically <1%. Strongly cardiovascular- and pulmonary-related neurons (SI > 0.5) were found. Results support the use of jitter-based SI in the context of intrinsic cardiac neurons.

A aquisição experimental de sinais neuronais é um dos principais avanços da neurociência. Por meio de observações da corrente e do potencial elétricos em uma região cerebral, é possível entender os processos fisiológicos envolvidos na geração do potencial de ação, e produzir modelos matemáticos capazes de simular o comportamento de uma célula neuronal. Uma prática comum nesse tipo de experimento é obter leituras a partir de um arranjo de eletrodos posicionado em um meio compartilhado por diversos neurônios, o que resulta em uma mistura de sinais neuronais em uma mesma série temporal. Este trabalho propõe um modelo linear de tempo discreto para o sinal produzido durante o disparo do neurônio. Os coeficientes desse modelo são calculados utilizando-se amostras reais dos sinais neuronais obtidas in vivo. O processo de modelagem concebido emprega técnicas de identificação de sistemas e processamento de sinais, e é dissociado de considerações sobre o funcionamento biofísico da célula, fornecendo uma alternativa de baixa complexidade para a modelagem do disparo neuronal. Além disso, a representação por meio de sistemas lineares permite idealizar um sistema inverso, cuja função é recuperar o sinal original de cada neurônio ativo em uma mistura extracelular. Nesse contexto, são discutidas algumas soluções baseadas em filtros adaptativos para a simulação do sistema inverso, introduzindo uma nova abordagem para o problema de separação de spikes neuronais. / The experimental acquisition of neuronal signals is a major advance in neuroscience. Through observations of electric current and potential in a brain region, it is possible to understand the physiological processes involved in the action potential generation, and create mathematical models capable of simulating the behavior of the neuronal cell. A common practice in this kind of experiment is to obtain readings from an array of electrodes positioned in a medium shared by several neurons, which results in a mixture of neuronal signals in the same time series. This work proposes a discrete-time linear model of the neuronal signal during the firing of the cell. The coefficients of this model are estimated using real samples of the neuronal signals obtained in vivo. The conceived modeling process employs system identification and signal processing concepts, and is dissociated from any considerations about the biophysical function of the neuronal cell, providing a low-complexity alternative to model the neuronal spike. In addition, the use of a linear representation allows the idealization of an inverse system, whose main purpose is to recover the original signal of each active neuron in a given extracellular mixture. In this context, some solutions based on adaptive filters are discussed for the inverse model simulation, introducing a new approach to the problem of neuronal spike separation.

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A aquisição experimental de sinais neuronais é um dos principais avanços da neurociência. Por meio de observações da corrente e do potencial elétricos em uma região cerebral, é possível entender os processos fisiológicos envolvidos na geração do potencial de ação, e produzir modelos matemáticos capazes de simular o comportamento de uma célula neuronal. Uma prática comum nesse tipo de experimento é obter leituras a partir de um arranjo de eletrodos posicionado em um meio compartilhado por diversos neurônios, o que resulta em uma mistura de sinais neuronais em uma mesma série temporal. Este trabalho propõe um modelo linear de tempo discreto para o sinal produzido durante o disparo do neurônio. Os coeficientes desse modelo são calculados utilizando-se amostras reais dos sinais neuronais obtidas in vivo. O processo de modelagem concebido emprega técnicas de identificação de sistemas e processamento de sinais, e é dissociado de considerações sobre o funcionamento biofísico da célula, fornecendo uma alternativa de baixa complexidade para a modelagem do disparo neuronal. Além disso, a representação por meio de sistemas lineares permite idealizar um sistema inverso, cuja função é recuperar o sinal original de cada neurônio ativo em uma mistura extracelular. Nesse contexto, são discutidas algumas soluções baseadas em filtros adaptativos para a simulação do sistema inverso, introduzindo uma nova abordagem para o problema de separação de spikes neuronais. / The experimental acquisition of neuronal signals is a major advance in neuroscience. Through observations of electric current and potential in a brain region, it is possible to understand the physiological processes involved in the action potential generation, and create mathematical models capable of simulating the behavior of the neuronal cell. A common practice in this kind of experiment is to obtain readings from an array of electrodes positioned in a medium shared by several neurons, which results in a mixture of neuronal signals in the same time series. This work proposes a discrete-time linear model of the neuronal signal during the firing of the cell. The coefficients of this model are estimated using real samples of the neuronal signals obtained in vivo. The conceived modeling process employs system identification and signal processing concepts, and is dissociated from any considerations about the biophysical function of the neuronal cell, providing a low-complexity alternative to model the neuronal spike. In addition, the use of a linear representation allows the idealization of an inverse system, whose main purpose is to recover the original signal of each active neuron in a given extracellular mixture. In this context, some solutions based on adaptive filters are discussed for the inverse model simulation, introducing a new approach to the problem of neuronal spike separation.

