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- A simple Hidden Markov Model for midbrain dopaminergic neurons (2009)
- Poster presentation: Introduction Dopaminergic neurons in the midbrain show a variety of firing patterns, ranging from very regular firing pacemaker cells to bursty and irregular neurons. The effects of different experimental conditions (like pharmacological treatment or genetical manipulations) on these neuronal discharge patterns may be subtle. Applying a stochastic model is a quantitative approach to reveal these changes. ...

- A model for the joint evaluation of burstiness and regularity in oscillatory spike trains (2009)
- Poster presentation: Introduction The ability of neurons to emit different firing patterns is considered relevant for neuronal information processing. In dopaminergic neurons, prominent patterns include highly regular pacemakers with separate spikes and stereotyped intervals, processes with repetitive bursts and partial regularity, and irregular spike trains with nonstationary properties. In order to model and quantify these processes and the variability of their patterns with respect to pharmacological and cellular properties, we aim to describe the two dimensions of burstiness and regularity in a single model framework. Methods We present a stochastic spike train model in which the degree of burstiness and the regularity of the oscillation are described independently and with two simple parameters. In this model, a background oscillation with independent and normally distributed intervals gives rise to Poissonian spike packets with a Gaussian firing intensity. The variability of inter-burst intervals and the average number of spikes in each burst indicate regularity and burstiness, respectively. These parameters can be estimated by fitting the model to the autocorrelograms. This allows to assign every spike train a position in the two-dimensional space described by regularity and burstiness and thus, to investigate the dependence of the firing patterns on different experimental conditions. Finally, burst detection in single spike trains is possible within the model because the parameter estimates determine the appropriate bandwidth that should be used for burst identification. Results and Discussion We applied the model to a sample data set obtained from dopaminergic substantia nigra and ventral tegmental area neurons recorded extracellularly in vivo and studied differences between the firing activity of dopaminergic neurons in wildtype and K-ATP channel knock-out mice. The model is able to represent a variety of discharge patterns and to describe changes induced pharmacologically. It provides a simple and objective classification scheme for the observed spike trains into pacemaker, irregular and bursty processes. In addition to the simple classification, changes in the parameters can be studied quantitatively, also including the properties related to bursting behavior. Interestingly, the proposed algorithm for burst detection may be applicable also to spike trains with nonstationary firing rates if the remaining parameters are unaffected. Thus, the proposed model and its burst detection algorithm can be useful for the description and investigation of neuronal firing patterns and their variability with cellular and experimental conditions.

- Detection and localization of multiple rate changes in Poisson spike trains : poster presentation from Twentieth Annual Computational Neuroscience Meeting CNS*2011 Stockholm, Sweden, 23 - 28 July 2011 (2011)
- Poster presentation from Twentieth Annual Computational Neuroscience Meeting: CNS*2011 Stockholm, Sweden. 23-28 July 2011. In statistical spike train analysis, stochastic point process models usually assume stationarity, in particular that the underlying spike train shows a constant firing rate (e.g. [1]). However, such models can lead to misinterpretation of the associated tests if the assumption of rate stationarity is not met (e.g. [2]). Therefore, the analysis of nonstationary data requires that rate changes can be located as precisely as possible. However, present statistical methods focus on rejecting the null hypothesis of stationarity without explicitly locating the change point(s) (e.g. [3]). We propose a test for stationarity of a given spike train that can also be used to estimate the change points in the firing rate. Assuming a Poisson process with piecewise constant firing rate, we propose a Step-Filter-Test (SFT) which can work simultaneously in different time scales, accounting for the high variety of firing patterns in experimental spike trains. Formally, we compare the numbers N1=N1(t,h) and N2=N2(t,h) of spikes in the time intervals (t-h,t] and (h,t+h]. By varying t within a fine time lattice and simultaneously varying the interval length h, we obtain a multivariate statistic D(h,t):=(N1-N2)/V(N1+N2), for which we prove asymptotic multivariate normality under homogeneity. From this a practical, graphical device to spot changes of the firing rate is constructed. Our graphical representation of D(h,t) (Figure 1A) visualizes the changes in the firing rate. For the statistical test, a threshold K is chosen such that under homogeneity, |D(h,t)|<K holds for all investigated h and t with probability 0.95. This threshold can indicate potential change points in order to estimate the inhomogeneous rate profile (Figure 1B). The SFT is applied to a sample data set of spontaneous single unit activity recorded from the substantia nigra of anesthetized mice. In this data set, multiple rate changes are identified which agree closely with visual inspection. In contrast to approaches choosing one fixed kernel width [4], our method has advantages in the flexibility of h.