An interspike interval method for computing phase locking from neural firing

Inner hair cells (IHCs) transform the mechanical movements of the basilar membrane into electrical impulses. The impulse coding of the IHCs is the main information carrier in the auditory process and is the basis for improvements of cochlea implants as well as for low rate, high-quality speech processing and compression. This paper shows how to compute the speech signal from the neural firing based on the analysis of the interspike interval histogram. This new approach solves problems that other standard analysis methods do not solve sufficiently well. Received 18 September 1998 / Accepted in revised form 15 October 1999     

Nonlinear sequence-dependent structure of nigral dopamine neuron interspike interval firing patterns.

Firing patterns of 15 dopamine neurons in the rat substantia nigra were studied. These cells alternated between two firing modes, single-spike and bursting, which interwove to produce irregular, aperiodic interspike interval (ISI) patterns. When examined by linear autocorrelation analysis, these patterns appeared to reflect a primarily stochastic or random process. However, dynamical analysis revealed that the sequential behavior of a majority of these cells expressed "higher-dimensional" nonlinear deterministic structure. Dimensionality refers to the number of degrees of freedom or complexity of a time series. Bursting was statistically associated with some aspects of nonlinear ISI sequence dependence. Controlling for the effects of nonstationarity substantially increased overall predictability of ISI sequences. We hypothesize that the nonlinear deterministic structure of ISI firing patterns reflects the neuron's response to coordinated synaptic inputs emerging from neural circuit interactions.     

Changes in interspike interval during propagation: Quantitative description

The intervals between nerve impulses can change substantially during propagation because of conduction velocity aftereffects of previous impulse activity. Effects of such changes on interval histograms and on statistical parameters of spike trains were evaluated for Poisson spike trains and for trains generated by a clock with added random delays. The distribution of short intervals was significantly changed during propagation for these spike trains. Substantial changes in serial correlation coefficients were found in trains with certain initial interval distributions. The relevance of these effects to neural coding is discussed.     

Discharge frequency and excitability of human firing motoneurone

The excitability of firing motoneurones activated by voluntary contraction of the flexor carpi ulnaris or tibialis anterior was tested by single excitatory Ia afferent volleys. In order to estimate the stimulation effects, the peri-stimulus time histograms of single motoneurones were plotted, and the firing indices were calculated. It was shown that the firing-frequency effect was absent within the range of 4-14 imp/s during testing by low-intensity excitatory volley. At higher intensity of afferent volley, the excitability increased at a low firing rate. It is suggested that the characteristics of the interspike-interval excitability trajectories underlie these relations. These findings made it possible to explicate some conflicting literature data which were usually reported without taking the afferent volley intensity effect into account. The mechanisms controlling the firing motoneurone excitability and possible trajectories of interspike-interval membrane potential in human motoneurones are discussed.     

Reciprocal inhibition of human motoneurons with different firing frequencies

A study was made of the effect of reciprocal inhibition on individual firing motoneurons in the extensor carpi ulnaris and soleus muscle in human subjects. Peristimulus histograms (PSH) were plotted at different average frequency of motoneuron firing ( ) and the change in duration of interspike intervals (ISI) was analyzed. For reciprocal inhibition, as for other types of inhibition, is a factor in the effectiveness of motoneuron inhibition. The duration of inhibition apparent in the PSH, the sizes of zones of inhibition effectiveness in the ISIs and lengthening of the intervals are dependent on . For all motoneurons, the low range is most favorable for effective inhibition. The dependence of effectiveness of a volley on the time of its arrival within the ISI is also analyzed.Institute for Problems of Information Transmission, Russian Academy of Sciences, Moscow. Translated from Neirofiziologiya, Vol. 24, No. 6, pp. 643–653, November–December, 1992.     

