Critical dynamics of Hopf bifurcations in the corticothalamic system: Transitions from normal arousal states to epileptic seizures

Yang, Dong-Ping; Robinson, P. A.

doi:10.1103/physreve.95.042410

Cited by 33 publications

(38 citation statements)

References 33 publications

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“…The examples of dynamics provided in this work represent perturbations around a fixed point to follow what has been done in previous analytic work. However, NFTsim is not limited to the simulation of such dynamics and can produce a range of oscillatory [6, 56], chaotic [57] and bursting dynamics [58]. …”

Section: Introductionmentioning

confidence: 99%

NFTsim: Theory and Simulation of Multiscale Neural Field Dynamics

et al. 2018

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A user ready, portable, documented software package, NFTsim, is presented to facilitate numerical simulations of a wide range of brain systems using continuum neural field modeling. NFTsim enables users to simulate key aspects of brain activity at multiple scales. At the microscopic scale, it incorporates characteristics of local interactions between cells, neurotransmitter effects, synaptodendritic delays and feedbacks. At the mesoscopic scale, it incorporates information about medium to large scale axonal ranges of fibers, which are essential to model dissipative wave transmission and to produce synchronous oscillations and associated cross-correlation patterns as observed in local field potential recordings of active tissue. At the scale of the whole brain, NFTsim allows for the inclusion of long range pathways, such as thalamocortical projections, when generating macroscopic activity fields. The multiscale nature of the neural activity produced by NFTsim has the potential to enable the modeling of resulting quantities measurable via various neuroimaging techniques. In this work, we give a comprehensive description of the design and implementation of the software. Due to its modularity and flexibility, NFTsim enables the systematic study of an unlimited number of neural systems with multiple neural populations under a unified framework and allows for direct comparison with analytic and experimental predictions. The code is written in C++ and bundled with Matlab routines for a rapid quantitative analysis and visualization of the outputs. The output of NFTsim is stored in plain text file enabling users to select from a broad range of tools for offline analysis. This software enables a wide and convenient use of powerful physiologically-based neural field approaches to brain modeling. NFTsim is distributed under the Apache 2.0 license.

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Section: Introductionmentioning

confidence: 99%

NFTsim: Theory and Simulation of Multiscale Neural Field Dynamics

et al. 2018

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“…min as seen in Eq (19),. where f max and f min are the maximum and minimum 414 values of f (t) actually encountered in a given instance.…”

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Effects of physiological parameter evolution on the dynamics of tonic-clonic seizures

Deeba

Sanz‐Leon

Robinson

2019

Preprint

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AbstractThe temporal and spectral characteristics of tonic-clonic seizures are investigated using a neural field model of the corticothalamic system in the presence of a temporally varying connection strength between the cerebral cortex and thalamus. Increasing connection strength drives the system into ∼ 10 Hz seizure oscillations once a threshold is passed and a subcritical Hopf bifurcation occurs. In this study, the spectral and temporal characteristics of tonic-clonic seizures are explored as functions of the relevant properties of physiological connection strengths, such as maximum strength, time above threshold, and the ramp rate at which the strength increases or decreases. Analysis shows that the seizure onset time decreases with the maximum connection strength and time above threshold, but increases with the ramp rate. Seizure duration and offset time increase with maximum connection strength, time above threshold, and rate of change. Spectral analysis reveals that the power of nonlinear harmonics and the duration of the oscillations increase as the maximum connection strength and the time above threshold increase. A secondary limit cycle at ∼ 18 Hz, termed a saddle-cycle, is also seen during seizure onset and becomes more prominent and robust with increasing ramp rate. If the time above the threshold is too small, the system does not reach the 10 Hz limit cycle, and only exhibits 18 Hz saddle-cycle oscillations. It is also seen that the times to reach the saturated large amplitude limit-cycle seizure oscillation from both the instability threshold and from the end of the saddle-cycle oscillations are inversely proportional to the square root of the ramp rate.Author SummaryEpilepsy, which is characterized by recurrent seizures, affects around 1% of the world population at some point in their lives. Tonic-clonic seizures are the most commonly encountered primary generalized seizures and it is widely considered that they can be induced by an increase in the connection strength between the cerebral cortex and the thalamus. In this paper, we analyze the detailed dynamics of tonic-clonic seizures along with their dependence on the parameters of the changing connection strength. We study the relationship of the seizure onset, offset, oscillation strength, and oscillation frequency to the duration, amplitude, and rate of change of the connection strength. A detailed understanding of the dynamics and their dependence on the physiological parameters of the brain may explain the variability of seizure dynamics among patients. It may also help to constitute successful seizure prediction.

