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

Oscillator-based neuronal modeling for seizure progression investigation and seizure control strategy

The coupled oscillator model has previously been used for the simulation of neuronal activities in in vitro rat hippocampal slice seizure data and the evaluation of seizure suppression algorithms. Each model unit can be described as either an oscillator which can generate action potential spike trains without inputs, or a threshold-based unit. With the change of only one parameter, each unit can either be an oscillator or a threshold-based spiking unit. This would eliminate the need for a new set of equations for each type of unit. Previous analysis has suggested that long kernel duration and imbalance of inhibitory feedback can cause the system to intermittently transition into and out of ictal activities. The state transitions of seizure-like events were investigated here; specifically, how the system excitability may change when the system undergoes transitions in the preictal and postictal processes. Analysis showed that the area of the excitation kernel is positively correlated with the mean firing rate of the ictal activity. The kernel duration is also correlated to the amount of ictal activity. The transition into ictal activity involved the escape from the saddle point foci in the state space trajectory identified by using Newton\u27s method. The ability to accurately anticipate and suppress seizures is an important endeavor that has tremendous impact on improving the quality of lives for epileptic patients. The stimulation studies have suggested that an electrical stimulation strategy that uses the intrinsic high complexity dynamics of the biological system may be more effective in reducing the duration of seizure-like activities in the computer model. In this research, we evaluate this strategy on an in vitro rat hippocampal slice magnesium-free model. Simulated postictal field potential data generated by an oscillator-based hippocampal network model was applied to the CA1 region of the rat hippocampal slices through a multi-electrode array (MEA) system. It was found to suppress and delay the onset of future seizures temporarily. The average inter-seizure time was found to be significantly prolonged after postictal stimulation when compared to the negative control trials and bipolar square wave signals. The result suggests that neural signal-based stimulation related to resetting may be suitable for seizure control in the clinical environment

Computational study of resting state network dynamics

Lo scopo di questa tesi è quello di mostrare, attraverso una simulazione con il software The Virtual Brain, le più importanti proprietà della dinamica cerebrale durante il resting state, ovvero quando non si è coinvolti in nessun compito preciso e non si è sottoposti a nessuno stimolo particolare. Si comincia con lo spiegare cos’è il resting state attraverso una breve revisione storica della sua scoperta, quindi si passano in rassegna alcuni metodi sperimentali utilizzati nell’analisi dell’attività cerebrale, per poi evidenziare la differenza tra connettività strutturale e funzionale. In seguito, si riassumono brevemente i concetti dei sistemi dinamici, teoria indispensabile per capire un sistema complesso come il cervello. Nel capitolo successivo, attraverso un approccio ‘bottom-up’, si illustrano sotto il profilo biologico le principali strutture del sistema nervoso, dal neurone alla corteccia cerebrale. Tutto ciò viene spiegato anche dal punto di vista dei sistemi dinamici, illustrando il pionieristico modello di Hodgkin-Huxley e poi il concetto di dinamica di popolazione. Dopo questa prima parte preliminare si entra nel dettaglio della simulazione. Prima di tutto si danno maggiori informazioni sul software The Virtual Brain, si definisce il modello di network del resting state utilizzato nella simulazione e si descrive il ‘connettoma’ adoperato. Successivamente vengono mostrati i risultati dell’analisi svolta sui dati ricavati, dai quali si mostra come la criticità e il rumore svolgano un ruolo chiave nell'emergenza di questa attività di fondo del cervello. Questi risultati vengono poi confrontati con le più importanti e recenti ricerche in questo ambito, le quali confermano i risultati del nostro lavoro. Infine, si riportano brevemente le conseguenze che porterebbe in campo medico e clinico una piena comprensione del fenomeno del resting state e la possibilità di virtualizzare l’attività cerebrale

An organizing center in a planar model of neuronal excitability

The paper studies the excitability properties of a generalized FitzHugh-Nagumo model. The model differs from the purely competitive FitzHugh-Nagumo model in that it accounts for the effect of cooperative gating variables such as activation of calcium currents. Excitability is explored by unfolding a pitchfork bifurcation that is shown to organize five different types of excitability. In addition to the three classical types of neuronal excitability, two novel types are described and distinctly associated to the presence of cooperative variables

Investigation of pattern generating mechanisms during atrial fibrillation based on the FitzHugh Nagumo equations

