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An algorithm for the EEG frequency architecture of consciousness and brain body coupling.

Klimesch W - Front Hum Neurosci (2013)

View Article: PubMed Central - PubMed

Affiliation: Department of Physiological Psychology, University of Salzburg Salzburg, Austria.

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The EEG is traditionally categorized into a handful of different frequency bands (δ, θ, α, β, γ; c.f... Schomer and Lopes da Silva, )... This implies that EEG frequencies do not represent an unstructured continuum... A good estimate for δ, θ, α, β and γ is 2.5, 5, 10, 20, and 40 Hz. (b) The width of a band is defined on the basis of the “golden mean role” (Klimesch, ; for an illustration, see Figure 1A left panel) to guarantee minimal interference between bands... Variable I(i) describes the numerical relation between δ, θ, α, γ as a series of harmonic frequencies that increase (or decrease) with i... If we would assume that δ, θ, α, β, γ are associated with long range white matter connections, each frequency domain would be associated with about 20% of all white matter fibers, as is illustrated in the left panel of Figure 1B... We can overcome this problem by assuming that loop time can stay constant when longer fibers are stronger myelinated than shorter fibers (conduction velocity is positively associated with myelin shield thickness; e.g., Rushton, ; Goldman and Albus, ; Sabah, )... Thus, a differential and selective myelination allows us to predict that loop times do not overlap between different frequency domains, although they have (different) fibers with the same length... This idea is illustrated in the middle panel of Figure 1B, where each bar is replaced by an asymmetric inverted u shape distribution, with the right part representing strongly and the left part weakly myelinated fibers... The resulting distribution is represented by the red dotted line... Second, and most importantly, the predicted distribution is strikingly similar to the empirically observed distribution of fiber lengths as shown in the right panel of Figure 1B (data are from Hagmann et al.,, provided by Olaf Sporns)... It should also be noted that the predicted shape of the distribution does not agree with the concept of “random connectivity. ” When the cortex is modeled as the surface of a sphere, the resulting distribution of connections between all points of the surface exhibits an inverted u-shape distribution around the radius as mean... Three groups of empirical data are also in support of this view, the task dependent emergence of between frequency phase coupling (e.g., Palva et al., ), the observation that ERP's can be described by a superposition of transiently phase coupled frequencies (Klimesch et al., ) and—most importantly—that a change in the state of consciousness from active cognition to drowsiness and slow wave sleep (SWS) is accompanied by a dramatic change in the frequency architecture... It is characterized by a decoupling between those frequency domains that are described by formula (2a) and the emergence of frequencies (slow waves and spindles) that do not play a role during conscious cognition... As an example, if HR is increased to 90 bpm (1.5 Hz; period of 667 ms) a transient decrease to 75 bpm (i.e., an increase in the period of 800 ms for a few heart beats) or increase to 150 bpm (a decrease in the period to 400 ms for a few heart beats) would still allow for a transient task-related harmonic coupling with brain oscillations.

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Illustration of the doubling-halving algorithm as described by formula (2a). (A) The distribution of the frequency domains, together with their bandwidths is shown in the left panel for brain oscillations and in the middle panel for body oscillations. The frequency boundaries are calculated according to the “golden mean role”: The upper frequency boundary of domain i is that frequency which is maximally separated from domain i + 1 and the lower boundary is that frequency which is maximally separated from domain i − 1 (see the inset in the left panel for an example). The predicted frequency architecture for a mouse with a heart rate of 600 bpm (=10 Hz) is shown in the right panel. Note that the values for the center frequencies are the same as for humans but the relation to the index of a domain is changed. (B) Formula (2) can be used to predict the distribution of long-range white matter connectivity. The areas of the yellow rectangles in the left and middle panel represent the percentage of bundles for a frequency domain. Note that the area of each rectangle is constant and that the two sides of the rectangles change according to the doubling-halving algorithm of formula (2). The empirical distribution is shown in the right panel (data are from Hagmann et al. (2008), provided by Olaf Sporns).
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Figure 1: Illustration of the doubling-halving algorithm as described by formula (2a). (A) The distribution of the frequency domains, together with their bandwidths is shown in the left panel for brain oscillations and in the middle panel for body oscillations. The frequency boundaries are calculated according to the “golden mean role”: The upper frequency boundary of domain i is that frequency which is maximally separated from domain i + 1 and the lower boundary is that frequency which is maximally separated from domain i − 1 (see the inset in the left panel for an example). The predicted frequency architecture for a mouse with a heart rate of 600 bpm (=10 Hz) is shown in the right panel. Note that the values for the center frequencies are the same as for humans but the relation to the index of a domain is changed. (B) Formula (2) can be used to predict the distribution of long-range white matter connectivity. The areas of the yellow rectangles in the left and middle panel represent the percentage of bundles for a frequency domain. Note that the area of each rectangle is constant and that the two sides of the rectangles change according to the doubling-halving algorithm of formula (2). The empirical distribution is shown in the right panel (data are from Hagmann et al. (2008), provided by Olaf Sporns).

