Linear Analysis of the Corticothalamic Model with Time Delay

Yamaguchi, Ikuhiro; Ogawa, Yutaro; Nakao, Hiroya; Jimbo, Yasuhiko; Kotani, Kiyoshi

doi:10.1002/ecj.11581

Cited by 6 publications

(7 citation statements)

References 16 publications

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“…The mean value and the standard deviation were 0.077 s and 0.00449 s, respectively. This result is consistent with those from with previous studies where t 0 was estimated with other methods such as curve fitting [22,23,27] or particle filter [24] and supports the validity of our method based on Eq. (8).…”

Section: Delay Of the Cortico-thalamo-cortical Loopsupporting

confidence: 93%

“…In contrast, our method elucidated that the cortico-thalamo-cortical loop strength c 2 decreases at the wake-to-sleep transition. It is notable that the simulation works with the same model that showed that a positive c 2 and a negative c 2 correspond to "alpha mode" and "theta mode", respectively [27]. Considering this, we can attribute the two phenomena, decreasing alpha and increasing theta, to the change of c 2 in the positiveto-negative direction.…”

Section: Discussionmentioning

confidence: 77%

“…First, the RTF corresponding to the system described by Eq. (1) can be derived from the equation as (2) where ω is the angular frequency and j is the imaginary unit [25,26,27]. To eliminate c 1 and t e , we took the third and fourth derivatives of Eq.…”

Section: Analytical Methods To Estimate Cortico-thalamo-cortical Loop mentioning

confidence: 99%

“…(4) and (1). In this study, M was set to 10 by using t 0 ≅80 ms, which was shown in previous studies [22,23,24,27], and T s =1/128 Hz. The RTF for the AR model is expressed as The same procedure that was used to derive Eq.…”

Section: Analytical Methods To Estimate Cortico-thalamo-cortical Loop mentioning

confidence: 99%

“…To deal with these issues, we use two kinds of lowfrequency approximation. One of these involves adopting a compact model proposed by Kim and Robinson, in which the number of parameters is extremely reduced by low-frequency approximation [25,26,27]. The other is Taylor expansion for reciprocal-transfer functions (TFs) at zero frequency.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

A Robust Method with High Time Resolution for Estimating the Cortico-Thalamo-Cortical Loop Strength and the Delay when Using a Scalp Electroencephalography Applied to the Wake-Sleep Transition

Yamaguchi¹,

Kishi²,

Togo³

et al. 2018

Methods Inf Med

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Section: Delay Of the Cortico-thalamo-cortical Loopsupporting

confidence: 93%

Section: Discussionmentioning

confidence: 77%

Section: Analytical Methods To Estimate Cortico-thalamo-cortical Loop mentioning

confidence: 99%

Section: Analytical Methods To Estimate Cortico-thalamo-cortical Loop mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

A Robust Method with High Time Resolution for Estimating the Cortico-Thalamo-Cortical Loop Strength and the Delay when Using a Scalp Electroencephalography Applied to the Wake-Sleep Transition

Yamaguchi¹,

Kishi²,

Togo³

et al. 2018

Methods Inf Med

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Estimating the parameters of neural mass models including time delay and nonlinearity using a particle filter: a preliminary study toward model‐based EEG analysis

Ogawa

Yamaguchi

Kotani

et al. 2017

IEEJ Transactions Elec Engng

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Electroencephalogram (EEG) and local field potential (LFP) signals are measured for both experimental and clinical purposes which include sleep stage analyses, brain–computer interfaces, and disease diagnosis. EEG and LFP data analyses are typically based on models assuming that the measured data is generated from a biological system and estimate the model parameter values that most accurately reproduce the measured data. Thus, use of a biologically plausible model is important for a model‐based analysis. However, analyses using models that include time delay and nonlinearity have not been reported, even though they are biologically important for EEG generation mechanisms. In this study, we developed a parameter estimation method that uses a particle filter for models with time delay and nonlinearity, which was evaluated with simulations. Simulated EEG data were generated from neural mass models (NMMs). The NMM parameters were estimated from the generated data. Furthermore, parameters for modeling EEG features of patients with Alzheimer's disease were included in the NMM; the disease parameters were estimated from the simulated EEG data. We observed that NMM parameters, as well as the disease parameters, were accurately estimated from the simulated data. We conclude that the validity of our method for estimating parameters of NMMs including time delay and nonlinearity is confirmed for simulated EEG data, and these results show the possibility of using our method for model‐based analysis with real EEG data. © 2017 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.

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

Yang

Robinson

2017

Phys. Rev. E

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A physiologically based corticothalamic model of large-scale brain activity is used to analyze critical dynamics of transitions from normal arousal states to epileptic seizures, which correspond to Hopf bifurcations. This relates an abstract normal form quantitatively to underlying physiology that includes neural dynamics, axonal propagation, and time delays. Thus, a bridge is constructed that enables normal forms to be used to interpret quantitative data. The normal form of the Hopf bifurcations with delays is derived using Hale's theory, the center manifold theorem, and normal form analysis, and it is found to be explicitly expressed in terms of transfer functions and the sensitivity matrix of a reduced open-loop system. It can be applied to understand the effect of each physiological parameter on the critical dynamics and determine whether the Hopf bifurcation is supercritical or subcritical in instabilities that lead to absence and tonic-clonic seizures. Furthermore, the effects of thalamic and cortical nonlinearities on the bifurcation type are investigated, with implications for the roles of underlying physiology. The theoretical predictions about the bifurcation type and the onset dynamics are confirmed by numerical simulations and provide physiologically based criteria for determining bifurcation types from first principles. The results are consistent with experimental data from previous studies, imply that new regimes of seizure transitions may exist in clinical settings, and provide a simplified basis for control-systems interventions. Using the normal form, and the full equations from which it is derived, more complex dynamics, such as quasiperiodic cycles and saddle cycles, are discovered near the critical points of the subcritical Hopf bifurcations.

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Linear Analysis of the Corticothalamic Model with Time Delay

Cited by 6 publications

References 16 publications

A Robust Method with High Time Resolution for Estimating the Cortico-Thalamo-Cortical Loop Strength and the Delay when Using a Scalp Electroencephalography Applied to the Wake-Sleep Transition

A Robust Method with High Time Resolution for Estimating the Cortico-Thalamo-Cortical Loop Strength and the Delay when Using a Scalp Electroencephalography Applied to the Wake-Sleep Transition

Estimating the parameters of neural mass models including time delay and nonlinearity using a particle filter: a preliminary study toward model‐based EEG analysis

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

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