Successive Spikes Research Articles

Simple model to incorporate statistical noise based on a modified hodgkin-huxley approach for external electrical field driven neural responses

Noise activity is known to affect neural networks, enhance the system response to weak external signals, and lead to stochastic resonance phenomenon that can effectively amplify signals in nonlinear systems. In most treatments, channel noise has been modeled based on multi-state Markov descriptions or the use stochastic differential equation models. Here we probe a computationally simple approach based on a minor modification of the traditional Hodgkin-Huxley approach to embed noise in neural response. Results obtained from numerous simulations with different excitation frequencies and noise amplitudes for the action potential firing show very good agreement with output obtained from well-established models. Furthermore, results from the Mann–Whitney U Test reveal a statistically insignificant difference. The distribution of the time interval between successive potential spikes obtained from this simple approach compared very well with the results of complicated Fox and Lu type methods at much reduced computational cost. This present method could also possibly be applied to the analysis of spatial variations and/or differences in characteristics of random incident electromagnetic signals.

Intrinsic and Synaptic Contributions to Repetitive Spiking in Dentate Granule Cells.

Repetitive firing of granule cells (GCs) in the dentate gyrus (DG) facilitates synaptic transmission to the CA3 region. This facilitation can gate and amplify the flow of information through the hippocampus. High-frequency bursts in the DG are linked to behavior and plasticity, but GCs do not readily burst. Under normal conditions, a single shock to the perforant path in a hippocampal slice typically drives a GC to fire a single spike, and only occasionally more than one spike is seen. Repetitive spiking in GCs is not robust, and the mechanisms are poorly understood. Here, we used a hybrid genetically encoded voltage sensor to image voltage changes evoked by cortical inputs in many mature GCs simultaneously in hippocampal slices from male and female mice. This enabled us to study relatively infrequent double and triple spikes. We found GCs are relatively homogeneous and their double spiking behavior is cell autonomous. Blockade of GABA type A receptors increased multiple spikes and prolonged the interspike interval, indicating inhibitory interneurons limit repetitive spiking and set the time window for successive spikes. Inhibiting synaptic glutamate release showed that recurrent excitation mediated by hilar mossy cells contributes to, but is not necessary for, multiple spiking. Blockade of T-type Ca2+ channels did not reduce multiple spiking but prolonged interspike intervals. Imaging voltage changes in different GC compartments revealed that second spikes can be initiated in either dendrites or somata. Thus, pharmacological and biophysical experiments reveal roles for both synaptic circuitry and intrinsic excitability in GC repetitive spiking.

Experimental and numerical study of wave-in-deck loads due to oblique transient wave groups

Wave-in-deck loads due to 45° oblique transient focus wave groups are investigated using model-scale experiments and computational fluid dynamics simulations with emphasis on comparing with head-on wave impacts for a solid cuboid deck model without and with an I-beam grillage beneath. After validation with experiments, numerical results are extended to consider wave-in-deck loads with 22.5° and 67.5° oblique wave directions. Generally, the head-on wave impacts cause larger longitudinal forces on the deck whereas the oblique cases result in larger downward vertical forces. For the deck with grillage case, Santo et al. (2020) and Wang et al. (2022) show that successive large spikes are observed in the force time series of head-on wave impact due to entrapped air-pocket effects in the grillage. However, here it is found that the large spikes are absent in the force time series for the oblique wave impacts and the patterns of forces are similar to the deck without grillage with rather small or no spikes in the force time series. Interrogation of the numerical flowfield reveals evidence that the asynchronous and less effective air entrapment in the grillage for the oblique cases are responsible for the difference. The maximum positive pressure on the underside of the deck is found to be much larger for the deck with grillage than without due to local slamming of jets formed in the grillage.

Analysis of spatio-temporal propagation of occipito-frontal spikes in childhood epilepsies by 3D sequential voltage mapping and dipole localization.

