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A generalized framework for quantifying the dynamics of EEG event-related desynchronization.

Lemm S, Müller KR, Curio G - PLoS Comput. Biol. (2009)

Bottom Line: Here, we establish a novel generalized concept to measure event-related desynchronization (ERD), which allows one to model neural oscillatory dynamics also in the presence of dynamical cortical states.Specifically, we demonstrate that a somatosensory stimulus causes a stereotypic sequence of first an ERD and then an ensuing amplitude overshoot (event-related synchronization), which at a dynamical cortical state becomes evident only if the natural relaxation dynamics of unperturbed EEG rhythms is utilized as reference dynamics.Moreover, this computational approach also encompasses the more general notion of a "conditional ERD," through which candidate explanatory variables can be scrutinized with regard to their possible impact on a particular oscillatory dynamics under study.

View Article: PubMed Central - PubMed

Affiliation: Intelligent Data Analysis Group, Fraunhofer Institute FIRST, Berlin, Germany. steven.lemm@first.fraunhofer.de

ABSTRACT
Brains were built by evolution to react swiftly to environmental challenges. Thus, sensory stimuli must be processed ad hoc, i.e., independent--to a large extent--from the momentary brain state incidentally prevailing during stimulus occurrence. Accordingly, computational neuroscience strives to model the robust processing of stimuli in the presence of dynamical cortical states. A pivotal feature of ongoing brain activity is the regional predominance of EEG eigenrhythms, such as the occipital alpha or the pericentral mu rhythm, both peaking spectrally at 10 Hz. Here, we establish a novel generalized concept to measure event-related desynchronization (ERD), which allows one to model neural oscillatory dynamics also in the presence of dynamical cortical states. Specifically, we demonstrate that a somatosensory stimulus causes a stereotypic sequence of first an ERD and then an ensuing amplitude overshoot (event-related synchronization), which at a dynamical cortical state becomes evident only if the natural relaxation dynamics of unperturbed EEG rhythms is utilized as reference dynamics. Moreover, this computational approach also encompasses the more general notion of a "conditional ERD," through which candidate explanatory variables can be scrutinized with regard to their possible impact on a particular oscillatory dynamics under study. Thus, the generalized ERD represents a powerful novel analysis tool for extending our understanding of inter-trial variability of evoked responses and therefore the robust processing of environmental stimuli.

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Comparison of both methods for the estimation of state conditional ERD by means of surrugate data.The figure contrasts the true conditional ERD (left column), the estimated conventional conditional ERD (central column) and the estimated generalized conditional ERD (right column). Each row corresponds to a particular artificial data set (I–III, top to bottom). The panels share an identical color coding scheme, where blue and red refer to ERD and ERS, respectively. The vertical and horizontal axes represent the state variable  and the time, respectively.
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pcbi-1000453-g003: Comparison of both methods for the estimation of state conditional ERD by means of surrugate data.The figure contrasts the true conditional ERD (left column), the estimated conventional conditional ERD (central column) and the estimated generalized conditional ERD (right column). Each row corresponds to a particular artificial data set (I–III, top to bottom). The panels share an identical color coding scheme, where blue and red refer to ERD and ERS, respectively. The vertical and horizontal axes represent the state variable and the time, respectively.

Mentions: Before comparing the results of the empirical estimators for the conditional ERD, let us begin with some analytical considerations. From the common setup of the artificial datasets we can attain the true conditional ERD as:(13)Where denotes the conditional probability distribution. Moreover, from the definition of the conventional and the generalized conditional ERD (cf. Eqn 4 and 5) and using the instantaneous power at the single time instance for estimating the static baseline level in the conventional framework we obtain:(14)(15)Considering further the particular settings of the three data sets, Table 1 presents the corresponding analytic solutions for the three artificial data sets. So, based on these preceding considerations, we expect the conventional estimator to incorrectly measure the conditional ERD for all three data sets, while the generalized estimator should be capable to retrieve the given underlying functional relationship between the explanatory variable and the ERD dynamics. In Fig. 3 we depict the true conditional ERD and the results of the two competing methods. Comparing the empirical estimates clearly reveals that the generalized ERD is capable of recovering the functional dependency of the ERD dynamics on the explanatory variable , while the conventional estimator miscalculate the conditional ERD and even gives rise to the observation of spurious ERS. On closer examination we can track down the static baseline as the failure cause in the conventional conditional ERD setting. To see this, first note that the conventional setting, using a fixed baseline, implicitly assumes that the expected power of the unperturbed dynamics does not vary with time (weak stationarity). Notably, weak stationarity of the overall distribution does not imply weak stationarity of the conditional distributions, which can be easily verified considering the second data set. Here the (unconditional) expectation , i.e., the average across all catch trials is given as(16)So it is constant and hence weak stationarity is fulfilled. However, conditioning the expectation on the state results in(17)To see this, please note the particular setting according to Eqn 10. Consequently, the conditional expectation of the unperturbed dynamics is a function of , that exhibits a clear non-constant time pattern. Apparently, any constant baseline does not sufficiently represent the intrinsic trends in the unperturbed dynamics. Accordingly, the conventional ERD measure, which relies on the static baseline assumption, incorrectly specifies the conditional unperturbed dynamics and therefore misvalues the true conditional ERD.


A generalized framework for quantifying the dynamics of EEG event-related desynchronization.

