Optimizing electrical brain stimulation for seizure disorders

University of Minnesota Ph.D. dissertation. March 2017. Major: Neuroscience. Advisor: Theoden Netoff. 1 computer file (PDF); x, 145 pages.Approximately 1% of the world population is afflicted with Epilepsy. For many patients, antiepileptic drugs do not fully control seizures. Electrical brain stimulation therapies have been effective in reducing seizure rates in some patients. While current neuromodulation devices provide a benefit to patients, efficacy can be improved by optimizing brain stimulation so that the therapy is tuned on a patient by patient basis. One optimization approach is to target deep brain regions that strongly modulate seizure prone regions. I will present data on the effects of stimulation of two different anatomical regions for seizure control, and establish my experimental platform for testing closed-loop algorithms. There are two general methods to implementing closed-loop algorithms to modulate neural activity: 1) Model-free algorithms that require a learning period to establish an optimal mapping between neural states and best therapeutic parameters, and 2) Model-based algorithms that use forward predictions of the neural system to determine the appropriate stimulation therapy to be administered. In this thesis, I will propose and test two closed-loop control schemes to control the brain activity to prevent epileptogenic activity while reducing stimulation energy. I will also present techniques to remove stimulation artifacts so that neural biomarkers can be measured while simultaneously applying stimulation. The methods I will present could potentially be implemented in next generation electrical brain stimulation hardware for seizure disorders and other neurological diseases

Mean field modelling of human EEG: application to epilepsy

Aggregated electrical activity from brain regions recorded via an electroencephalogram (EEG), reveal that the brain is never at rest, producing a spectrum of ongoing oscillations that change as a result of different behavioural states and neurological conditions. In particular, this thesis focusses on pathological oscillations associated with absence seizures that typically affect 2–16 year old children. Investigation of the cellular and network mechanisms for absence seizures studies have implicated an abnormality in the cortical and thalamic activity in the generation of absence seizures, which have provided much insight to the potential cause of this disease. A number of competing hypotheses have been suggested, however the precise cause has yet to be determined. This work attempts to provide an explanation of these abnormal rhythms by considering a physiologically based, macroscopic continuum mean-field model of the brain's electrical activity. The methodology taken in this thesis is to assume that many of the physiological details of the involved brain structures can be aggregated into continuum state variables and parameters. The methodology has the advantage to indirectly encapsulate into state variables and parameters, many known physiological mechanisms underlying the genesis of epilepsy, which permits a reduction of the complexity of the problem. That is, a macroscopic description of the involved brain structures involved in epilepsy is taken and then by scanning the parameters of the model, identification of state changes in the system are made possible. Thus, this work demonstrates how changes in brain state as determined in EEG can be understood via dynamical state changes in the model providing an explanation of absence seizures. Furthermore, key observations from both the model and EEG data motivates a number of model reductions. These reductions provide approximate solutions of seizure oscillations and a better understanding of periodic oscillations arising from the involved brain regions. Local analysis of oscillations are performed by employing dynamical systems theory which provide necessary and sufficient conditions for their appearance. Finally local and global stability is then proved for the reduced model, for a reduced region in the parameter space. The results obtained in this thesis can be extended and suggestions are provided for future progress in this area