A joint interspike interval difference stochastic spike train analysis: detecting local trends in the temporal firing patterns of single neurons

We introduce a stochastic spike train analysis method called joint interspike interval difference (JISID) analysis. By design, this method detects changes in firing interspike intervals (ISIs), called local trends, within a 4-spike pattern in a spike train. This analysis classifies 4-spike patterns that have similar incremental changes. It characterizes the higher-order serial dependence in spike firing relative to changes in the firing history. Mathematically, this spike train analysis describes the statistical joint distribution of consecutive changes in ISIs, from which the serial dependence of the changes in higher-order intervals can be determined. It is similar to the joint interspike interval (JISI) analysis, except that the joint distribution of consecutive ISI differences (ISIDs) is quantified. The graphical location of points in the JISID scatter plot reveals the local trends in firing (i.e., monotonically increasing, monotonically decreasing, or transitional firing). The trajectory of these points in the serial-JISID plot traces the time evolution of these trends represented by a 5-spike pattern, while points in the JISID scatter plot represent trends of a 4-spike pattern. We provide complete theoretical interpretations of the JISID analysis. We also demonstrate that this method indeed identifies firing trends in both simulated spike trains and spike trains recorded from cultured neurons. Received: 13 May 1997 / Accepted in revised form: 9 December 1998     

Reproducing bursting interspike interval statistics of the gustatory cortex

Cortical neurons in vivo generate highly irregular spike sequences. Recently, it was experimentally found that the local variation of interspike intervals, LV, is nearly constant for every spike sequence for the same neurons. On the contrary, the coefficient of variation, CV, varies over different spike sequences. Here, we first show that these characteristic features are also applicable in bursting spike sequences that are obtained from the rat gustatory cortex. Next, we show that the conventional leaky integrate-and-fire model does not fully account for reproducing these statistical features in data of real bursting spike sequences. We resolve this difficulty by proposing an alternative neuron model which is a reduction of the bursting neuron model involving the persistent sodium current. Our study implies that (1) the characteristic features of CV and LV are the results of the endogenous bursting and (2) the bursting behavior in the gustatory cortex is caused mainly by the persistent sodium current.     

Changes in cortical unit activity during selective reinforcement of a chosen interspike interval range

In experiments on immobilized unanesthetized rabbits selective automatic reinforcement of certain ranges of short and long interspike intervals in spontaneous unit activity recorded from single cortical units was given by means of a nociceptive stimulus. Analysis of postinterval histograms showed that the total number of intervals reinforceable by nociceptive stimuli is reduced as a result of the consequent reorganization of the firing pattern. If short intervals are reinforced the mean firing rate is reduced and the probability of appearance of long intervals immediately after the short reinforcements is increased. After reinforcement of long intervals the mean firing rate was increased in one group of cortical neurons, with a corresponding decrease in the total number of long intervals. In the other group of cells a decrease in the number of long intervals was accompanied by a decrease in the mean firing rate of the cells. It is postulated that reorganization of the firing pattern is determined by the level of synchronization of ascending activating influences and by their summation with phases of excitation and inhibition in reciprocally interacting neuron populations.Institute of Experimental Medicine, Academy of Medical Sciences of the USSR, Leningrad. Translated from Neirofiziologiya, Vol. 4, No. 4, pp. 339–348, July–August, 1972.     

Neural mechanism generating firing patterns in jaw motoneurons during the food-induced response in Aplysia kurodai

1. In each right and left buccal ganglia of Aplysia kurodai, we identified 4 premotor neurons impinging on the ipsilateral jaw-closing and -opening motoneurons. Three of them (MA1 neurons) had features of multifunctional neurons. Current-induced spikes in the MA1 neurons produced excitatory junction potentials (EJPs) in the buccal muscle fibers. In addition, tactile stimulation of the buccal muscle surface produced a train of spikes in the MA1 neurons without synaptic input. The other neuron (MA2) had only a premotor function. 2. The MA1 and MA2 neurons had similar synaptic effects on the jaw-closing and -opening motoneurons. Current-induced spikes in the premotor neurons gave rise to monosynaptic inhibitory postsynaptic potentials (IPSPs) in the ipsilateral jaw-closing motoneurons. Simultaneously, spikes in one of the MA1 neurons and the MA2 also gave rise to monosynaptic excitatory postsynaptic potentials (EPSPs) in the ipsilateral jaw-opening motoneuron. 3. The IPSPs and the EPSPs induced by spikes in the premotor neurons were reversibly blocked by d-tubocurarine and hexamethonium, respectively, suggesting that the MA1 and MA2 neurons are cholinergic. 4. When depolarizing and hyperpolarizing current pulses were passed into one premotor neuron, attenuated but similar potential changes were produced in another randomly selected premotor neuron in the same ganglion, suggesting that they are electronically coupled.     

