Interspike Interval Series Research Articles

A hidden Markov model approach to neuron firing patterns

Analysis and characterization of neuronal discharge patterns are of interest to neurophysiologists and neuropharmacologists. In this paper we present a hidden Markov model approach to modeling single neuron electrical activity. Basically the model assumes that each interspike interval corresponds to one of several possible states of the neuron. Fitting the model to experimental series of interspike intervals by maximum likelihood allows estimation of the number of possible underlying neuron states, the probability density functions of interspike intervals corresponding to each state, and the transition probabilities between states. We present an application to the analysis of recordings of a locus coeruleus neuron under three pharmacological conditions. The model distinguishes two states during halothane anesthesia and during recovery from halothane anesthesia, and four states after administration of clonidine. The transition probabilities yield additional insights into the mechanisms of neuron firing.

Low dimensional attractors in discharges of sensory neurons of the rat spinal dorsal horn are maintained by supraspinal descending systems.

Background activity was recorded from sensory neurons in laminae I-V of the lumbar spinal dorsal horn of the rat prior to and during cold block spinalization at the cervical cord. To graphically and quantitatively describe the complexity of the discharge patterns, phase space portraits were plotted and the correlation dimension D2 was calculated by using the Grassberger-Procaccia algorithm adopted for point processes, i.e. for series of interspike intervals. The algorithm is validated both for the Baker transformation, which is a simple point process, and for the Lorenz model, whereby a transformation from continuous to point process variables is achieved. A method of surrogate data is provided in order to show the difference between original neuronal patterns and their surrogate stochastic data. Therefore, this method shows that neuronal discharge patterns cannot be fully described in terms of interspike interval histograms. However, in the intact cord most (73%) of the neurons displayed background activity with low (0.28-4.3) D2 values. During spinalization, D2 values significantly increased in 68% of the neurons showing previously low D2 values, irrespective of classification and laminar location of neurons, thus proving that tonic descending systems may maintain a high order in the discharge of sensory dorsal horn neurons.

Interspike interval embedding of chaotic signals.

According to a theorem of Takens [Lecture Notes in Mathematics (Springer-Verlag, Berlin, 1981), Vol. 898], dynamical state information can be reproduced from a time series of amplitude measurements. In this paper we investigate whether the same information can be reproduced from interspike interval (ISI) measurements. Assuming an integrate-and-fire model coupling the dynamical system to the spike train, there is a one-to-one correspondence between the system states and interspike interval vectors of sufficiently large dimension. The correspondence implies in particular that a data series of interspike intervals, formed in this manner, can be forecast from past history. This capability is demonstrated using a nonlinear prediction algorithm, and is found to be robust to noise. A set of interspike intervals measured from a simple neuronal circuit is studied for deterministic structure using a prediction error statistic. (c) 1995 American Institute of Physics.

Reconstruction of dynamical systems from interspike intervals.

Attractor reconstruction from interspike interval (ISI) data is described, in rough analogy with Taken's theorem for attractor reconstruction from time series. Assuming a generic integrate-and-fire model coupling the dynamical system to the spike train, there is a one-to-one correspondence between the system states and interspike interval vectors of sufficiently large dimension. The correspondence has an important implication: interspike intervals can be forecast from past history. We show that deterministically driven ISI series can be distinguished from stochastically driven ISI series on the basis of prediction error.

Discharge patterns of the slowly adapting mechanoreceptor afferent units innervating the non-warty skin of the frog.

Discharge patterns of slowly adapting (SA) mechanoreceptor afferent units innervating the non-warty skin of frogs, were analyzed statistically. Because SA units in the frog did not always produce sustained discharges for a long period, analysis was carried out on ensembles of interspike intervals (ISIs) obtained in two ways: (1) a series of successive ISIs obtained in the quasi-stationary state of maintained discharges and (2) an ensemble of ISIs (X(1),X(2),..., X(50)), obtained on repeated trials of stimulation at about 1,000 msec following the onset of stimulation. In some units these two types of ensembles of ISIs were collected. Statistical analysis of a series of successive ISIs in the quasi-stationary state disclosed two kinds of discharge patterns, irregular and regular, corresponding to those of the SA cutaneous units of mammals and reptiles. We named these two types of units Frog type I and Frog type II (Ft I and Ft II) units, respectively. In addition, the quantitative study of an ensemble of ISIs in the non-stationary state revealed that Ft II units discharged regularly in response to an optimum range of indentation but irregularly to indentation outside this range, although Ft I units produced irregular discharges irrespective of the magnitude of indentation applied.