Noise-induced synchronization and anti-resonance in excitable systems; Implications for information processing in Parkinson's Disease and Deep Brain Stimulation

We study the statistical physics of a surprising phenomenon arising in large networks of excitable elements in response to noise: while at low noise, solutions remain in the vicinity of the resting state and large-noise solutions show asynchronous activity, the network displays orderly, perfectly synchronized periodic responses at intermediate level of noise. We show that this phenomenon is fundamentally stochastic and collective in nature. Indeed, for noise and coupling within specific ranges, an asymmetry in the transition rates between a resting and an excited regime progressively builds up, leading to an increase in the fraction of excited neurons eventually triggering a chain reaction associated with a macroscopic synchronized excursion and a collective return to rest where this process starts afresh, thus yielding the observed periodic synchronized oscillations. We further uncover a novel anti-resonance phenomenon: noise-induced synchronized oscillations disappear when the system is driven by periodic stimulation with frequency within a specific range. In that anti-resonance regime, the system is optimal for measures of information capacity. This observation provides a new hypothesis accounting for the efficiency of Deep Brain Stimulation therapies in Parkinson's disease, a neurodegenerative disease characterized by an increased synchronization of brain motor circuits. We further discuss the universality of these phenomena in the class of stochastic networks of excitable elements with confining coupling, and illustrate this universality by analyzing various classical models of neuronal networks. Altogether, these results uncover some universal mechanisms supporting a regularizing impact of noise in excitable systems, reveal a novel anti-resonance phenomenon in these systems, and propose a new hypothesis for the efficiency of high-frequency stimulation in Parkinson's disease

Stochastic resonance and finite resolution in a network of leaky integrate-and-fire neurons.

This thesis is a study of stochastic resonance (SR) in a discrete implementation of a leaky integrate-and-fire (LIF) neuron network. The aim was to determine if SR can be realised in limited precision discrete systems implemented on digital hardware. How neuronal modelling connects with SR is discussed. Analysis techniques for noisy spike trains are described, ranging from rate coding, statistical measures, and signal processing measures like power spectrum and signal-to-noise ratio (SNR). The main problem in computing spike train power spectra is how to get equi-spaced sample amplitudes given the short duration of spikes relative to their frequency. Three different methods of computing the SNR of a spike train given its power spectrum are described. The main problem is how to separate the power at the frequencies of interest from the noise power as the spike train encodes both noise and the signal of interest. Two models of the LIF neuron were developed, one continuous and one discrete, and the results compared. The discrete model allowed variation of the precision of the simulation values allowing investigation of the effect of precision limitation on SR. The main difference between the two models lies in the evolution of the membrane potential. When both models are allowed to decay from a high start value in the absence of input, the discrete model does not completely discharge while the continuous model discharges to almost zero. The results of simulating the discrete model on an FPGA and the continuous model on a PC showed that SR can be realised in discrete low resolution digital systems. SR was found to be sensitive to the precision of the values in the simulations. For a single neuron, we find that SR increases between 10 bits and 12 bits resolution after which it saturates. For a feed-forward network with multiple input neurons and one output neuron, SR is stronger with more than 6 input neurons and it saturates at a higher resolution. We conclude that stochastic resonance can manifest in discrete systems though to a lesser extent compared to continuous systems

Adaptive dynamical networks

It is a fundamental challenge to understand how the function of a network is related to its structural organization. Adaptive dynamical networks represent a broad class of systems that can change their connectivity over time depending on their dynamical state. The most important feature of such systems is that their function depends on their structure and vice versa. While the properties of static networks have been extensively investigated in the past, the study of adaptive networks is much more challenging. Moreover, adaptive dynamical networks are of tremendous importance for various application fields, in particular, for the models for neuronal synaptic plasticity, adaptive networks in chemical, epidemic, biological, transport, and social systems, to name a few. In this review, we provide a detailed description of adaptive dynamical networks, show their applications in various areas of research, highlight their dynamical features and describe the arising dynamical phenomena, and give an overview of the available mathematical methods developed for understanding adaptive dynamical networks

