An important goal in neuroscience is to identify instances when EEG signals are coupled. We employ a method to measure the coupling strength between gamma signals (40–100？Hz) on a short time scale as the maximum cross-correlation over a range of time lags within a sliding variable-width window. Instances of coupling states among several signals are also identified, using a mixed multivariate beta distribution to model coupling strength across multiple gamma signals with reference to a common base signal. We first apply our variable-window method to simulated signals and compare its performance to a fixed-window approach. We then focus on gamma signals recorded in two regions of the rat hippocampus. Our results indicate that this may be a useful method for mapping coupling patterns among signals in EEG datasets. 1. Introduction Current neuroscience research is focused not only on identification of brain regions associated with particular cognitive tasks, but also on how those regions interact during the execution of the these tasks on a short time scale [1–3]. In this paper, we investigate methods for identifying brief instances in time when groups of gamma-band signals (40–100？Hz) extracted from electroencephalogram (EEG) recordings become synchronized. Our methods are developed to address the specific problem of analyzing EEG recordings from the rat hippocampal formation. Recent studies [2] have demonstrated dynamic coordination at these frequencies between the dentate gyrus, CA1, and CA3 during tasks with high cognitive demand and during REM sleep. Typically in situations where a signal is suspected to be changing with time, methods from signal analysis, such as the short-time Fourier transform, can be applied quite successfully. For pairs of signals, coherency, a measure of signal coherence in the frequency domain, can be computed with confidence bounds, using for example a multitaper [4]. In both of these cases software has been developed to compute these quantities. For example, the spectrogram function in Matlab [5] computes the short-time Fourier transform along segments of an individual signal, and the coherence function in the Chronux package [6] computes the windowed coherence between pairs of signals. However, for signals with synchrony lasting just a few cycles at a time, frequency-domain methods can be less sensitive and may yield unrealistically large confidence bounds. Alternative methods for detecting synchronization of neuroelectric signals are based on transient phase locking [7, 8]. For the case of many EEG signals, other approaches
References
[1]
G. Buszaki, Rhythms of the Brain, Oxford University Press, Oxford, UK, 2006.
[2]
S. M. Montgomery and G. Buzsáki, “Gamma oscillations dynamically couple hippocampal CA3 and CA1 regions during memory task performance,” Proceedings of the National Academy of Sciences of the United States of America, vol. 104, no. 36, pp. 14495–14500, 2007.
[3]
M. A. Kramer, U. T. Eden, S. S. Cash, and E. D. Kolaczyk, “Network inference with confidence from multivariate time series,” Physical Review E, vol. 79, no. 6, Article ID 061916, 2009.
[4]
R. H. Shumway and D. S. Stoffer, Time Series Analysis and Its Applications: With R Examples, Springer, New York, NY, USA, 2nd edition, 2006.
[5]
“MATLAB,” The Mathworks, Natick, Mass, USA, http://www.mathworks.com/.
[6]
P. Mitra and H. Bokil, Observed Brain Dynamics, Oxford University Press, New York, NY, USA, 2008, Chronux Analysis Software, Mitra Lab, Cold Spring Harbor Laboratory, Cold Spring, NY, USA, 2008, http://chronux.org/.
[7]
P. Tass, M. G. Rosenblum, J. Weule et al., “Detection of n: m phase locking from noisy data: application to magnetoencephalography,” Physical Review Letters, vol. 81, no. 15, pp. 3291–3294, 1998.
[8]
J.-P. Lachaux, E. Rodriguez, J. Martinerie, and F. J. Varela, “Measuring phase synchrony in brain signals,” Human Brain Mapping, vol. 8, no. 4, pp. 194–208, 1999.
[9]
C. W. J. Granger, “Investigating causal relations by econometric models and cross-spectral methods,” Econometrica, vol. 37, no. 3, pp. 424–438, 1969.
[10]
W. Gersh and B. R. Tharp, “Spectral regression|amount of information analysis of seizures in humans,” in Quantitative Analytic Studies in Epilepsy, P. Kellaway and I. Petersén, Eds., pp. 509–532, Raven Press, NY, USA, 1976.
[11]
J. C. Rajapakse and J. Zhou, “Learning effective brain connectivity with dynamic Bayesian networks,” NeuroImage, vol. 37, no. 3, pp. 749–760, 2007.
[12]
A. P. Dempster, N. M. Laird, and D. B. Rubin, “Maximum likelihood from incomplete data via the EM algorithm,” Journal of the Royal Statistical Society: Series A, vol. 39, pp. 1–38, 1977.
[13]
M. A. Kramer, E. D. Kolaczyk, and H. E. Kirsch, “Emergent network topology at seizure onset in humans,” Epilepsy Research, vol. 79, no. 2-3, pp. 173–186, 2008.
[14]
R Development Core Team, R: A Language and Environment for Statistical Computing, R Foundation for Statistical Computing, Vienna, Austria, 2009.
[15]
J. A. Hartigan and M. A. Wong, “A K-means clustering algorithm,” Applied Statistics, vol. 28, pp. 100–108, 1979.
[16]
C. Fraley and A. E. Raftery, “How many clusters? Which clustering method? Answers via model-based cluster analysis,” The Computer Journal, vol. 41, no. 8, pp. 578–588, 1998.
[17]
I. Olkin and R. Liu, “A bivariate beta distribution,” Statistics & Probability Letters, vol. 62, no. 4, pp. 407–412, 2003.
