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PubMed2004

Contributions of the input signal and prior activation history to the discharge behaviour of rat motoneurones.

The principal computational operation of neurones is the transformation of synaptic inputs into spike train outputs. The probability of spike occurrence in neurones is determined by the time course and magnitude of the total current reaching the spike initiation zone. The features of this current that are most effective in evoking spikes can be determined by injecting a Gaussian current waveform into a neurone and using spike-triggered reverse correlation to calculate the average current trajectory (ACT) preceding spikes. The time course of this ACT (and the related first-order Wiener kernel) provides a general description of a neurone's response to dynamic stimuli. In many different neurones, the ACT is characterized by a shallow hyperpolarizing trough followed by a more rapid depolarizing peak immediately preceding the spike. The hyperpolarizing phase is thought to reflect an enhancement of excitability by partial removal of sodium inactivation. Alternatively, this feature could simply reflect the fact that interspike intervals that are longer than average can only occur when the current is lower than average toward the end of the interspike interval. Thus, the ACT calculated for the entire spike train displays an attenuated version of the hyperpolarizing trough associated with the long interspike intervals. This alternative explanation for the characteristic shape of the ACT implies that it depends upon the time since the previous spike, i.e. the ACT reflects both previous stimulus history and previous discharge history. The present study presents results based on recordings of noise-driven discharge in rat hypoglossal motoneurones that support this alternative explanation. First, we show that the hyperpolarizing trough is larger in ACTs calculated from spikes preceded by long interspike intervals, and minimal or absent in those based on short interspike intervals. Second, we show that the trough is present for ACTs calculated from the discharge of a threshold-crossing neurone model with a postspike afterhyperpolarization (AHP), but absent from those calculated from the discharge of a model without an AHP. We show that it is possible to represent noise-driven discharge using a two-component linear model that predicts discharge probability based on the sum of a feedback kernel and a stimulus kernel. The feedback kernel reflects the influence of prior discharge mediated by the AHP, and it increases in amplitude when AHP amplitude is increased by pharmacological manipulations. Finally, we show that the predictions of this model are virtually identical to those based on the first-order Wiener kernel. This suggests that the Wiener kernels derived from standard white-noise analysis of noise-driven discharge in neurones actually reflect the effects of both stimulus and discharge history.

Action Potentials↗

PubMed1998

Coexistence of multiple propagating wave-fronts in a regulated enzyme reaction model: link with birhythmicity and multi-threshold excitability.

We analyze the spatial propagation of wave-fronts in a biochemical model for a product-activated enzyme reaction with non-linear recycling of product into substrate. This model was previously studied as a prototype for the coexistence of two distinct types of periodic oscillations (birhythmicity). The system is initially in a stable steady state characterized by the property of multi-threshold excitability, by which it is capable of amplifying in a pulsatory manner perturbations exceeding two distinct thresholds. In such conditions, when the effect of diffusion is taken into account, two distinct wave-fronts are shown to propagate in space, with distinct amplitudes and velocities, for the same set of parameter values, depending on the magnitude of the initial perturbation. Such a multiplicity of propagating wave-fronts represents a new type of coexistence of multiple modes of dynamic behavior, besides the coexistence involving, under spatially homogeneous conditions, multiple steady states, multiple periodic regimes, or a combination of steady and periodic regimes.

Journal Article↗

PubMed1994

A model of dendritic spine Ca2+ concentration exploring possible bases for a sliding synaptic modification threshold.

We used a biophysical model of an isolated dendritic spine to assess quantitatively the impact of changes in spine geometry, Ca2+ buffer concentration, and channel kinetics on Ca2+ dynamics following high-frequency activation of N-methyl-D-aspartate receptors. We found that varying the buffer concentration in the postsynaptic density from 50 to 500 microM can result in an 8-fold difference in the peak Ca2+ concentration following three pulses at 100 Hz. Similarly, varying the spine neck diameter from 0.1 to 0.55 micron can result in a 15-fold difference in the peak Ca2+ concentration. The amplification of peak Ca2+ concentration also depended on temporal summation of N-methyl-D-aspartate-mediated excitatory postsynaptic currents. Variation of the current duration on the order of 100 msec can significantly affect summation at a given stimulation frequency, resulting in a 10-fold difference in the peak Ca2+ concentration at 100 Hz. It is suggested that activity-dependent modifications of these parameters may be important for the regulation of synaptic plasticity in the brain.

