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W Gerstner

Publications and source records attributed to W Gerstner.

18 recordsLinked to original sources
PubMed1998

Extracting oscillations. Neuronal coincidence detection with noisy periodic spike input.

How does a neuron vary its mean output firing rate if the input changes from random to oscillatory coherent but noisy activity? What are the critical parameters of the neuronal dynamics and input statistics? To answer these questions, we investigate the coincidence-detection properties of an integrate-and-fire neuron. We derive an expression indicating how coincidence detection depends on neuronal parameters. Specifically, we show how coincidence detection depends on the shape of the postsynaptic response function, the number of synapses, and the input statistics, and we demonstrate that there is an optimal threshold. Our considerations can be used to predict from neuronal parameters whether and to what extent a neuron can act as a coincidence detector and thus can convert a temporal code into a rate code.

Membrane Potentials↗
PubMed1997

Neural codes: firing rates and beyond.

Computational neuroscience has contributed significantly to our understanding of higher brain function by combining experimental neurobiology, psychophysics, modeling, and mathematical analysis. This article reviews recent advances in a key area: neural coding and information processing. It is shown that synapses are capable of supporting computations based on highly structured temporal codes. Such codes could provide a substrate for unambiguous representations of complex stimuli and be used to solve difficult cognitive tasks, such as the binding problem. Unsupervised learning rules could generate the circuitry required for precise temporal codes. Together, these results indicate that neural systems perform a rich repertoire of computations based on action potential timing.

Action Potentials↗
PubMed1997

Therapeutic management of grade IV aneurysm patients.

BACKGROUND: The timing of surgery in patients suffering from subarachnoid hemorrhage grade IV and V according to Hunt and Hess, is still controversial. Several authors advocate early surgery for patients in poor clinical condition. Improved outcome and decreased mortality rates were reported. Others exclude patients in poor condition from early aneurysm surgery. METHODS: Forty grade IV aneurysm patients were admitted to our department. After ventriculostomy and cerebral angiography, 28 of them were operated on within 72 hours. The postoperative treatment included hypertensive, hypervolemic, hemodilutional therapy (triple-H therapy) and intensive monitoring (intracerebral pressure, blood pressure, hemodynamic parameters). The mean follow-up time was 6 months. RESULTS: Out of the 28 patients who underwent early surgery, 64% were in good health, 11% in poor health, 25% died; there were no survivors in a vegetative state. Twelve patients were treated conservatively; 50% died from infarction and rebleeding, before the operation was performed. Six underwent delayed aneurysm surgery after clinical improvement. In this group, 25% had good clinical outcome. CONCLUSIONS: Our results favor an aggressive treatment of grade IV aneurysm patients by means of ventricular drainage, early surgery and triple-H therapy.

Critical Care↗
PubMed1997

Learning navigational maps through potentiation and modulation of hippocampal place cells.

We analyze a model of navigational map formation based on correlation-based, temporally asymmetric potentiation and depression of synapses between hippocampal place cells. We show that synaptic modification during random exploration of an environment shifts the location encoded by place cell activity in such a way that it indicates the direction from any location to a fixed target avoiding walls and other obstacles. Multiple maps to different targets can be simultaneously stored if we introduce target-dependent modulation of place cell activity. Once maps to a number of target locations in a given environment have been stored, novel maps to previously unknown target locations are automatically constructed by interpolation between existing maps.

Animals↗
PubMed1997

Three-dimensional computer-assisted stereotactic-guided microneurosurgery combined with cortical mapping of the motor area by direct electrostimulation.

TIM (Zeppelin Chirurgische Instrumente GmbH, 82 049 Pullach, Germany) is a tomographic imaging system which enables surgeons to visualize the pathologic lesions three dimensionally in relationship to the surrounding structures. The distance and the angle between the pathologic lesion and the anatomical and/or bony landmarks as well as the volume of the mass lesion can be measured. Therefore an accurate localization of the lesion is possible with this technique. It is very applicable for planning of surgery on skull base tumors. The surgical procedure for small and well-defined, intrinsic pathologic deep-seated brain lesions, however, becomes much easier by using the stereotactic techniques of this system. The target point and the direction brain-surface-to-lesion can be determined within seconds. Before the aiming probe is inserted to the target, the cortical motor area is mapped by direct electrical stimulation. The approach can be varied depending on the results of these neurophysiologic investigations of the brain surface. The dissection is made along the aiming probe up to the target point. Because of the fixation of the brain with the needle, a brain shifting due to the dissection as well as to CSF release is diminished. Forty patients with deep-seated intracerebral lesions were operated on during a 13 months period by these combined techniques in our service. Using this technique, we never made a negative exploration. In all but three patients, total removal of the mass lesion was achieved. Permanent neurological deficits were observed in two patients only. In our opinion, this combined imaging and neurophysiological technique is easy to perform, and of major benefit for the patients due to its accuracy and is preferable in comparison with other single computer localizer techniques without neurophysiological monitoring.