We sought to study the spatio-temporal propagation of occipito-frontal spikes in childhood epilepsies by voltage mapping and dipole localization and identify types of occipito-frontal spikes based on onset, propagation, and stability of their dipoles. Sleep EEG data of children, aged 1-14 years, with a minimum 1 h of recording from June 2018 to June 2021, were analyzed to identify occipito-frontal spikes. In total, 150 successive occipito-frontal spikes were manually selected from each EEG and using a source localization software were averaged using automated pattern matching with a threshold of 80%, and sequential 3D voltage maps of averaged spike were analyzed. Stability quotient (SQ) was calculated as the total number of averages/150. Stable dipole was defined as SQ ≥ .8. Dipole analysis was performed with principal component analysis using an age-appropriate template head model. Ten children with occipito-frontal spikes were identified; five with self-limited epilepsy with autonomic seizures (SeLEAS) and five with non-SeLEAS epilepsies. Three types of occipito-frontal spikes were identified: (1) narrow occipito-frontal spikes with stable dipoles seen in all five children with SeLEAS which were "apparently" synchronous and bilateral clone-like with an occipito-frontal interval of 10-30 ms and a homogeneous propagation pattern from a unilateral medial parieto-occipital region to an ipsilateral mesial frontal region; (2) wide occipito-frontal spikes with stable dipoles seen in one child with non-SeLEAS and developmental and/or epileptic encephalopathy with spike-wave activation in sleep (D/EE-SWAS) with an occipito-frontal interval of 45 ms, caused by focal spike propagation from a deeper temporal focus to ipsilateral peri-rolandic cortex; and (3) wide occipito-frontal spikes with unstable dipoles seen in four children with non-SeLEAS lesional epilepsies with an occipito-frontal latency of >50 ms and heterogeneous propagation patterns with poor intra-individual dipole stability. We successfully identified different types of occipito-frontal spikes in childhood epilepsies. Although the term "occipito-frontal" is used to describe these spikes on the 10-20 EEG system, true propagation from occipital to frontal regions is not necessary. It is possible to differentiate idiopathic from symptomatic cases by analyzing the stability quotient and the occipito-frontal interval of occipito-frontal spikes.

Spontaneous activity in cortical neurons is stereotyped and non-Poisson.

Neurons fire even in the absence of sensory stimulation or task demands. Numerous theoretical studies have modeled this spontaneous activity as a Poisson process with uncorrelated intervals between successive spikes and a variance in firing rate equal to the mean. Experimental tests of this hypothesis have yielded variable results, though most have concluded that firing is not Poisson. However, these tests say little about the ways firing might deviate from randomness. Nor are they definitive because many different distributions can have equal means and variances. Here, we characterized spontaneous spiking patterns in extracellular recordings from monkey, cat, and mouse cerebral cortex neurons using rate-normalized spike train autocorrelation functions (ACFs) and a logarithmic timescale. If activity was Poisson, this function should be flat. This was almost never the case. Instead, ACFs had diverse shapes, often with characteristic peaks in the 1-700ms range. Shapes were stable over time, up to the longest recording periods used (51min). They did not fall into obvious clusters. ACFs were often unaffected by visual stimulation, though some abruptly changed during brain state shifts. These behaviors may have their origin in the intrinsic biophysics and dendritic anatomy of the cells or in the inputs they receive.

Wave impacts on a solid deck in transient wave groups

Wave impacts on an elevated solid deck due to transient focused wave groups are studied numerically. Previously reported experiments with and without an I-beam grillage beneath the deck by Santo et al. (2020) are reproduced successfully in a three-dimensional numerical wave tank based on a two-phase Navier–Stokes solver. The impact loads on the solid deck are relatively simple. The three-dimensional horizontal force, characterised by a single peak in time, is close to two-dimensional, whereas the vertical force consists of upward force and downward suction force. The downward suction force is related to triangularisation of the wetted area underneath the deck and dominated by the added mass effect, which is a three-dimensional effect and therefore any two-dimensional simulation will overpredict the strongly three-dimensional process and the vertical impact loads. The wave impact loads on the solid deck with a grillage are more complicated, with successive force spikes observed for both the horizontal and vertical loads. The significance of entrapped air pockets in the grillage to global wave impact loads is ascertained through interrogating flow field of numerical experiments. It is found that large upward vertical impulsive forces are caused by high local pressures when entrapped down-wave air-pockets are formed, while large downward suction forces are resulted from both high-frequency up-wave air-pocket effect and the low-frequency added mass effect. Large horizontal impulsive forces are due to the combined effects of the down-wave air-pocket and the upward jetting motion of the wave crests. The entrapped air-pocket effects are found to be more important for vertical than horizontal forces.