Calcium↗

PubMed1999

Threshold-linear versus linear-linear analysis of birth weight and calving ease using an animal model: II. Comparison of models.

Several models were evaluated in terms of predictive ability for calving difficulty. Data included birth weight and calving difficulty scores provided by the American Gelbvieh Association from 26,006 calves born to first-parity cows and five simulated populations of 6,200 animals each. Included in the model were fixed age of dam x sex interaction effects, random herd-year-season effects, and random animal direct and maternal effects. Bivariate linear-threshold and linear-linear models for birth weight/calving ease and univariate threshold and linear models for calving ease were applied to the data sets. For each data set and model, one-half of calving ease records were randomly discarded. Predictive ability of the different models was defined with the mean square error (MSE) for the difference between a deleted calving ease score and its prediction obtained from the remaining data. In terms of correlation between simulated and predicted breeding values, the threshold models had a 1% advantage for direct genetic effects and 3% for maternal genetic effects. In simulation, the average MSE was .29 for linear-threshold, .32 for linear-linear, .37 for threshold, and .39 for linear model. For the field data set, the MSE was .31, .33, .39, and .40, respectively. Although the bivariate models for calving ease/birth weight were more accurate than univariate models, the threshold models showed a greater advantage under the bivariate model. For the purpose of genetic evaluation for calving difficulty in beef cattle, the use of the linear-threshold model seems justified. In dairy cattle, the evaluation for calving ease can benefit from recording birth weight.

Animals↗

PubMed2003

Predicting the threshold of single-pulse electrical stimuli using a stochastic auditory nerve model: the effects of noise.

An important factor that may play a role in speech recognition by individuals with cochlear implants is that electrically stimulated nerves respond with a much higher level of synchrony than is normally observed in acoustically stimulated nerves. Recent work has indicated that the addition of noise to an electrical stimulus may result in neural responses whose statistical characteristics are more similar to those observed in acoustically driven neurons. Psychophysical data have indicated that performance on some tasks might also be enhanced by the addition of noise. However, little theoretical work has been done toward predicting the effect of noise on psychoacoustic measurements. In this paper, theoretical predictions of these effects are developed through the use of a stochastic computational model. The effect of additive noise on the input and output characteristics and aggregate threshold behavior of modeled auditory nerves (ANs) is specifically studied. This paper derives the stochastic properties of the model input and output when using adaptive threshold procedures. A closed form solution for the input, or amplitude, probability distribution is obtained via Markov models for both one-down one-up (1D1U) and two-down one-up (2D1U) experimental paradigms. The output statistics are derived by integrating over the noise-free probability mass function (PMF). All theoretical PMFs are verified by simulations with the model. Theoretical threshold is predicted as a function of noise level based on these PMFs and the predictions match simulated performance. The results indicate that threshold may be adversely affected by the presence of high levels of noise.

Action Potentials↗

PubMed1982

A model for the speech-reception threshold in noise without and with a hearing aid.

This paper presents a summary of the main results of our current research programme on the speech-reception threshold for sentences as a function of the sound-pressure level of interfering noise. The experimental results agree with a simple quantitative model in which every hearing loss for speech is interpreted as the sum of a class-A loss (attenuation), characterized by a reduction in the levels of both speech signal and noise, and a class-D loss (distortion), comparable to a reduction in S/N ratio. The experiments confirm the model's prediction that a hearing aid can compensate for class-A hearing losses but, generally, not for class-D hearing losses. The implies that the problem of having difficulties in understanding speech in a noisy environment, which is the primary handicap of hearing-impaired subjects, is not solved by the hearing aid.

Audiometry, Speech↗

PubMed2004

Time course and cellular distribution of hsp27 and hsp72 stress protein expression in a quantitative gerbil model of ischemic injury and tolerance: thresholds for hsp72 induction and hilar lesioning in the context of ischemic preconditioning.

