Frequency-difference-dependent stochastic resonance in neural systems

Inter-areal transmission of multiple neural signals through frequency-division-multiplexing communication

Inter-areal information transmission in the brain cortex relates to cognitive functions. Researches used to pay attention to activity pattern transmission, signals gating, or routing in neuronal networks. However, the underlying mechanism of simultaneous transmission of multiple neural signals in the same channel across networks remains unclear. In this work, we construct a two-layer feedforward neuronal network (sender-receiver) with each layer's intrinsic rhythms consisting of slow- (low-frequency) and fast- gamma rhythms (high-frequency), investigating how to realize simultaneous transmission of multiple signals in neuronal systems. With the aid of resonance and frequency analysis, it is shown that low- and high-frequency signals can be transmitted simultaneously in such a feedforward network through frequency division multiplexing (FDM) communication. The transmission performance is related to the local resonance, connectivity, as well as background noise. Moreover, low- and high-frequency signals can also be gated or selected with appropriate adjustments of recurrent connection strength and delay, and background noise. Our model might provide a novel insight into the underlying mechanism of complex signals communication between different cortex areas.

Research on constrained localization of ultrasound geometric distribution based on FHN neurons

The autopilot positioning process is mainly affected by three aspects: the first is the spatial geometric distribution of positioning sensors; the second is the screening of spurious observations; and the third is the equivalent ranging error. A constrained positioning method based on the geometric distribution of FitzHugh-Nagumo (FHN) neurons is proposed. To reduce the geometric accuracy factor, a Horizontal Dilution Of Precision value algorithm with a weight factor was proposed by considering the spatial geometric distribution of base stations and the geometric relationship of anchor points. This paper proposes a geometric constraint data processing method for the error of the pseudo-observation value. Finally, considering the significant weak signal perception ability of the biological nervous system, and the stochastic resonance phenomenon caused by noise can enhance the ability of the neuronal system to detect weak signals, an ultrasonic receiving method based on the stochastic resonance characteristics of FHN neuronal system is proposed, to enhance the signal and reduce noise. The results show that under the optimized base station layout and data geometric constraint processing, the ultrasonic wave based on FHN neuron improves the accuracy of spurious observations, reduces the calculation amount of geometric constraint processing, and reduces the positioning error by 66.67%, which provides a new direction for improving the positioning accuracy.

Interlayer Connectivity Affects the Coherence Resonance and Population Activity Patterns in Two-Layered Networks of Excitatory and Inhibitory Neurons

The firing patterns of neuronal populations often exhibit emergent collective oscillations, which can display substantial regularity even though the dynamics of individual elements is very stochastic. One of the many phenomena that is often studied in this context is coherence resonance, where additional noise leads to improved regularity of spiking activity in neurons. In this work, we investigate how the coherence resonance phenomenon manifests itself in populations of excitatory and inhibitory neurons. In our simulations, we use the coupled FitzHugh-Nagumo oscillators in the excitable regime and in the presence of neuronal noise. Formally, our model is based on the concept of a two-layered network, where one layer contains inhibitory neurons, the other excitatory neurons, and the interlayer connections represent heterotypic interactions. The neuronal activity is simulated in realistic coupling schemes in which neurons within each layer are connected with undirected connections, whereas neurons of different types are connected with directed interlayer connections. In this setting, we investigate how different neurophysiological determinants affect the coherence resonance. Specifically, we focus on the proportion of inhibitory neurons, the proportion of excitatory interlayer axons, and the architecture of interlayer connections between inhibitory and excitatory neurons. Our results reveal that the regularity of simulated neural activity can be increased by a stronger damping of the excitatory layer. This can be accomplished with a higher proportion of inhibitory neurons, a higher fraction of inhibitory interlayer axons, a stronger coupling between inhibitory axons, or by a heterogeneous configuration of interlayer connections. Our approach of modeling multilayered neuronal networks in combination with stochastic dynamics offers a novel perspective on how the neural architecture can affect neural information processing and provide possible applications in designing networks of artificial neural circuits to optimize their function via noise-induced phenomena.