Nonlinear mechanism for the enhanced bursting activities induced by fast inhibitory autapse and reduced activities by fast excitatory autapse.

The paradoxical phenomena that excitatory modulation does not enhance but reduces or inhibitory modulation not suppresses but promotes neural firing activities have attracted increasing attention. In the present study, paradoxical phenomena induced by both fast excitatory and inhibitory autapses in a "Fold/Big Homoclinic" bursting are simulated, and the corresponding nonlinear and biophysical mechanisms are presented. Firstly, the enhanced conductance of excitatory autapse induces the number of spikes per burst and firing rate reduced, while the enhanced inhibitory autapse cause both indicators increased. Secondly, with fast-slow variable dissection, the burst of bursting is identified to locate between a fold bifurcation and a big saddle-homoclinic orbit bifurcation of the fast subsystem. Enhanced excitatory or inhibitory autapses cannot induce changes of both bifurcation points, i.e., burst width. However, width of slow variable between two successive spikes within a burst becomes wider for the excitatory autapse and narrower for the inhibitory autapse, resulting in the less and more spikes per burst, respectively. Last, the autaptic current of fast autapse mainly plays a role during the peak of action potential, differing from the slow autaptic current with exponential decay, which can play roles following the peak of action potential. The fast excitatory autaptic current enhances the amplitude of the action potential and reduces the repolarization of the action potential to lengthen the interspike interval (ISI) of the spiking of the fast subsystem, resulting in the wide width of slow variable between successive spikes. The fast inhibitory autaptic current reduces the amplitude of action potential and ISI of spiking, resulting in narrow width of slow variable. The novel example of the paradoxical responses for both fast modulations and nonlinear mechanism extend the contents of neurodynamics, which presents potential functions of the fast autapse.

Multiple Phase Transitions for an Infinite System of Spiking Neurons

We consider a stochastic model describing the spiking activity of a countable set of neurons spatially organized into a homogeneous tree of degree $d$, $d \geq 2$; the degree of a neuron is just the number of connections it has. Roughly, the model is as follows. Each neuron is represented by its membrane potential, which takes non-negative integer values. Neurons spike at Poisson rate 1, provided they have strictly positive membrane potential. When a spike occurs, the potential of the spiking neuron changes to 0, and all neurons connected to it receive a positive amount of potential. Moreover, between successive spikes and without receiving any spiking inputs from other neurons, each neuron's potential behaves independently as a pure death process with death rate $\gamma \geq 0$. In this article, we show that if the number $d$ of connections is large enough, then the process exhibits at least two phase transitions depending on the choice of rate $\gamma$: For large values of $\gamma$, the neural spiking activity almost surely goes extinct; For small values of $\gamma$, a fixed neuron spikes infinitely many times with a positive probability, and for "intermediate" values of $\gamma$, the system has a positive probability of always presenting spiking activity, but, individually, each neuron eventually stops spiking and remains at rest forever.

Integrating peroxidase-mimicking NH2-MIL-101(Fe) with molecular imprinting for high-performance ratiometric fluorescence sensing of domoic acid

Ingestion of shellfish and water containing excessive domoic acid (DA) threatens human health tremendously, and even causes death in severe cases. Herein, we have integrated the bifunctional NH2-MIL-101(Fe) with molecular imprinting to design a ratiometric fluorescent sensor for quantitative analysis of DA. In this research, NH2-MIL-101(Fe) itself can supply an intrinsic peak at 452 nm, and trigger oxidation of o-phenylenediamine (OPD) to 2,3-diaminophenazine (DAP) with peak at 556 nm owing to its excellent peroxidase-like activity. The two signal probes that influence each other owing to the inner filter effect (IFE) can form a highly sensitive composite fluorescent probe. Additionally, the introduction of molecular imprinting technology (MIT) instead of expensive antibodies can endow the ratiometric fluorescent sensor outstanding selectivity and specificity toward DA. Thus, the proposed ratiometric fluorescent sensor exhibits outstanding sensitivity, super anti-interference ability, and excellent selectivity. The experimental results demonstrate that the sensor exhibits good performance for DA sensing in the scope of 0.01–10 μM with low limit of detection (LOD) as 8.2 nM. More attractively, the successful spike and recovery experiments in real samples with the complicated matrix indicate the considerable practical application promise of our proposed ratiometric fluorescent sensor.