Recurrent inhibition of human firing motoneurons (experimental and modeling study)

Recurrent inhibition between tonically activated single human motoneurons was studied experimentally and by means of a computer simulation. Motor unit activity was recorded during weak isometric constant-force muscle contractions of brachial biceps (BB) and soleus (SOL) muscles. Three techniques (cross correlogram, frequencygram, and interspike interval analysis) were used to gauge the relations between single motor unit potential trains. Pure inhibition was detected in 5.6% of 54 BB motoneuron pairs and in 5.2% of 43 SOL motoneuron pairs. In 27.8% (BB) and 23.7% (SOL) presumed inhibition symptoms were accompanied by a synchrony peak; 37% (BB) and 48.8% (SOL) exhibited synchrony alone. The demonstrated inhibition was very weak, at the edge of detectability. Computer simulations were based on the threshold-crossing model of a tonically firing motoneuron. The model included synaptic noise as well as threshold and postsynaptic potential (PSP) amplitude change within interspike interval. Inhibition efficiency of the model neurons increased with IPSP amplitude and duration, and with increasing source firing rate. The efficiency depended on target motoneuron interspike interval in a manner similar to standard deviation of ISI. The minimum detectable amplitude estimated in the simulations was about 50V, which, compared with the experimental results, suggests that amplitudes of detectable recurrent IPSPs in human motoneurons during weak muscle contractions do not exceed this magnitude. Since recurrent inhibition is known to be progressively depressed with an increase in the force of voluntary contraction, it is concluded that the recurrent inhibition hardly plays any important role in the isometric muscle contractions of constant force.     

Altered excitability of and synaptic effects of motoneurons during the establishing of a locomotor generation in the cat

Research was performed on spinal cats injected with DOPA and decorticate (decerebrated at level A 13) and spinal cats. It was found that formation (activation) of the spinal locomotor generator is accompanied by heightened excitability in the extensor and the reverse trend in the flexor motoneurons, by an increase in the efficacy of recurrent and reciprocal Ia inhibition of -motoneurons, and by a weakening of the influence of Ib afferents and extensor reflex afferents on these same motoneurons. The likely functional role of these changes in tuning of the spinal segmental apparatus in the generation of locomotor rhythm is discussed.A. A. Bogomolets Institute of Physiology, Academy of Sciences of the Ukrainian SSR, Kiev. Translated from Neirofiziologiya, Vol. 18, No. 5, pp. 679–687, September–October, 1986.     

Detecting chaotic structures in noisy pulse trains based on interspike interval reconstruction

The nonlinear prediction method based on the interspike interval (ISI) reconstruction is applied to the ISI sequence of noisy pulse trains and the detection of the deterministic structure is performed. It is found that this method cannot discriminate between the noisy periodic pulse train and the noisy chaotic one when noise-induced pulses exist. When the noise-induced pulses are eliminated by the grouping of ISI sequence with the genetic algorithm, the chaotic structure of the chaotic firings becomes clear, and the noisy chaotic pulse train could be discriminated from the periodic one.     

Changes in the excitability of and synaptic effects on motoneurons during formation of the scratch motion generator in the cat

Studies on immobilized decerebrate (at intracollicular level) cats in which the scratch generator had been set up following bicuculline application to the upper cervical segments of the spinal cord, showed that the state of the segmental apparatus of the lumbosacral section of the spinal cord differs substantially from that seen in the spinal animal. Direct excitability of motoneurons of the "aiming" and "scratching" muscles rises, while recurrent and reciprocal Ia inhibition of motoneurons intensifies and the influence of Ib afferents on motoneurons declines. Afferents of the flexor reflex exert a primarily inhibitory influence on motoneurons of the "aiming" muscles. This influence becomes predominantly excitatory following spinalization, while the inhibitory effects of these afferents on motoneurons of the "scratch" muscles declines. The functional significance of the changes discovered in generation of scratch routine is discussed.A. A. Bogomolets Institute of Physiology, Academy of Sciences of the Ukrainian SSR, Kiev. Translated from Neirofiziologiya, Vol. 19, No. 2, pp. 244–250, March–April, 1987.     