Die häufigste Arrhythmie des Herzens im klinischen Alltag ist Vorhofflimmern. Sie ist die Ursache von einem Drittel aller Behandlungen von Herzrhythmusstörungen. Obwohl das Phänomen des Vorhofflimmerns seit Anfang des letzten Jahrhunderts bekannt ist, sind die zugrunde liegenden Mechanismen noch nicht ausreichend verstanden. Als mögliche generierende Mechanismen werden in dieser Arbeit ektopische Zentren und Spiralwellen auf der Grundlage der FitzHugh-Nagumo- Gleichungen untersucht. Zur Darstellung von lokalen Gewebeveränderungen und der mit ihnen verbundenen Entstehung von ektopischen Zentren und Spiralwellen werden Zelleigenschaften wie die Anregbarkeit und die Stabilität des Ruhezustandes in räumlich begrenzten Gebieten variiert. Das Auftreten von Aktivitätsmustern in Abhängigkeit der linearen Ausdehnung der modifizierten Zellbereiche und der Stärke der Modifikation wird in dynamischen Phasendiagrammen erfasst und die mit den verschiedenen Mustern verbundenen Eigenschaften werden analysiert. Der abschließende Teil betrifft die Untersuchung von Mustern, welche durch Interferenz von regelmässigen, periodisch angeregten Wellen im rechten Vorhof mit Wellen ausgehend von einer stabilen Spiralwelle im linken Vorhof entstehen. Es wird gezeigt, dass diese Interferenz Ursache eines Flimmerzustandes im rechten Vorhof sein kann. Dabei führt insbesondere eine hohe Anregungsrate zu einem irregulären, flimmerähnlichen Zustand im rechten Vorhof. Sie erweist sich als Schlüsselfaktor für das Auftreten von Flimmerepisoden.Atrial fibrillation is the most important arrhythmia in clinical practice, accounting for one third of hospitalisations for cardiac disrhythms. Although it is known since the beginning of the last century, the underlying mechanisms are still under disucssion. In this work two proposed mechanisms are investigated, ectopic activity and spiral waves, with focus on their generating conditions, characteristic properties and wether they can be a possible cause of atrial fibrillation. Thereby, the cell properties like excitability and resting state stability are spatially varied to model possible generating conditions. The calculations are carried out on the basis of the FitzHugh Nagumo model. Dynamical phase diagrams are constructed for the ectopic activity as well as for the spiral waves, which classify the behaviour of the system in dependence on the properties of the spatial variation of the cell properties. The fibrillation rate is analysed and a transition from anatomical to functional reentry is observed for the spiral waves. Moreover, interference patterns of waves are studied in comparison to patterns found in recent experiments. The interference of waves from a stable spiral wave in the left atrium with regular paced waves in the right atrium, as a model of the sinus node, is shown to be a possible cause of fibrillation in the right atrium. A high pacing rate can yield an irregular, fibrillatory state, which describes the generation of fibrillation episodes and is seen as a key factor for the occurrence of fibrillation episodes.Ilmenau, Techn. Univ., Diplomarbeit, 200

Modeling the coupling of action potential and electrodes

The present monograph is a study of pulse propagation in nerves. The main project of this work is modeling and simulation of the action potential propagation in a neuron and its interaction with the electrodes in the context of neurochip application. In the first part, I work with an adapted model of FitzHugh-Nagumo derived from the Hodgkin-Huxley model. The second part was the result of turning the spotlight-on onto the drawbacks of Hodgkin-Huxley model and to bring forth, an alternative model: soliton model. The purpose is to comprehend the role of membrane state in the pulse propagation

Flipping Biological Switches: Solving for Optimal Control: A Dissertation

Switches play an important regulatory role at all levels of biology, from molecular switches triggering signaling cascades to cellular switches regulating cell maturation and apoptosis. Medical therapies are often designed to toggle a system from one state to another, achieving a specified health outcome. For instance, small doses of subpathologic viruses activate the immune system’s production of antibodies. Electrical stimulation revert cardiac arrhythmias back to normal sinus rhythm. In all of these examples, a major challenge is finding the optimal stimulus waveform necessary to cause the switch to flip. This thesis develops, validates, and applies a novel model-independent stochastic algorithm, the Extrema Distortion Algorithm (EDA), towards finding the optimal stimulus. We validate the EDA’s performance for the Hodgkin-Huxley model (an empirically validated ionic model of neuronal excitability), the FitzHugh-Nagumo model (an abstract model applied to a wide range of biological systems that that exhibit an oscillatory state and a quiescent state), and the genetic toggle switch (a model of bistable gene expression). We show that the EDA is able to not only find the optimal solution, but also in some cases excel beyond the traditional analytic approaches. Finally, we have computed novel optimal stimulus waveforms for aborting epileptic seizures using the EDA in cellular and network models of epilepsy. This work represents a first step in developing a new class of adaptive algorithms and devices that flip biological switches, revealing basic mechanistic insights and therapeutic applications for a broad range of disorders

Analysis of periodic oscillations of APDs in reaction diffusion waves with nonlinear diffusion in tissues with peripheral nerve injury (PNI)

Millions of people suffer from peripheral nerve injury every year. Previous works have predominantly focused on surgical means of injury treatment without sufficient attention to studying distinct mechanisms of electrical conduction in small peripheral nerves. In this study, we examined the effects of nonlinear diffusion on wave propagation generated in normal and injured (with altered electrical conduction) peripheral nerves using one-dimensional Fitzhugh-Nagumo model. We modified this model by adding an additional power function type nonlinear diffusion term to account for fundamental changes in charge balance in excitable cells of small peripheral nerves. It was found that nonlinear diffusion played a critical role in stabilization of action potential propagation in healthy and injured peripheral nerves. In addition, it was observed that conditions for stable propagation of action potential in injured nerves significantly depended not only on the magnitude of nonlinear diffusion but also on location of zones of injury. These results may be helpful in elucidating physiological mechanisms of various electrical conduction pathologies which occur in injured peripheral nerves