A Wiener-type neuronal model in the presence of exponential refractoriness

An instantaneous return process in the presence of random refractoriness for Wiener model of single neuron activity is considered. The case of exponential distributed refractoriness is analyzed and expressions for output distributions and interspike intervals density are obtained in closed form. A computational study is performed to elucidate the role played by the model parameters in affecting the firing probabilities and the interspike distribution.     

A model for the variability of interspike intervals during sustained firing of a retinal neuron.

The statistics of the variability of interspike intervals of ganglion cells in the retina of goldfish are modeled by assuming the noise in an integrate-and-fire mechanism is proportional to the reciprocal of a normally distributed variable. This model meets the constraint that the coefficient of variation of the interspike. This does not change when the mean firing rate of the neuron changes. Alternative sources of variability of interspike intervals are discussed.     

A stochastic model for the membrane potential of a stimulated neuron

We present a simple model describing the transition between the prefiring, firing and postfiring phases of a single neuron in a large neural net. Using typical values for the physiological parameters that enter the model, we find average interspike times that are close to those reported in experimental measurements.     

Natural history of cervical intraepithelial neoplasia: a meta-analysis

OBJECTIVE: To determine the probabilities of transition of stages in the cervical cancer by conducting a meta-studies on the topic. STUDY DESIGN: We identified health states of interest in the natural history of cervical precancer, identified all possible papers that could meet selection criteria, developed relevance and acceptability criteria for inclusion, then thoroughly reviewed the selected studies. To determine the transition probability data we used a random effects model. We determined probabilities for 4 health state transitions. The 6-month mean predictive transition probability (95% confidence intervals with "prediction interval" in parentheses) for high grade squamous intraepithelial lesions (HSIL) to cancer was 0.0037 (0.00004, 0.03386), for low grade squamous intraepithelial lesions (LSIL) to HSIL was 0.0362 (0.00055, 0.23220), for HSIL to LSIL was 0.0282 (0.00027, 0.35782), and for LSIL to normal was 0.0740 (0.00119, 0.42672). CONCLUSION: The transition probabilities between cervical cancer health states for 6-month intervals are small; however, the cumulative risk of cervical cancer is significant. Markers to identify the cervical precursors that will lead to the transition to cervical cancer are needed.     

Effects of afterhyperpolarization on neuronal firing.

Stein's model for a neuron is studied. This model is modified to take into account the effects of afterhyperpolarization on the neuronal firing. The relative refractory phase, following the absolute one, is modelled by a time-increasing amplitude of postsynaptic potentials and it is also incorporated into the model. Besides the simulation of the model, some theoretical results and approximation methods are derived. Afterhyperpolarization tends to preserve the linearity of the frequency transfer characteristic and it has a limited effect on the moments of the interspike intervals in general. The main effects are seen at high firing rates and in the removal of short intervals in the interspike interval histogram.     

Relationship between applicability of current-based synapses and uniformity of firing patterns

The purpose of this paper is to identify situations in neural network modeling where current-based synapses are applicable. The applicability of current-based synapse model for studying post-transient behavior of neural networks is discussed in terms of average synaptic current strength induced by per spike during one firing cycle of a neuron (or briefly per spike synaptic current strength). It was found that current-based synapse models are applicable in both situations where both the interspike intervals of the neurons and the distribution of firing times of the neurons are uniform, and where the firing of all neurons is synchronized. If neither the interspike intervals nor the distribution of firing times of the neurons is uniform or the reversal potential is between the rest and threshold potentials, current-based synapse models may be oversimplified.     

Decoding Input Signals in Time Domain—A Model Approach

From an observation of efferent interspike intervals of a neuron, we consider how to decode the input temporal information. It is found that the integrate-and-fire model is blind in the temporal domain due to the fact that its efferent firing rate is independent of the input temporal frequency. The conclusion is then confirmed for the integrate-and-fire model with correlated inputs, with reversal potentials, with a nonlinear leakage and with a subthreshold oscillation. For the Hodgkin-Huxley model, however, in terms of efferent firing rates alone, it is possible to read out the input temporal information.     

