Emmanuelle Tognoli & J. A. Scott Kelso Center for Complex Systems and Brain Sciences, Florida Atlantic University, Boca Raton, FL – USA ;

AIM Historically, “alpha” band has either been (1) treated as a coherent whole, (2) divided into “low-” and “high-alpha” or (3) subdivided into a limited set of anatomo-functional processes such as alpha, rolandic mu, tau and sometimes parietal mu. High-resolution spectral analysis (Tognoli et al., 2007) opened up the discovery of numerous rhythms in the 10Hz band, i.e. stable, reproducible peaks in induced EEG spectra that emerge as properties of a diversity of brain functional networks. A tentative functional dictionary of these rhythms is presented below. The main goals of this communication are to stress the heterogeneity of 10Hz rhythms, to discuss strategies for their proper measurements and to propose a theory of rhythms and temporal scales in which inter- individual and intra-individual variability may be explained.

A non-exhaustive list of 10Hz rhythms in human waking EEG Induced EEG rhythms were obtained with high-resolution FFT of multiple EEG epochs each lasting between 1 and 16 sec. Epochs were multiplied with a Tukey window to prevent leakage, and were padded when necessary to achieve high-spectral resolution. EEG spectra are visualized with a 4D colorimetric mapping to identify spatial organization. Rhythms are distinguished on the basis of three criteria: spatial distribution, spectral localization and reactivity/functional significance.

 AL Seen during behavioral arrest following right hand or finger movement Hz typical.  M Seen during rest states, and modulated during movement steady-states. 8-10Hz typical  CR Seen during imitation tasks (data from Bernier, Dawson, Webb & Murias, 2007). Is associated with  CL Hz typical.  Seen during covert attention tasks. Is associated with  Hz typical.  Seen during covert movements of spatial attention. Sometimes associated with  Hz typical.  CL Seen during imitation tasks (data from Bernier et al., 2007). Is generally associated with  CR Hz typical.     Seen during social coordination and possibly during multisensory integration. Composed of 2 components that are independently modulated Hz typical. Seen during imitation tasks. Signification unknown. 8-10Hz typical. Bilateral  variant Asymmetrical variant seen with eyes open. Possibly related to asymmetrical selective attention to left and right hemifields. 9-10Hz typical.  Seen during eye closed and drowsy states. 9-10Hz typical.

Example of a spectrum with a large number of 10Hz rhythms. Power is best measured at peak electrode, where confound from other rhythms is minimal.

STRATEGIES FOR PROPER MEASUREMENT RHYTHMS SEPARATION AND ACCURATE POWER ESTIMATES: When distinct rhythms are not separated, power is distorted by confound in respective changes from each peak (see example below). Condition- dependent change may be missed if one rhythm decreases and another increases nearby. The change may be ascribed to a location that reflect neither of the rhythms...etc. Peaks should be separated either by careful identification of each peak boundary or by spectral decomposition.

Example of bias in power measurement due to improper separation of 2 distinct rhythms.

SPECTRAL OVERLAP AND SPECTRAL-SPATIAL DISTORTION: Because of the crowding in the 10Hz band, there is potential for overlap: 2 rhythms close enough in frequency to be embedded in one another. The consequence is merging of spatial and spectral features: apparent peak is displaced at the intersection domain of both originating components (well known examples are bilateral rhythms that appear medially –e.g. alpha–). Spatial and spectral distortion are harmful to the proper interpretation of components’ functional properties. Frequency analysis with a fine spectral resolution (in the order of Hz) greatly minimizes this problem. Choice of the time scale (principle 4, right) also helps, with shorter temporal windows most likely to reveal the true properties of each rhythm.

FREQUENCY BOUNDARIES AND POWER ESTIMATION: In several subjects, the same rhythm may appear at different frequencies and peaks may exhibit different width (see example of in 4 subjects on the left). Rhythm identification and power estimation should be performed on a subject-by subject basis.

, small amplitude, 9Hz, large amplitude, 11Hz, broad band, 9Hz, partially buried, 9Hz

A THEORY OF EEG OSCILLATIONS AND TEMPORAL SCALES Atoms of EEG spectra are instantaneous spatio-temporal patterns (Tognoli & Kelso, 2009; see left picture below). Those patterns arise from self-organized neural activity in two basic types of cortical structures: sulci (e.g. first pattern) and gyri (e.g. last pattern).