The distribution and time course of expression of the heat shock/stress proteins, hsp27 and hsp72, were evaluated in a highly controlled gerbil model of ischemic injury and tolerance induction, in which the duration of ischemic depolarization in each hippocampus provides a precise quantitative index of insult severity. Gerbils were subjected to brief priming insults (2- to 3.5-minute depolarization) that produce optimal preconditioning, to severe test insults (6- to 8.5-minute depolarization) that produce complete CA1 neuron loss in naive animals, or to combined insults administered 1 week apart, after which almost complete tolerance to CA1 neuron injury is observed. Immunoreactivities of hsp27, hsp72, glial fibrillary acidic protein and microtubule-associated protein 2 (MAP2) were evaluated in animals perfused at defined intervals after the final insult in each treatment group, using a variation of established antigen-retrieval procedures that significantly improves detection of many proteins in vibratome brain sections. Hsp72 was detected in CA1 neurons of some hippocampi 2 to 4 days after preconditioning, but this was only seen after the longest priming depolarizations, whereas shorter insults that still induced optimal tolerance failed to induce hsp72. Hsp72 was induced after test insults in preconditioned hippocampi, but at a higher depolarization threshold than observed for naive animals. An astrocytic localization of hsp27 was observed in regions of neuron injury, as indicated by reduced MAP2 immunoreactivity, and was primarily restricted to dentate hilus after preconditioning insults. These results establish that limited hilar lesions are characteristic of optimal preconditioning, whereas prior neuronal expression of either hsp72 or hsp27 is not required for ischemic tolerance.

Animals↗

PubMed1997

Exclusion of linkage between bipolar affective disorder and chromosome 16 in 12 Australian pedigrees.

Several recent reports of possible susceptibility loci for bipolar affective disorder (BAD) have identified sites on a number of chromosomes. Specifically, two Danish studies have suggested the presence of a susceptibility locus for BAD on chromosome 16p13. As the first step of a whole genome scan, we screened 12 Australian families with markers at 16p13 and also a number of markers spanning the entirety of chromosome 16. Linkage analysis was undertaken using both the parametric lod score method (two- and multipoint) with different models and diagnostic thresholds, and the nonparametric affected pedigree member (APM) method. Results of lod score analysis convincingly excluded the 16p13 region from linkage to BAD in these families, while APM provided no support for linkage. Furthermore, using the broad definition of BAD, with individuals affected by bipolar I and II and recurrent unipolar disorders included, the entire chromosome was excluded from linkage to BAD with autosomal-dominant transmission at a maximum age-specific penetrance of 60%, and with autosomal-dominant and recessive modes of transmission at a maximum age-specific penetrance level of 90%. Diagnostic thresholds which did not include unipolar affected individuals were somewhat less informative. However, a majority (between 63-96%, depending upon the model) of the chromosome was clearly excluded using narrow diagnostic thresholds. Moreover, no positive lod scores were obtained at theta = 0.00 for any tested model or diagnostic threshold. Our results indicate that no linkage exists between BAD and chromosome 16 markers in this group of Australian families.

Australia↗

PubMed2002

A tuned-trace theory of interval-timing dynamics.

Animals on interval schedules of reinforcement can rapidly adjust a temporal dependent variable, such as wait time, to changes in the prevailing interreinforcement interval. We describe data on the effects of impulse, step, sine-cyclic, and variable-interval schedules and show that they can be explained by a tuned-trace timing model with a one-back threshold-setting rule. The model can also explain steady-state timing properties such as proportional and Weber law timing and the effects of reinforcement magnitude. The model assumes that food reinforcers and other time markers have a decaying effect (trace) with properties that can be derived from the rate-sensitive property of habituation (the multiple-time-scale model). In timing experiments, response threshold is determined by the trace value at the time of the most recent reinforcement. The model provides a partial account for the learning of multiple intervals, but does not account for scalloping and other postpause features of responding on interval schedules and has some problems with square-wave schedules.

Animals↗

PubMed2005

An application of threshold-versus-intensity functions in automated static perimetry.