Interval analysis of bursting discharges in aplysia neurons

Time intervals of 12 records of bursting discharges in Aplysia neurons were analysed by digital computer to determine the interrelations between the burst period, the interburst interval and the burst duration. The effects of membrane potential changes on the parameters of bursting discharges were examined also. A low correlation was found between burst duration and burst period in the majority of cases, and this was interpreted as an indication of probable independence between the mechanisms governing these parameters. Also, a specific temporal organization of interspike intervals seems to be present in each type of neuron. The results suggest that the mechanism governing the burst period is characterized by a slow membrane potential oscillation resembling that observed in bursting neurons when actions potentials are blocked by tetrodotoxin. The burst duration would be determined by the response of the neuron to suprathreshold depolarization.     

The parameters of the stochastic leaky integrate-and-fire neuronal model

Five parameters of one of the most common neuronal models, the diffusion leaky integrate-and-fire model, also known as the Ornstein-Uhlenbeck neuronal model, were estimated on the basis of intracellular recording. These parameters can be classified into two categories. Three of them (the membrane time constant, the resting potential and the firing threshold) characterize the neuron itself. The remaining two characterize the neuronal input. The intracellular data were collected during spontaneous firing, which in this case is characterized by a Poisson process of interspike intervals. Two methods for the estimation were applied, the regression method and the maximum-likelihood method. Both methods permit to estimate the input parameters and the membrane time constant in a short time window (a single interspike interval). We found that, at least in our example, the regression method gave more consistent results than the maximum-likelihood method. The estimates of the input parameters show the asymptotical normality, which can be further used for statistical testing, under the condition that the data are collected in different experimental situations. The model neuron, as deduced from the determined parameters, works in a subthreshold regimen. This result was confirmed by both applied methods. The subthreshold regimen for this model is characterized by the Poissonian firing. This is in a complete agreement with the observed interspike interval data. Action Editor: Nicolas Brunel     

Cardiopulmonary,hematological, serum biochemical and behavioral effects of sevoflurane compared with isoflurane or halothane in spontaneously ventilating goats

This study compares cardiopulmonary, hematological, serum biochemical and behavioral effects of sevoflurane, isoflurane or halothane anesthesia in spontaneously breathing, conventionally medicated goats. Six male adult goats were anesthetized repeatedly at 2-week intervals with three anesthetics. Goats were administered atropine (0.1 mg/kg) intramuscularly, and 10 min later, induced to anesthesia by an intravenous infusion of thiopental (mean 14.3 mg/kg). After intubation, goats were anesthetized with halothane, isoflurane or sevoflurane in oxygen and maintained at surgical depth of anesthesia for 3 h. Recovery from anesthesia with sevoflurane was more rapid than that with isoflurane or halothane. Time-related hypercapnia and acidosis were observed during halothane anesthesia, but not observed during sevoflurane or isoflurane anesthesia. Both hypercapnia and acidosis during sevoflurane anesthesia did not differ from isoflurane anesthesia, but were less during halothane anesthesia, especially at prolonged maintenance period. There were no significant differences between anesthetics in respiration and heart rates, arterial pressures, hematological and serum biochemical values. It was concluded that sevoflurane is an effective inhalant for use in goats showing the most rapid recovery from anesthesia, and that cardiopulmonary effects of sevoflurane are similar to isoflurane than halothane.     

A qualitative comparison of some diffusion models for neural activity via stochastic ordering

A number of diffusion processes have been proposed as a continuous analog of Stein's model for the subthreshold membrane potential of a neuron. Interspike intervals are then described as the first-passage-time of the corresponding diffusion model through a suitable threshold. Various biological considerations suggest the use of more sophisticated models in lieu of the Ornstein-Uhlenbeck model. However, the advantages of the additional complexity are not always clear. Comparisons among different models generally use numerical methods in specific examples without a general sensitivity analysis on the role of the model parameters. Here, we compare the distribution of interspike intervals from different models using the method of stochastic ordering. The qualitative comparison of the role of each parameter extends the results obtained from numerical simulations. One result on neurons with high positive net excitation is that the reversal potential models considered do not greatly differ from the Ornstein-Uhlenbeck model. For neurons with increased inhibition, the models give greater differences among the interspike interval distributions. In particular, when the mean trajectories are matched, the Feller model gives shorter times than the Ornstein-Uhlenbeck model but longer times than our double reversal potential model. Received: 5 August 1999 / Accepted in revised form: 8 May 2000     

A review of the methods for signal estimation in stochastic diffusion leaky integrate-and-fire neuronal models

