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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 N2.Qualitative comparison of (a) human EEG data of sleep stage N2 from electrode Cz with (b) the isolated cortical module in regime N2 (region IV in the bifurcation diagram in Figure 2). The traces illustrate the medium-amplitude background oscillations and the stereotypical shape of spontaneous KCs at the EEG level. It may or may not have an initial bump followed by a large negative peak and a pronounced positive overshoot. The model-KC is noise induced and represents a single relaxation cycle. An evoked KC in the noise-free case is shown in Figure 4a. Model output is excitatory membrane voltage Ve, and both time series are z-scored (Parameters as in Table 2).
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pcbi-1003923-g005: Comparison of human EEG with model output in regime N2.Qualitative comparison of (a) human EEG data of sleep stage N2 from electrode Cz with (b) the isolated cortical module in regime N2 (region IV in the bifurcation diagram in Figure 2). The traces illustrate the medium-amplitude background oscillations and the stereotypical shape of spontaneous KCs at the EEG level. It may or may not have an initial bump followed by a large negative peak and a pronounced positive overshoot. The model-KC is noise induced and represents a single relaxation cycle. An evoked KC in the noise-free case is shown in Figure 4a. Model output is excitatory membrane voltage Ve, and both time series are z-scored (Parameters as in Table 2).

Mentions: To verify the ability of the model to reproduce sleep stage N2 we set the model to parameter configuration “N2” from Figure 2 (See Table 2). The chosen parameter set is within region I close to the border of region III, an example time series is shown in Figure 5.


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 N2.Qualitative comparison of (a) human EEG data of sleep stage N2 from electrode Cz with (b) the isolated cortical module in regime N2 (region IV in the bifurcation diagram in Figure 2). The traces illustrate the medium-amplitude background oscillations and the stereotypical shape of spontaneous KCs at the EEG level. It may or may not have an initial bump followed by a large negative peak and a pronounced positive overshoot. The model-KC is noise induced and represents a single relaxation cycle. An evoked KC in the noise-free case is shown in Figure 4a. Model output is excitatory membrane voltage Ve, and both time series are z-scored (Parameters as in Table 2).
© Copyright Policy
Related In: Results  -  Collection

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

pcbi-1003923-g005: Comparison of human EEG with model output in regime N2.Qualitative comparison of (a) human EEG data of sleep stage N2 from electrode Cz with (b) the isolated cortical module in regime N2 (region IV in the bifurcation diagram in Figure 2). The traces illustrate the medium-amplitude background oscillations and the stereotypical shape of spontaneous KCs at the EEG level. It may or may not have an initial bump followed by a large negative peak and a pronounced positive overshoot. The model-KC is noise induced and represents a single relaxation cycle. An evoked KC in the noise-free case is shown in Figure 4a. Model output is excitatory membrane voltage Ve, and both time series are z-scored (Parameters as in Table 2).
Mentions: To verify the ability of the model to reproduce sleep stage N2 we set the model to parameter configuration “N2” from Figure 2 (See Table 2). The chosen parameter set is within region I close to the border of region III, an example time series is shown in Figure 5.

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