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Chaos game representation of human pallidal spike trains

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Abstract

Many studies have demonstrated the presence of scale invariance and long-range correlation in animal and human neuronal spike trains. The methodologies to extract the fractal or scale-invariant properties, however, do not address the issue as to the existence within the train of fine temporal structures embedded in the global fractal organisation. The present study addresses this question in human spike trains by the chaos game representation (CGR) approach, a graphical analysis with which specific temporal sequences reveal themselves as geometric structures in the graphical representation. The neuronal spike train data were obtained from patients whilst undergoing pallidotomy. Using this approach, we observed highly structured regions in the representation, indicating the presence of specific preferred sequences of interspike intervals within the train. Furthermore, we observed that for a given spike train, the higher the magnitude of its scaling exponent, the more pronounced the geometric patterns in the representation and, hence, higher probability of occurrence of specific subsequences. Given its ability to detect and specify in detail the preferred sequences of interspike intervals, we believe that CGR is a useful adjunct to the existing set of methodologies for spike train analysis.

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Acknowledgements

We thank the three reviewers for their comments and suggestions. This research was supported by grants from the Toronto East General Hospital Research Foundation and the NIH to FAL (RO1:NS38493 and RO1:40059).

Authors’ contributions

MR was the primary author and, along with GR, wrote the programs and analysed the results. FAL, DSB, LV and HCK contributed to the writing of the paper. In addition, FAL performed the surgeries and acquired the data.

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Authors and Affiliations

  1. Department of Ophthalmology, University of Alberta, 2319, 10240 Kingsway Avenue NW, Edmonton, AB, Canada, T5H 3V9

    Mahta Rasouli

  2. Chicago Medical School, 3333 Green Bay Road, North Chicago, IL, 60064, USA

    Golta Rasouli

  3. Department of Neurosurgery, Johns Hopkins Hospital, Baltimore, MD, 21278-7713, USA

    Fredrick A. Lenz

  4. Division of Neurology, Toronto East General Hospital, Toronto, ON, Canada

    Donald S. Borrett

  5. Department of Neurology, Rush University, Chicago, IL, USA

    Leo Verhagen

  6. Department of Physiology, University of Toronto, 1 King’s College Circle, Toronto, ON, Canada, M5S 1A8

    Hon C. Kwan

Authors
  1. Mahta Rasouli
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  2. Golta Rasouli
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  3. Fredrick A. Lenz
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  4. Donald S. Borrett
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  5. Leo Verhagen
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  6. Hon C. Kwan
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Correspondence to Mahta Rasouli.

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Rasouli, M., Rasouli, G., Lenz, F.A. et al. Chaos game representation of human pallidal spike trains. J Biol Phys 36, 197–205 (2010). https://doi.org/10.1007/s10867-009-9172-x

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  • DOI: https://doi.org/10.1007/s10867-009-9172-x

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