Magteld Zeitler

Assessing Neuronal Coherence with Single-Unit, Multi-Unit, and Local Field Potentials

The purpose of this study was to obtain a better understanding of neuronal responses to correlated input, in particular focusing on the aspect of synchronization of neuronal activity. The first aim was to obtain an analytical expression for the coherence between the output spike train and correlated input and for the coherence between output spike trains of neurons with correlated input. For Poisson neurons, we could derive that the peak of the coherence between the correlated input and multi-unit activity increases proportionally with the square root of the number of neurons in the multi-unit recording. The coherence between two typical multi-unit recordings (2 to 10 single units) with partially correlated input increases proportionally with the number of units in the multi-unit recordings. The second aim of this study was to investigate to what extent the amplitude and signal-to-noise ratio of the coherence between input and output varied for single-unit versus multi-unit activity and how they are affected by the duration of the recording. The same problem was addressed for the coherence between two single-unit spike series and between two multi-unit spike series. The analytical results for the Poisson neuron and numerical simulations for the conductance-based leaky integrate-and-fire neuron and for the conductance-based Hodgkin-Huxley neuron show that the expectation value of the coherence function does not increase for a longer duration of the recording. The only effect of a longer duration of the spike recording is a reduction of the noise in the coherence function. The results of analytical derivations and computer simulations for model neurons show that the coherence for multi-unit activity is larger than that for single-unit activity. This is in agreement with the results of experimental data obtained from monkey visual cortex (V4). Finally, we show that multitaper techniques greatly contribute to a more accurate estimate of the coherence by reducing the bias and variance in the coherence estimate.

Biased competition through variations in amplitude of gamma-oscillations.

Experiments in visual cortex have shown that the firing rate of a neuron in response to the simultaneous presentation of a preferred and non-preferred stimulus within the receptive field is intermediate between that for the two stimuli alone (stimulus competition). Attention directed to one of the stimuli drives the response towards the response induced by the attended stimulus alone (selective attention). This study shows that a simple feedforward model with fixed synaptic conductance values can reproduce these two phenomena using synchronization in the gamma-frequency range to increase the effective synaptic gain for the responses to the attended stimulus. The performance of the model is robust to changes in the parameter values. The model predicts that the phase locking between presynaptic input and output spikes increases with attention.

When Long-Range Zero-Lag Synchronization is Feasible in Cortical Networks.

Many studies have reported long-range synchronization of neuronal activity between brain areas, in particular in the beta and gamma bands with frequencies in the range of 14–30 and 40–80 Hz, respectively. Several studies have reported synchrony with zero phase lag, which is remarkable considering the synaptic and conduction delays inherent in the connections between distant brain areas. This result has led to many speculations about the possible functional role of zero-lag synchrony, such as for neuronal communication, attention, memory, and feature binding. However, recent studies using recordings of single-unit activity and local field potentials report that neuronal synchronization may occur with non-zero phase lags. This raises the questions whether zero-lag synchrony can occur in the brain and, if so, under which conditions. We used analytical methods and computer simulations to investigate which connectivity between neuronal populations allows or prohibits zero-lag synchrony. We did so for a model where two oscillators interact via a relay oscillator. Analytical results and computer simulations were obtained for both type I Mirollo–Strogatz neurons and type II Hodgkin–Huxley neurons. We have investigated the dynamics of the model for various types of synaptic coupling and importantly considered the potential impact of Spike-Timing Dependent Plasticity (STDP) and its learning window. We confirm previous results that zero-lag synchrony can be achieved in this configuration. This is much easier to achieve with Hodgkin–Huxley neurons, which have a biphasic phase response curve, than for type I neurons. STDP facilitates zero-lag synchrony as it adjusts the synaptic strengths such that zero-lag synchrony is feasible for a much larger range of parameters than without STDP.

Gamma oscillations as a mechanism for selective information transmission

In the past decades, many studies have focussed on the relation between the input and output of neurons with the aim to understand information processing by neurons. A particular aspect of neuronal information, which has not received much attention so far, concerns the problem of information transfer when a neuron or a population of neurons receives input from two or more (populations of) neurons, in particular when these (populations of) neurons carry different types of information. The aim of the present study is to investigate the responses of neurons to multiple inputs modulated in the gamma frequency range. By a combination of theoretical approaches and computer simulations, we test the hypothesis that enhanced modulation of synchronized excitatory neuronal activity in the gamma frequency range provides an advantage over a less synchronized input for various types of neurons. The results of this study show that the spike output of various types of neurons [i.e. the leaky integrate and fire neuron, the quadratic integrate and fire neuron and the Hodgkin–Huxley (HH) neuron] and that of excitatory–inhibitory coupled pairs of neurons, like the Pyramidal Interneuronal Network Gamma (PING) model, is highly phase-locked to the larger of two gamma-modulated input signals. This implies that the neuron selectively responds to the input with the larger gamma modulation if the amplitude of the gamma modulation exceeds that of the other signals by a certain amount. In that case, the output of the neuron is entrained by one of multiple inputs and that other inputs are not represented in the output. This mechanism for selective information transmission is enhanced for short membrane time constants of the neuron.

