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

Frequency-dependent phase entrainment of cortical cell types during tACS: computational modeling evidence

Objective. Transcranial alternating current stimulation (tACS) enables non-invasive modulation of brain activity, holding promise for clinical and research applications. Yet, it remains unclear how the stimulation frequency differentially impacts various neuron types. Here, we aimed to quantify the frequency-dependent behavior of key neocortical cell types.Approach. We used both detailed (anatomical multicompartments) and simplified (three compartments) single-cell modeling approaches based on the Hodgkin-Huxley formalism to study neocortical excitatory and inhibitory cells under various tACS intensities and frequencies within the 5-50 Hz range at rest and during basal 10 Hz activity.Main results. L5 pyramidal cells (PCs) exhibited the highest polarizability at direct current, ranging from 0.21 to 0.25 mm and decaying exponentially with frequency. Inhibitory neurons displayed membrane resonance in the 5-15 Hz range with lower polarizability, although bipolar cells had higher polarizability. Layer 5 PC demonstrated the highest entrainment close to 10 Hz, which decayed with frequency. In contrast, inhibitory neurons entrainment increased with frequency, reaching levels akin to PC. Results from simplified models could replicate phase preferences, while amplitudes tended to follow opposite trends in PC.Significance. tACS-induced membrane polarization is frequency-dependent, revealing observable resonance behavior. Whilst optimal phase entrainment of sustained activity is achieved in PC when tACS frequency matches endogenous activity, inhibitory neurons tend to be entrained at higher frequencies. Consequently, our results highlight the potential for precise, cell-specific targeting for tACS.

Frequency-domain analysis of membrane polarization in two-compartment model neurons with weak alternating electric fields

Transcranial alternating current stimulation (tACS) is widely used in studying brain functions and the treatment of neuropsychiatric diseases in a frequency-specific manner. However, how tACS works on neuronal activity has been poorly understood. In this paper, we use linear system analysis to investigate how weak alternating electric fields (EFs) affect the membrane polarization of neurons in the frequency domain. Two biophysically realistic conductance-based two-compartment models of cortical pyramidal neurons are developed to simulate subthreshold membrane polarization with weak alternating EFs. We linearize the original nonlinear models at the stable equilibrium points and further simplify them to the two- or three-dimensional linear systems. Thus, we calculate the transfer functions of the low-dimensional linear models to model neuronal polarization patterns. Based on the transfer functions, we compute the amplitude- and phase-frequency characteristics to describe the relationship between weak EFs and membrane polarization. We also computed the parameters (gain, zeros, and poles) and structures (the number of zeros and poles) of transfer functions to reveal how neuronal intrinsic properties affect the parameters and structure of transfer functions and thus the frequency-dependent membrane polarization with alternating EFs. We find that the amplitude and phase of membrane polarization both strongly depended on EF frequency, and these frequency responses are modulated by the intrinsic properties of neurons. The compartment geometry, internal coupling conductance, and ionic currents (except Ih) affect the frequency-dependent polarization by mainly changing the gain and pole of transfer functions. Larger gain contributes to larger amplitude-frequency characteristics. The closer the pole is to the imaginary axis, the lower phase-frequency characteristics. However, Ih changes the structure of transfer function in the dendrite by introducing a new pair of zero-pole points, which decrease the amplitude at low frequencies and thus lead to a visible resonance. These results highlight the effects of passive properties and active ion currents on subthreshold membrane polarization with alternating EFs in the frequency domain, which provide an explainable connection of how intrinsic properties of neurons modulate the neuronal input-output functions with weak EF stimulation.

