Emergence and combinatorial accumulation of jittering regimes in spiking oscillators with delayed feedback

Interaction via pulses is common in many natural systems, especially neuronal. In this article we study one of the simplest possible systems with pulse interaction: a phase oscillator with delayed pulsatile feedback. When the oscillator reaches a specific state, it emits a pulse, which returns after propagating through a delay line. The impact of an incoming pulse is described by the oscillator's phase reset curve (PRC). In such a system we discover an unexpected phenomenon: for a sufficiently steep slope of the PRC, a periodic regular spiking solution bifurcates with several multipliers crossing the unit circle at the same parameter value. The number of such critical multipliers increases linearly with the delay and thus may be arbitrary large. This bifurcation is accompanied by the emergence of numerous "jittering" regimes with non-equal interspike intervals (ISIs). Each of these regimes corresponds to a periodic solution of the system with a period roughly proportional to the delay. The number of different "jittering" solutions emerging at the bifurcation point increases exponentially with the delay. We describe the combinatorial mechanism that underlies the emergence of such a variety of solutions. In particular, we show how a periodic solution exhibiting several distinct ISIs can imply the existence of multiple other solutions obtained by rearranging of these ISIs. We show that the theoretical results for phase oscillators accurately predict the behavior of an experimentally implemented electronic oscillator with pulsatile feedback

Proceedings of the Sixth Deep Brain Stimulation Think Tank Modulation of Brain Networks and Application of Advanced Neuroimaging, Neurophysiology, and Optogenetics

The annual deep brain stimulation (DBS) Think Tank aims to create an opportunity for a multidisciplinary discussion in the field of neuromodulation to examine developments, opportunities and challenges in the field. The proceedings of the Sixth Annual Think Tank recapitulate progress in applications of neurotechnology, neurophysiology, and emerging techniques for the treatment of a range of psychiatric and neurological conditions including Parkinson’s disease, essential tremor, Tourette syndrome, epilepsy, cognitive disorders, and addiction. Each section of this overview provides insight about the understanding of neuromodulation for specific disease and discusses current challenges and future directions. This year’s report addresses key issues in implementing advanced neurophysiological techniques, evolving use of novel modulation techniques to deliver DBS, ans improved neuroimaging techniques. The proceedings also offer insights into the new era of brain network neuromodulation and connectomic DBS to define and target dysfunctional brain networks. The proceedings also focused on innovations in applications and understanding of adaptive DBS (closed-loop systems), the use and applications of optogenetics in the field of neurostimulation and the need to develop databases for DBS indications. Finally, updates on neuroethical, legal, social, and policy issues relevant to DBS research are discussed

Proceedings of the Sixth Deep Brain Stimulation Think Tank Modulation of Brain Networks and Application of Advanced Neuroimaging, Neurophysiology, and Optogenetics

The annual deep brain stimulation (DBS) Think Tank aims to create an opportunity for a multidisciplinary discussion in the field of neuromodulation to examine developments, opportunities and challenges in the field. The proceedings of the Sixth Annual Think Tank recapitulate progress in applications of neurotechnology, neurophysiology, and emerging techniques for the treatment of a range of psychiatric and neurological conditions including Parkinson’s disease, essential tremor, Tourette syndrome, epilepsy, cognitive disorders, and addiction. Each section of this overview provides insight about the understanding of neuromodulation for specific disease and discusses current challenges and future directions. This year’s report addresses key issues in implementing advanced neurophysiological techniques, evolving use of novel modulation techniques to deliver DBS, ans improved neuroimaging techniques. The proceedings also offer insights into the new era of brain network neuromodulation and connectomic DBS to define and target dysfunctional brain networks. The proceedings also focused on innovations in applications and understanding of adaptive DBS (closed-loop systems), the use and applications of optogenetics in the field of neurostimulation and the need to develop databases for DBS indications. Finally, updates on neuroethical, legal, social, and policy issues relevant to DBS research are discussed

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

Plastic neural network with transmission delays promotes equivalence between function and structure

Acknowledgements The authors acknowledge the financial support from São Paulo Research Foundation (FAPESP, Brazil) (Grants Nos. 2016/23398-8, 2017/13502-5, 2018/03211-6, 2020/04624-2, 2022/05153-9, 2022/13761-9), National Council for Scientific and Technological Development (CNPq), Fundação Araucária and Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - Brasil (CAPES) .Peer reviewedPublisher PD

The Dynamic Brain in Action: Cortical Oscillations and Coordination Dynamics

Cortical oscillations are electrical activities with rhythmic and/or repetitive nature generated spontaneously and in response to stimuli. Study of cortical oscillations has become an area of converging interests since the last two decades and has deepened our understanding of its physiological basis across different behavioral states. Experimental and modeling work has taught us that there is a wide diversity of cellular and circuit mechanisms underlying the generation of cortical rhythms. A wildly diverse set of functions has pertained to synchronous oscillations but their significance in cognition should be better appraised in the more general framework of correlation between spike times of neurons. Oscillations are the core mechanism in adjusting neuronal interactions and shaping temporal coordination of neural activity. In the first part of this thesis, we review essential feature of cortical oscillations in membrane potentials and local field potentials recorded from turtle ex vivo preparation. Then we develop a simple computational model that reproduces the observed features. This modeling investigation suggests a plausible underlying mechanism for rhythmogenesis through cellular and circuit properties. The second part of the thesis is about temporal coordination dynamics quantified by signal and noise correlations. Here, again, we present a computational model to show how temporal coordination and synchronous oscillations can be sewn together. More importantly, what biophysical ingrediants are necessary for a network to reproduce the observed coordination dynamics

Functional Brain Oscillations: How Oscillations Facilitate Information Representation and Code Memories

The overall aim of the modelling works within this thesis is to lend theoretical evidence to empirical findings from the brain oscillations literature. We therefore hope to solidify and expand the notion that precise spike timing through oscillatory mechanisms facilitates communication, learning, information processing and information representation within the brain. The primary hypothesis of this thesis is that it can be shown computationally that neural de-synchronisations can allow information content to emerge. We do this using two neural network models, the first of which shows how differential rates of neuronal firing can indicate when a single item is being actively represented. The second model expands this notion by creating a complimentary timing mechanism, thus enabling the emergence of qualitive temporal information when a pattern of items is being actively represented. The secondary hypothesis of this thesis is that it can be also be shown computationally that oscillations might play a functional role in learning. Both of the models presented within this thesis propose a sparsely coded and fast learning hippocampal region that engages in the binding of novel episodic information. The first model demonstrates how active cortical representations enable learning to occur in their hippocampal counterparts via a phase-dependent learning rule. The second model expands this notion, creating hierarchical temporal sequences to encode the relative temporal position of cortical representations. We demonstrate in both of these models, how cortical brain oscillations might provide a gating function to the representation of information, whilst complimentary hippocampal oscillations might provide distinct phasic reference points for learning