Stochastic Resonance in Organic Electronic Devices

Stochastic Resonance (SR) is a phenomenon in which noise improves the performance of a system. With the addition of noise, a weak input signal to a nonlinear system, which may exceed its threshold, is transformed into an output signal. In the other words, noise-driven signal transfer is achieved. SR has been observed in nonlinear response systems, such as biological and artificial systems, and this review will focus mainly on examples of previous studies of mathematical models and experimental realization of SR using poly(hexylthiophene)-based organic field-effect transistors (OFETs). This phenomenon may contribute to signal processing with low energy consumption. However, the generation of SR requires a noise source. Therefore, the focus is on OFETs using materials such as organic materials with unstable electrical properties and critical elements due to unidirectional signal transmission, such as neural synapses. It has been reported that SR can be observed in OFETs by application of external noise. However, SR does not occur under conditions where the input signal exceeds the OFET threshold without external noise. Here, we present an example of a study that analyzes the behavior of SR in OFET systems and explain how SR can be made observable. At the same time, the role of internal noise in OFETs will be explained.

Emergence of stochastic resonance in a two-compartment hippocampal pyramidal neuron model

In vitro studies have shown that hippocampal pyramidal neurons employ a mechanism similar to stochastic resonance (SR) to enhance the detection and transmission of weak stimuli generated at distal synapses. To support the experimental findings from the perspective of multicompartment model analysis, this paper aimed to elucidate the phenomenon of SR in a noisy two-compartment hippocampal pyramidal neuron model, which was a variant of the Pinsky-Rinzel neuron model with smooth activation functions and a hyperpolarization-activated cation current. With a bifurcation analysis of the model, we demonstrated the underlying dynamical structure responsible for the occurrence of SR. Furthermore, using a stochastically generated biphasic pulse train and broadband noise generated by the Orenstein-Uhlenbeck process as noise perturbation, both SR and suprathreshold SR were observed and quantified. Spectral analysis revealed that the distribution of spectral power under noise perturbations, in addition to inherent neurodynamics, is the main factor affecting SR behavior. The research results suggested that noise enhances the transmission of weak stimuli associated with elongated dendritic structures of hippocampal pyramidal neurons, thereby providing support for related laboratory findings.

Control of noise-induced coherent oscillations in three-neuron motifs

The phenomenon of self-induced stochastic resonance (SISR) requires a nontrivial scaling limit between the deterministic and the stochastic timescales of an excitable system, leading to the emergence of coherent oscillations which are absent without noise. In this paper, we numerically investigate SISR and its control in single neurons and three-neuron motifs made up of the Morris–Lecar model. In single neurons, we compare the effects of electrical and chemical autapses on the degree of coherence of the oscillations due to SISR. In the motifs, we compare the effects of altering the synaptic time-delayed couplings and the topologies on the degree of SISR. Finally, we provide two enhancement strategies for a particularly poor degree of SISR in motifs with chemical synapses: (1) we show that a poor SISR can be significantly enhanced by attaching an electrical or an excitatory chemical autapse on one of the neurons, and (2) we show that by multiplexing the motif with a poor SISR to another motif (with a high SISR in isolation), the degree of SISR in the former motif can be significantly enhanced. We show that the efficiency of these enhancement strategies depends on the topology of the motifs and the nature of synaptic time-delayed couplings mediating the multiplexing connections.

Effects of chaotic activity and time delay on signal transmission in FitzHugh-Nagumo neuronal system

The influences of chaotic activity and time delay on the transmission of the sub-threshold signal (STS) in a single FitzHugh-Nagumo neuron and coupled neuronal networks are studied. It is found that a moderate chaotic activity level can enhance the system's detection and transmission of STS. This phenomenon is known as chaotic resonance (CR). In a single neuron, the large amplitude and small period of the STS have a positive effect on the CR phenomenon. In the coupled neuronal network, however, the signal transmission performance of chemical synapses is better than that of electrical synapses. The time delay can determine the trend of the system response, and the multiple chaotic resonances phenomenon is observed upon fine-tuning the time delay length. Both sub-harmonic chaotic resonance and chaotic anti-resonance appear when the STS period and time delay are locked. In chained networks, the signal transmission performance between electrical synapses attenuates continuously. Conversely, the performance between chemical synapses reaches a steady state.