Mentions: The EEG is traditionally categorized into a handful of different frequency bands (δ, θ, α, β, γ; c.f. Schomer and Lopes da Silva, 2011). This implies that EEG frequencies do not represent an unstructured continuum. But what could be the reasons for that? One obvious reason is that frequency bands such as e.g., θ and α exhibit a clear task and event related behavior (Klimesch, 1999, 2012; Buzsaki, 2006). But here the emphasis is on a formal aspect, which is to avoid unwanted “spurious” phase synchronization. If the numerical ratio between two frequencies (f1, f2; f1 < f2) is harmonic (f2 = I * f1; I = integer), the excitatory phases of the two frequencies can meet and synchronize according to a strict and regular pattern. This is of great advantage when phase coupling between frequencies is an important aspect of neuronal communication. If the ratio differs from a harmonic, spurious (unwanted) phase synchronization will appear in an uncontrolled way. Pletzer et al. (2010) have shown mathematically that the golden mean (g = 1.618 ….) is the best possible ratio to avoid spurious phase synchronization (see also Roopun et al., 2008). These aspects of phase synchronization can be summarized by two assumptions. (a) The center frequency of each EEG band is harmonically related to those of neighboring bands. A good estimate for δ, θ, α, β and γ is 2.5, 5, 10, 20, and 40 Hz. (b) The width of a band is defined on the basis of the “golden mean role” (Klimesch, 2012; for an illustration, see Figure 1A left panel) to guarantee minimal interference between bands. EEG center frequencies which have these properties are termed frequency domains in the following.


An algorithm for the EEG frequency architecture of consciousness and brain body coupling.

Klimesch W - Front Hum Neurosci (2013)

Illustration of the doubling-halving algorithm as described by formula (2a). (A) The distribution of the frequency domains, together with their bandwidths is shown in the left panel for brain oscillations and in the middle panel for body oscillations. The frequency boundaries are calculated according to the “golden mean role”: The upper frequency boundary of domain i is that frequency which is maximally separated from domain i + 1 and the lower boundary is that frequency which is maximally separated from domain i − 1 (see the inset in the left panel for an example). The predicted frequency architecture for a mouse with a heart rate of 600 bpm (=10 Hz) is shown in the right panel. Note that the values for the center frequencies are the same as for humans but the relation to the index of a domain is changed. (B) Formula (2) can be used to predict the distribution of long-range white matter connectivity. The areas of the yellow rectangles in the left and middle panel represent the percentage of bundles for a frequency domain. Note that the area of each rectangle is constant and that the two sides of the rectangles change according to the doubling-halving algorithm of formula (2). The empirical distribution is shown in the right panel (data are from Hagmann et al. (2008), provided by Olaf Sporns).
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC3824085&req=5