Frequency-dependent membrane polarization across neocortical cell types and subcellular elements by transcranial alternating current stimulation

Objective.Transcranial alternating current stimulation (tACS) is a non-invasive brain stimulation technique that directly interacts with ongoing brain oscillations in a frequency-dependent manner. However, it remains largely unclear how the cellular effects of tACS vary between cell types and subcellular elements.Approach.In this study, we use a set of morphologically realistic models of neocortical neurons to simulate the cellular response to uniform oscillating electric fields (EFs). We systematically characterize the membrane polarization in the soma, axons, and dendrites with varying field directions, intensities, and frequencies.Main results.Pyramidal cells are more sensitive to axial EF that is roughly parallel to the cortical column, while interneurons are sensitive to axial EF and transverse EF that is tangent to the cortical surface. Membrane polarization in each subcellular element increases linearly with EF intensity, and its slope, i.e. polarization length, highly depends on the stimulation frequency. At each frequency, pyramidal cells are more polarized than interneurons. Axons usually experience the highest polarization, followed by the dendrites and soma. Moreover, a visible frequency resonance presents in the apical dendrites of pyramidal cells, while the other subcellular elements primarily exhibit low-pass filtering properties. In contrast, each subcellular element of interneurons exhibits complex frequency-dependent polarization. Polarization phase in each subcellular element of cortical neurons lags that of field and exhibits high-pass filtering properties. These results demonstrate that the membrane polarization is not only frequency-dependent, but also cell type- and subcellular element-specific. Through relating effective length and ion mechanism with polarization, we emphasize the crucial role of cell morphology and biophysics in determining the frequency-dependent membrane polarization.Significance.Our findings highlight the diverse polarization patterns across cell types as well as subcellular elements, which provide some insights into the tACS cellular effects and should be considered when understanding the neural spiking activity by tACS.

Neurophysiological mechanisms of transcranial alternating current stimulation

Neuronal oscillations are the primary basis for precise temporal coordination of neuronal processing and are linked to different brain functions. Transcranial alternating current stimulation (tACS) has demonstrated promising potential in improving cognition by entraining neural oscillations. Despite positive findings in recent decades, the results obtained are sometimes rife with variance and replicability problems, and the findings translation to humans is quite challenging. A thorough understanding of the mechanisms underlying tACS is necessitated for accurate interpretation of experimental results. Animal models are useful for understanding tACS mechanisms, optimizing parameter administration, and improving rational design for broad horizons of tACS. Here, we review recent electrophysiological advances in tACS from animal models, as well as discuss some critical issues for results coordination and translation. We hope to provide an overview of neurophysiological mechanisms and recommendations for future consideration to improve its validity, specificity, and reproducibility.

Excitatory and inhibitory effects of HCN channel modulation on excitability of layer V pyramidal cells

Dendrites of cortical pyramidal cells are densely populated by hyperpolarization-activated cyclic nucleotide-gated (HCN) channels, a.k.a. Ih channels. Ih channels are targeted by multiple neuromodulatory pathways, and thus are one of the key ion-channel populations regulating the pyramidal cell activity. Previous observations and theories attribute opposing effects of the Ih channels on neuronal excitability due to their mildly hyperpolarized reversal potential. These effects are difficult to measure experimentally due to the fine spatiotemporal landscape of the Ih activity in the dendrites, but computational models provide an efficient tool for studying this question in a reduced but generalizable setting. In this work, we build upon existing biophysically detailed models of thick-tufted layer V pyramidal cells and model the effects of over- and under-expression of Ih channels as well as their neuromodulation. We show that Ih channels facilitate the action potentials of layer V pyramidal cells in response to proximal dendritic stimulus while they hinder the action potentials in response to distal dendritic stimulus at the apical dendrite. We also show that the inhibitory action of the Ih channels in layer V pyramidal cells is due to the interactions between Ih channels and a hot zone of low voltage-activated Ca2+ channels at the apical dendrite. Our simulations suggest that a combination of Ih-enhancing neuromodulation at the proximal part of the apical dendrite and Ih-inhibiting modulation at the distal part of the apical dendrite can increase the layer V pyramidal excitability more than either of the two alone. Our analyses uncover the effects of Ih-channel neuromodulation of layer V pyramidal cells at a single-cell level and shed light on how these neurons integrate information and enable higher-order functions of the brain.