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“…The model is simulated using the recently published NFTsim code written in C++ [36] 134 to investigate the spatiotemporal dynamics [27,32,33], which solves our damped and 135 retarded 2D wave equation in Eqs (2) and (4)−(6) with given initial conditions and 136 boundary conditions.…”

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confidence: 99%

“…The spatially homogeneous case 187 Many previous studies of the corticothalamic system investigated its global (spatially 188 uniform) dynamics; e.g., steady states, bifurcations from normal arousal states to 189 epileptic seizures [27,32,33]. Specifically, bifurcations have been intensively investigated 190 via changes of the parameter ν se , and demonstrated that this system can explain 191 primary generalized absence seizures [27,32].…”

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confidence: 99%

“…Specifically, bifurcations have been intensively investigated 190 via changes of the parameter ν se , and demonstrated that this system can explain 191 primary generalized absence seizures [27,32]. Furthermore, recent analysis has 192 established a bridge explicitly linking the tractable normal-form dynamical parameters 193 with the underlying physiological ones [33]. 194 In the homogeneous case of generalized absence seizures, the system has spatially with clinical data in detail and thus was employed to explain the pathological transition 203 from normal arousal states to primary generalized absence seizures [27,32].…”

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Unified Analysis of Global and Focal Aspects of Absence Epilepsy via Neural Field Theory of the Corticothalamic System

Yang

Robinson

2018

Preprint

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A physiology-based corticothalamic model is investigated with focal spatial heterogeneity, to unify global and focal aspects of absence epilepsy. Numerical and analytical calculations are employed to investigate the emergent spatiotemporal dynamics induced by focal activity as well as their underlying dynamical mechanisms. The spatiotemporal dynamics can be categorized into three scenarios: suppression, localization, and generalization of the focal activity, as summarized from a phase diagram vs. focal width and characteristic axon range. The corresponding temporal frequencies and spatial extents of wave activity during seizure generalization and localization agree well with experimental observations of global and focal aspects of absence epilepsy, respectively. The emergent seizure localization provide a biophysical explanation of the temporally higher frequency but spatially more localized cortical waves observed in genetic rat models that display characteristics of human absence epilepsy. Predictions are also presented for further experimental test. Author SummaryAbsence epilepsy is characterized by a sudden paroxysmal loss of consciousness accompanied by oscillatory activity propagating over many brain areas. Although primary generalized absence seizures are supported by the global corticothalamic system, converging experimental evidence supports a focal theory of absence epilepsy. Here we propose a dynamical mechanism to unify the global and focal aspects of absence epilepsy, with focal absence seizures associated with seizure localization, and the global ones associated with seizure generalization. Our corticothalamic model is used to investigate how seizure rhythms and spatial extents are related in these two different aspects of absence epilepsy. The results account for the difference of the experimentally observed seizure rhythms and spatial extents between humans and genetic rat models, which has previously been used to argue against the validity of such rats as animal models of absence epilepsy in humans.

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Critical dynamics of Hopf bifurcations in the corticothalamic system: Transitions from normal arousal states to epileptic seizures

Cited by 33 publications

References 33 publications

NFTsim: Theory and Simulation of Multiscale Neural Field Dynamics

NFTsim: Theory and Simulation of Multiscale Neural Field Dynamics

Effects of physiological parameter evolution on the dynamics of tonic-clonic seizures

Unified Analysis of Global and Focal Aspects of Absence Epilepsy via Neural Field Theory of the Corticothalamic System

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