Augmented brain function by coordinated reset stimulation with slowly varying sequences.

Several brain disorders are characterized by abnormally strong neuronal synchrony. Coordinated Reset (CR) stimulation was developed to selectively counteract abnormal neuronal synchrony by desynchronization. For this, phase resetting stimuli are delivered to different subpopulations in a timely coordinated way. In neural networks with spike timing-dependent plasticity CR stimulation may eventually lead to an anti-kindling, i.e., an unlearning of abnormal synaptic connectivity and abnormal synchrony. The spatiotemporal sequence by which all stimulation sites are stimulated exactly once is called the stimulation site sequence, or briefly sequence. So far, in simulations, pre-clinical and clinical applications CR was applied either with fixed sequences or rapidly varying sequences (RVS). In this computational study we show that appropriate repetition of the sequence with occasional random switching to the next sequence may significantly improve the anti-kindling effect of CR. To this end, a sequence is applied many times before randomly switching to the next sequence. This new method is called SVS CR stimulation, i.e., CR with slowly varying sequences. In a neuronal network with strong short-range excitatory and weak long-range inhibitory dynamic couplings SVS CR stimulation turns out to be superior to CR stimulation with fixed sequences or RVS.

Hippocampal theta modulation of neocortical spike times and gamma rhythm: a biophysical model study

The hippocampal theta and neocortical gamma rhythms are two prominent examples of oscillatory neuronal activity. The hippocampus has often been hypothesized to influence neocortical networks by its theta rhythm, and, recently, evidence for such a direct influence has been found. We examined a possible mechanism for this influence by means of a biophysical model study using conductance-based model neurons. We found, in agreement with previous studies, that networks of fast-spiking GABA -ergic interneurons, coupled with shunting inhibition, synchronize their spike activity at a gamma frequency and are able to impose this rhythm on a network of pyramidal cells to which they are coupled. When our model was supplied with hippocampal theta-modulated input fibres, the theta rhythm biased the spike timings of both the fast-spiking and pyramidal cells. Furthermore, both the amplitude and frequency of local field potential gamma oscillations were influenced by the phase of the theta rhythm. We show that the fast-spiking cells, not pyramidal cells, are essential for this latter phenomenon, thus highlighting their crucial role in the interplay between hippocampus and neocortex.

Anti-kindling Induced by Two-Stage Coordinated Reset Stimulation with Weak Onset Intensity

Abnormal neuronal synchrony plays an important role in a number of brain diseases. To specifically counteract abnormal neuronal synchrony by desynchronization, Coordinated Reset (CR) stimulation, a spatiotemporally patterned stimulation technique, was designed with computational means. In neuronal networks with spike timing–dependent plasticity CR stimulation causes a decrease of synaptic weights and finally anti-kindling, i.e., unlearning of abnormally strong synaptic connectivity and abnormal neuronal synchrony. Long-lasting desynchronizing aftereffects of CR stimulation have been verified in pre-clinical and clinical proof of concept studies. In general, for different neuromodulation approaches, both invasive and non-invasive, it is desirable to enable effective stimulation at reduced stimulation intensities, thereby avoiding side effects. For the first time, we here present a two-stage CR stimulation protocol, where two qualitatively different types of CR stimulation are delivered one after another, and the first stage comes at a particularly weak stimulation intensity. Numerical simulations show that a two-stage CR stimulation can induce the same degree of anti-kindling as a single-stage CR stimulation with intermediate stimulation intensity. This stimulation approach might be clinically beneficial in patients suffering from brain diseases characterized by abnormal neuronal synchrony where a first treatment stage should be performed at particularly weak stimulation intensities in order to avoid side effects. This might, e.g., be relevant in the context of acoustic CR stimulation in tinnitus patients with hyperacusis or in the case of electrical deep brain CR stimulation with sub-optimally positioned leads or side effects caused by stimulation of the target itself. We discuss how to apply our method in first in man and proof of concept studies.

