Biological Cybernetics

, Volume 109, Issue 4–5, pp 421–433 | Cite as

Modeling neural activity with cumulative damage distributions

  • Víctor Leiva
  • Mauricio Tejo
  • Pierre Guiraud
  • Oliver Schmachtenberg
  • Patricio Orio
  • Fernando Marmolejo-Ramos
Original Paper


Neurons transmit information as action potentials or spikes. Due to the inherent randomness of the inter-spike intervals (ISIs), probabilistic models are often used for their description. Cumulative damage (CD) distributions are a family of probabilistic models that has been widely considered for describing time-related cumulative processes. This family allows us to consider certain deterministic principles for modeling ISIs from a probabilistic viewpoint and to link its parameters to values with biological interpretation. The CD family includes the Birnbaum–Saunders and inverse Gaussian distributions, which possess distinctive properties and theoretical arguments useful for ISI description. We expand the use of CD distributions to the modeling of neural spiking behavior, mainly by testing the suitability of the Birnbaum–Saunders distribution, which has not been studied in the setting of neural activity. We validate this expansion with original experimental and simulated electrophysiological data.


Birnbaum–Saunders and inverse Gaussian distributions Integrate-and-fire model Inter-spike intervals Maximum likelihood method Model selection and goodness of fit 



The authors thank the Editor-in-Chief, Prof. Dr. J. Leo van Hemmen, and two anonymous referees for their valuable comments on an earlier version of this manuscript, which resulted in this improved version. The authors thank Rosie Gronthos from Australia for proofreading the first revised version of this manuscript and Patricia Van Roon from Canada for proofreading its second version. The research of V. Leiva was supported by FONDECYT 1120879 grant from the Chilean government; of M. Tejo by FONDECYT 3140613 postdoctorate grant; of P. Guiraud by PIA-Anillo ACT1112 grant from the Chilean government; of P. Orio by FONDECYT 1130862 and PIA-Anillo ACT-1113; and of P. Orio and O. Schmachtenberg by The Centro Interdisciplinario de Neurociencia de Valparaíso, which is a Millennium Institute supported by the Millennium Scientific Initiative of the Ministerio de Economía, Fomento y Turismo of the Chilean government.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  • Víctor Leiva
    • 1
    • 2
  • Mauricio Tejo
    • 3
  • Pierre Guiraud
    • 4
  • Oliver Schmachtenberg
    • 5
  • Patricio Orio
    • 5
  • Fernando Marmolejo-Ramos
    • 6
  1. 1.Faculty of Engineering and SciencesUniversidad Adolfo IbáñezViña del MarChile
  2. 2.Institute of StatisticsUniversidad de ValparaisoValparaisoChile
  3. 3.Faculty of Natural and Exact SciencesUniversidad de Playa AnchaValparaisoChile
  4. 4.Centro de Investigación y Modelamiento de Fenómenos Aleatorios - Valparaíso, Faculty of EngineeringUniversidad de ValparaísoValparaisoChile
  5. 5.Centro Interdisciplinario de Neurociencia de Valparaíso and Institute of NeuroscienceUniversidad de ValparaísoValparaisoChile
  6. 6.Gösta Ekman Laboratory, Department of PsychologyStockholm UniversityStockholmSweden

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