Parameters in diffusion neuronal models are divided into two groups; intrinsic and input parameters. Intrinsic parameters are related to the properties of the neuronal membrane and are assumed to be known throughout the paper. Input parameters characterize processes generated outside the neuron and methods for their estimation are reviewed here. Two examples of the diffusion neuronal model, which are based on the integrate-and-fire concept, are investigated--the Ornstein--Uhlenbeck model as the most common one and the Feller model as an illustration of state-dependent behavior in modeling the neuronal input. Two types of experimental data are assumed-intracellular describing the membrane trajectories and extracellular resulting in knowledge of the interspike intervals. The literature on estimation from the trajectories of the diffusion process is extensive and thus the stress in this review is set on the inference made from the interspike intervals.     

无噪声Hodgkin-Huxley神经元对正弦信号的响应

研究了无噪声影响下的Hcdgkin-Huxley神经元在正弦信号刺激下的动力学行为,并利用“魔梯”图和峰峰间期分布图来分别描述。数值模拟结果表明,当信号振幅一定时,神经元的发放情况随频率而改变;当信号的频率一定时,峰峰间期分布随振幅而改变,相应地,峰峰间期序列也具有不同的特点。     

基于复杂性度量的心率变异信号非线性分析

假设心率变异信号是累积－发放模型（Ｉｎｔｅｇｒａｔｅ－ｆｉｒｅ）与非线性动力学系统耦合产生的峰电位链（ＳｐｉｋｅＴｒａｉｎ）。以符号动力学为基础,提出利用峰电位间隔（ｉｎｔｅｒｓｐｉｋｅｉｎｔｅｒｖａｌ,ＩＳＩ）及其随机替代数据的Ｃ１、Ｃ２复杂度来定量刻划非线性动力学系统特性。结果表明：确定性驱动产生的峰电位间隔序列可以与随机性驱动产生的峰电位间隔序列区分开。因此,在噪声干扰较强的生理信号中,尤其是在不清楚非线性动力系统变量和峰电位间隔序列之间是否存在微分同胚的情况下,以复杂性度量来代替以Ｔａｋｅｎｓ嵌入定理为基础的关联维数、Ｌｙａｐｎｏｖ指数等描述动力系统特征的方法是合适的。最后通过２类共３７个个体,每个个体的心电数据为１０００个Ｒ－Ｒ间期的微分序列检验心率变异信号的非线性结构。     

Influence of temporal correlation of synaptic input on the rate and variability of firing in neurons

The spike trains that transmit information between neurons are stochastic. We used the theory of random point processes and simulation methods to investigate the influence of temporal correlation of synaptic input current on firing statistics. The theory accounts for two sources for temporal correlation: synchrony between spikes in presynaptic input trains and the unitary synaptic current time course. Simulations show that slow temporal correlation of synaptic input leads to high variability in firing. In a leaky integrate-and-fire neuron model with spike afterhyperpolarization the theory accurately predicts the firing rate when the spike threshold is higher than two standard deviations of the membrane potential fluctuations. For lower thresholds the spike afterhyperpolarization reduces the firing rate below the theory's predicted level when the synaptic correlation decays rapidly. If the synaptic correlation decays slower than the spike afterhyperpolarization, spike bursts can occur during single broad peaks of input fluctuations, increasing the firing rate over the prediction. Spike bursts lead to a coefficient of variation for the interspike intervals that can exceed one, suggesting an explanation of high coefficient of variation for interspike intervals observed in vivo.     

Interactions Between Neuronal Histamine and Halothane Anesthesia in Rats

Abstract: Using an in vivo microdialysis method, we measured the release of histamine in the anterior hypothalamic area (AHy) of rats under several concentrations of halothane anesthesia (1, 0.5, and 0.2%). The release of histamine increased to 341 and 325% at halothane concentrations of 0.5 and 0.2%, compared with the basal level at anesthesia induced by 1% halothane. α-Fluoromethylhistidine (100 mg/kg i.v.), a specific and irreversible inhibitor of histidine decarboxylase, reduced the histamine release to <35% of the basal value at 1% halothane anesthesia in the AHy, and also decreased the anesthetic requirement for halothane, evaluated as the minimum alveolar concentration (MAC), by 26%. Furthermore, pyrilamine (20 mg/kg i.v.), a brain-penetrating H₁ antagonist, and zolantidine (20 mg/kg i.v.), a brain-penetrating H₂ antagonist, reduced the MAC for halothane by 28.5 and 16%, respectively. Although thioperamide (5 mg/kg i.v.), an antagonist of presynaptic H₃ autoreceptor, induced an approximate twofold increase in the level of histamine release in conscious freely moving rats, the same dose of thioperamide had little effect on the release of histamine under 1% halothane anesthesia in the AHy. Furthermore, thioperamide did not change the anesthetic requirement (MAC) for halothane. The present findings indicate that halothane anesthesia inhibits the release of neuronal histamine and that histaminergic neuron activities change the anesthetic requirement (MAC) for halothane through H₁ as well as H₂ receptors.     

