Oscillatory Input Research Articles

Beta-Band Resonance and Intrinsic Oscillations in a Biophysically Detailed Model of the Subthalamic Nucleus-Globus Pallidus Network.

Increased beta-band oscillatory activity in the basal ganglia network is associated with Parkinsonian motor symptoms and is suppressed with medication and deep brain stimulation (DBS). The origins of the beta-band oscillations, however, remains unclear with both intrinsic oscillations arising within the subthalamic nucleus (STN)—external globus pallidus (GPe) network and exogenous beta-activity, originating outside the network, proposed as potential sources of the pathological activity. The aim of this study was to explore the relative contribution of autonomous oscillations and exogenous oscillatory inputs in the generation of pathological oscillatory activity in a biophysically detailed model of the parkinsonian STN-GPe network. The network model accounts for the integration of synaptic currents and their interaction with intrinsic membrane currents in dendritic structures within the STN and GPe. The model was used to investigate the development of beta-band synchrony and bursting within the STN-GPe network by changing the balance of excitation and inhibition in both nuclei, and by adding exogenous oscillatory inputs with varying phase relationships through the hyperdirect cortico-subthalamic and indirect striato-pallidal pathways. The model showed an intrinsic susceptibility to beta-band oscillations that was manifest in weak autonomously generated oscillations within the STN-GPe network and in selective amplification of exogenous beta-band synaptic inputs near the network's endogenous oscillation frequency. The frequency at which this resonance peak occurred was determined by the net level of excitatory drive to the network. Intrinsic or endogenously generated oscillations were too weak to support a pacemaker role for the STN-GPe network, however, they were considerably amplified by sparse cortical beta inputs and were further amplified by striatal beta inputs that promoted anti-phase firing of the cortex and GPe, resulting in maximum transient inhibition of STN neurons. The model elucidates a mechanism of cortical patterning of the STN-GPe network through feedback inhibition whereby intrinsic susceptibility to beta-band oscillations can lead to phase locked spiking under parkinsonian conditions. These results point to resonance of endogenous oscillations with exogenous patterning of the STN-GPe network as a mechanism of pathological synchronization, and a role for the pallido-striatal feedback loop in amplifying beta oscillations.

Chaotic dynamics as a mechanism of rapid transition of hippocampal local field activity between theta and non-theta states.

We propose a dynamical model of the local hippocampal circuit realizing the transition between the theta and non-theta states. We model the interaction between hippocampal local rhythm generators and the external periodic input from the medial septum and diagonal band of Broca (MS-DBB). With our model, bifurcation of the nonlinear dynamics serves as a mechanism that realizes two distinctive oscillations in the hippocampus, where the amplitude of the oscillatory input from the MS-DBB works as a bifurcation parameter. We model the network of the hippocampal interneurons with a network of simple class 1 neuron models connected mutually with gap junctions. The model neurons exhibit highly synchronous periodic oscillations under the existence of an external force from the MS-DBB, just as the real hippocampus shows theta oscillation under the rhythmic input from the MS-DBB. The model shows diffusion-induced chaotic dynamics under an aperiodic MS-DBB activity, just as the large amplitude irregular activity appears following the disappearance of the rhythmicity of the MS-DBB neurons in the real brain. The model is consistent with both previous experimental findings reporting the existence of local rhythm generators in the hippocampus and the executive role of the MS-DBB in synchronizing theta oscillation in vivo. Our model also replicates the traveling waves of theta oscillations in two-dimensionally coupled networks.

Asymmetrical voltage response in resonant neurons shaped by nonlinearities.

