Transcranial alternating current stimulation entrains alpha oscillations by preferential phase synchronization of fast-spiking cortical neurons to stimulation waveform.

Computational modeling and human studies suggest that transcranial alternating current stimulation (tACS) modulates alpha oscillations by entrainment. Yet, a direct examination of how tACS interacts with neuronal spiking activity that gives rise to the alpha oscillation in the thalamo-cortical system has been lacking. Here, we demonstrate how tACS entrains endogenous alpha oscillations in head-fixed awake ferrets. We first show that endogenous alpha oscillations in the posterior parietal cortex drive the primary visual cortex and the higher-order visual thalamus. Spike-field coherence is largest for the alpha frequency band, and presumed fast-spiking inhibitory interneurons exhibit strongest coupling to this oscillation. We then apply alpha-tACS that results in a field strength comparable to what is commonly used in humans (<0.5 mV/mm). Both in these ferret experiments and in a computational model of the thalamo-cortical system, tACS entrains alpha oscillations by following the theoretically predicted Arnold tongue. Intriguingly, the fast-spiking inhibitory interneurons exhibit a stronger entrainment response to tACS in both the ferret experiments and the computational model, likely due to their stronger endogenous coupling to the alpha oscillation. Our findings demonstrate the in vivo mechanism of action for the modulation of the alpha oscillation by tACS.

Stimulus-specific regulation of visual oddball differentiation in posterior parietal cortex.

The frequency at which a stimulus is presented determines how it is interpreted. For example, a repeated image may be of less interest than an image that violates the prior sequence. This process involves integration of sensory information and internal representations of stimulus history, functions carried out in higher-order sensory areas such as the posterior parietal cortex (PPC). Thus far, there are few detailed reports investigating the single-neuron mechanisms for processing of stimulus presentation frequency in PPC. To address this gap in knowledge, we recorded PPC activity using 2-photon calcium imaging and electrophysiology during a visual oddball paradigm. Calcium imaging results reveal differentiation at the level of single neurons for frequent versus rare conditions which varied depending on whether the stimulus was preferred or non-preferred by the recorded neural population. Such differentiation of oddball conditions was mediated primarily by stimulus-independent adaptation in the frequent condition.

Neuromodulation-dependent effect of gated high-frequency, LFMS-like electric field stimulation in mouse cortical slices.

Low-field magnetic stimulation (LFMS) is a gated high-frequency non-invasive brain stimulation method (500 Hz gated at 2 Hz) with a proposed antidepressant effect. However, it has remained unknown how such stimulation paradigms modulate neuronal network activity and how the induced changes depend on network state. Here we examined the immediate and outlasting effects of the gated high-frequency electric field associated with LFMS on the cortical activity as a function of neuromodulatory tone that defines network state. We used a sham-controlled study design to investigate effects of stimulation (20 min of 0.5 s trains of 500 Hz charge-balanced pulse stimulation patterned at 0.5 Hz) on neural activity in mouse medial prefrontal cortex in vitro. Bath application of cholinergic and noradrenergic agents enabled us to examine the stimulation effects as a function of neuromodulatory tone. The stimulation attenuated the increase in firing rate of layer V cortical neurons during the post-stimulation period in the presence of cholinergic activation. The same stimulation had no significant immediate or outlasting effect in the absence of exogenous neuromodulators or in the presence of noradrenergic activation. These results provide electrophysiological insights into the neuromodulatory-dependent effects of gated high-frequency stimulation. More broadly, our results are the first to provide a mechanistic demonstration of how behavioral states and arousal levels may modify the effects of non-invasive brain stimulation.

Non-linear transfer characteristics of stimulation and recording hardware account for spurious low-frequency artifacts during amplitude modulated transcranial alternating current stimulation (AM-tACS).