Vibrational resonance in a neuron-astrocyte coupled model

Recent findings have revealed that not only neurons but also astrocytes, a special type of glial cells, are major players of neuronal information processing. It is now widely accepted that they contribute to the regulation of their microenvironment by cross-talking with neurons via gliotransmitters. In this context, we here study the phenomenon of vibrational resonance in neurons by considering their interaction with astrocytes. Our analysis of a neuron-astrocyte pair reveals that intracellular dynamics of astrocytes can induce a double vibrational resonance effect in the weak signal detection performance of a neuron, exhibiting two distinct wells centred at different high-frequency driving amplitudes. We also identify the underlying mechanism of this behaviour, showing that the interaction of widely separated time scales of neurons, astrocytes and driving signals is the key factor for the emergence and control of double vibrational resonance. This article is part of the theme issue 'Vibrational and stochastic resonance in driven nonlinear systems (part 2)'.

Enhanced logical chaotic resonance

It was demonstrated recently that logical chaotic resonance (LCR) can be observed in a bistable system. In other words, the system can operate robustly as a specific logic gate in an optimal window of chaotic signal intensity. Here, we report that the size of the optimal window of chaotic signal intensity can be remarkably extended by exploiting the constructive interaction of chaotic signal and periodic force, as well as coupling, in a coupled bistable system. In addition, medium-frequency periodic force and an increasing system size can also lead to an improvement in the response speed of logic devices. The results are corroborated by circuit experiments. Taken together, a reliable and rapid-response logic operation can be realized based on periodic force- and array-enhanced LCR.

EEG, MEG and neuromodulatory approaches to explore cognition: Current status and future directions

Neural oscillations and their association with brain states and cognitive functions have been object of extensive investigation over the last decades. Several electroencephalography (EEG) and magnetoencephalography (MEG) analysis approaches have been explored and oscillatory properties have been identified, in parallel with the technical and computational advancement. This review provides an up-to-date account of how EEG/MEG oscillations have contributed to the understanding of cognition. Methodological challenges, recent developments and translational potential, along with future research avenues, are discussed.

The Relationship between Sparseness and Energy Consumption of Neural Networks

About 50-80% of total energy is consumed by signaling in neural networks. A neural network consumes much energy if there are many active neurons in the network. If there are few active neurons in a neural network, the network consumes very little energy. The ratio of active neurons to all neurons of a neural network, that is, the sparseness, affects the energy consumption of a neural network. Laughlin's studies show that the sparseness of an energy-efficient code depends on the balance between signaling and fixed costs. Laughlin did not give an exact ratio of signaling to fixed costs, nor did they give the ratio of active neurons to all neurons in most energy-efficient neural networks. In this paper, we calculated the ratio of signaling costs to fixed costs by the data from physiology experiments. The ratio of signaling costs to fixed costs is between 1.3 and 2.1. We calculated the ratio of active neurons to all neurons in most energy-efficient neural networks. The ratio of active neurons to all neurons in neural networks is between 0.3 and 0.4. Our results are consistent with the data from many relevant physiological experiments, indicating that the model used in this paper may meet neural coding under real conditions. The calculation results of this paper may be helpful to the study of neural coding.