Adolescent↗
PubMed1996

What matters in neuronal locking?

Exploiting local stability, we show what neuronal characteristics are essential to ensure that coherent oscillations are asymptotically stable in a spatially homogeneous network of spiking neurons. Under standard conditions, a necessary and, in the limit of a large number of interacting neighbors, also sufficient condition is that the postsynaptic potential is increasing in time as the neurons fire. If the postsynaptic potential is decreasing, oscillations are bound to be unstable. This is a kind of locking theorem and boils down to a subtle interplay of axonal delays, postsynaptic potentials, and refractory behavior. The theorem also allows for mixtures of excitatory and inhibitory interactions. On the basis of the locking theorem, we present a simple geometric method to verify the existence and local stability of a coherent oscillation.

Action Potentials↗
PubMed1996

A neuronal learning rule for sub-millisecond temporal coding.

A paradox that exists in auditory and electrosensory neural systems is that they encode behaviorally relevant signals in the range of a few microseconds with neurons that are at least one order of magnitude slower. The importance of temporal coding in neural information processing is not clear yet. A central question is whether neuronal firing can be more precise than the time constants of the neuronal processes involved. Here we address this problem using the auditory system of the barn owl as an example. We present a modelling study based on computer simulations of a neuron in the laminar nucleus. Three observations explain the paradox. First, spiking of an 'integrate-and-fire' neuron driven by excitatory postsynaptic potentials with a width at half-maximum height of 250 micros, has an accuracy of 25 micros if the presynaptic signals arrive coherently. Second, the necessary degree of coherence in the signal arrival times can be attained during ontogenetic development by virtue of an unsupervised hebbian learning rule. Learning selects connections with matching delays from a broad distribution of axons with random delays. Third, the learning rule also selects the correct delays from two independent groups of inputs, for example, from the left and right ear.

Animals↗
PubMed1996

Vertical signal flow and oscillations in a three-layer model of the cortex.

A model of vertical signal flow across a layered cortical structure is presented and analyzed. Neurons communicate through spikes, which evoke an excitatory or inhibitory postsynaptic potential (spike response model). The layers incorporate two anatomical features-dendritic and axonal arborization patterns and distance-dependent time delays. The vertical signal flow through the network is discussed for various stimulus conditions using two different, but typical, axonal arborization patterns. We find stationary as well as oscillatory response, but the oscillatory response may be restricted to a single layer. Confronted with conflicting stimuli the network separates the patterns through phase-shifted oscillations. We also discuss two hypothetical animals, to be called "cat" and "mouse." These have different axonal arborizations, which give rise to a different oscillatory response (if any) of the various layers.

Axons↗
PubMed1995

Intracellular Ca2+ stores can account for the time course of LTP induction: a model of Ca2+ dynamics in dendritic spines.

1. A model of Ca2+ dynamics in spines of CA1 hippocampal neurons is presented. In contrast to traditional models, which concentrate on the effects of Ca2+ influx, diffusion, buffering, and extrusion, we also consider the additional effect of intracellular Ca2+ stores. 2. It is shown that traditional models without Ca2+ stores cannot account for the time course of long-term potentiation (LTP) induction as found in recent experiments. Experimental data suggest that the intracellular Ca2+ concentration should be elevated for up to 2 s, whereas the Ca2+ concentration in standard models of Ca2+ dynamics decays much faster. 3. When intracellular Ca2+ stores are taken into account, a much slower decay is found. In particular, a model simulation with a stimulation paradigm consisting of two bursts of four impulses at 100 Hz each and variable interburst intervals can reproduce experimental results found for primed or theta-burst stimulation. 4. In our model, Ca2+ release from the store has a nonlinear, bell-shaped dependence on the intracellular Ca2+ concentration, similar to the one found for inositoltrisphosphate and ryanodine receptors. These receptors are known to control calcium release from intracellular stores. 5. Our model suggests an important role of intracellular calcium stores in the induction of LTP. The stores serve as a long-term calcium source that can sustain an intracellular Ca2+ concentration above the resting level for 1-2 s.

Animals↗
PubMed1995

Spontaneous excitations in the visual cortex: stripes, spirals, rings, and collective bursts.

As a simple model of the cortical sheet, we study a locally connected net of spiking neurons. Refractoriness, noise, axonal delays, and the time course of excitatory and inhibitory postsynaptic potentials are taken into account explicitly. In addition to a low-activity state and depending on the synaptic efficacy, four different scenarios evolve spontaneously, viz., stripes, spirals, rings, and collective bursts. Our results can be related to experimental observations of drug-induced epilepsy and hallucinations.

Action Potentials↗
PubMed1994

A biologically motivated and analytically soluble model of collective oscillations in the cortex. II. Application to binding and pattern segmentation.