Detection and analysis of recurrent inhibition of firing motoneurons in man

During regular firing of "small" motor units, activated during weak voluntary contraction of the human soleus muscle, thick efferent fibers of n. tibialis were stimulated (a small M response was evoked, in which the small units did not participate). Peristimulus histograms of potentials of single motor units were constructed and the effect of stimulation on interspike interval duration was analyzed. The firing rate of the motor units was 4.5–7.6 spikes/sec. Stimulation of the nerve led to a sharp decrease in probability of their discharge or even complete temporary cessation of firing, i.e., it had a well marked inhibitory effect (lasting 10–20 msec). The latent period of inhibition (35–40 msec) was only a little longer than the latent period of the monosynaptic reflex of the soleus muscle. The effect of an inhibitory volley on duration of the interspike interval of the motor units depended on the time when the volley arrived during the interval. Lengthening of the interval was observed only if the inhibitory volley arrived in the second half or at the end of the interval. It is concluded that inhibition of firing of small motor units is due to Renshaw cells, activated on stimulation of axons of large motoneurons. The efficiency of a short (compared with the duration of the interspike interval) inhibitory volley reaching a motoneuron firing at low frequency characteristic of its adequate activation, is discussed.Institute for Problems of Information Transmission, Academy of Sciences of the USSR, Moscow. Translated from Neirofiziologiya, Vol. 16, No. 1, pp. 88–96, January–February, 1984.     

Reduction in maximal firing rate of motoneurons after 1-week immobilization of finger muscle in human subjects.

We investigated the effects of immobilization on the maximal motoneuronal firing rate recorded from the first dorsal interosseous (FDI) during voluntary isometric contraction. In five human subjects, the middle finger, index finger, and thumb were immobilized for 1 week in a fiber-glass cast, which kept FDI in a shortened position. During a maximal voluntary contraction, single muscle-fiber action potentials were recorded using a tungsten microelectrode, and mean firing rate was calculated for each action-potential train. Three recording sessions were held: before immobilization (pre), after immobilization (post), and after a 1-week recovery period (recovery). The mean firing rate of FDI motoneurons during maximal voluntary contraction was decreased immediately after the 1-week immobilization (pre: 39.0+/-3.2 Hz, number of detected spike trains (n)=353; post: 33.1+/-1.5 Hz, n=285; p<0.05), and there was a return to control after the recovery period (40.2+/-3.4 Hz, n=236). This suggests that the maximal motoneuronal firing rate achieved during maximal voluntary contraction is reduced after short-term immobilization. The functional implications and the contribution of this phenomenon to the immobilization-induced reduction in maximal voluntary force are discussed.     

Double discharges in human motoneurons

Potentials of motor units from the trapezius and rectus femoris muscles were recorded with selective needle electrodes during weak and moderately strong voluntary isometric contraction. The sequence of interspike intervals was analyzed. Double discharges (interspike interval not exceeding 20 msec) were found most commonly during recruiting of the motor units, but also at its end. Intervals between double discharges arising while the motor units were firing at a mean rate of 10–18 spikes/sec were outside the limits of statistical scatter of the remaining intervals. Double discharges were recorded chiefly in high-threshold units. The mean interval between double discharges recorded from the trapezius muscle was significantly smaller and the double discharges appeared considerably more often than in the rectus femoris muscle. Comparison of the results of these experiments with those obtained by other workers showed correlation between the mean duration of the interval between the double discharges and the duration of delayed depolarization of the motoneuron; this fact probably plays an important role in the creation of double discharges.     

On modelling the variability of interspike intervals during epileptic unit activity

In spite of the fact that the participation of well defined ionic particles in generating convulsive unit discharges is established, there is a gap between the data on ionic movements and on first-order statistics of firing patterns. Our aim was to tight this gap by studying the effectiveness of functionally separated electrical conductances of membrane during the generation of consecutive interspike interval histograms (IIHs) of unitary discharges. On account of the non-stationarity of the process curve fitting analysis which based on the simple modifications of the integrate-and-fire model has been implemented in the sequential interspike interval histogram procedure (SIIH). The experimental data were recorded from cat cortex treated with 3-Aminopyridine (3-Ap) by glass microelectrodes during nembutal anesthezia. Assuming the normal distribution of input parameters it is concluded, that the efficiency of the fluctuations of the active spike-generating conductance g_g and the passive diffusional conductance g_l may increase during the generation of the unimodal IIHs and the first mode of the bimodal IIHs. The simple conductance coupling g_l=a·g_g+b may participate in g_l activation, moreover, the reciprocally coupled mechanism g_g=c/g_l may be driven by g_l activation (a, b, c are the coupling constants). A temporal separation of processes governed by g_g or g_l respectively was observed. The timeindependent occurrences of the reciprocally coupled conductance processes may be involved in the unit activities represented by the prolonged IIHs and second modes of the bimodal IIHs.