Investigating well potential parameters on neural spike enhancement in a stochastic-resonance pre-emphasis algorithm

Objective. Background noise experienced during extracellular neural recording limits the number of spikes that can be reliably detected, which ultimately limits the performance of next-generation neuroscientific work. In this study, we aim to utilize stochastic resonance (SR), a technique that can help identify weak signals in noisy environments, to enhance spike detectability. Approach. Previously, an SR-based pre-emphasis algorithm was proposed, where a particle inside a 1D potential well is exerted by a force defined by the extracellular recording, and the output is obtained as the displacement of the particle. In this study, we investigate how the well shape and damping status impact the output signal-to-noise ratio (SNR). We compare the overdamped and underdamped solutions of shallow- and steep-wall monostable wells and bistable wells in terms of SNR improvement using two synthetic datasets. Then, we assess the spike detection performance when thresholding is applied on the output of the well shape-damping status configuration giving the best SNR enhancement. Main results. The SNR depends on the well-shape and damping-status type as well as the input noise level. The underdamped solution of the shallow-wall monostable well can yield to more than four orders of magnitude greater SNR improvement compared to other configurations for low noise intensities. Using this configuration also results in better spike detection sensitivity and positive predictivity than the state-of-the-art spike detection algorithms for a public synthetic dataset. For larger noise intensities, the overdamped solution of the steep-wall monostable well provides better spike enhancement than the others. Significance. The dependence of SNR improvement on the input signal noise level can be used to design a detector with multiple outputs, each more sensitive to a certain distance from the electrode. Such a detector can potentially enhance the performance of a successive spike sorting stage.

Maximum Likelihood Estimation for an Ornstein–Uhlenbeck Model for Neural Activity

The Ornstein–Uhlenbeck process arises from a leaky stochastic integrate-and-fire model of the membrane potential of a neuron, in which its firing corresponds to the first time the process hits a barrier. We address the problem of estimating the parameters of the underlying process when the available data are the neuron’s successive spikes, or spike train. The first-hitting time density is not tractable, so we use its Laplace transform to determine the identifiable parameters of the model, show that their maximum likelihood estimates are consistent and asymptotically normal, and describe computational methods to obtain the estimates and their standard errors.

Analysis of Whole-Body Coordination Patterning in Successful and Faulty Spikes Using Self-Organising Map-Based Cluster Analysis: A Secondary Analysis.

This study investigated the whole-body coordination patterning in successful and faulty spikes using self-organising map-based cluster analysis. Ten young, elite volleyball players (aged 15.5 ± 0.7 years) performed 60 volleyball spikes in a real-game environment. Adopting the cluster analysis, based on a self-organising map, whole-body coordination patterning was explored between successful and faulty spikes of individual players. The self-organising maps (SOMs) portrayed whole body, lower and upper limb coordination dissimilarities during the jump phase and the ball impact phases between the successful and faulty spikes. The cluster analysis illustrated that the whole body, upper limb and lower limb coordination patterning of each individual’s successful spikes were similar to their faulty spikes. Range of motion patterning also demonstrated no differences in kinematics between spike outcomes. Further, the upper limb angular velocity patterning of the players’ successful/faulty spikes were similar. The SPM analysis portrayed significant differences between the normalized upper limb angular velocities from 35% to 45% and from 76% to 100% of the spike movement. Although the lower limb angular velocities are vital for achieving higher jumps in volleyball spikes, the results of this study portrayed that the upper limb angular velocities distinguish the differences between successful and faulty spikes among the attackers. This confirms the fact that volleyball coaches should shift their focus toward the upper limb velocity and coordination training for higher success rates in spiking for volleyball attackers.

Superradiance in Quantum Vacuum

A new process associated with the nonlinear optical properties of the electromagnetic quantum vacuum is described. It corresponds to the superradiant emission of photons, resulting from the interaction of an intense laser pulse with frequency ω0 with a counter-propagating high-harmonic signal with a spectrum of frequencies nω1, for n integer, in the absence of matter. Under certain conditions, photon emission from vacuum will be enhanced by the square of the number of intense spikes associated with the high-harmonic pulse. This occurs when the field created by the successive spikes is coherently emitted, as in typical superradiant processes involving atoms. Subradiant conditions, where the nonlinearity of quantum vacuum is entirely suppressed, can equally be defined.