Predicting and identifying signs of criticality near neuronal phase transition

This thesis examines the critical transitions between distinct neural states associated with the transition to neuron spiking and with the induction of anaesthesia. First, mathematical and electronic models of a single spiking neuron are investigated, focusing on stochastic subthreshold dynamics on close approach to spiking and to depolarisation-blocked quiescence (spiking death) transition points. Theoretical analysis of subthreshold neural behaviour then shifts to the anaesthetic-induced phase transition into unconsciousness using a mean-field model for interacting populations of excitatory and inhibitory neurons. The anaesthetic-induced changes are validated experimentally using published electrophysiological data recorded in anaesthetised rats. The criticality hypothesis associated with brain state change is examined using neuronal avalanches for experimentally recorded rat local field potential (LFP) data and mean-field pseudoLFP simulation data. We compare three different implementations of the FitzHugh--Nagumo single spiking neuron model: a mathematical model by H. R. Wilson, an alternative due to Keener and Sneyd, and an op-amp based nonlinear oscillator circuit. Although all three models can produce nonlinear ``spiking" oscillations, our focus is on the altering characteristics of noise-induced fluctuations near spiking onset and death via Hopf bifurcation. We introduce small-amplitude white noise to enable a linearised stochastic analyses using Ornstein--Uhlenbeck theory to predict variance, power spectrum and correlation of voltage fluctuations during close approach to the critical point, identified as the point at which the real part of the dominant eigenvalue becomes zero. We validate the theoretical predictions with numerical simulations and show that the fluctuations exhibit critical slowing down divergences when approaching the critical point: power-law increases in the variance of the fluctuations simultaneous with prolongation of the system response. We expand the study of stochastic behaviour to two spatial dimensions using the Waikato mean-field model operating near phase transition points controlled by the infusion or elimination of anaesthetic inhibition. Specifically, we investigate close approach to the critical point (CP), and to the points of loss of consciousness (LOC) and recovery of consciousness (ROC). We select the equilibrium states using $\lambda$ anaesthetic inhibition and $\Delta V^{\text{rest}}_e$ cortical excitation as control parameters, then analyse the voltage fluctuations evoked by small-amplitude spatiotemporal white noise. We predict the variance and power spectrum of voltage fluctuations near the marginally stable LOC and ROC transition points, then validate via numerical simulation. The results demonstrate a marked increase in voltage fluctuations and spectral power near transition points. This increased susceptibility to low-intensity white noise stimulation provides an early warning of impending phase transition. Effects of anaesthetic agents on cortical activity are reflected in local field potentials (LFPs) by the variation of amplitude and frequency in voltage fluctuations. To explore these changes, we investigate LFPs acquired from published electrophysiological experiments of anaesthetised rats to extract amplitude distribution, variance and time-correlation statistics. The analysis is broadened by applying detrended fluctuation analysis (DFA) to detect long-range dependencies in the time-series, and we compare DFA results with power spectral density (PSD). We find that the DFA exponent increases with anaesthetic concentration, but is always close to 1. The penultimate chapter investigates the evidence of criticality in anaesthetic induced phase-transitions using avalanche analysis. Rat LFP data reveal an avalanche power-law exponent close to $\alpha = 1.5$, but this value depends on both the time-bin width chosen to separate the events and the \textit{z}-score threshold used to detect these events. Power-law behaviour is only evident at lower anaesthetic concentrations; at higher concentrations the avalanche size distribution fails to align with a power-law nature. Criticality behaviour is also indicated in the Waikato mean-field model for anaesthetic-induced phase-transition using avalanches detected from the pseudoLFP time-series, but only at the critical point (CP) and at the secondary phase-transition points of LOC and ROC. In summary, this thesis unveils evidence of characteristic changes near phase transition points using computer-based mathematical modelling and electrophysiological data analysis. We find that noise-driven fluctuations become larger and persist for longer as the critical point is closely approached, with similar properties being seen not only in single-neuron and neural population models, but also in biological LFP signals. These results consistent with an increase of susceptibility to noise perturbations near phase transition point. Identification of neuronal avalanches in rat LFP data for low anaesthetic concentrations provides further support for the criticality hypothesis

Network resilience

Many systems on our planet are known to shift abruptly and irreversibly from one state to another when they are forced across a "tipping point," such as mass extinctions in ecological networks, cascading failures in infrastructure systems, and social convention changes in human and animal networks. Such a regime shift demonstrates a system's resilience that characterizes the ability of a system to adjust its activity to retain its basic functionality in the face of internal disturbances or external environmental changes. In the past 50 years, attention was almost exclusively given to low dimensional systems and calibration of their resilience functions and indicators of early warning signals without considerations for the interactions between the components. Only in recent years, taking advantages of the network theory and lavish real data sets, network scientists have directed their interest to the real-world complex networked multidimensional systems and their resilience function and early warning indicators. This report is devoted to a comprehensive review of resilience function and regime shift of complex systems in different domains, such as ecology, biology, social systems and infrastructure. We cover the related research about empirical observations, experimental studies, mathematical modeling, and theoretical analysis. We also discuss some ambiguous definitions, such as robustness, resilience, and stability.Comment: Review chapter

Complex Dynamics in Dedicated / Multifunctional Neural Networks and Chaotic Nonlinear Systems

