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Biomedical subjects

W Gerstner

Publications and source records attributed to W Gerstner.

At least 19 recordsLinked to original sources
PubMed2000

Noise in integrate-and-fire neurons: from stochastic input to escape rates.

We analyze the effect of noise in integrate-and-fire neurons driven by time-dependent input and compare the diffusion approximation for the membrane potential to escape noise. It is shown that for time-dependent subthreshold input, diffusive noise can be replaced by escape noise with a hazard function that has a gaussian dependence on the distance between the (noise-free) membrane voltage and threshold. The approximation is improved if we add to the hazard function a probability current proportional to the derivative of the voltage. Stochastic resonance in response to periodic input occurs in both noise models and exhibits similar characteristics.

Membrane Potentials↗
PubMed2000

Population dynamics of spiking neurons: fast transients, asynchronous states, and locking.

An integral equation describing the time evolution of the population activity in a homogeneous pool of spiking neurons of the integrate-and-fire type is discussed. It is analytically shown that transients from a state of incoherent firing can be immediate. The stability of incoherent firing is analyzed in terms of the noise level and transmission delay, and a bifurcation diagram is derived. The response of a population of noisy integrate-and-fire neurons to an input current of small amplitude is calculated and characterized by a linear filter L. The stability of perfectly synchronized"locked"solutions is analyzed.

Animals↗
PubMed1999

Noise shaping in populations of coupled model neurons.

Biological information-processing systems, such as populations of sensory and motor neurons, may use correlations between the firings of individual elements to obtain lower noise levels and a systemwide performance improvement in the dynamic range or the signal-to-noise ratio. Here, we implement such correlations in networks of coupled integrate-and-fire neurons using inhibitory coupling and demonstrate that this can improve the system dynamic range and the signal-to-noise ratio in a population rate code. The improvement can surpass that expected for simple averaging of uncorrelated elements. A theory that predicts the resulting power spectrum is developed in terms of a stochastic point-process model in which the instantaneous population firing rate is modulated by the coupling between elements.

Mathematics↗
PubMed1999

Cerebral vasodilatation causing acute intracranial hypertension: a method for noninvasive assessment.

Deep spontaneous vasodilatatory events are frequently recorded in various cerebral diseases, causing dramatic increases (A-waves) in intracranial pressure (ICP) and subsequently provoking ischemic brain insults. The relationship between fluctuations in CBF, ICP, and arterial blood pressure (ABP) is influenced by properties of cerebrovascular control mechanisms and the cerebrospinal pressure-volume compensation. The goal of this study was to construct a mathematical model of this relationship and to assess its ability to predict the occurrence and time course of A-waves. A group of 17 severely head-injured patients were included in the study. In our model ICP was derived from the ABP waveform using a linear signal transformation. The transformation was modified during the simulation by a relationship between ABP and flow velocity, i.e., by the characterization of the cerebrovascular bed. In this way the ICP could be calculated from the ABP waveform. This model was verified by comparison of simulated and directly measured ICP during A-waves recorded in seven of the patients. In all simulations, plateau elevations of ICP were well replicated. The mean absolute error between real and simulated ICP was 8.3 +/- 5.4 mm Hg at the baseline and 7.9 +/- 4.3 mm Hg at the top of plateau waves. The correlation coefficient between real and simulated increase in ICP was R = 0.98; P < .001. Similarly, correlation between real and simulated increase in pulse amplitude of ICP was highly significant (R = 0.94; P < .001). The mathematical model of the relationship between ABP, flow velocity, and ICP is of potential clinical use for the noninvasive detection of A-waves in patients in whom invasive ICP assessment is not conducted.

Adolescent↗
PubMed1999

Noise spectrum and signal transmission through a population of spiking neurons.

How reliably can a population of spiking neurons transmit a continuous-time signal? We study the noise spectrum of a fully connected population of spiking neurons with relative and absolute refractoriness. Spikes are generated stochastically with a rate that depends on the postsynaptic potential. The analytical solution of the noise spectrum of the population activity is compared with simulations. We find that strong inhibitory couplings can considerably reduce the noise level in a certain frequency band. This allows the population to reliably transmit signals at frequencies close to or even above the single-neuron firing rate.

Action Potentials↗
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↗
PubMed1998

Analysis of a correlation-based model for the development of orientation-selective receptive fields in the visual cortex.

We analyse a model for the development of orientation-selective receptive fields of simple cells in a locally connected network of cortical neurons. The Hebbian learning rule that underlies the development is described by a linear differential equation. The structure of the emerging cortical map can be predicted by deriving the eigenfunctions corresponding to the leading eigenvalues of the associated matrix. We show that the receptive fields have the typical form of a wavelet. Mathematically, receptive fields are given by a Hermitian polynomial with Gaussian cut-off and a phase factor. Both the phase of the wavelet and the orientation are changing periodically along the surface of the cortical map as suggested by previous simulation studies and as also found in experiments. In order to get orientation-selective receptive fields, the spatial correlation function of the inputs that drive the development must have a zero crossing.

Algorithms↗
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↗