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.

Effects of Ih and TASK-like shunting current on dendritic impedance in layer 5 pyramidal-tract neurons

Pyramidal neurons in neocortex have complex input-output relationships that depend on their morphologies, ion channel distributions, and the nature of their inputs, but which cannot be replicated by simple integrate-and-fire models. The impedance properties of their dendritic arbors, such as resonance and phase shift, shape neuronal responses to synaptic inputs and provide intraneuronal functional maps reflecting their intrinsic dynamics and excitability. Experimental studies of dendritic impedance have shown that neocortical pyramidal tract neurons exhibit distance-dependent changes in resonance and impedance phase with respect to the soma. We, therefore, investigated how well several biophysically detailed multicompartment models of neocortical layer 5 pyramidal tract neurons reproduce the location-dependent impedance profiles observed experimentally. Each model tested here exhibited location-dependent impedance profiles, but most captured either the observed impedance amplitude or phase, not both. The only model that captured features from both incorporates hyperpolarization-activated cyclic nucleotide-gated (HCN) channels and a shunting current, such as that produced by Twik-related acid-sensitive K+ (TASK) channels. TASK-like channel density in this model was proportional to local HCN channel density. We found that although this shunting current alone is insufficient to produce resonance or realistic phase response, it modulates all features of dendritic impedance, including resonance frequencies, resonance strength, synchronous frequencies, and total inductive phase. We also explored how the interaction of HCN channel current (Ih) and a TASK-like shunting current shape synaptic potentials and produce degeneracy in dendritic impedance profiles, wherein different combinations of Ih and shunting current can produce the same impedance profile.NEW & NOTEWORTHY We simulated chirp current stimulation in the apical dendrites of 5 biophysically detailed multicompartment models of neocortical pyramidal tract neurons and found that a combination of HCN channels and TASK-like channels produced the best fit to experimental measurements of dendritic impedance. We then explored how HCN and TASK-like channels can shape the dendritic impedance as well as the voltage response to synaptic currents.

Temporal interference stimulation targets deep brain regions by modulating neural oscillations

BACKGROUND

Temporal interference (TI) stimulation of the brain generates amplitude-modulated electric fields oscillating in the kHz range with the goal of non-invasive targeted deep brain stimulation. Yet, the current intensities required in human (sensitivity) to modulate deep brain activity and if superficial brain region are spared (selectivity) at these intensities remains unclear.

OBJECTIVE

We developed an experimentally constrained theory for TI sensitivity to kHz electric field given the attenuation by membrane low-pass filtering property, and for TI selectivity to deep structures given the distribution of modulated and unmodulated electric fields in brain.

METHODS

The electric field threshold to modulate carbachol-induced gamma oscillations in rat hippocampal slices was determined for unmodulated 0.05-2 kHz sine waveforms, and 5 Hz amplitude-modulated waveforms with 0.1-2 kHz carrier frequencies. The neuronal effects are replicated with a computational network model to explore the underlying mechanisms, and then coupled to a validated current-flow model of the human head.

RESULTS

Amplitude-modulated electric fields are stronger in deep brain regions, while unmodulated electric fields are maximal at the cortical regions. Both experiment and model confirmed the hypothesis that spatial selectivity of temporal interference stimulation depends on the phasic modulation of neural oscillations only in deep brain regions. Adaptation mechanism (e.g. GABA_b) enhanced sensitivity to amplitude modulated waveform in contrast to unmodulated kHz and produced selectivity in modulating gamma oscillation (i.e. Higher gamma modulation in amplitude modulated vs unmodulated kHz stimulation). Selection of carrier frequency strongly affected sensitivity to amplitude modulation stimulation. Amplitude modulated stimulation with 100 Hz carrier frequency required ∼5 V/m (corresponding to ∼13 mA at the scalp surface), whereas, 1 kHz carrier frequency ∼60 V/m (∼160 mA) and 2 kHz carrier frequency ∼80 V/m (∼220 mA) to significantly modulate gamma oscillation. Sensitivity is increased (scalp current required decreased) for theoretical neuronal membranes with faster time constants.