To circumvent the issue of Signal-to-Noise Ratio and obtain “stable” frequency estimates, investigators usually compute the power spectrum over a cumulative time of minutes. In the 10Hz range, patterns typically last one or two cycles. Five minutes of EEG may contain ~2000 patterns. Which of these patterns contribute to spectral peaks and how?

PRINCIPLE 1: ONLY SUSTAINED PATTERNS SURVIVE INTO SPECTRAL PEAKS If a pattern can be sustained over a significant period of time over the time-scale of spectral analysis (duration and recurrence), it may be seen as a spectral peak. If a pattern cannot be sustained, it will blend in the floor of EEG spectra with other transient oscillations, irrespective of its importance for brain dynamics and function. PRINCIPLE 2: SPECTRAL PEAKS ARE SPATIALLY REORGANIZED Spectral peaks never show spatial organization of sulcal patterns (two spatially distinct maxima). It suggests that cumulative power maps are composed of a non-uniform group of spatio-temporal patterns sharing some spatial and spectral properties.

Slowly changing drowsy EEG

Fast changing active EEG

PRINCIPLE 3: ACTIVATION AFFECTS PATTERNS’ RATE OF CHANGE In drowsy EEG, patterns’ rate of change is slow. The longer the time window over which EEG spectra are computed, the most likely rhythm will appear. In active EEG, many patterns occur, none of which may stand out from the crowd. The longer the time window over which EEG spectra are computed, the least likely rhythms will appear : transient peaks will blend in the “spectral floor”.

PRINCIPLE 4: SHORTER (WELL-DEFINED) TEMPORAL WINDOWS ARE BETTER Most mental processes may not have the ability to be sustained over seconds to minutes (either at once or in iterations). In such cases, long spectral windows favor task-unrelated brain rhythms (fillers) and are detrimental to understanding task-related brain rhythms. To emphasize task-related transient rhythms, task should be shorter, and dependent variables should be collected to pinpoint the temporal onset of mental processes.

CONCLUSION Ten Hz oscillations are often conceived as resting EEG states of little cognitive or behavioral relevance. It has further been shown that this band had no correlation with the bold signal (Niessing et al., 2005). Yet the time scale of this oscillation (~ msec) is of prime importance for cognition and behavior and an excess peak at 10Hz over the 1/f distribution of EEG power spectra suggests that it is a preferred frequency in the human brain. We present a tentative dictionary of 10Hz rhythms, advance guidelines for their accurate measurement and analysis, and propose a theory that relates EEG rhythms in spectral average with instantaneous patterns in continuous EEG. Distinguishing the variety of 10Hz rhythms, understanding their functional significance and properly estimating their individual contributions in spectral studies are challenges that will be determinant for advance in non-invasive electrophysiology: a lexicon of brain functional processes is sketched that could be useful for basic and clinical science, neuro-feedback, brain computer interface and neuro- pharmacological studies.

REFERENCES Bernier, R., Dawson, G., Webb, S. & Murias, M. (2007). EEG mu rhythm and imitation impairments in individuals with autism spectrum disorder. Brain and Cognition, 64: Kelso, J. A. S Dynamic Patterns: the Self-Organization of Brain and Behavior. MIT Press: Cambridge, MA. Niessing, J., Ebisch, B., Schmidt, K.E., Niessing, M., Singer W., Galuske, R.A. (2005). Hemodynamic signals correlate tightly with synchronized gamma oscillations. Science, 309: Tognoli, E., Lagarde, J., De Guzman, G. C., Kelso, J. A. S The phi complex as a neuromarker of human social coordination. Proc. Natl. Acad. Sci. U.S.A. 104, Tognoli E., (2008). EEG coordination dynamics: neuromarkers of social coordination. In Fuchs A, Jirsa VK (eds.) Coordination: Neural, Behavioral and Social Dynamics. Springer. Tognoli E., Kelso J.A.S (2009). Brain Coordination Dynamics: True and False Faces of Phase Synchrony and Metastability. Progress in Neurobiology, 87(1):