Figure 1: Illustration of the doubling-halving algorithm as described by formula (2a). (A) The distribution of the frequency domains, together with their bandwidths is shown in the left panel for brain oscillations and in the middle panel for body oscillations. The frequency boundaries are calculated according to the “golden mean role”: The upper frequency boundary of domain i is that frequency which is maximally separated from domain i + 1 and the lower boundary is that frequency which is maximally separated from domain i − 1 (see the inset in the left panel for an example). The predicted frequency architecture for a mouse with a heart rate of 600 bpm (=10 Hz) is shown in the right panel. Note that the values for the center frequencies are the same as for humans but the relation to the index of a domain is changed. (B) Formula (2) can be used to predict the distribution of long-range white matter connectivity. The areas of the yellow rectangles in the left and middle panel represent the percentage of bundles for a frequency domain. Note that the area of each rectangle is constant and that the two sides of the rectangles change according to the doubling-halving algorithm of formula (2). The empirical distribution is shown in the right panel (data are from Hagmann et al. (2008), provided by Olaf Sporns).
Mentions: The EEG is traditionally categorized into a handful of different frequency bands (δ, θ, α, β, γ; c.f. Schomer and Lopes da Silva, 2011). This implies that EEG frequencies do not represent an unstructured continuum. But what could be the reasons for that? One obvious reason is that frequency bands such as e.g., θ and α exhibit a clear task and event related behavior (Klimesch, 1999, 2012; Buzsaki, 2006). But here the emphasis is on a formal aspect, which is to avoid unwanted “spurious” phase synchronization. If the numerical ratio between two frequencies (f1, f2; f1 < f2) is harmonic (f2 = I * f1; I = integer), the excitatory phases of the two frequencies can meet and synchronize according to a strict and regular pattern. This is of great advantage when phase coupling between frequencies is an important aspect of neuronal communication. If the ratio differs from a harmonic, spurious (unwanted) phase synchronization will appear in an uncontrolled way. Pletzer et al. (2010) have shown mathematically that the golden mean (g = 1.618 ….) is the best possible ratio to avoid spurious phase synchronization (see also Roopun et al., 2008). These aspects of phase synchronization can be summarized by two assumptions. (a) The center frequency of each EEG band is harmonically related to those of neighboring bands. A good estimate for δ, θ, α, β and γ is 2.5, 5, 10, 20, and 40 Hz. (b) The width of a band is defined on the basis of the “golden mean role” (Klimesch, 2012; for an illustration, see Figure 1A left panel) to guarantee minimal interference between bands. EEG center frequencies which have these properties are termed frequency domains in the following.

View Article: PubMed Central - PubMed

Affiliation: Department of Physiological Psychology, University of Salzburg Salzburg, Austria.

AUTOMATICALLY GENERATED EXCERPT
Please rate it.

The EEG is traditionally categorized into a handful of different frequency bands (δ, θ, α, β, γ; c.f... Schomer and Lopes da Silva, )... This implies that EEG frequencies do not represent an unstructured continuum... A good estimate for δ, θ, α, β and γ is 2.5, 5, 10, 20, and 40 Hz. (b) The width of a band is defined on the basis of the “golden mean role” (Klimesch, ; for an illustration, see Figure 1A left panel) to guarantee minimal interference between bands... Variable I(i) describes the numerical relation between δ, θ, α, γ as a series of harmonic frequencies that increase (or decrease) with i... If we would assume that δ, θ, α, β, γ are associated with long range white matter connections, each frequency domain would be associated with about 20% of all white matter fibers, as is illustrated in the left panel of Figure 1B... We can overcome this problem by assuming that loop time can stay constant when longer fibers are stronger myelinated than shorter fibers (conduction velocity is positively associated with myelin shield thickness; e.g., Rushton, ; Goldman and Albus, ; Sabah, )... Thus, a differential and selective myelination allows us to predict that loop times do not overlap between different frequency domains, although they have (different) fibers with the same length... This idea is illustrated in the middle panel of Figure 1B, where each bar is replaced by an asymmetric inverted u shape distribution, with the right part representing strongly and the left part weakly myelinated fibers... The resulting distribution is represented by the red dotted line... Second, and most importantly, the predicted distribution is strikingly similar to the empirically observed distribution of fiber lengths as shown in the right panel of Figure 1B (data are from Hagmann et al.,, provided by Olaf Sporns)... It should also be noted that the predicted shape of the distribution does not agree with the concept of “random connectivity. ” When the cortex is modeled as the surface of a sphere, the resulting distribution of connections between all points of the surface exhibits an inverted u-shape distribution around the radius as mean... Three groups of empirical data are also in support of this view, the task dependent emergence of between frequency phase coupling (e.g., Palva et al., ), the observation that ERP's can be described by a superposition of transiently phase coupled frequencies (Klimesch et al., ) and—most importantly—that a change in the state of consciousness from active cognition to drowsiness and slow wave sleep (SWS) is accompanied by a dramatic change in the frequency architecture... It is characterized by a decoupling between those frequency domains that are described by formula (2a) and the emergence of frequencies (slow waves and spindles) that do not play a role during conscious cognition... As an example, if HR is increased to 90 bpm (1.5 Hz; period of 667 ms) a transient decrease to 75 bpm (i.e., an increase in the period of 800 ms for a few heart beats) or increase to 150 bpm (a decrease in the period to 400 ms for a few heart beats) would still allow for a transient task-related harmonic coupling with brain oscillations.

No MeSH data available.