The conventional impedance profile of a neuron can identify the presence of resonance and other properties of the neuronal response to oscillatory inputs, such as nonlinear response amplifications, but it cannot distinguish other nonlinear properties such as asymmetries in the shape of the voltage response envelope. Experimental observations have shown that the response of neurons to oscillatory inputs preferentially enhances either the upper or lower part of the voltage envelope in different frequency bands. These asymmetric voltage responses arise in a neuron model when it is submitted to high enough amplitude oscillatory currents of variable frequencies. We show how the nonlinearities associated to different ionic currents or present in the model as captured by its voltage equation lead to asymmetrical response and how high amplitude oscillatory currents emphasize this response. We propose a geometrical explanation for the phenomenon where asymmetries result not only from nonlinearities in their activation curves but also from nonlinearites captured by the nullclines in the phase-plane diagram and from the system's time-scale separation. In addition, we identify an unexpected frequency-dependent pattern which develops in the gating variables of these currents and is a product of strong nonlinearities in the system as we show by controlling such behavior by manipulating the activation curve parameters. The results reported in this paper shed light on the ionic mechanisms by which brain embedded neurons process oscillatory information.

Functional Connectivity of Organic Neuromorphic Devices by Global Voltage Oscillations

Global oscillations in the brain synchronize neural populations and lead to dynamic binding between different regions. This functional connectivity reconfigures as needed for the architecture of the neural network, thereby transcending the limitations of its hardwired structure. Despite the fact that it underlies the versatility of biological computational systems, this concept is not captured in current neuromorphic device architectures. Herein, functional connectivity in an array of organic neuromorphic devices connected through an electrolyte is demonstrated. The output of these devices is shown to be synchronized by a global oscillatory input despite the fact that individual inputs are stochastic and independent. This temporal coupling is induced at a specific phase of the global oscillation in a way that is reminiscent of phase locking of neurons to brain oscillations. This demonstration provides a pathway toward new neuromorphic architectural paradigms, where dynamic binding transcends the limitations of structural connectivity, and could enable architectural concepts of hierarchical information flow.

Biased competition in the absence of input bias revealed through corticostriatal computation

Classical accounts of biased competition require an input bias to resolve the competition between neuronal ensembles driving downstream processing. However, flexible and reliable selection of behaviorally relevant ensembles can occur with unbiased stimulation: striatal D1 and D2 spiny projection neurons (SPNs) receive balanced cortical input, yet their activity determines the choice between GO and NO-GO pathways in the basal ganglia. We here present a corticostriatal model identifying three mechanisms that rely on physiological asymmetries to effect rate- and time-coded biased competition in the presence of balanced inputs. First, tonic input strength determines which one of the two SPN phenotypes exhibits a higher mean firing rate. Second, low-strength oscillatory inputs induce higher firing rate in D2 SPNs but higher coherence between D1 SPNs. Third, high-strength inputs oscillating at distinct frequencies can preferentially activate D1 or D2 SPN populations. Of these mechanisms, only the latter accommodates observed rhythmic activity supporting rule-based decision making in prefrontal cortex.

Preactuated Multirate Feedforward Control for Independent Stable Inversion of Unstable Intrinsic and Discretization Zeros

A plant with unstable zeros is known to be difficult to be controlled, because of the initial undershoot of its step response and the unstable poles in its inversion system. There are two reasons why a plant has unstable zeros in the discrete-time domain: 1) noncollocation of actuators and sensors; and 2) discretization by the zero-order hold. Addressing problems 1) and 2) simultaneously, approximate and discrete-time stable inversion methods have been proposed as model-based feedforward control for unstable zeros. However, the approximated inversion methods compromise tracking performance, and the discrete-time stable inversion methods obtain oscillatory control inputs owing to the direct cancellation of discretization zeros. Therefore, this paper proposes a preactuated multirate feedforward control, which is an independent stable inversion of the two types of zeros: unstable intrinsic zeros from noncollocation and unstable discretization zeros from the zero-order hold. The proposed method combines both a state trajectory generation based on a time- and imaginary-axis reversal to address problem 1) and a multirate feedforward implementation to address problem 2), independently. Moreover, this study verifies the tracking performance improvement by performing simulations and experiments in comparison with well-known model-based feedforward control methods using a high-precision motion stage. The role and importance of multirate feedforward control are also demonstrated by comparing it to a continuous-time domain approach with preactuation.

Membrane potential resonance in non-oscillatory neurons interacts with synaptic connectivity to produce network oscillations.

