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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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Comparison of human EEG with model output in regime N3.Qualitative comparison of (a) human EEG data of sleep stage N3 from electrode Cz with (b) the isolated cortical module in regime N3 (region I in the bifurcation diagram in Figure 2). As the system is close to the Hopf bifurcation noise leads to quasiperiodic oscillations around the stable focus (up state). Large amplitude oscillations resemble KCs as both are shaped by the same homoclinic orbit. The model output is excitatory membrane voltage Ve, and both time series are z-scored (Parameters as in Table 3).
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pcbi-1003923-g006: Comparison of human EEG with model output in regime N3.Qualitative comparison of (a) human EEG data of sleep stage N3 from electrode Cz with (b) the isolated cortical module in regime N3 (region I in the bifurcation diagram in Figure 2). As the system is close to the Hopf bifurcation noise leads to quasiperiodic oscillations around the stable focus (up state). Large amplitude oscillations resemble KCs as both are shaped by the same homoclinic orbit. The model output is excitatory membrane voltage Ve, and both time series are z-scored (Parameters as in Table 3).

Mentions: Following our route for the sleep/wake transition in Figure 2 we then moved along the Hopf bifurcation to a setting beyond the cusp and close to region II, labeled as “N3”. In Figure 6 a representative time series is shown with the parameters given in Table 3. There the cortex shows high amplitude oscillations around 0.8 Hz. In contrast to the N2 stage, the cortex does not produce KCs in the sense of isolated events that differ from the background oscillations. Rather, the response increases until it approaches the form of a KC, depending on the strength of the perturbation.


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)

Comparison of human EEG with model output in regime N3.Qualitative comparison of (a) human EEG data of sleep stage N3 from electrode Cz with (b) the isolated cortical module in regime N3 (region I in the bifurcation diagram in Figure 2). As the system is close to the Hopf bifurcation noise leads to quasiperiodic oscillations around the stable focus (up state). Large amplitude oscillations resemble KCs as both are shaped by the same homoclinic orbit. The model output is excitatory membrane voltage Ve, and both time series are z-scored (Parameters as in Table 3).
© Copyright Policy
Related In: Results  -  Collection

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

pcbi-1003923-g006: Comparison of human EEG with model output in regime N3.Qualitative comparison of (a) human EEG data of sleep stage N3 from electrode Cz with (b) the isolated cortical module in regime N3 (region I in the bifurcation diagram in Figure 2). As the system is close to the Hopf bifurcation noise leads to quasiperiodic oscillations around the stable focus (up state). Large amplitude oscillations resemble KCs as both are shaped by the same homoclinic orbit. The model output is excitatory membrane voltage Ve, and both time series are z-scored (Parameters as in Table 3).
Mentions: Following our route for the sleep/wake transition in Figure 2 we then moved along the Hopf bifurcation to a setting beyond the cusp and close to region II, labeled as “N3”. In Figure 6 a representative time series is shown with the parameters given in Table 3. There the cortex shows high amplitude oscillations around 0.8 Hz. In contrast to the N2 stage, the cortex does not produce KCs in the sense of isolated events that differ from the background oscillations. Rather, the response increases until it approaches the form of a KC, depending on the strength of the perturbation.

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