Observation of stochastic resonance in a liquid-crystal light valve with optical feedback induced by colored noise in the driving voltage

Stochastic resonance is a noise phenomenon that benefits applications such as pattern formation, neural systems, microelectromechanical systems, and image processing. This study experimentally clarifies that the orientation of the liquid crystal molecules was switched between two stable positions when stochastic resonance was induced by colored noises in a liquid crystal light valve with optical feedback. Ornstein-Uhlenbeck and dichotomous noises were used for colored noise, and the noise was applied to the drive voltage of the liquid crystal light valve. The signal-to-noise ratio was measured with respect to changes in the noise type, noise intensity, and autocorrelation time of the noise. It was found that typical stochastic resonance was observed with a noise autocorrelation time of approximately 20 ms or more for both noise types, and dichotomous noise further enhanced the stochastic resonance compared to the Ornstein-Uhlenbeck noise. This suggests that it is possible to maximize stochastic resonance in a liquid crystal light valve by optimizing the conditions of colored noise.

Ionic channel blockage in stochastic Hodgkin-Huxley neuronal model driven by multiple oscillatory signals

Ionic channel blockage and multiple oscillatory signals play an important role in the dynamical response of pulse sequences. The effects of ionic channel blockage and ionic channel noise on the discharge behaviors are studied in Hodgkin-Huxley neuronal model with multiple oscillatory signals. It is found that bifurcation points of spontaneous discharge are altered through tuning the amplitude of multiple oscillatory signals, and the discharge cycle is changed by increasing the frequency of multiple oscillatory signals. The effects of ionic channel blockage on neural discharge behaviors indicate that the neural excitability can be suppressed by the sodium channel blockage, however, the neural excitability can be reversed by the potassium channel blockage. There is an optimal blockage ratio of potassium channel at which the electrical activity is the most regular, while the order of neural spike is disrupted by the sodium channel blockage. In addition, the frequency of spike discharge is accelerated by increasing the ionic channel noise, the firing of neuron becomes more stable if the ionic channel noise is appropriately reduced. Our results might provide new insights into the effects of ionic channel blockages, multiple oscillatory signals, and ionic channel noises on neural discharge behaviors.

Resonance phenomena controlled by external feedback signals and additive noise in neural systems

Chaotic resonance is a phenomenon that can replace the fluctuation source in stochastic resonance from additive noise to chaos. We previously developed a method to control the chaotic state for suitably generating chaotic resonance by external feedback even when the external adjustment of chaos is difficult, establishing a method named reduced region of orbit (RRO) feedback. However, a feedback signal was utilized only for dividing the merged attractor. In addition, the signal sensitivity in chaotic resonance induced by feedback signals and that of stochastic resonance by additive noise have not been compared. To merge the separated attractor, we propose a negative strength of the RRO feedback signal in a discrete neural system which is composed of excitatory and inhibitory neurons. We evaluate the features of chaotic resonance and compare it to stochastic resonance. The RRO feedback signal with negative strength can merge the separated attractor and induce chaotic resonance. We also confirm that additive noise induces stochastic resonance through attractor merging. The comparison of these resonance modalities verifies that chaotic resonance provides more applicability than stochastic resonance given its capability to handle attractor separation and merging.

Stability Analysis for Delayed Neural Networks via Improved Auxiliary Polynomial-Based Functions

This brief is concerned with stability analysis for delayed neural networks (DNNs). By establishing polynomials and introducing slack variables reasonably, some improved delay-product type of auxiliary polynomial-based functions (APFs) is developed to exploit additional degrees of freedom and more information on extra states. Then, by constructing Lyapunov-Krasovskii functional using APFs and integrals of quadratic forms with high order scalar functions, a novel stability criterion is derived for DNNs, in which the benefits of the improved inequalities are fully integrated and the information on delay and its derivative is well reflected. By virtue of the advantages of APFs, more desirable performance is achieved through the proposed approach, which is demonstrated by the numerical examples.