Hopf bifurcation in a Mean-Field model of spiking neurons

We study a family of non-linear McKean-Vlasov SDEs driven by a Poisson measure, modelling the mean-field asymptotic of a network of generalized Integrate-and-Fire neurons. We give sufficient conditions to have periodic solutions through a Hopf bifurcation. Our spectral conditions involve the location of the roots of an explicit holomorphic function. The proof relies on two main ingredients. First, we introduce a discrete time Markov Chain modeling the phases of the successive spikes of a neuron. The invariant measure of this Markov Chain is related to the shape of the periodic solutions. Secondly, we use the Lyapunov-Schmidt method to obtain self-consistent oscillations. We illustrate the result with a toy model for which all the spectral conditions can be analytically checked.

Kinematic differences between successful and faulty spikes in young volleyball players

ABSTRACT This study was designated to investigate the kinematical differences between successful and faulty spikes, in order to identify the best strategies leading to better spike performance. Simulating a real-game condition, 13 elite youth attackers performed 6 spikes in the presence of 2 blocks. The kinematic variables of the spike performances were recorded using 6 optoelectronic cameras (Vicon Motion systems, Oxford, UK). The paired sample t-test was used to compare the kinematic variables recorded during the delivery of successful and faulty spikes. Among the successful trials, both the angular velocities of the knees (≈12.4%) and hips (≈13.3%), and the vertical velocity of the centre of mass at take-off (≈6.5%) and arm swing (≈8.2%) were considerably higher during the plant phase. Consequently, the jump (≈4.3%) and spike (≈1.5%) heights, as well as the wrist velocity (≈5.5%), were significantly higher during the jump phase of successful spikes. In successful spike performances, the attackers adopted higher hip and knee angular velocities, combined with efficient arm swings, to produce higher take-off velocities and reach higher jump heights. This approach provides them with the better position regarding the ball and the blockers to find the best path and hit the ball with higher arm velocities.

Conditional propagation of chaos for mean field systems of interacting neurons

We study the stochastic system of interacting neurons introduced in [5] and in [10] in a diffusive scaling. The system consists of N neurons, each spiking randomly with rate depending on its membrane potential. At its spiking time, the potential of the spiking neuron is reset to 0 and all other neurons receive an additional amount of potential which is a centred random variable of order 1∕ N. In between successive spikes, each neuron’s potential follows a deterministic flow. We prove the convergence of the system, as N→∞, to a limit nonlinear jumping stochastic differential equation driven by Poisson random measure and an additional Brownian motion W which is created by the central limit theorem. This Brownian motion is underlying each particle’s motion and induces a common noise factor for all neurons in the limit system. Conditionally on W, the different neurons are independent in the limit system. This is the conditional propagation of chaos property. We prove the well-posedness of the limit equation by adapting the ideas of [12] to our frame. To prove the convergence in distribution of the finite system to the limit system, we introduce a new martingale problem that is well suited for our framework. The uniqueness of the limit is deduced from the exchangeability of the underlying system.

A Template-Based Sequential Algorithm for Online Clustering of Spikes in Extracellular Recordings

In order to discriminate different spikes in an extracellular recording, a multitude of successful spike sorting algorithms has been proposed up to now. However, new implantable neuroprosthetics containing a spike sorting block necessitate the use of a real-time and a preferably unsupervised method. The aim of this article is to propose a new unsupervised spike sorting algorithm which could work in real-time. As opposed to most traditional frameworks that consist of separate noise cancelation and feature extraction steps, here a sequential algorithm is proposed which makes use of noise statistics and uses data samples as features. For each detected spike, the difference between the detected spike and all the previously detected spike templates are calculated. If the output is a signal similar to noise, this indicates that the new spike is fired from a previously observed neuron. Two varieties of the general method are illustrated and a set of clustering indices which determine an optimal clustering is used to set the parameters. Clustering indices surpassed 0.90 (out of 1) for synthetic data with modest noise level. Experiments with our recorded signals showed satisfactory results in clustering and template identification. Spike sorting is an active field. A deficiency in conventional spike sorting algorithms is that most of them are either supervised or offline. Here, we present an online unsupervised algorithm which could be developed as a solution for current neuroprosthetics. Since the present method clustered real spikes data appropriately without a need for training data, the methodology could be adapted to be used in implantable devices.