Increment thresholds were measured over a range of adapting illuminances using a modified automated static perimeter. The data were fitted to a threshold versus intensity model (logT - logT(0) + log((A + A(0))/A(0))n) and the values logT(0) and logA(0) estimated. The effect of eccentricity and age on logT(0) and logA(0) was examined in normal subjects. A small group of patients with ocular disease were then assessed. Macular degeneration appeared to act as disease processes acting near the photoreceptor (d1 model). Glaucoma seemed to act near the site of retinal gain (d3 model). This analysis method may be of value in developing light adaptation strategies in people with ocular disease.

Adaptation, Ocular↗

PubMed1991

A model of the T-type calcium current and the low-threshold spike in thalamic neurons.

1. A model of the transient, low-threshold voltage-dependent (T-type) Ca2+ current is constructed using recent whole-cell voltage-clamp data from enzymatically isolated rat thalamocortical relay neurons. The T-type Ca2+ current is described according to the Hodgkin-Huxley scheme, using the m3h format, with rate constants determined from the experimental data (22-24 degrees C; extracellular Ca2+ concentration [Ca2+]o = 3 mM). 2. The T-type Ca2+ current inactivates rapidly during maintained depolarization (time constant, Tau h approximately 20 ms at -20 mV), yet recovery from inactivation is slow (time constant, Tau r approximately 270 ms at -80 mV). To reconcile these observations, a two-step kinetic scheme is proposed for the inactivation gate. Each of the time constants in this scheme is voltage dependent, with a maximum at about -85 mV (45 ms for one and 275 ms for the other). 3. Numerical simulations of recovery in a two-pulse, voltage-clamp protocol compare favorably with experimental results obtained by Coulter et al. as well as those obtained in an independent series of experiments with guinea pig thalamic neurons ([Ca2+]o = 10 mM). 4. For current-clamp simulations, a leakage current gL (V-VL) is included; with VL = -65 mV, the calculated resting membrane potential is -63 mV. 5. It is shown that the T-type Ca2+ current together with the leakage current suffices to describe the low-threshold spike (LTS), a slow, triangular-shaped depolarizing event that can be evoked only from relatively hyperpolarized membrane potentials and that underlies the burst firing of Na(+)-dependent action potentials in thalamic neurons. Outward currents are not required to reproduce the basic shape of the LTS. 6. The LTS can be activated with either a depolarizing current step from a sufficiently hyperpolarized level or on termination of a hyperpolarizing current step. In either case, the amplitude of the LTS is a monotonically increasing, sigmoid-shape function of the hyperpolarizing current step intensity. 7. Because of the slower kinetic step of the channel's inactivation gate, our model predicts that recovery of the LTS to greater than one-half amplitude would require a prolonged hyperpolarization of greater than 100 ms (at body temperature). This imposes an upper limit (approximately 10 Hz) on the frequency of repetitive hyperpolarization that can elicit a train of LTSs and hence on the frequency of any rhythm that requires LTS-mediated bursting of thalamic neurons.(ABSTRACT TRUNCATED AT 400 WORDS)

Action Potentials↗

PubMed1994

Low-threshold calcium current and resonance in thalamic neurons: a model of frequency preference.