Die vorliegende Arbeit befasst sich mit dem Einfluss von nicht-weißem oder nicht-Gauß’schem synaptischen Rauschen auf die Informationsübertragung in stochastischen Neuronenmodellen. Ziel ist es, zu verstehen, wie eine Nervenzelle ein Signal in ihrer Pulsaktivität kodiert. Synaptisches Rauschen beschreibt hier den Einfluss anderer Nervenzellen, die nicht das interessierende Signal tragen, aber seine Übertragung durch ihre synaptische Wirkung auf die betrachtete Zelle beeinflussen. In stochastischen Neuronenmodellen wird diese Hintergrundaktivität durch einen stochastischen Prozess mit geeigneter Statistik beschrieben. Ist die Rate, mit der präsynaptische Pulse auftreten, hoch und zeitlich konstant, die Wirkung einzelner Pulse aber verschwindend gering, so wird das synaptische Rauschen durch einen Gauß’schen Prozess beschrieben. Oft wird zudem angenommen, dass das Rauschen unkorreliert (weiß) ist. In dieser Arbeit wird neuronale Signalübertragung in dem Fall untersucht, dass eine solche Näherung nicht mehr gerechtfertigt ist, d.h. wenn der synaptische Hintergrund durch einen stochastischen Prozess beschrieben werden muss, der nicht weiß, nicht Gauß’sch, oder weder weiß noch Gauß’sch ist. Mittels Simulationen und analytischer Rechnungen werden drei Szenarien behandelt: Zunächst betrachten wir eine Zelle, die nicht ein, sondern zwei Signale empfängt, welche zusätzlich durch synaptische Kurzzeitplastizität gefiltert werden. In diesem Fall muss der Hintergrund durch ein farbiges Rauschen beschrieben werden. Im zweiten Szenario betrachten wir den Fall, dass der Effekt einzelner Pulse nicht mehr als schwach angenommen werden kann. Das Rauschen ist dann nicht mehr Gauß’sch, sondern ein Schrotrauschen. Schließlich untersuchen wir den Einfluss einer präsynaptischen Population, deren Feuerrate nicht zeitlich konstant ist, sondern zwischen Phasen hoher und niedriger Aktivität, sogenannten up und down states, springt. In diesem Fall ist das Rauschen weder weiß noch Gauß’sch. / This thesis is concerned with the effect of non-white or non-Gaussian synaptic noise on the information transmission properties of single neurons. Synaptic noise subsumes the massive input that a cell receives from thousands of other neurons. In the framework of stochastic neuron models, this input is described by a stochastic process with suitably chosen statistics. If the overall arrival rate of presynaptic action potentials is high and constant in time and if each individual incoming spike has only a small effect on the dynamics of the cell, the massive synaptic input can be modeled as a Gaussian process. For mathematical tractability, one often assumes that furthermore, the input is devoid of temporal structure, i.e. that it is well described by a Gaussian white noise. This is the so-called diffusion approximation (DA). The present thesis explores neuronal signal transmission when the conditions that underlie the DA are no longer met, i.e. when one must describe the synaptic background activity by a stochastic process that is not white, not Gaussian, or neither. We explore three distinct scenarios by means of simulations and analytical calculations: First, we study a cell that receives not one but two signals, additionally filtered by synaptic short-term plasticity (STP), so that the background has to be described by a colored noise. The second scenario deals with synaptic weights that cannot be considered small; here, the effective noise is no longer Gaussian and the shot-noise nature of the input has to be taken into account. Finally, we study the effect of a presynaptic population that does not fire at a rate which is constant in time but instead undergoes transitions between states of high and low activity, so-called up and down states.