Several neuron types have been shown to exhibit (subthreshold) membrane potential resonance (MPR), defined as the occurrence of a peak in their voltage amplitude response to oscillatory input currents at a preferred (resonant) frequency. MPR has been investigated both experimentally and theoretically. However, whether MPR is simply an epiphenomenon or it plays a functional role for the generation of neuronal network oscillations and how the latent time scales present in individual, non-oscillatory cells affect the properties of the oscillatory networks in which they are embedded are open questions. We address these issues by investigating a minimal network model consisting of (i) a non-oscillatory linear resonator (band-pass filter) with 2D dynamics, (ii) a passive cell (low-pass filter) with 1D linear dynamics, and (iii) nonlinear graded synaptic connections (excitatory or inhibitory) with instantaneous dynamics. We demonstrate that (i) the network oscillations crucially depend on the presence of MPR in the resonator, (ii) they are amplified by the network connectivity, (iii) they develop relaxation oscillations for high enough levels of mutual inhibition/excitation, and (iv) the network frequency monotonically depends on the resonators resonant frequency. We explain these phenomena using a reduced adapted version of the classical phase-plane analysis that helps uncovering the type of effective network nonlinearities that contribute to the generation of network oscillations. We extend our results to networks having cells with 2D dynamics. Our results have direct implications for network models of firing rate type and other biological oscillatory networks (e.g, biochemical, genetic).

The development of functional and directed corticomuscular connectivity during tonic ankle muscle contraction across childhood and adolescence

In adults, oscillatory activity in the sensorimotor cortex is coherent with contralateral muscle activity at beta frequencies (15–35 Hz) during tonic contraction. This functional coupling reflects the involvement of the sensorimotor cortex, the corticospinal pathway, and likely also ascending sensory feedback in the task at hand. However, little is known about the developmental trajectory of task-related corticomuscular connectivity relating to the voluntary control of the ankle muscles. To address this, we recorded electroencephalography (EEG) from the vertex (Cz) and electromyography (EMG) from ankle muscles (proximal and distal anterior tibial, TA; soleus, SOL; gastrocnemius medialis, GM) in 33 participants aged 7–23 yr during tonic dorsi- and plantar flexion requiring precise maintenance of a submaximal torque level. Coherence was calculated for Cz-TA, Cz-SOL, TA-TA, and SOL-GM signal pairs. We found strong, positive associations between age and beta band coherence for Cz-TA, Cz-SOL, and TA-TA, suggesting that oscillatory corticomuscular connectivity is strengthened during childhood development and adolescence. Directionality analysis indicated that the primary interaction underlying this age-related increase was in the descending direction. In addition, performance during dorsi- and plantar flexion tasks was positively associated with age, indicating more precise control of the ankle joint in older participants. Performance was also positively associated with beta band coherence, suggesting that participants with greater coherence also exhibited greater precision. We propose that these results indicate an age-related increase in oscillatory corticospinal input to the ankle muscle motoneuron pools during childhood development and adolescence, with possible implications for maturation of precision force control. Within the theoretical framework of predictive coding, we suggest that our results may reflect an age-related increase in reliance on feedforward control as the developing nervous system becomes better at predicting the sensory consequences of movement. These findings may contribute to the development of novel intervention strategies targeting improved sensorimotor control in children and adolescents with central motor disorders.

Planar Multi-Link Swimmers: Experiments and Theoretical Investigation using “Perfect Fluid” Model

SummaryRobotic swimmers are currently a subject of extensive research and development for several underwater applications. Clever design and planning must rely on simple theoretical models that account for the swimmer’s hydrodynamics in order to optimize its structure and control inputs. In this work, we study a planar snake-like multi-link swimmer by using the “perfect fluid” model that accounts for inertial hydrodynamic forces while neglecting viscous drag effects. The swimmer’s dynamic equations of motion are formulated and reduced into a first-order system due to symmetries and conservation of generalized momentum variables. Focusing on oscillatory inputs of joint angles, we study optimal gaits for 3-link and 5-link swimmers via numerical integration. For the 3-link swimmer, we also provide a small-amplitude asymptotic solution which enables obtaining closed-form approximations for optimal gaits. The theoretical results are then corroborated by experiments and motion measurement of untethered robotic prototypes with three and five links floating in a water pool, showing a reasonable agreement between the experiments and the theoretical model.