Simplified Cardiodynamic Tissue Electrophysiology Characterization, Reduced Order Modeling with Therapeutic Perspective

Atrial fibrillation (Afib) is the most common cardiac arrhythmia affecting millions of people around the world. Mapping and analysis of electrical activation patterns such as electric rotors during Afib is crucial in understanding arrhythmic mechanisms and assessment of diagnostic measures. To this end, there exists various mapping studies where textit{'quantitative'} features such as local activation time, dominant frequency, wave direction, and conduction velocity are extracted from recorded intracardiac electrograms (EGMs). However, obtaining quantitative features further adds to multiplicity of the data and henceforth does not help interpretation of measured signals as opposed to using a more compressed diagnostic terms such as linking the measurements to reentry mechanisms. Through some techniques it is possible to construct isopotential and phase mappings by the help of monophasic action potential recordings in higher spatial resolution. In those cases, however, both expensive mapping tools performing multi-site simultaneous recordings which are not available to most of electrophysiologists are required. On the other hand, the most commonly used catheters which provide high resolution but local measurements remain rather rudimentary in mapping a spatially more global arrhythmic behaviors in a simultaneous fashion. Spiral waves are tissue level phenomena observed in both clinical and experimental settings. They are the product of electrical rotors which are associated with reentry mechanisms during Afib. They can be reproduced using computer models of cardiac electrical activity. Current computer models vary in complexity, accuracy, and efficiency. One particular type is called biophysical models which are based on detailed ion channel interactions. Besides being computationally demanding, they are exceedingly complex and intractable preventing their use in a systems approach where multilevel events are generally considered together. Phenomenological models, on the other hand, include summarized details of ionic events yet preserve fundamental biophysical accuracy. A particular one of them, a minimal resistor model (MRM), was shown to reproduce relevant basic electrophysiological behaviors such as (action potential) AP and electrical restitution properties for human ventricular tissue. The objective in present thesis is to 'qualitatively' characterize fibrillatory wavefront propagation dynamics in cardiac tissue using simulated intracardiac EGMs obtained from most commonly used and lower cost catheter types providing high resolution but localized readings. Another purpose connected to the previous is to show adequacy of a phenomenological model, MRM, in reproducing biophysically related behaviors for human atria. In this respect, two category of problems are handled throughout the thesis: (1) parameter estimation of MRM and (2) discrimination of spiral wave behaviors through intracardiac EGMs simulated using MRM. In the first part, representativeness of MRM for human atrial electrophysiology is established through adaptation of it to a biophysically detailed model originated from experimental data. Specifically, a method is proposed for parameter estimation of the simple model, MRM, to match a targeted behavior such as AP and electrical restitutions first generated from a complex model, by using extended Kalman filter (EKF). In the second part, a method that receives intracardiac EGMs and returns corresponding wavefront propagation patterns classified in terms of electric rotor dynamics is introduced. The method incorporates an information theoretical distance which is called normalized compression distance (NCD) used for assessment of distance measure between simulated behaviors. Achieving outstanding performance together with robustness in discrimination through usage of simulated data enables a theoretical validation of the method. Proposed frameworks collectively yield (1) potential usability of a computationally efficient and easier in analysis model for tissue level cardiac events and (2) simplicity and practicality in clinics through a mapping from a multiple, complex EGM signals to electric rotor behaviors, symptoms more relevant to the diagnosis.Ph.D., Electrical Engineering -- Drexel University, 201