Feature linking and pattern separation are shown to be performed as simultaneous processes by a highly connected auto-associative network of spiking neurons (spike response model). In principle, many (e.g., with nine) patterns can be separated, but with a biological set of parameters the number is limited to four. The patterns have been learned by an asymmetric hebbian rule that can handle a low activity which may vary from pattern to pattern (in a range between 4% and 7%). Spikes are generated by a threshold process and--with some delay--transmitted to postsynaptic neurons. There they evoke an excitatory or inhibitory postsynaptic potential (EPSP or IPSP). Spike emission is followed by an absolute refractory period (1 ms) and activates an inhibitory delay loop that prevents continuous firing. Three different network topologies are discussed, i.e., a structureless fully connected system, a network composed of two 'hemispheres', and finally a hierarchical network with four subsystems that represent different 'functions' and interact via feedforward and feedback connections. Functional feedback turns out to be essential for context-sensitive binding. The coherence between the two hemispheres is dependent on the interhemispheric delays. If these are on average too large, the two hemispheres oscillate coherently by themselves but phase-shifted by half a period with respect to each other.

Animals↗
PubMed1993

A biologically motivated and analytically soluble model of collective oscillations in the cortex. I. Theory of weak locking.

A model of an associative network of spiking neurons with stationary states, globally locked oscillations, and weakly locked oscillatory states is presented and analyzed. The network is close to biology in the following sense. First, the neurons spike and our model includes an absolute refractory period after each spike. Second, we consider a distribution of axonal delay times. Finally, we describe synaptic signal transmission by excitatory and inhibitory potentials (EPSP and IPSP) with a realistic shape, that is, through a response kernel. During retrieval of a pattern, all active neurons exhibit periodic spike bursts which may or may not be synchronized ('locked') into a coherent oscillation. We derive an analytical condition of locking and calculate the period of collective activity during oscillatory retrieval. In a stationary retrieval state, the overlap assumes a constant value proportional to the mean firing rate of the neurons. It is argued that in a biological network an intermediate scenario of 'weak locking' is most likely.

Animals↗
PubMed1993

Why spikes? Hebbian learning and retrieval of time-resolved excitation patterns.

Hebbian learning allows a network of spiking neurons to store and retrieve spatio-temporal patterns with a time resolution of 1 ms, despite the long postsynaptic and dendritic integration times. To show this, we introduce and analyze a model of spiking neurons, the spike response model, with a realistic distribution of axonal delays and with realistic postsynaptic potentials. Learning is performed by a local Hebbian rule which is based on the synchronism of presynaptic neurotransmitter release and some short-acting postsynaptic process. The time window of this synchronism determines the temporal resolution of pattern retrieval, which can be initiated by applying a short external stimulus pattern. Furthermore, a rate quantization is found in dependence upon the threshold value of the neurons, i.e., in a given time a pattern runs n times as often as learned, when n is a positive integer (n > or = 0). We show that all information about the spike pattern is lost if only mean firing rates (temporal average) or ensemble activities (spatial average) are considered. An average over several retrieval runs in order to generate a post-stimulus time histogram may also deteriorate the signal. The full information on a pattern is contained in the spike raster of a single run. Our results stress the importance, and advantage, of coding by spatio-temporal spike patterns instead of firing rates and average ensemble activity. The implications regarding modelling and experimental data analysis are discussed.

Animals↗
PubMed1992

Universality in neural networks: the importance of the 'mean firing rate'.

We present a general analysis of highly connected recurrent neural networks which are able to learn and retrieve a finite number of static patterns. The arguments are based on spike trains and their interval distribution and require no specific model of a neuron. In particular, they apply to formal two-state neurons as well as to more refined models like the integrate-and-fire neuron or the Hodgkin-Huxley equations. We show that the mean firing rate defined as the inverse of the mean interval length is the only relevant parameter (apart from the synaptic weights) that determines the existence of retrieval solutions with a large overlap with one of the learnt patterns. The statistics of the spiking noise (Gaussian, Poisson or other) and hence the shape of the interval distribution does not matter. Thus our unifying approach explains why, and when, all the different associative networks which treat static patterns yield basically the same results, i.e., belong to the same universality class.

Mathematics↗
PubMedDate not supplied

How the threshold of a neuron determines its capacity for coincidence detection.

Coherent oscillatory activity of a population of neurons is thought to be a vital feature of temporal coding in the brain. We focus on the question of whether a single neuron can transform a spike code into a rate code. More precisely, how does a neuron vary its mean output firing rate, if its input changes from random to coherent? We investigate the coincidence detection properties of an integrate-and-fire neuron in dependence upon internal parameters and input statistics. In particular, we show how coincidence detection depends on the membrane time constant and the threshold. Furthermore, we demonstrate that there is an optimal threshold for coincidence detection and that there is a broad range of near-optimal threshold values. Fine-tuning is not necessary.

Action Potentials↗