Inhibition-based relaxation oscillations emerge in resonator networks

We investigate the mechanisms responsible for the generation of oscillations in mutually inhibitory cells of non-oscillatory neurons and the transitions from non-relaxation (sinusoidal-like) oscillations to relaxation oscillations. We use a minimal model consisting of a 2D linear resonator, a 1D linear cell and graded synaptic inhibition described by a piecewise linear sigmoidal function. Individually, resonators exhibit a peak in their response to oscillatory inputs at a preferred (resonant) frequency, but they do not show intrinsic (damped) oscillations in response to constant perturbations. We show that network oscillations emerge in this model for appropriate balance of the model parameters, particularly the connectivity strength and the steepness of the connectivity function. For fixed values of the latter, there is a transition from sinusoidal-like to relaxation oscillations as the connectivity strength increases. Similarly, for fixed connectivity strength values, increasing the connectivity steepness also leads to relaxation oscillations. Interestingly, relaxation oscillations are not observed when the 2D linear node is a damped oscillator. We discuss the role of the intrinsic properties of the participating nodes by focusing on the effect that the resonator’s resonant frequency has on the network frequency and amplitude.

Oscillations and Spike Entrainment.

Oscillatory input to networks, as indicated by field potentials, must entrain neuronal firing to be a causal agent in brain activity. Even when the oscillatory input is prominent, entrainment of firing is not a foregone conclusion but depends on the intrinsic dynamics of the postsynaptic neurons, including cell type-specific resonances, and background firing rates. Within any local network of neurons, only a subset of neurons may have their firing entrained by an oscillating synaptic input, and oscillations of different frequency may engage separate subsets of neurons.

Propagation of Oscillating Chemical Signals through Reaction Networks.

Akin to electronic systems that can tune to and process signals of select frequencies, systems/networks of chemical reactions also "propagate" time-varying concentration inputs in a frequency-dependent manner. Whereas signals of low frequencies are transmitted, higher frequency inputs are dampened and converted into steady-concentration outputs. Such behavior is observed in both idealized reaction chains as well as realistic signaling cascades, in the latter case explaining the experimentally observed responses of such cascades to input calcium oscillations. These and other results are supported by numerical simulations within the freely available Kinetix web application we developed to study chemical systems of arbitrary architectures, reaction kinetics, and boundary conditions.

Oscillatory IL-2 stimulus reveals pertinent signaling timescales of T cell responsiveness.

Cell response to extracellular ligand is affected not only by ligand availability, but also by pre-existing cell-to-cell variability that enables a range of responses within a cell population. We developed a computational model that incorporates cell heterogeneity in order to investigate Jurkat T cell response to time dependent extracellular IL-2 stimulation. Our model predicted preferred timing of IL-2 oscillatory input for maximizing downstream intracellular STAT5 nuclear translocation. The modeled cytokine exposure was replicated experimentally through the use of a microfluidic platform that enabled the parallelized capture of dynamic single cell response to precisely delivered pulses of IL-2 stimulus. The in vitro results demonstrate that single cell response profiles vary with pulsatile IL-2 input at pre-equilibrium levels. These observations confirmed our model predictions that Jurkat cells have a preferred range of extracellular IL-2 fluctuations, in which downstream response is rapidly initiated. Further investigation into this filtering behavior could increase our understanding of how pre-existing cellular states within immune cell populations enable a systems response within a preferred range of ligand fluctuations, and whether the observed cytokine range corresponds to in vivo conditions.

Network mechanisms underlying the role of oscillations in cognitive tasks.

