# American Institute of Mathematical Sciences

2014, 11(1): 27-48. doi: 10.3934/mbe.2014.11.27

## Cross nearest-spike interval based method to measure synchrony dynamics

 1 Department of Mathematics, Facultad de Informática, Campus de Elviña s/n, 15071, Universidade da Coruña, A Coruña, Spain, Spain 2 Interuniversity Institute for Biostatistics and statistical Bionformatics, Hasselt University and KULeuven, Hasselt, Belgium, Belgium 3 Neuroscience and Motor Control Group (NEUROcom), Department of Medicine, Facultad de Ciencias de la Salud, Campus de Oza s/n, 15006, Universidade da Coruña, A Coruña, Spain, Spain, Spain

Received  December 2012 Revised  June 2013 Published  September 2013

A new synchrony index for neural activity is defined in this paper. The method is able to measure synchrony dynamics in low firing rate scenarios. It is based on the computation of the time intervals between nearest spikes of two given spike trains. Generalized additive models are proposed for the synchrony profiles obtained by this method. Two hypothesis tests are proposed to assess for differences in the level of synchronization in a real data example. Bootstrap methods are used to calibrate the distribution of the tests. Also, the expected synchrony due to chance is computed analytically and by simulation to assess for actual synchronization.
Citation: Aldana M. González Montoro, Ricardo Cao, Christel Faes, Geert Molenberghs, Nelson Espinosa, Javier Cudeiro, Jorge Mariño. Cross nearest-spike interval based method to measure synchrony dynamics. Mathematical Biosciences & Engineering, 2014, 11 (1) : 27-48. doi: 10.3934/mbe.2014.11.27
##### References:
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##### References:
 [1] M. Bazhenov, I. Timofeev, M. Steriade and T. Sejnowski, Model of thalamocortical slow-wave sleep oscillations and transitions to activated states, The Journal of Neuroscience, 22 (2002), 8691-8704. [2] C. E. Bonferroni, Il calcolo delle assicurazioni su gruppi di teste, Studi in Onore del Professore Salvatore Ortu Carboni, Rome, (1935), 13-60. [3] E. N. Brown, R. E. Kass and P. P. Mitra, Multiple neural spike train data analysis: State-of-the-art and future challenges, Nature Neuroscience, 7 (2004), 456-461. doi: 10.1038/nn1228. [4] R. Cao, M. Francisco-Fernández and E. J. Quinto, A random effect multiplicative heteroscedastic model for bacterial growth, BMC Bioinformatics, 11 (2010), 77. doi: 10.1186/1471-2105-11-77. [5] C. Faes, H. Geys, G. Molenberghs, M. Aerts, C. Cadarso-Suárez, C. Acuña and M. Cano, A flexible method to measure synchrony in neuronal firing, J. Amer. Statist. Assoc., 103 (2008), 149-161. doi: 10.1198/016214507000000419. [6] G. L. Gerstein and D. H. Perkel, Simultaneously recorded trains of action potentials: Analysis and functional interpretation, Science, 164 (1969), 828-830. doi: 10.1126/science.164.3881.828. [7] S. Grün, "Unitary Joint-Events in Multiple-Neuron Spiking Activity: Detection, Significance, and Interpretation," Reihe Physik, Band 60, Verlag Harri Deutsch, Thun, Frankfurt/Main, 1996. [8] S. Grün, M. Diesmann and A. Aertsen, Unitary events in multiple single-neuron spiking activity: I. Detection and significance, Neural Computation, 14 (2002), 43-80. [9] T. J. Hastie and R. J. Tibshirani, "Generalized Additive Models," Monographs on Statistics and Applied Probability, 43, Chapman & Hall, Ltd., London, 1990. [10] R. E. Kass, V. Ventura and E. N. Brown, Statistical issues in the analysis of neuronal data, Journal of Neurophysiology, 94 (2005), 8-25. doi: 10.1152/jn.00648.2004. [11] J. Mariño and J. Cudeiro, Nitric oxide-mediated cortical activation: A diffuse wake-up system, The Journal of Neuroscince, 23 (2003), 4299-4307. [12] M. Nawrot, A. Aertsen and E. Rotter, Single-trial estimation of neural firing rates: From single-neuron spike trains to population activity, Journal of Neuroscience Methods, 94 (1999), 81-92. [13] R. Q. Quiroga, T. Kreuz and P. Grassberger, Event synchronization: A simple and fast method to measure synchronicity and time delay patterns, Physical Review E (3), 66 (2002), 041904, 9 pp. doi: 10.1103/PhysRevE.66.041904. [14] M. Steriade, D. A. McCormick and T. J. Sejnowski, Thalamocortical oscillations in the sleeping and arousal brain, Science, 262 (1993), 679-685. doi: 10.1126/science.8235588. [15] M. Steriade, Sleep oscillations and their blockage by activating systems, Journal of Psychiatry and Neuroscience, 19 (1994), 354-358. [16] M. P. Wand and M. C. Jones, "Kernel Smoothing," Monographs on Statistics and Applied Probability, 60, Chapman & Hall, London, 1995. [17] S. Wood, "Generalized Additive Models. An Introduction with R," Texts in Statistical Science Series, Chapman & Hall/CRC, Boca Raton, FL, 2006.
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