A Game-Theoretical Network Formation Model for C. elegans Neural Network

Studying and understanding human brain structures and functions have become one of the most challenging issues in neuroscience today. However, the mammalian nervous system is made up of hundreds of millions of neurons and billions of synapses. This complexity made it impossible to reconstruct such a huge nervous system in the laboratory. So, most researchers focus on C. elegans neural network. The C. elegans neural network is the only biological neural network that is fully mapped. This nervous system is the simplest neural network that exists. However, many fundamental behaviors like movement emerge from this basic network. These features made C. elegans a convenient case to study the nervous systems. Many studies try to propose a network formation model for C. elegans neural network. However, these studies could not meet all characteristics of C. elegans neural network, such as significant factors that play a role in the formation of C. elegans neural network. Thus, new models are needed to be proposed in order to explain all aspects of C. elegans neural network. In this paper, a new model based on game theory is proposed in order to understand the factors affecting the formation of nervous systems, which meet the C. elegans frontal neural network characteristics. In this model, neurons are considered to be agents. The strategy for each neuron includes either making or removing links to other neurons. After choosing the basic network, the utility function is built using structural and functional factors. In order to find the coefficients for each of these factors, linear programming is used. Finally, the output network is compared with C. elegans frontal neural network and previous models. The results implicate that the game-theoretical model proposed in this paper can better predict the influencing factors in the formation of C. elegans neural network compared to previous models.

Temperature effect on memristive ion channels

Neuron shows distinct dependence of electrical activities on membrane patch temperature, and the mode transition of electrical activity is induced by the patch temperature through modulating the opening and closing rates of ion channels. In this paper, inspired by the physical effect of memristor, the potassium and sodium ion channels embedded in the membrane patch are updated by using memristor-based voltage gate variables, and an external stimulus is applied to detect the variety of mode selection in electrical activities under different patch temperatures. It is found that each ion channel can be regarded as a physical memristor, and the shape of pinched hysteresis loop of memristor is dependent on both input voltage and patch temperature. The pinched hysteresis loops of two ion-channel memristors are dramatically enlarged by increasing patch temperature, and the hysteresis lobe areas are monotonously reduced with the increasing of excitation frequency if the frequency of external stimulus exceeds certain threshold. However, for the memristive potassium channel, the AREA1 corresponding to the threshold frequency is increased with the increasing of patch temperature. The amplitude of conductance for two ion-channel memristors depends on the variation of patch temperature. The results of this paper might provide insights to modulate the neural activities in appropriate temperature condition completely, and involvement of external stimulus enhance the effect of patch temperature.

Routing information flow by separate neural synchrony frequencies allows for "functionally labeled lines" in higher primate cortex

Dynamical coordination of the neural activity between individual neurons is known to have a key role in the efficient transfer of sensory information to associative areas. Here, we report a role of interneuronal synchrony within the high-gamma (180 to 220 Hz) frequency range of activity in macaque area MT (a visual area in the dorsal visual pathway) in determining behavioral performance. This is, however, in contrast to previous reports for the ventral visual pathway (such as area V4), where only gamma range (40 to 70 Hz) was observed to play a role. We propose that such a difference between the functional coordination in different visual pathways might be used to unambiguously identify the source of input to the higher areas.

Efficient transfer of sensory information to higher (motor or associative) areas in primate visual cortical areas is crucial for transforming sensory input into behavioral actions. Dynamically increasing the level of coordination between single neurons has been suggested as an important contributor to this efficiency. We propose that differences between the functional coordination in different visual pathways might be used to unambiguously identify the source of input to the higher areas, ensuring a proper routing of the information flow. Here we determined the level of coordination between neurons in area MT in macaque visual cortex in a visual attention task via the strength of synchronization between the neurons’ spike timing relative to the phase of oscillatory activities in local field potentials. In contrast to reports on the ventral visual pathway, we observed the synchrony of spikes only in the range of high gamma (180 to 220 Hz), rather than gamma (40 to 70 Hz) (as reported previously) to predict the animal’s reaction speed. This supports a mechanistic role of the phase of high-gamma oscillatory activity in dynamically modulating the efficiency of neuronal information transfer. In addition, for inputs to higher cortical areas converging from the dorsal and ventral pathway, the distinct frequency bands of these inputs can be leveraged to preserve the identity of the input source. In this way source-specific oscillatory activity in primate cortex can serve to establish and maintain “functionally labeled lines” for dynamically adjusting cortical information transfer and multiplexing converging sensory signals.