1. We constructed a mathematical model of the subthreshold electrical behavior of neurons in the nucleus mediodorsalis thalami (MDT) to elucidate the basis of a Ni(2+)-sensitive low-frequency (2-4 Hz) resonance found previously in these neurons. 2. A model that included the low- and high-threshold Ca2+ currents (IT and IL), a Ca(2+)-activated K+ current (IC), a rapidly inactivating K+ current (IA), a voltage-dependent K+ current which we call IKx, and a voltage-independent leak current (Il), successfully simulated the low-threshold spike observed in MDT neurons. This model (the MDT model) and a minimal version of the model containing only IT and I1 (the minimal MDT model) were used in the analysis. 3. An impedance function was derived for a linearized version of the MDT model. This showed that the model predicts a low-frequency (2-4 Hz) resonance in the voltage response to "small" oscillatory current inputs (producing voltage changes of < 10 mV) when the membrane potential is between -60 and -85 mV. 4. Further examination of the impedances for the MDT and minimal MDT models shows that IT underlies the frequency- and voltage-dependent resonance. The slow inactivation of IT results in an attenuation of voltage responses to low frequencies, resulting in a band-pass behavior. The fast activation of IT amplifies the resonance and modulates the peak frequency but does not, in itself, cause resonance. 5. When voltage responses are small (< 10 mV), the strength and voltage-dependence of resonance of the minimal MDT model are determined by the steady-state window conductance, gw, due to IT. This steady-state conductance arises where the steady-state activation, m(infinity2)(V), and inactivation, h(infinity) (V), curves overlap. Parallel shifts in the inactivation curve can eliminate or enhance resonance with little effect on the IT-dependent low-threshold spike evoked after hyperpolarizing current pulses. When the peak magnitude of gw was large, the minimal MDT model showed spontaneous oscillations at 3 Hz with amplitudes > 30 mV. 6. Large oscillatory current inputs evoked significantly nonlinear voltage responses in the minimal MDT model, but the 2- to 4-Hz frequency selectivity (predicted from the linearized impedance) remained. 7. We conclude that the properties of the low-threshold Ca2+ current, IT, are sufficient to explain the Ni(2+)-sensitive 2- to 4-Hz resonance seen in MDT neurons.(ABSTRACT TRUNCATED AT 400 WORDS)

Animals↗

PubMed2003

Bayesian estimation of dose thresholds.

An example is described of Bayesian estimation of radiation absorbed dose thresholds (subsequently simply referred to as dose thresholds) using a specific parametric model applied to a data set on mice exposed to 60Co gamma rays and fission neutrons. A Weibull based relative risk model with a dose threshold parameter was used to analyse, as an example, lung cancer mortality and determine the posterior density for the threshold dose after single exposures to 60Co gamma rays or fission neutrons from the JANUS reactor at Argonne National Laboratory. The data consisted of survival, censoring times and cause of death information for male B6CF1 unexposed and exposed mice. The 60Co gamma whole-body doses for the two exposed groups were 0.86 and 1.37 Gy. The neutron whole-body doses were 0.19 and 0.38 Gy. Marginal posterior densities for the dose thresholds for neutron and gamma radiation were calculated with numerical integration and found to have quite different shapes. The density of the threshold for 60Co is unimodal with a mode at about 0.50 Gy. The threshold density for fission neutrons declines monotonically from a maximum value at zero with increasing doses. The posterior densities for all other parameters were similar for the two radiation types.

Adenocarcinoma↗

PubMed2006

Time scale for magnetic reversal and the topological nonconnectivity threshold.

Anisotropic classical Heisenberg models with all-to-all spin coupling display a topological nonconnectivity threshold (TNT) for any number N of spins. Below this threshold, the energy surface is disconnected in two components with positive and negative total magnetizations, respectively, so that magnetization cannot reverse its sign and ergodicity is broken, even at finite N. Here, we solve the model in the microcanonical ensemble, using a recently developed method based on large deviation techniques, and show that a phase transition is present at an energy higher than the TNT energy. In the energy range between the TNT energy and the phase transition, magnetization changes sign stochastically and its behavior can be fully characterized by an average magnetization reversal time. The time scale for magnetic reversal can be computed analytically, using statistical mechanics. Numerical simulations confirm this calculation and further show that the magnetic reversal time diverges with a power law at the TNT threshold, with a size-dependent exponent. This exponent can be computed in the thermodynamic limit N-->(infinity), by the knowledge of entropy as a function of magnetization, and turns out to be in reasonable agreement with finite numerical simulations. We finally generalize our results to other models: Heisenberg chains with distance-dependent coupling, small 3D clusters with nearest-neighbor interactions, metastable states. We conjecture that the power-law divergence of the magnetic reversal time scale might be a universal signature of the presence of a TNT.

Journal Article↗

PubMed1992

Factors affecting neural stimulation with magnetic fields.