Amplitude modulated transcranial alternating current stimulation (AM-tACS) has been recently proposed as a possible solution to overcome the pronounced stimulation artifact encountered when recording brain activity during tACS. In theory, AM-tACS does not entail power at its modulating frequency, thus avoiding the problem of spectral overlap between brain signal of interest and stimulation artifact. However, the current study demonstrates how weak non-linear transfer characteristics inherent to stimulation and recording hardware can reintroduce spurious artifacts at the modulation frequency. The input-output transfer functions (TFs) of different stimulation setups were measured. Setups included recordings of signal-generator and stimulator outputs and M/EEG phantom measurements. 6th-degree polynomial regression models were fitted to model the input-output TFs of each setup. The resulting TF models were applied to digitally generated AM-tACS signals to predict the frequency of spurious artifacts in the spectrum. All four setups measured for the study exhibited low-frequency artifacts at the modulation frequency and its harmonics when recording AM-tACS. Fitted TF models showed non-linear contributions significantly different from zero (all p < .05) and successfully predicted the frequency of artifacts observed in AM-signal recordings. Results suggest that even weak non-linearities of stimulation and recording hardware can lead to spurious artifacts at the modulation frequency and its harmonics. These artifacts were substantially larger than alpha-oscillations of a human subject in the MEG. Findings emphasize the need for more linear stimulation devices for AM-tACS and careful analysis procedures, taking into account low-frequency artifacts to avoid confusion with effects of AM-tACS on the brain.

Targeting alpha-band oscillations in a cortical model with amplitude-modulated high-frequency transcranial electric stimulation.

Non-invasive brain stimulation to target specific network activity patterns, e.g. transcranial alternating current stimulation (tACS), has become an essential tool to understand the causal role of neuronal oscillations in cognition and behavior. However, conventional sinusoidal tACS limits the ability to record neuronal activity during stimulation and lacks spatial focality. One particularly promising new tACS stimulation paradigm uses amplitude-modulated (AM) high-frequency waveforms (AM-tACS) with a slow signal envelope that may overcome the limitations. Moreover. AM-tACS using high-frequency carrier signals is more tolerable than conventional tACS, e.g. in terms of skin irritation and occurrence of phosphenes, when applied at the same current intensities (e.g. 1-2 mA). Yet, the fundamental mechanism of neuronal target-engagement by AM-tACS waveforms has remained unknown. We used a computational model of cortex to investigate how AM-tACS modulates endogenous oscillations and compared the target engagement mechanism to the case of conventional (unmodulated) low-frequency tACS. Analysis of stimulation amplitude and frequency indicated that cortical oscillations were phase-locked to the envelope of the AM stimulation signal, which thus exhibits the same target engagement mechanism as conventional (unmodulated) low frequency tACS. However, in the computational model substantially higher current intensities were needed for AM-tACS than for low-frequency (unmodulated) tACS waveforms to achieve pronounced phase synchronization. Our analysis of the carrier frequency suggests that there might be a trade-off between the use of high-frequency carriers and the stimulation amplitude required for successful entrainment. Together, our computational simulations support the use of slow-envelope high frequency carrier AM waveforms as a tool for noninvasive modulation of brain oscillations. More empirical data will be needed to identify the optimal stimulation parameters and to evaluate tolerability and safety of both, AM- and conventional tACS.

Ih interacts with somato-dendritic structure to determine frequency response to weak alternating electric field stimulation.

