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Characterization of K-complexes and slow wave activity in a neural mass model.

Weigenand A, Schellenberger Costa M, Ngo HV, Claussen JC, Martinetz T - PLoS Comput. Biol. (2014)

Bottom Line: While the underlying dynamics on the neuronal level is well known and can be easily measured, the resulting behavior on the macroscopic population level remains unclear.Importantly, there is a canard phenomenon arising from a homoclinic bifurcation, whose orbit determines the shape of large amplitude SOs.The model generates both time series and spectra that strikingly resemble real electroencephalogram data and points out possible differences between the different stages of natural sleep.

View Article: PubMed Central - PubMed

Affiliation: Institute for Neuro- and Bioinformatics, University of Lübeck, Lübeck, Germany; Graduate School for Computing in Medicine and Life Science, University of Lübeck, Lübeck, Germany.

ABSTRACT
NREM sleep is characterized by two hallmarks, namely K-complexes (KCs) during sleep stage N2 and cortical slow oscillations (SOs) during sleep stage N3. While the underlying dynamics on the neuronal level is well known and can be easily measured, the resulting behavior on the macroscopic population level remains unclear. On the basis of an extended neural mass model of the cortex, we suggest a new interpretation of the mechanisms responsible for the generation of KCs and SOs. As the cortex transitions from wake to deep sleep, in our model it approaches an oscillatory regime via a Hopf bifurcation. Importantly, there is a canard phenomenon arising from a homoclinic bifurcation, whose orbit determines the shape of large amplitude SOs. A KC corresponds to a single excursion along the homoclinic orbit, while SOs are noise-driven oscillations around a stable focus. The model generates both time series and spectra that strikingly resemble real electroencephalogram data and points out possible differences between the different stages of natural sleep.

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Response of the noise-free cortex to artificial stimuli.Excitatory bursts of 50 ms duration were applied to both populations. The spike rate of the stimuli  varies uniformly from 5 Hz (dark blue) to 100 Hz (dark red). The stimulus is shown in grey. (a) Bifurcation parameters are set to the mark N2 close to region III (see Table 2). There, a canard explosion leads to large amplitude responses that qualitatively resemble a typical evoked KC with its P200, N550 and P900 components. (b) Parameters are set to mark N3, so that the cortex is beyond the cusp close to region II (see Table 3). The canard vanished, leading to an even increase in the amplitude of the response.
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pcbi-1003923-g004: Response of the noise-free cortex to artificial stimuli.Excitatory bursts of 50 ms duration were applied to both populations. The spike rate of the stimuli varies uniformly from 5 Hz (dark blue) to 100 Hz (dark red). The stimulus is shown in grey. (a) Bifurcation parameters are set to the mark N2 close to region III (see Table 2). There, a canard explosion leads to large amplitude responses that qualitatively resemble a typical evoked KC with its P200, N550 and P900 components. (b) Parameters are set to mark N3, so that the cortex is beyond the cusp close to region II (see Table 3). The canard vanished, leading to an even increase in the amplitude of the response.

Mentions: There, positive as well as negative inputs may cause a reverse spike resembling a KC. Additionally, close to the curve of Hopf points the stable active state turns into a stable focus, i.e. the system behaves like a damped oscillator upon perturbation. In Figure 4a we show the response to artificial stimuli of varying strength, when the cortex is set close to the Hopf bifurcation between region I and III.


Characterization of K-complexes and slow wave activity in a neural mass model.

Weigenand A, Schellenberger Costa M, Ngo HV, Claussen JC, Martinetz T - PLoS Comput. Biol. (2014)

Response of the noise-free cortex to artificial stimuli.Excitatory bursts of 50 ms duration were applied to both populations. The spike rate of the stimuli  varies uniformly from 5 Hz (dark blue) to 100 Hz (dark red). The stimulus is shown in grey. (a) Bifurcation parameters are set to the mark N2 close to region III (see Table 2). There, a canard explosion leads to large amplitude responses that qualitatively resemble a typical evoked KC with its P200, N550 and P900 components. (b) Parameters are set to mark N3, so that the cortex is beyond the cusp close to region II (see Table 3). The canard vanished, leading to an even increase in the amplitude of the response.
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4230734&req=5

pcbi-1003923-g004: Response of the noise-free cortex to artificial stimuli.Excitatory bursts of 50 ms duration were applied to both populations. The spike rate of the stimuli varies uniformly from 5 Hz (dark blue) to 100 Hz (dark red). The stimulus is shown in grey. (a) Bifurcation parameters are set to the mark N2 close to region III (see Table 2). There, a canard explosion leads to large amplitude responses that qualitatively resemble a typical evoked KC with its P200, N550 and P900 components. (b) Parameters are set to mark N3, so that the cortex is beyond the cusp close to region II (see Table 3). The canard vanished, leading to an even increase in the amplitude of the response.
Mentions: There, positive as well as negative inputs may cause a reverse spike resembling a KC. Additionally, close to the curve of Hopf points the stable active state turns into a stable focus, i.e. the system behaves like a damped oscillator upon perturbation. In Figure 4a we show the response to artificial stimuli of varying strength, when the cortex is set close to the Hopf bifurcation between region I and III.

Bottom Line: While the underlying dynamics on the neuronal level is well known and can be easily measured, the resulting behavior on the macroscopic population level remains unclear.Importantly, there is a canard phenomenon arising from a homoclinic bifurcation, whose orbit determines the shape of large amplitude SOs.The model generates both time series and spectra that strikingly resemble real electroencephalogram data and points out possible differences between the different stages of natural sleep.

View Article: PubMed Central - PubMed

Affiliation: Institute for Neuro- and Bioinformatics, University of Lübeck, Lübeck, Germany; Graduate School for Computing in Medicine and Life Science, University of Lübeck, Lübeck, Germany.

ABSTRACT
NREM sleep is characterized by two hallmarks, namely K-complexes (KCs) during sleep stage N2 and cortical slow oscillations (SOs) during sleep stage N3. While the underlying dynamics on the neuronal level is well known and can be easily measured, the resulting behavior on the macroscopic population level remains unclear. On the basis of an extended neural mass model of the cortex, we suggest a new interpretation of the mechanisms responsible for the generation of KCs and SOs. As the cortex transitions from wake to deep sleep, in our model it approaches an oscillatory regime via a Hopf bifurcation. Importantly, there is a canard phenomenon arising from a homoclinic bifurcation, whose orbit determines the shape of large amplitude SOs. A KC corresponds to a single excursion along the homoclinic orbit, while SOs are noise-driven oscillations around a stable focus. The model generates both time series and spectra that strikingly resemble real electroencephalogram data and points out possible differences between the different stages of natural sleep.

Show MeSH