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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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Bifurcation diagram of the cortex with respect to  and .Overview over the models dynamic regimes, obtained via numerical bifurcation analysis of the cortex with respect to  and . Hopf bifurcations are drawn in red, while the black line depicts saddle-node bifurcations. The bottom gray line marks the intersection of Hopf and saddle curves, the top gray line the cusp bifurcation. The green line depicts the proposed route for the transition from wake to sleep stage N3. The region around wake corresponds to parameter settings commonly used for wake EEG. N2 and N3 are settings used within this study for the respective sleep stages, as given in Table 2 and 3. Regions I-VI are described in the text and Table 1 (Parameters as in Table S1).
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pcbi-1003923-g002: Bifurcation diagram of the cortex with respect to and .Overview over the models dynamic regimes, obtained via numerical bifurcation analysis of the cortex with respect to and . Hopf bifurcations are drawn in red, while the black line depicts saddle-node bifurcations. The bottom gray line marks the intersection of Hopf and saddle curves, the top gray line the cusp bifurcation. The green line depicts the proposed route for the transition from wake to sleep stage N3. The region around wake corresponds to parameter settings commonly used for wake EEG. N2 and N3 are settings used within this study for the respective sleep stages, as given in Table 2 and 3. Regions I-VI are described in the text and Table 1 (Parameters as in Table S1).

Mentions: As can be seen in Figure 2 the dynamics of the system is shaped by two bifurcations. The first one is a fold created by two saddle node bifurcations (black), that vanishes in a cusp. Between the two saddle nodes there are three equilibrium states, leading to bistability or excitability, see Figure 3a or Figure 3b. This is in good agreement with [31] and [70], as in the case of a fixed sodium concentration is constant, and an increase in acts as a decrease in resting potential.


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)

Bifurcation diagram of the cortex with respect to  and .Overview over the models dynamic regimes, obtained via numerical bifurcation analysis of the cortex with respect to  and . Hopf bifurcations are drawn in red, while the black line depicts saddle-node bifurcations. The bottom gray line marks the intersection of Hopf and saddle curves, the top gray line the cusp bifurcation. The green line depicts the proposed route for the transition from wake to sleep stage N3. The region around wake corresponds to parameter settings commonly used for wake EEG. N2 and N3 are settings used within this study for the respective sleep stages, as given in Table 2 and 3. Regions I-VI are described in the text and Table 1 (Parameters as in Table S1).
© Copyright Policy
Related In: Results  -  Collection

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

pcbi-1003923-g002: Bifurcation diagram of the cortex with respect to and .Overview over the models dynamic regimes, obtained via numerical bifurcation analysis of the cortex with respect to and . Hopf bifurcations are drawn in red, while the black line depicts saddle-node bifurcations. The bottom gray line marks the intersection of Hopf and saddle curves, the top gray line the cusp bifurcation. The green line depicts the proposed route for the transition from wake to sleep stage N3. The region around wake corresponds to parameter settings commonly used for wake EEG. N2 and N3 are settings used within this study for the respective sleep stages, as given in Table 2 and 3. Regions I-VI are described in the text and Table 1 (Parameters as in Table S1).
Mentions: As can be seen in Figure 2 the dynamics of the system is shaped by two bifurcations. The first one is a fold created by two saddle node bifurcations (black), that vanishes in a cusp. Between the two saddle nodes there are three equilibrium states, leading to bistability or excitability, see Figure 3a or Figure 3b. This is in good agreement with [31] and [70], as in the case of a fixed sodium concentration is constant, and an increase in acts as a decrease in resting potential.

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