Fast regular firings induced by intra- and inter-time delays in two clustered neuronal networks

In this paper, we consider two clustered neuronal networks with dense intra-synaptic links within each cluster and sparse inter-synaptic links between them. We focus on the effects of intra- and inter-time delays on the spiking regularity and timing in both clusters. With the aid of simulation results, we show that intermediate intra- and inter-time delays are able to separately induce fast regular firing - spiking activity with a high firing rate as well as a high spiking regularity. Moreover, when both intra- and inter-time delays are present, we find that fast regular firings are induced much more frequently than if only a single type of delay is present in the system. Our results indicate that appropriately adjusted intra- and inter-time delays can significantly facilitate fast regular firing in neuronal networks. Based on a detailed analysis, we conjecture that this is most likely when the largest value of common divisors of the intra- and inter-time delays falls into a range where fast regular firings are induced by suitable intra- or inter-time delays alone.

Fractional Gaussian noise-enhanced information capacity of a nonlinear neuron model with binary signal input

This paper reveals the effect of fractional Gaussian noise with Hurst exponent H∈(1/2,1) on the information capacity of a general nonlinear neuron model with binary signal input. The fGn and its corresponding fractional Brownian motion exhibit long-range, strong-dependent increments. It extends standard Brownian motion to many types of fractional processes found in nature, such as the synaptic noise. In the paper, for the subthreshold binary signal, sufficient conditions are given based on the "forbidden interval" theorem to guarantee the occurrence of stochastic resonance, while for the suprathreshold binary signal, the simulated results show that additive fGn with Hurst exponent H∈(1/2,1) could increase the mutual information or bits count. The investigation indicated that the synaptic noise with the characters of long-range dependence and self-similarity might be the driving factor for the efficient encoding and decoding of the nervous system.

An oscillatory neural network model that demonstrates the benefits of multisensory learning

Since the world consists of objects that stimulate multiple senses, it is advantageous for a vertebrate to integrate all the sensory information available. However, the precise mechanisms governing the temporal dynamics of multisensory processing are not well understood. We develop a computational modeling approach to investigate these mechanisms. We present an oscillatory neural network model for multisensory learning based on sparse spatio-temporal encoding. Recently published results in cognitive science show that multisensory integration produces greater and more efficient learning. We apply our computational model to qualitatively replicate these results. We vary learning protocols and system dynamics, and measure the rate at which our model learns to distinguish superposed presentations of multisensory objects. We show that the use of multiple channels accelerates learning and recall by up to 80%. When a sensory channel becomes disabled, the performance degradation is less than that experienced during the presentation of non-congruent stimuli. This research furthers our understanding of fundamental brain processes, paving the way for multiple advances including the building of machines with more human-like capabilities.

Periodic Visual Stimulation Induces Resting-State Brain Network Reconfiguration

Periodic visual stimulation can evoke the steady-state visual potential (SSVEP) in the brain. Owing to its superior characteristics, the SSVEP has been widely used in neural engineering and cognitive neuroscience studies. However, the underlying mechanisms of the SSVEP are not well understood. In this study, we introduced a brain reconfiguration methodology to explore the possible mechanisms of the SSVEP. The EEG data from five periodic stimuli consistently indicated that the periodic visual stimulation could induce resting-state brain network reconfiguration and that the responses evoked by the stimuli were correlated to the network reconfiguration indexes. For each stimulus frequency, larger response amplitudes corresponded to higher reconfiguration indexes from the resting-state network to a stimulus-evoked network. These findings demonstrate that an external periodic visual stimulation can induce the modification of intrinsic oscillatory activities by reconfiguring resting-state activity at a network level, which could facilitate the responses evoked by the stimulus. These findings provide new insights into the response mechanisms of periodic visual stimulation.

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 Parkinson's therapy and acoustic CR stimulation for tinnitus therapy. Promising first in human data is available for vibrotactile CR stimulation for Parkinson's 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.