Oscillatory activity robustly correlates with task demands during many cognitive tasks. However, not only are the network mechanisms underlying the generation of these rhythms poorly understood, but it is also still unknown to what extent they may play a functional role, as opposed to being a mere epiphenomenon. Here we study the mechanisms underlying the influence of oscillatory drive on network dynamics related to cognitive processing in simple working memory (WM), and memory recall tasks. Specifically, we investigate how the frequency of oscillatory input interacts with the intrinsic dynamics in networks of recurrently coupled spiking neurons to cause changes of state: the neuronal correlates of the corresponding cognitive process. We find that slow oscillations, in the delta and theta band, are effective in activating network states associated with memory recall. On the other hand, faster oscillations, in the beta range, can serve to clear memory states by resonantly driving transient bouts of spike synchrony which destabilize the activity. We leverage a recently derived set of exact mean-field equations for networks of quadratic integrate-and-fire neurons to systematically study the bifurcation structure in the periodically forced spiking network. Interestingly, we find that the oscillatory signals which are most effective in allowing flexible switching between network states are not smooth, pure sinusoids, but rather burst-like, with a sharp onset. We show that such periodic bursts themselves readily arise spontaneously in networks of excitatory and inhibitory neurons, and that the burst frequency can be tuned via changes in tonic drive. Finally, we show that oscillations in the gamma range can actually stabilize WM states which otherwise would not persist.

Modeling and Operational Analysis of an Automotive Shock Absorber with a Tuned Mass Damper

Abstract Recently, the topic of energy dissipation efficiency of vehicle suspension dampers has become a research and engineering problem due to structural requirements of vehicle manufacturers and the introduction of electric/hybrid cars. By principle, any disturbances in the damping force generation process translate into pressure fluctuations to be then transferred to the body of the vehicle. The effect known as rattling within the damper engineering community is perceived as detrimental to ride comfort. To improve the performance of a vehicle damper several methods can be devised and used. One approach is to optimize the settings of the valves in the damper. The approach, however, often influences the force output of the damper. Another technique involves the application of add-on systems. One such system is the tuned mass damper concept originally developed by Frahm for structural engineering applications. In the paper the author proposes a damper concept equipped with an external/internal tuned mass damper component for improving the dynamic characteristics of vehicle dampers. The author presents modeling details followed by simulations of the damper with the tuned mass damper concept subjected to oscillatory inputs, and a critical analysis of the presented results.

BrAHMs V1.0: a fast, physically based subglacial hydrology model for continental-scale application

Abstract. We present BrAHMs (BAsal Hydrology Model): a physically based basal hydrology model which represents water flow using Darcian flow in the distributed drainage regime and a fast down-gradient solver in the channelized regime. Switching from distributed to channelized drainage occurs when appropriate flow conditions are met. The model is designed for long-term integrations of continental ice sheets. The Darcian flow is simulated with a robust combination of the Heun and leapfrog–trapezoidal predictor–corrector schemes. These numerical schemes are applied to a set of flux-conserving equations cast over a staggered grid with water thickness at the centres and fluxes defined at the interface. Basal conditions (e.g., till thickness, hydraulic conductivity) are parameterized so the model is adaptable to a variety of ice sheets. Given the intended scales, basal water pressure is limited to ice overburden pressure, and dynamic time stepping is used to ensure that the Courant–Friedrichs–Lewy (CFL) condition is met for numerical stability. The model is validated with a synthetic ice sheet geometry and different bed topographies to test basic water flow properties and mass conservation. Synthetic ice sheet tests show that the model behaves as expected with water flowing down gradient, forming lakes in a potential well or reaching a terminus and exiting the ice sheet. Channel formation occurs periodically over different sections of the ice sheet and, when extensive, displays the arborescent configuration expected of Röthlisberger channels. The model is also shown to be stable under high-frequency oscillatory meltwater inputs.

Robustness of Clocks to Input Noise.

To estimate the time, many organisms, ranging from cyanobacteria to animals, employ a circadian clock which is based on a limit-cycle oscillator that can tick autonomously with a nearly 24h period. Yet, a limit-cycle oscillator is not essential for knowing the time, as exemplified by bacteria that possess an "hourglass": a system that when forced by an oscillatory light input exhibits robust oscillations from which the organism can infer the time, but that in the absence of driving relaxes to a stable fixed point. Here, using models of the Kai system of cyanobacteria, we compare a limit-cycle oscillator with two hourglass models, one that without driving relaxes exponentially and one that does so in an oscillatory fashion. In the limit of low input noise, all three systems are equally informative on time, yet in the regime of high input-noise the limit-cycle oscillator is far superior. The same behavior is found in the Stuart-Landau model, indicating that our result is universal.