Mean-field analysis of selective persistent activity in presence of short-term synaptic depression

Mean-Field theory is extended to recurrent networks of spiking neurons endowed with short-term depression (STD) of synaptic transmission. The extension involves the use of the distribution of interspike intervals of an integrate-and-fire neuron receiving a Gaussian current, with a given mean and variance, in input. This, in turn, is used to obtain an accurate estimate of the resulting postsynaptic current in presence of STD. The stationary states of the network are obtained requiring self-consistency for the currents—those driving the emission processes and those generated by the emitted spikes. The model network stores in the distribution of two-state efficacies of excitatory-to-excitatory synapses, a randomly composed set of external stimuli. The resulting synaptic structure allows the network to exhibit selective persistent activity for each stimulus in the set. Theory predicts the onset of selective persistent, or working memory (WM) activity upon varying the constitutive parameters (e.g. potentiated/depressed long-term efficacy ratio, parameters associated with STD), and provides the average emission rates in the various steady states. Theoretical estimates are in remarkably good agreement with data “recorded” in computer simulations of the microscopic model. Action Editor: Karen Sigvardt     

From complex spatial dynamics to simple Markov chain models: do predators and prey leave footprints?

In this paper we present a concept for using presence–absence data to recover information on the population dynamics of predator–prey systems. We use a highly complex and spatially explicit simulation model of a predator–prey mite system to generate simple presence–absence data: the number of patches with both prey and predators, with prey only, with predators only, and with neither species, along with the number of patches that change from one state to another in each time step. The average number of patches in the four states, as well as the average transition probabilities from one state to another, are then depicted in a state transition diagram, constituting the "footprints" of the underlying population dynamics. We investigate to what extent changes in the population processes modeled in the complex simulation (i.e. the predator's functional response and the dispersal rates of both species) are reflected by different footprints
The transition probabilities can be used to forecast the expected fate of a system given its current state. However, the transition probabilities in the modeled system depend on the number of patches in each state. We develop a model for the dependence of transition probabilities on state variables, and combine this information in a Markov chain transition matrix model. Finally, we use this extended model to predict the long-term dynamics of the system and to reveal its asymptotic steady state properties.     

The dependence of impulse propagation speed on firing frequency, dispersion, for the Hodgkin-Huxley model.

Propagation speed of an impulse is influenced by previous activity. A pulse following its predecessor too closely may travel more slowly than a solitary pulse. In contrast, for some range of interspike intervals, a pulse may travel faster than normal because of a possible superexcitable phase of its predecessor's wake. Thus, in general, pulse speeds and interspike intervals will not remain constant during propagation. We consider these issues for the Hodgkin-Huxley cable equations. First, the relation between speed and frequency or interspike interval, the dispersion relation, is computed for particular solutions, steadily propagating periodic wave trains. For each frequency, omega, below some maximum frequency, omega max, we find two such solutions, one fast and one slow. The latter are likely unstable as a computational example illustrates. The solitary pulse is obtained in the limit as omega tends to zero. At high frequency, speed drops significantly below the solitary pulse speed; for 6.3 degrees C, the drop at omega max is greater than 60%. For an intermediate range of frequencies, supernormal speeds are found and these are correlated with oscillatory swings in sub- and superexcitability in the return to rest of an impulse. Qualitative consequences of the dispersion relation are illustrated with several different computed pulse train responses of the full cable equations for repetitively applied current pulses. Moreover, changes in pulse speed and interspike interval during propagation are predicted quantitatively by a simple kinematic approximation which applies the dispersion relation, instantaneously, to individual pulses. One example shows how interspike time intervals can be distorted during propagation from a ratio of 2:1 at input to 6:5 at a distance of 6.5 cm.