Aspects of Signal Processing in Noisy Neurons

In jüngerer Zeit hat sich die Erkenntnis durchgesetzt, daß statistische Einflüsse, oft Rauschen genannt, die Verarbeitung von Signalen nicht notwendig behindern, sondern unterstützen können. Dieser Effekt ist als stochastische Resonanz bekannt geworden. Es liegt nahe, daß die Evolution Wege gefunden hat, diese Phänomen zur Optimierung der Informationsverarbeitung im Nervensystem auszunutzen. Diese Dissertation untersucht am Beispiel des pulserzeugenden Integratorneurons mit Leckstrom, ob die Kodierung periodischer Signale in Neuronen durch das ohnehin im Nervensystem vorhandene Rauschen verbessert wird. Die Untersuchung erfolgt mit den Methoden der Theorie der Punktprozesse. Die Verteilung der Intervalle zwischen zwei beliebigen aufeinanderfolgenden Pulsen, die das Neuron aussendet, wird aus einem Integralgleichungsansatz numerisch bestimmt und die zeitliche Ordnung der Pulsfolgen relativ zum periodischen Signal als Markoffkette beschrieben. Daneben werden einige Näherungsmodelle für die Pulsintervallverteilung, die weitergehende analytische Untersuchungen erlauben, vorgestellt und ihre Zuverlässigkeit geprüft. Als wesentliches Ergebnis wird gezeigt, daß im Modellneuron zwei Arten rauschinduzierter Resonanz auftreten: zum einen klassiche stochastische Resonanz, d.h. ein optimales Signal-Rausch-Verhältnis der evozierten Pulsfolge bei einer bestimmten Amplitude des Eingangsrauschens. Hinzu tritt eine Resonanz bezüglich der Frequenz des Eingangssignals oder Reizes. Reize eines bestimmten Frequenzbereichs werden in Pulsfolgen kodiert, die zeitlich deutlich strukturiert sind, währ! end Stimuli außerhalb des bevorzugten Frequenzbandes zeitlich homogenere Pulsfolgen auslösen. Für diese zweifache Resonanz wird der Begriff stochastische Doppelresonanz eingeführt. Der Effekt wird auf elementare Mechanismen zurückgeführt und seine Abhängigkeit von den Eigenschaften des Reizes umfassend untersucht. Dabei zeigt sich ,daß die Reizantwort des Neurons einfachen Skalengesetzen unterliegt. Insbesondere ist die optimale skalierte Rauschamplitude ein universeller Parameter des Modells, der vom Reiz unabhängig zu sein scheint. Die optimale Reizfrequenz hängt hingegen linear von der skalierten Reizamplitude ab, wobei die Proportionalitätskonstante vom Gleichstromanteil des Reizes bestimmt wird (Basisstrom). Während große Basisströme Frequenz und Amplitude nahezu entkoppeln, so daß Reize beliebiger Amplitude in zeitlich wohlstrukturierten Pulsfolgen kodiert werden, erlauben es kleine Basisströme, das optimale Frequenzband durch Veränderung der Reizamplitude zu wählen

Phase Transitions Induced by Diversity and Examples in Biological Systems

Tesis leída en l'Universitat de les Illes Balears en diciembre de 2010The present thesis covers various topics that range over di erent aspects of scientific research. On one end there is the specific analysis of a precise form that models some experimental observations. A good theoretical understanding of the mathematics that describe the observations can be a guide to the experimentalist and help estimate the validity of the measurements. On the other end there are abstract models whose relation to physical systems seem far but they are prototypic for a broad range of di erent systems and the drawn conclusions tend to be quite general. Depending on the abstraction and on the simplifications in use the distinction between both ends might not be sharp. The ordering of the research results presented in part II of this thesis somehow reflects the seamless transition from one end to the other. To introduce the reader into the context of the genuine results we provide introductory material in the chapters of the present part I.Peer reviewe

Dynamics of Macrosystems; Proceedings of a Workshop, September 3-7, 1984

There is an increasing awareness of the important and persuasive role that instability and random, chaotic motion play in the dynamics of macrosystems. Further research in the field should aim at providing useful tools, and therefore the motivation should come from important questions arising in specific macrosystems. Such systems include biochemical networks, genetic mechanisms, biological communities, neutral networks, cognitive processes and economic structures. This list may seem heterogeneous, but there are similarities between evolution in the different fields. It is not surprising that mathematical methods devised in one field can also be used to describe the dynamics of another. IIASA is attempting to make progress in this direction. With this aim in view this workshop was held at Laxenburg over the period 3-7 September 1984. These Proceedings cover a broad canvas, ranging from specific biological and economic problems to general aspects of dynamical systems and evolutionary theory