Transcranial current stimulation (tCS) modulates brain dynamics using weak electric fields. Given the pathological changes in brain network oscillations in neurological and psychiatric illnesses, using alternating electric field waveforms that engage rhythmic activity has been proposed as a targeted, network-level treatment approach. Previous studies have investigated the effects of electric fields at the neuronal level. However, the biophysical basis of the cellular response to electric fields has remained limited. Here, we characterized the frequency-dependent response of different compartments in a layer V pyramidal neuron to exogenous electric fields to dissect the relative contributions of voltage-gated ion channels and neuronal morphology. Hyperpolarization-activated cation current (Ih) in the distal dendrites was the primary ionic mechanism shaping the model's response to electric field stimulation and caused subthreshold resonance in the tuft at 20 ± 4 Hz. In contrast, subthreshold Ih-mediated resonance in response to local sinusoidal current injection was present in all model compartments at 11 ± 2 Hz. The frequencies of both resonance responses were modulated by Ih conductance density. We found that the difference in resonance frequency between the two stimulation types can be explained by the fact that exogenous electric fields simultaneously polarize the membrane potentials at the distal ends of the neuron (relative to field direction) in opposite directions. Our results highlight the role of Ih in shaping the cellular response to electric field stimulation and suggest that the common model of tCS as a weak somatic current injection fails to capture the cellular effects of electric field stimulation. NEW & NOTEWORTHY Modulation of cortical oscillation by brain stimulation serves as a tool to understand the causal role of network oscillations in behavior and is a potential treatment modality that engages impaired network oscillations in disorders of the central nervous system. To develop targeted stimulation paradigms, cellular-level effects must be understood. We demonstrate that hyperpolarization-activated cation current (Ih) and cell morphology cooperatively shape the response to applied alternating electric fields.

Which System Variables Carry Robust Early Signs of Upcoming Phase Transition? An Ecological Example.

Growth of critical fluctuations prior to catastrophic state transition is generally regarded as a universal phenomenon, providing a valuable early warning signal in dynamical systems. Using an ecological fisheries model of three populations (juvenile prey J, adult prey A and predator P), a recent study has reported silent early warning signals obtained from P and A populations prior to saddle-node (SN) bifurcation, and thus concluded that early warning signals are not universal. By performing a full eigenvalue analysis of the same system we demonstrate that while J and P populations undergo SN bifurcation, A does not jump to a new state, so it is not expected to carry early warning signs. In contrast with the previous study, we capture a significant increase in the noise-induced fluctuations in the P population, but only on close approach to the bifurcation point; it is not clear why the P variance initially shows a decaying trend. Here we resolve this puzzle using observability measures from control theory. By computing the observability coefficient for the system from the recordings of each population considered one at a time, we are able to quantify their ability to describe changing internal dynamics. We demonstrate that precursor fluctuations are best observed using only the J variable, and also P variable if close to transition. Using observability analysis we are able to describe why a poorly observable variable (P) has poor forecasting capabilities although a full eigenvalue analysis shows that this variable undergoes a bifurcation. We conclude that observability analysis provides complementary information to identify the variables carrying early-warning signs about impending state transition.

Noise-induced precursors of state transitions in the stochastic Wilson-cowan model.

The Wilson-Cowan neural field equations describe the dynamical behavior of a 1-D continuum of excitatory and inhibitory cortical neural aggregates, using a pair of coupled integro-differential equations. Here we use bifurcation theory and small-noise linear stochastics to study the range of a phase transitions-sudden qualitative changes in the state of a dynamical system emerging from a bifurcation-accessible to the Wilson-Cowan network. Specifically, we examine saddle-node, Hopf, Turing, and Turing-Hopf instabilities. We introduce stochasticity by adding small-amplitude spatio-temporal white noise, and analyze the resulting subthreshold fluctuations using an Ornstein-Uhlenbeck linearization. This analysis predicts divergent changes in correlation and spectral characteristics of neural activity during close approach to bifurcation from below. We validate these theoretical predictions using numerical simulations. The results demonstrate the role of noise in the emergence of critically slowed precursors in both space and time, and suggest that these early-warning signals are a universal feature of a neural system close to bifurcation. In particular, these precursor signals are likely to have neurobiological significance as early warnings of impending state change in the cortex. We support this claim with an analysis of the in vitro local field potentials recorded from slices of mouse-brain tissue. We show that in the period leading up to emergence of spontaneous seizure-like events, the mouse field potentials show a characteristic spectral focusing toward lower frequencies concomitant with a growth in fluctuation variance, consistent with critical slowing near a bifurcation point. This observation of biological criticality has clear implications regarding the feasibility of seizure prediction.