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A time-series model of phase amplitude cross frequency coupling and comparison of spectral characteristics with neural data.

Lepage KQ, Vijayan S - Biomed Res Int (2015)

Bottom Line: We introduce the full stochastic process time series model as a summation of three component weak-sense stationary (WSS) processes, namely, θ, γ, and η, with η a 1/f (α) noise process.The γ process is constructed as a product of a latent and unobserved high-frequency process x with a function of the lagged, low-frequency oscillatory component (θ).After demonstrating that the model process is WSS, an appropriate method of simulation is introduced based upon the WSS property.

View Article: PubMed Central - PubMed

Affiliation: The Department of Mathematics & Statistics, Boston University, 111 Cummington Mall, Boston, MA 02215, USA.

ABSTRACT
Stochastic processes that exhibit cross-frequency coupling (CFC) are introduced. The ability of these processes to model observed CFC in neural recordings is investigated by comparison with published spectra. One of the proposed models, based on multiplying a pulsatile function of a low-frequency oscillation (θ) with an unobserved and high-frequency component, yields a process with a spectrum that is consistent with observation. Other models, such as those employing a biphasic pulsatile function of a low-frequency oscillation, are demonstrated to be less suitable. We introduce the full stochastic process time series model as a summation of three component weak-sense stationary (WSS) processes, namely, θ, γ, and η, with η a 1/f (α) noise process. The γ process is constructed as a product of a latent and unobserved high-frequency process x with a function of the lagged, low-frequency oscillatory component (θ). After demonstrating that the model process is WSS, an appropriate method of simulation is introduced based upon the WSS property. This work may be of interest to researchers seeking to connect inhibitory and excitatory dynamics directly to observation in a model that accounts for known temporal dependence or to researchers seeking to examine what can occur in a multiplicative time-domain CFC mechanism.

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Spectra Sy of the stochastic model y. The sinusoidal, pulsatile, and biphasic γ's each contribute to the spectrum Sy in a different way. The spectrum associated with γ computed with the pulsatile function of θ is similar to the spectrum estimated from actual neural recordings (see [5]). The spectra associated with sinuosoidal, pulsatile, and biphasic γ exhibit side-lobes consistent with the convolution appearing in (13), (21).
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fig4: Spectra Sy of the stochastic model y. The sinusoidal, pulsatile, and biphasic γ's each contribute to the spectrum Sy in a different way. The spectrum associated with γ computed with the pulsatile function of θ is similar to the spectrum estimated from actual neural recordings (see [5]). The spectra associated with sinuosoidal, pulsatile, and biphasic γ exhibit side-lobes consistent with the convolution appearing in (13), (21).

Mentions: To explore the effect of θ center frequency upon cross frequency coupling, in simulation, two center frequencies are used. These frequencies are 6 Hz (Figure 4) and 15 Hz (Figure 5). The effect of making this change can be seen by comparing the spectra plotted in Figure 4 with those plotted in Figure 5.


A time-series model of phase amplitude cross frequency coupling and comparison of spectral characteristics with neural data.

Lepage KQ, Vijayan S - Biomed Res Int (2015)

Spectra Sy of the stochastic model y. The sinusoidal, pulsatile, and biphasic γ's each contribute to the spectrum Sy in a different way. The spectrum associated with γ computed with the pulsatile function of θ is similar to the spectrum estimated from actual neural recordings (see [5]). The spectra associated with sinuosoidal, pulsatile, and biphasic γ exhibit side-lobes consistent with the convolution appearing in (13), (21).
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4383361&req=5

fig4: Spectra Sy of the stochastic model y. The sinusoidal, pulsatile, and biphasic γ's each contribute to the spectrum Sy in a different way. The spectrum associated with γ computed with the pulsatile function of θ is similar to the spectrum estimated from actual neural recordings (see [5]). The spectra associated with sinuosoidal, pulsatile, and biphasic γ exhibit side-lobes consistent with the convolution appearing in (13), (21).
Mentions: To explore the effect of θ center frequency upon cross frequency coupling, in simulation, two center frequencies are used. These frequencies are 6 Hz (Figure 4) and 15 Hz (Figure 5). The effect of making this change can be seen by comparing the spectra plotted in Figure 4 with those plotted in Figure 5.

Bottom Line: We introduce the full stochastic process time series model as a summation of three component weak-sense stationary (WSS) processes, namely, θ, γ, and η, with η a 1/f (α) noise process.The γ process is constructed as a product of a latent and unobserved high-frequency process x with a function of the lagged, low-frequency oscillatory component (θ).After demonstrating that the model process is WSS, an appropriate method of simulation is introduced based upon the WSS property.

View Article: PubMed Central - PubMed

Affiliation: The Department of Mathematics & Statistics, Boston University, 111 Cummington Mall, Boston, MA 02215, USA.

ABSTRACT
Stochastic processes that exhibit cross-frequency coupling (CFC) are introduced. The ability of these processes to model observed CFC in neural recordings is investigated by comparison with published spectra. One of the proposed models, based on multiplying a pulsatile function of a low-frequency oscillation (θ) with an unobserved and high-frequency component, yields a process with a spectrum that is consistent with observation. Other models, such as those employing a biphasic pulsatile function of a low-frequency oscillation, are demonstrated to be less suitable. We introduce the full stochastic process time series model as a summation of three component weak-sense stationary (WSS) processes, namely, θ, γ, and η, with η a 1/f (α) noise process. The γ process is constructed as a product of a latent and unobserved high-frequency process x with a function of the lagged, low-frequency oscillatory component (θ). After demonstrating that the model process is WSS, an appropriate method of simulation is introduced based upon the WSS property. This work may be of interest to researchers seeking to connect inhibitory and excitatory dynamics directly to observation in a model that accounts for known temporal dependence or to researchers seeking to examine what can occur in a multiplicative time-domain CFC mechanism.

Show MeSH
Related in: MedlinePlus