A System of Interacting Neurons with Short Term Synaptic Facilitation

In this paper we present a simple microscopic stochastic model describing short term plasticity within a large homogeneous network of interacting neurons. Each neuron is represented by its membrane potential and by the residual calcium concentration within the cell at a given time. Neurons spike at a rate depending on their membrane potential. When spiking, the residual calcium concentration of the spiking neuron increases by one unit. Moreover, an additional amount of potential is given to all other neurons in the system. This amount depends linearly on the current residual calcium concentration within the cell of the spiking neuron. In between successive spikes, the potentials and the residual calcium concentrations of each neuron decrease at a constant rate. We show that in this framework, short time memory can be described as the tendency of the system to keep track of an initial stimulus by staying within a certain region of the space of configurations during a short but macroscopic amount of time before finally being kicked out of this region and relaxing to equilibrium. The main technical tool is a rigorous justification of the passage to a large population limit system and a thorough study of the limit equation.

Autophosphorylated CaMKII Facilitates Spike Propagation in Rat Optic Nerve.

Repeated spike firing can transmit information at synapses and modulate spike timing, shape, and conduction velocity. These latter effects have been found to result from voltage-induced changes in ion currents and could alter the signals carried by axons. Here, we test whether Ca2+/calmodulin-dependent protein kinase II (CaMKII) regulates spike propagation in adult rat optic nerve. We find that small-, medium-, and large-diameter axons bind anti-Thr286-phosphorylated CaMKII (pT286) antibodies and that, in isolated optic nerves, electrical stimulation reduces pT286 levels, spike propagation is hastened by CaMKII autophosphorylation and slowed by CaMKII dephosphorylation, single and multiple spikes slow propagation of subsequently activated spikes, and more frequent stimulation produces greater slowing. Likewise, exposing freely moving animals to flickering illumination reduces pT286 levels in optic nerves and electrically eliciting spikes in vivo in either the optic nerve or optic chiasm slows subsequent spike propagation in the optic nerve. By increasing the time that elapses between successive spikes as they propagate, pT286 dephosphorylation and activity-induced spike slowing reduce the frequency of propagated spikes below the frequency at which they were elicited and would thus limit the frequency at which axons synaptically drive target neurons. Consistent with this, the ability of retinal ganglion cells to drive at least some lateral geniculate neurons has been found to increase when presented with light flashes at low and moderate temporal frequencies but less so at high frequencies. Activity-induced decreases in spike frequency may also reduce the energy required to maintain normal intracellular Na+ and Ca2+ levels.SIGNIFICANCE STATEMENT By propagating along axons at constant velocities, spikes could drive synapses as frequently as they are initiated. However, the onset of spiking has been found to alter the conduction velocity of subsequent ("follower") spikes in various preparations. Here, we find that spikes reduce spike frequency in rat optic nerve by slowing follower spike propagation and that electrically stimulated spiking ex vivo and spike-generating flickering illumination in vivo produce net decreases in axonal Ca2+/calmodulin-dependent protein kinase II (CaMKII) autophosphorylation. Consistent with these effects, propagation speed increases and decreases, respectively, with CaMKII autophosphorylation and dephosphorylation. Lowering spike frequency by CaMKII dephosphorylation is a novel consequence of axonal spiking and light adaptation that could decrease synaptic gain as stimulus frequency increases and may also reduce energy use.

Hypoelliptic stochastic FitzHugh–Nagumo neuronal model: Mixing, up-crossing and estimation of the spike rate

The FitzHugh–Nagumo is a well-known neuronal model that describes the generation of spikes at the intracellular level. We study a stochastic version of the model from a probabilistic point of view. The hypoellipticity is proved, as well as the existence and uniqueness of the stationary distribution. The bi-dimensional stochastic process is $\beta$-mixing. The stationary density can be estimated with an adaptive nonparametric estimator. Then we focus on the distribution of the length between successive spikes. Spikes are difficult to define directly from the continuous stochastic process. We study the distribution of the number of up-crossings. We link it to the stationary distribution and propose an estimator of its expectation. We finally prove mathematically that the mean length of inter-up-crossings interval is equal to its up-crossings rate. We illustrate the proposed estimators on a simulation study. Different regimes are explored, with no, few or high generation of spikes.