Flexible resonance in prefrontal networks with strong feedback inhibition.

Oscillations are ubiquitous features of brain dynamics that undergo task-related changes in synchrony, power, and frequency. The impact of those changes on target networks is poorly understood. In this work, we used a biophysically detailed model of prefrontal cortex (PFC) to explore the effects of varying the spike rate, synchrony, and waveform of strong oscillatory inputs on the behavior of cortical networks driven by them. Interacting populations of excitatory and inhibitory neurons with strong feedback inhibition are inhibition-based network oscillators that exhibit resonance (i.e., larger responses to preferred input frequencies). We quantified network responses in terms of mean firing rates and the population frequency of network oscillation; and characterized their behavior in terms of the natural response to asynchronous input and the resonant response to oscillatory inputs. We show that strong feedback inhibition causes the PFC to generate internal (natural) oscillations in the beta/gamma frequency range (>15 Hz) and to maximize principal cell spiking in response to external oscillations at slightly higher frequencies. Importantly, we found that the fastest oscillation frequency that can be relayed by the network maximizes local inhibition and is equal to a frequency even higher than that which maximizes the firing rate of excitatory cells; we call this phenomenon population frequency resonance. This form of resonance is shown to determine the optimal driving frequency for suppressing responses to asynchronous activity. Lastly, we demonstrate that the natural and resonant frequencies can be tuned by changes in neuronal excitability, the duration of feedback inhibition, and dynamic properties of the input. Our results predict that PFC networks are tuned for generating and selectively responding to beta- and gamma-rhythmic signals due to the natural and resonant properties of inhibition-based oscillators. They also suggest strategies for optimizing transcranial stimulation and using oscillatory networks in neuromorphic engineering.

Multiplexed oscillations and phase rate coding in the basal forebrain.

Complex behaviors demand temporal coordination among functionally distinct brain regions. The basal forebrain's afferent and efferent structure suggests a capacity for mediating this coordination at a large scale. During performance of a spatial orientation task, synaptic activity in this region was dominated by four amplitude-independent oscillations temporally organized by the phase of the slowest, a theta-frequency rhythm. Oscillation amplitudes were also organized by task epoch and positively correlated to the task-related modulation of individual neuron firing rates. For many neurons, spiking was temporally organized through phase precession against theta band field potential oscillations. Theta phase precession advanced in parallel to task progression, rather than absolute spatial location or time. Together, the findings reveal a process by which associative brain regions can integrate independent oscillatory inputs and transform them into sequence-specific, rate-coded outputs that are adaptive to the pace with which organisms interact with their environment.

Suppression of Multimodality in Inter-Spike Interval Distribution: Role of External Damped Oscillatory Input.

A theoretical model based on the generalized neuronal model with distributed delay (GNMDD) is proposed to generate multimodal/bimodal inter-spike interval (ISI) distribution. The distributed delay is assumed to be general in the sense that it is a linear combination of gamma distributed weak and strong memory kernels. It is found that the expected membrane potential in the subthreshold regime exhibits damped oscillatory behavior. This causes the ISI pattern to become bimodal/multimodal. Furthermore, the effect of external damped oscillatory current in the GNMDD model is investigated. Based on extensive simulation study of a set of coupled stochastic differential equations in the presence of a threshold, a vast amount of spiking data are generated. Using the non-parametric modeling approach, the optimal bin width of the histogram is obtained by using the Freedman-Diaconis rule. It is to be noted that, with the increasing amplitude of the damped oscillatory current, the multimodal ISI distribution changes to unimodal ISI distribution when the magnitude of external current reaches a critical value. It is found that the entropy also shows a sudden transition around the critical point. This phenomenon is akin to a phase transition.