Short-Term Dosage Regimen for Stimulation-Induced Long-Lasting Desynchronization

In this paper, we computationally generate hypotheses for dose-finding studies in the context of desynchronizing neuromodulation techniques. Abnormally strong neuronal synchronization is a hallmark of several brain disorders. Coordinated Reset (CR) stimulation is a spatio-temporally patterned stimulation technique that specifically aims at disrupting abnormal neuronal synchrony. In networks with spike-timing-dependent plasticity CR stimulation may ultimately cause an anti-kindling, i.e., an unlearning of abnormal synaptic connectivity and neuronal synchrony. This long-lasting desynchronization was theoretically predicted and verified in several pre-clinical and clinical studies. We have shown that CR stimulation with rapidly varying sequences (RVS) robustly induces an anti-kindling at low intensities e.g., if the CR stimulation frequency (i.e., stimulus pattern repetition rate) is in the range of the frequency of the neuronal oscillation. In contrast, CR stimulation with slowly varying sequences (SVS) turned out to induce an anti-kindling more strongly, but less robustly with respect to variations of the CR stimulation frequency. Motivated by clinical constraints and inspired by the spacing principle of learning theory, in this computational study we propose a short-term dosage regimen that enables a robust anti-kindling effect of both RVS and SVS CR stimulation, also for those parameter values where RVS and SVS CR stimulation previously turned out to be ineffective. Intriguingly, for the vast majority of parameter values tested, spaced multishot CR stimulation with demand-controlled variation of stimulation frequency and intensity caused a robust and pronounced anti-kindling. In contrast, spaced CR stimulation with fixed stimulation parameters as well as singleshot CR stimulation of equal integral duration failed to improve the stimulation outcome. In the model network under consideration, our short-term dosage regimen enables to robustly induce long-term desynchronization at comparably short stimulation duration and low integral stimulation duration. Currently, clinical proof of concept is available for deep brain CR stimulation for Parkinsons therapy and acoustic CR stimulation for tinnitus therapy. Promising first in human data is available for vibrotactile CR stimulation for Parkinsons treatment. For the clinical development of these treatments it is mandatory to perform dose-finding studies to reveal optimal stimulation parameters and dosage regimens. Our findings can straightforwardly be tested in human dose-finding studies.

How stimulation frequency and intensity impact on the long-lasting effects of coordinated reset stimulation

Several brain diseases are characterized by abnormally strong neuronal synchrony. Coordinated Reset (CR) stimulation was computationally designed to specifically counteract abnormal neuronal synchronization processes by desynchronization. In the presence of spike-timing-dependent plasticity (STDP) this may lead to a decrease of synaptic excitatory weights and ultimately to an anti-kindling, i.e. unlearning of abnormal synaptic connectivity and abnormal neuronal synchrony. The long-lasting desynchronizing impact of CR stimulation has been verified in pre-clinical and clinical proof of concept studies. However, as yet it is unclear how to optimally choose the CR stimulation frequency, i.e. the repetition rate at which the CR stimuli are delivered. This work presents the first computational study on the dependence of the acute and long-term outcome on the CR stimulation frequency in neuronal networks with STDP. For this purpose, CR stimulation was applied with Rapidly Varying Sequences (RVS) as well as with Slowly Varying Sequences (SVS) in a wide range of stimulation frequencies and intensities. Our findings demonstrate that acute desynchronization, achieved during stimulation, does not necessarily lead to long-term desynchronization after cessation of stimulation. By comparing the long-term effects of the two different CR protocols, the RVS CR stimulation turned out to be more robust against variations of the stimulation frequency. However, SVS CR stimulation can obtain stronger anti-kindling effects. We revealed specific parameter ranges that are favorable for long-term desynchronization. For instance, RVS CR stimulation at weak intensities and with stimulation frequencies in the range of the neuronal firing rates turned out to be effective and robust, in particular, if no closed loop adaptation of stimulation parameters is (technically) available. From a clinical standpoint, this may be relevant in the context of both invasive as well as non-invasive CR stimulation.

Computationally Developed Sham Stimulation Protocol for Multichannel Desynchronizing Stimulation

A characteristic pattern of abnormal brain activity is abnormally strong neuronal synchronization, as found in several brain disorders, such as tinnitus, Parkinsons disease, and epilepsy. As observed in several diseases, different therapeutic interventions may induce a placebo effect that may be strong and hinder reliable clinical evaluations. Hence, to distinguish between specific, neuromodulation-induced effects and unspecific, placebo effects, it is important to mimic the therapeutic procedure as precisely as possibly, thereby providing controls that actually lack specific effects. Coordinated Reset (CR) stimulation has been developed to specifically counteract abnormally strong synchronization by desynchronization. CR is a spatio-temporally patterned multichannel stimulation which reduces the extent of coincident neuronal activity and aims at an anti-kindling, i.e., an unlearning of both synaptic connectivity and neuronal synchrony. Apart from acute desynchronizing effects, CR may cause sustained, long-lasting desynchronizing effects, as already demonstrated in pre-clinical and clinical proof of concept studies. In this computational study, we set out to computationally develop a sham stimulation protocol for multichannel desynchronizing stimulation. To this end, we compare acute effects and long-lasting effects of six different spatio-temporally patterned stimulation protocols, including three variants of CR, using a no-stimulation condition as additional control. This is to provide an inventory of different stimulation algorithms with similar fundamental stimulation parameters (e.g., mean stimulation rates) but qualitatively different acute and/or long-lasting effects. Stimulation protocols sharing basic parameters, but inducing nevertheless completely different or even no acute effects and/or after-effects, might serve as controls to validate the specific effects of particular desynchronizing protocols such as CR. In particular, based on our computational findings we propose a multichannel sham (i.e., inactive) stimulation protocol as control condition for phase 2 and phase 3 studies with desynchronizing multichannel stimulation techniques.