We study complex behaviors arising in neuroscience and other nonlinear systems by combining dynamical systems analysis with modern computational approaches including GPU parallelization and unsupervised machine learning. To gain insights into the behaviors of brain networks and complex central pattern generators (CPGs), it is important to understand the dynamical principles regulating individual neurons as well as the basic structural and functional building blocks of neural networks. In the first section, we discuss how symbolic methods can help us analyze neural dynamics such as bursting, tonic spiking and chaotic mixed-mode oscillations in various models of individual neurons, the bifurcations that underlie transitions between activity types, as well as emergent network phenomena through synergistic interactions seen in realistic neural circuits, such as network bursting from non-intrinsic bursters. The second section is focused on the origin and coexistence of multistable rhythms in oscillatory neural networks of inhibitory coupled cells. We discuss how network connectivity and intrinsic properties of the cells affect the dynamics, and how even simple circuits can exhibit a variety of mono/multi-stable rhythms including pacemakers, half-center oscillators, multiple traveling-waves, fully synchronous states, as well as various chimeras. Our analyses can help generate verifiable hypotheses for neurophysiological experiments on central pattern generators. In the last section, we demonstrate the inter-disciplinary nature of this research through the applications of these techniques to identify the universal principles governing both simple and complex dynamics, and chaotic structure in diverse nonlinear systems. Using a classical example from nonlinear laser optics, we elaborate on the multiplicity and self-similarity of key organizing structures in 2D parameter space such as homoclinic and heteroclinic bifurcation curves, Bykov T-point spirals, and inclination flips. This is followed by detailed computational reconstructions of the spatial organization and 3D embedding of bifurcation surfaces, parametric saddles, and isolated closed curves (isolas). The generality of our modeling approaches could lead to novel methodologies and nonlinear science applications in biological, medical and engineering systems

Mechanisms of the Coregulation of Multiple Ionic Currents for the Control of Neuronal Activity

An open question in contemporary neuroscience is how neuromodulators coregulate multiple conductances to maintain functional neuronal activity. Neuromodulators enact changes to properties of biophysical characteristics, such as the maximal conductance or voltage of half-activation of an ionic current, which determine the type and properties of neuronal activity. We apply dynamical systems theory to study the changes to neuronal activity that arise from neuromodulation. Neuromulators can act on multiple targets within a cell. The coregulation of mulitple ionic currents extends the scope of dynamic control on neuronal activity. Different aspects of neuronal activity can be independently controlled by different currents. The coregulation of multiple ionic currents provides precise control over the temporal characteristics of neuronal activity. Compensatory changes in multiple ionic currents could be used to avoid dangerous dynamics or maintain some aspect of neuronal activity. The coregulation of multiple ionic currents can be used as bifurcation control to ensure robust dynamics or expand the range of coexisting regimes. Multiple ionic currents could be involved in increasing the range of dynamic control over neuronal activity. The coregulation of multiple ionic currents in neuromodulation expands the range over which biophysical parameters support functional activity

Modelling human choices: MADeM and decision‑making

Research supported by FAPESP 2015/50122-0 and DFG-GRTK 1740/2. RP and AR are also part of the Research, Innovation and Dissemination Center for Neuromathematics FAPESP grant (2013/07699-0). RP is supported by a FAPESP scholarship (2013/25667-8). ACR is partially supported by a CNPq fellowship (grant 306251/2014-0)

29th Annual Computational Neuroscience Meeting: CNS*2020

Meeting abstracts This publication was funded by OCNS. The Supplement Editors declare that they have no competing interests. Virtual | 18-22 July 202

International Conference on Mathematical Analysis and Applications in Science and Engineering – Book of Extended Abstracts

The present volume on Mathematical Analysis and Applications in Science and Engineering - Book of Extended Abstracts of the ICMASC’2022 collects the extended abstracts of the talks presented at the International Conference on Mathematical Analysis and Applications in Science and Engineering – ICMA2SC'22 that took place at the beautiful city of Porto, Portugal, in June 27th-June 29th 2022 (3 days). Its aim was to bring together researchers in every discipline of applied mathematics, science, engineering, industry, and technology, to discuss the development of new mathematical models, theories, and applications that contribute to the advancement of scientific knowledge and practice. Authors proposed research in topics including partial and ordinary differential equations, integer and fractional order equations, linear algebra, numerical analysis, operations research, discrete mathematics, optimization, control, probability, computational mathematics, amongst others. The conference was designed to maximize the involvement of all participants and will present the state-of- the-art research and the latest achievements.info:eu-repo/semantics/publishedVersio