Modulated Renewal Process and Statistical Analysis of Multiple Spike-Trains
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1
University of Plymouth, CTCN, United Kingdom
Multi-Electrode Recording (MER) is a widely used neurophysiological technique to record simultaneous activities of many neurons. The data from MER can be used to investigate a functional connectivity of simultaneously recorded spike trains (Brown, Kass, & Mitra, 2004). A standard approach to study the functional connectivity is based on calculation of the pair wise cross-correlation function. This approach has several constrains: 1) Spike-trains are stationary; 2) Length of spike-trains should be significantly large; 3) Method estimates the only linear component of interconnectivity; 4) Analysis takes into account a pair of spike-trains and ignores information about others. To overcome these drawbacks of the cross-correlation function, an alternative statistical technique has been developed (Borisyuk et al. 1985). This method is based on the statistical analysis of inter-dependencies of point processes proposed by Cox (1972). To estimate influence of the spike-train B to the spike-train A, it is assumed that point process A is the modulated renewal process. The influence from B to A is formulated in terms of the hazard function which is a product of the hazard function of process A (without influence) and the function exp(βZB(t)), where the function ZB(t) describes the influence and the parameter β characterizes the strength. The same approach allows generalization to the case of several influences to the spike train A. In this case the function ZB(t) and parameter β are vectors. Statistical procedure (Cox, 1972) allows estimating parameters β based on conditional Maximum Likelihood principle. Borisyuk et al. (1985) used the Cox’s method to study spike-trains generated by a simplified neural network of Leaky Integrate and Fire (LIF) neurons. Here we develop further the Cox method and apply it to analyse functional connectivity of multiple spike-trains.
First, we investigate what is a proper function ZB(t) to describe influences between spike-trains generated by interacting neurons. Second, we compare the Cox’s method based on pair-wise influences with the Cox’s method on simultaneous analysis of three spike trains (one spike train is influenced by two others). We show that second approach has a significant advantage and higher sensitivity.
Third, we compare the result based on the cross-correlation function with the analysis based on the Cox’s method. We generate four spike-trains using a simple network of enhanced LIF neurons with prescribed architecture of connections (Borisyuk, 2002). We find that the Cox’s method have advantages and can better identify the functional connectivity than the technique based on the cross-correlation function.
References
1. Borisyuk, R.M. (2002) Oscillatory activity in the neural networks of spiking elements. BioSystems, 67, 3-16.
2. Borisyuk, G.N., Borisyuk, R.M., Kirillov, A.B., Kovalenko, E.I., & Kryukov, V.I. (1985) A new statistical method for identifying interconnections between neuronal network elements. Biological Cybernetics, 52, 301–306.
3. Brown, E.N., Kass, R.E., & Mitra, P.P. (2004) Multiple neural spike train data analysis: State-of-the-art and future challenges. Nature Neuroscience, 7, 456–461.
4. Cox, D.R. (1972) The statistical analysis of dependencies in point processes. In: Stochastic point processes. pp. 55-56. Lewis, P.A., ed. New York: Wiley 1972.
Conference:
Neuroinformatics 2009, Pilsen, Czechia, 6 Sep - 8 Sep, 2009.
Presentation Type:
Poster Presentation
Topic:
Computational neuroscience
Citation:
Masud
M and
Borisyuk
R
(2019). Modulated Renewal Process and Statistical Analysis of Multiple Spike-Trains.
Front. Neuroinform.
Conference Abstract:
Neuroinformatics 2009.
doi: 10.3389/conf.neuro.11.2009.08.003
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Received:
21 May 2009;
Published Online:
09 May 2019.
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Correspondence:
Mohammad Masud, University of Plymouth, CTCN, Plymouth, United Kingdom, mohammad.masud@plymouth.ac.uk