High amplitude magnetic field pulses produced by coils external to the body have been used for medical diagnosis since the mid-1980s to stimulate motor neurons in the brain cortex and peripheral nerves. While successful applications have since blossomed, it has only been during the last three years that quantitative dosimetric data have become available. The factors affecting neural stimulation can be divided into three categories broadly related to the characteristics of (i) the stimulus, (ii) the neuron, and (iii) the induced electric field as related to the configuration of the stimulating coil. The stimulus, in the case of magnetic field stimulation, has the form of an exponentially decaying pulse with a small overshoot of the opposite polarity. Physical and electrical properties of a neuron affect its electrical stimulation. Dosimetric considerations are limited to the linear model describing the threshold phenomena, where passive electrical properties and the cable model provide a reasonable approximation of neuron behavior. The electromagnetic variable responsible for stimulation is the spatial derivative of the induced electric field along the neuron axis. This paper examines the factors involved in eliciting threshold excitation of motor neurons by magnetic fields. The description of various factors is largely based on published data except for the analysis of the electromagnetic stimuli induced by various coils.

Animals↗

PubMedDate not supplied

[Limiting behavior of a model of the impulse activity of a neuron for large frequency of input flow and small contributions of a single synapse (non-diffusion approximation)].

The limit behavior of probability models of neuron's firing, viz. models with exponential decay and constant threshold is considered. These models differ from each other by F(v), distribution of jumps of potential after arrival of input impulse. If average number of input impulses arriving during the decaying time of one impulse in very large and threshold depolarisation, measured by unit of average jump of potential, is large too, than limit density of interspike interval distribution does not depend on form of F(v); and depends on other neuron's parameters mean and variance of F(v). Moreover, the form of this density depends on only one parameter--normalised threshold. Under this condition interspike interval distribution for diffusion model converges to the same limit. Lapase transform for limit distribution is found and results of its numeric inverts are given.

Action Potentials↗

PubMed1994

Objective detection of 40 Hz auditory evoked potentials: phase coherence vs. magnitude-squared coherence.

The relative performance of phase coherence (PC) and magnitude-squared coherence (MSC) for detection of steady-state evoked potentials was studied using 40 Hz auditory evoked potentials (AEPs) in 10 normal human subjects. In addition, simulation experiments were carried out to determine the effects of signal amplitude and phase variability on detection performance. All simulations showed MSC performance to be better than PC performance, with further improvements when MSC was supplemented with weighted averaging. However, human 40 Hz AEP data showed essentially identical detection performance for PC and MSC, with or without weighted averaging. These data support a "phase aggregation" model (at least near threshold) over the more usual model in which an AEP signal is added to a stationary noise. Human data collected under "no-stimulus" conditions agree well with theoretical distributions for both PC and MSC. For equal test time, long analysis periods (with less averaging) yielded equal performance to short analysis periods (with more averaging), for both PC and MSC.

Acoustic Stimulation↗

PubMed1999

Intensity discrimination of Gaussian-windowed tones: indications for the shape of the auditory frequency-time window.

The just-noticeable difference in intensity jnd(I) was measured for 1-kHz tones with a Gaussian-shaped envelope as a function of their spectro-temporal shape. The stimuli, with constant energy and a constant product of bandwidth and duration, ranged from a long-duration narrow-band "tone" to a short-duration broadband "click." The jnd(I) was measured in three normal-hearing listeners at sensation levels of 0, 10, 20, and 30 dB in 35 dB(A) SPL pink noise. At intermediate sensation levels, jnd(I) depends on the spectro-temporal shape: at the extreme shapes (tones and clicks), intensity discrimination performance is best, whereas at intermediate shapes the jnd(I) is larger. Similar results are observed at a higher overall sound level, and at a higher carrier frequency. The maximum jnd(I) is observed for stimuli with an effective bandwidth of about 1/3 octave and an effective duration of 4 ms at 1 kHz (1 ms at 4 kHz). A generalized multiple-window model is proposed that assumes that the spectro-temporal domain is partitioned into "internal" auditory frequency-time windows. The model predicts that intensity discrimination thresholds depend upon the number of windows excited by a signal: jnd(I) is largest for stimuli covering one window.

Adult↗