Lemm S, Müller KR, Curio G - PLoS Comput. Biol. (2009)

Comparison of both methods for the estimation of state conditional ERD by means of surrugate data.The figure contrasts the true conditional ERD (left column), the estimated conventional conditional ERD (central column) and the estimated generalized conditional ERD (right column). Each row corresponds to a particular artificial data set (I–III, top to bottom). The panels share an identical color coding scheme, where blue and red refer to ERD and ERS, respectively. The vertical and horizontal axes represent the state variable  and the time, respectively.
© Copyright Policy
Related In: Results  -  Collection

Show All Figures
getmorefigures.php?uid=PMC2713829&req=5

pcbi-1000453-g003: Comparison of both methods for the estimation of state conditional ERD by means of surrugate data.The figure contrasts the true conditional ERD (left column), the estimated conventional conditional ERD (central column) and the estimated generalized conditional ERD (right column). Each row corresponds to a particular artificial data set (I–III, top to bottom). The panels share an identical color coding scheme, where blue and red refer to ERD and ERS, respectively. The vertical and horizontal axes represent the state variable and the time, respectively.
Mentions: Before comparing the results of the empirical estimators for the conditional ERD, let us begin with some analytical considerations. From the common setup of the artificial datasets we can attain the true conditional ERD as:(13)Where denotes the conditional probability distribution. Moreover, from the definition of the conventional and the generalized conditional ERD (cf. Eqn 4 and 5) and using the instantaneous power at the single time instance for estimating the static baseline level in the conventional framework we obtain:(14)(15)Considering further the particular settings of the three data sets, Table 1 presents the corresponding analytic solutions for the three artificial data sets. So, based on these preceding considerations, we expect the conventional estimator to incorrectly measure the conditional ERD for all three data sets, while the generalized estimator should be capable to retrieve the given underlying functional relationship between the explanatory variable and the ERD dynamics. In Fig. 3 we depict the true conditional ERD and the results of the two competing methods. Comparing the empirical estimates clearly reveals that the generalized ERD is capable of recovering the functional dependency of the ERD dynamics on the explanatory variable , while the conventional estimator miscalculate the conditional ERD and even gives rise to the observation of spurious ERS. On closer examination we can track down the static baseline as the failure cause in the conventional conditional ERD setting. To see this, first note that the conventional setting, using a fixed baseline, implicitly assumes that the expected power of the unperturbed dynamics does not vary with time (weak stationarity). Notably, weak stationarity of the overall distribution does not imply weak stationarity of the conditional distributions, which can be easily verified considering the second data set. Here the (unconditional) expectation , i.e., the average across all catch trials is given as(16)So it is constant and hence weak stationarity is fulfilled. However, conditioning the expectation on the state results in(17)To see this, please note the particular setting according to Eqn 10. Consequently, the conditional expectation of the unperturbed dynamics is a function of , that exhibits a clear non-constant time pattern. Apparently, any constant baseline does not sufficiently represent the intrinsic trends in the unperturbed dynamics. Accordingly, the conventional ERD measure, which relies on the static baseline assumption, incorrectly specifies the conditional unperturbed dynamics and therefore misvalues the true conditional ERD.

Bottom Line: Here, we establish a novel generalized concept to measure event-related desynchronization (ERD), which allows one to model neural oscillatory dynamics also in the presence of dynamical cortical states.Specifically, we demonstrate that a somatosensory stimulus causes a stereotypic sequence of first an ERD and then an ensuing amplitude overshoot (event-related synchronization), which at a dynamical cortical state becomes evident only if the natural relaxation dynamics of unperturbed EEG rhythms is utilized as reference dynamics.Moreover, this computational approach also encompasses the more general notion of a "conditional ERD," through which candidate explanatory variables can be scrutinized with regard to their possible impact on a particular oscillatory dynamics under study.

View Article: PubMed Central - PubMed

Affiliation: Intelligent Data Analysis Group, Fraunhofer Institute FIRST, Berlin, Germany. steven.lemm@first.fraunhofer.de

ABSTRACT
Brains were built by evolution to react swiftly to environmental challenges. Thus, sensory stimuli must be processed ad hoc, i.e., independent--to a large extent--from the momentary brain state incidentally prevailing during stimulus occurrence. Accordingly, computational neuroscience strives to model the robust processing of stimuli in the presence of dynamical cortical states. A pivotal feature of ongoing brain activity is the regional predominance of EEG eigenrhythms, such as the occipital alpha or the pericentral mu rhythm, both peaking spectrally at 10 Hz. Here, we establish a novel generalized concept to measure event-related desynchronization (ERD), which allows one to model neural oscillatory dynamics also in the presence of dynamical cortical states. Specifically, we demonstrate that a somatosensory stimulus causes a stereotypic sequence of first an ERD and then an ensuing amplitude overshoot (event-related synchronization), which at a dynamical cortical state becomes evident only if the natural relaxation dynamics of unperturbed EEG rhythms is utilized as reference dynamics. Moreover, this computational approach also encompasses the more general notion of a "conditional ERD," through which candidate explanatory variables can be scrutinized with regard to their possible impact on a particular oscillatory dynamics under study. Thus, the generalized ERD represents a powerful novel analysis tool for extending our understanding of inter-trial variability of evoked responses and therefore the robust processing of environmental stimuli.

Show MeSH