Applications of optimal nonlinear control to a whole-brain network of FitzHugh-Nagumo oscillators

Chouzouris, Teresa; Roth, Nicolas; Cakan, Caglar; Obermayer, Klaus

doi:10.1103/physreve.104.024213

Cited by 10 publications

(8 citation statements)

References 70 publications

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“…Gradient-based optimization as investigated in this study may provide an alternative method to derive these optimal control strategies. With properly adapted precision measures (e.g., measures of synchronization, Chouzouris et al, 2021 ) and alternative constraints (if required), the formalism of OCT investigated in this work can be extended to a variety of novel control goals.…”

Section: Discussionmentioning

confidence: 99%

“…In general, our theoretical and algorithmic approach can be applied to a wide range of models of neural dynamics, including whole-brain network structures (cf. Cakan et al, 2022 ) and can be extended to different control tasks (e.g., Chouzouris et al, 2021 ). This could, for example, open up new ways to study the efficiency of neural interaction theoretically.…”

Section: Discussionmentioning

confidence: 99%

“…A recent work (Ref. Chouzouris et al, 2021 ) applied nonlinear OCT to a whole-brain network model of FitzHugh-Nagumo oscillators, discussing the predictions of linear control diagnostics vs. nonlinear optimal control for different control settings. These studies highlight the potential of control theoretic concepts in an “analytic” setting for a mechanistic understanding of neural dynamics.…”

Section: Introductionmentioning

confidence: 99%

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Nonlinear optimal control of a mean-field model of neural population dynamics

Salfenmoser

Obermayer

2022

Front. Comput. Neurosci.

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We apply the framework of nonlinear optimal control to a biophysically realistic neural mass model, which consists of two mutually coupled populations of deterministic excitatory and inhibitory neurons. External control signals are realized by time-dependent inputs to both populations. Optimality is defined by two alternative cost functions that trade the deviation of the controlled variable from its target value against the “strength” of the control, which is quantified by the integrated 1- and 2-norms of the control signal. We focus on a bistable region in state space where one low- (“down state”) and one high-activity (“up state”) stable fixed points coexist. With methods of nonlinear optimal control, we search for the most cost-efficient control function to switch between both activity states. For a broad range of parameters, we find that cost-efficient control strategies consist of a pulse of finite duration to push the state variables only minimally into the basin of attraction of the target state. This strategy only breaks down once we impose time constraints that force the system to switch on a time scale comparable to the duration of the control pulse. Penalizing control strength via the integrated 1-norm (2-norm) yields control inputs targeting one or both populations. However, whether control inputs to the excitatory or the inhibitory population dominate, depends on the location in state space relative to the bifurcation lines. Our study highlights the applicability of nonlinear optimal control to understand neuronal processing under constraints better.

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Section: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Nonlinear optimal control of a mean-field model of neural population dynamics

Salfenmoser

Obermayer

2022

Front. Comput. Neurosci.

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“…1 The various human brain parcellation studies, which divide the brain in structural or functional centers, have used a number of brain parcels (nodes) varying from 70 to 360 (Rolls et al, 2015;Arslan et al, 2018;Albers et al, 2021;Chouzouris et al, 2021). Therefore, a number of nodes of the order of 500 for each ring covers adequately the computational brain division.…”

Section: Synchronization Patterns For Positive Inter-ring Couplingmentioning

confidence: 99%

“…MRI imaging has, up to now, depicted different functional regions and axons bundles at a resolution of the order of 0.1 mm (Finn et al, 2015). In addition, the various human brain parcellation projects have identified a number of functional or structural regions in each hemisphere, with complementary inter-hemispheric connections (Rolls et al, 2015;Arslan et al, 2018;Albers et al, 2021;Chouzouris et al, 2021). In the present multiplex network approach, each hemisphere is roughly represented by one ring (denoted as L-ring for the left ring and R-ring for the right one), while the inter-connections between the L-and R-rings correspond to the neuron axons bundles connecting the left and right hemispheres (Finn et al, 2015).…”

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confidence: 99%

Synchronization in Multiplex Leaky Integrate-and-Fire Networks With Nonlocal Interactions

Anesiadis

Provata

2022

Front. Netw. Physiol.

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We study synchronization phenomena in a multiplex network composed of two rings with identical Leaky Integrate-and-Fire (LIF) oscillators located on the nodes of the rings. Within each ring the LIF oscillators interact nonlocally, while between rings there are one-to-one inter-ring interactions. This structure is motivated by the observed connectivity between the two hemispheres of the brain: within each hemisphere the various brain regions interact with neighboring regions, while across hemispheres each region interacts, primarily, with the functionally homologous region. We consider both positive (excitatory) and negative (inhibitory) linking. We identify numerically various parameter regimes where the multiplex network develops coexistence of active and subthreshold domains, chimera states, solitary states, full coherence or incoherence. In particular, for weak inter-ring coupling (weak multiplexing) different synchronization patterns on the two rings are supported. These are stable and are obtained when the intra-ring coupling values are near the critical points separating qualitatively distinct synchronization regimes, e.g., between the travelling fronts regime and the chimera state one.

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neurolib: A Simulation Framework for Whole-Brain Neural Mass Modeling

2021

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Abstractneurolib is a computational framework for whole-brain modeling written in Python. It provides a set of neural mass models that represent the average activity of a brain region on a mesoscopic scale. In a whole-brain network model, brain regions are connected with each other based on biologically informed structural connectivity, i.e., the connectome of the brain. neurolib can load structural and functional datasets, set up a whole-brain model, manage its parameters, simulate it, and organize its outputs for later analysis. The activity of each brain region can be converted into a simulated BOLD signal in order to calibrate the model against empirical data from functional magnetic resonance imaging (fMRI). Extensive model analysis is made possible using a parameter exploration module, which allows one to characterize a model’s behavior as a function of changing parameters. An optimization module is provided for fitting models to multimodal empirical data using evolutionary algorithms. neurolib is designed to be extendable and allows for easy implementation of custom neural mass models, offering a versatile platform for computational neuroscientists for prototyping models, managing large numerical experiments, studying the structure–function relationship of brain networks, and for performing in-silico optimization of whole-brain models.

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Applications of optimal nonlinear control to a whole-brain network of FitzHugh-Nagumo oscillators

Cited by 10 publications

References 70 publications

Nonlinear optimal control of a mean-field model of neural population dynamics

Nonlinear optimal control of a mean-field model of neural population dynamics

Synchronization in Multiplex Leaky Integrate-and-Fire Networks With Nonlocal Interactions

neurolib: A Simulation Framework for Whole-Brain Neural Mass Modeling

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