CONCLUSION

The TI sensitivity (current required at the scalp) depends on the neuronal membrane time-constant (e.g. axons) approaching the kHz carrier frequency. TI selectivity is governed by network adaption (e.g. GABA_b) that is faster than the amplitude-modulation frequency. Thus, we show neuronal and network oscillations time-constants determine the scalp current required and the selectivity achievable with TI in humans.

Age-Dependent Effect of Transcranial Alternating Current Stimulation on Motor Skill Consolidation

Transcranial alternating current stimulation (tACS) is the application of subthreshold, sinusoidal current to modulate ongoing brain rhythms related to sensory, motor and cognitive processes. Electrophysiological studies suggested that the effect of tACS applied at an alpha frequency (8–12 Hz) was state-dependent. The effects of tACS, that is, an increase in parieto-occipital electroencephalography (EEG) alpha power and magnetoencephalography (MEG) phase coherence, was only observed when the eyes were open (low alpha power) and not when the eyes were closed (high alpha power). This state-dependency of the effects of alpha tACS might extend to the aging brain characterized by general slowing and decrease in spectral power of the alpha rhythm. We additionally hypothesized that tACS will influence the motor cortex, which is involved in motor skill learning and consolidation. A group of young and old healthy adults performed a serial reaction time task (SRTT) with their right hand before and after the tACS stimulation. Each participant underwent three sessions of stimulation: sham, stimulation applied at the individual participant’s alpha peak frequency or individual alpha peak frequency (iAPF; α-tACS) and stimulation with iAPF plus 2 Hz (α2-tACS) to the left motor cortex for 10 min (1.5 mA). We measured the effect of stimulation on general motor skill (GMS) and sequence-specific skill (SS) consolidation. We found that α-tACS and α2-tACS improved GMS and SS consolidation in the old group. In contrast, α-tACS minimally improved GMS consolidation but impaired SS consolidation in the young group. On the other hand, α2-tACS was detrimental to the consolidation of both skills in the young group. Our results suggest that individuals with aberrant alpha rhythm such as the elderly could benefit more from tACS stimulation, whereas for young healthy individuals with intact alpha rhythm the stimulation could be detrimental.

Implantable Direct Current Neural Modulation: Theory, Feasibility, and Efficacy

Implantable neuroprostheses such as cochlear implants, deep brain stimulators, spinal cord stimulators, and retinal implants use charge-balanced alternating current (AC) pulses to recover delivered charge and thus mitigate toxicity from electrochemical reactions occurring at the metal-tissue interface. At low pulse rates, these short duration pulses have the effect of evoking spikes in neural tissue in a phase-locked fashion. When the therapeutic goal is to suppress neural activity, implants typically work indirectly by delivering excitation to populations of neurons that then inhibit the target neurons, or by delivering very high pulse rates that suffer from a number of undesirable side effects. Direct current (DC) neural modulation is an alternative methodology that can directly modulate extracellular membrane potential. This neuromodulation paradigm can excite or inhibit neurons in a graded fashion while maintaining their stochastic firing patterns. DC can also sensitize or desensitize neurons to input. When applied to a population of neurons, DC can modulate synaptic connectivity. Because DC delivered to metal electrodes inherently violates safe charge injection criteria, its use has not been explored for practical applicability of DC-based neural implants. Recently, several new technologies and strategies have been proposed that address this safety criteria and deliver ionic-based direct current (iDC). This, along with the increased understanding of the mechanisms behind the transcutaneous DC-based modulation of neural targets, has caused a resurgence of interest in the interaction between iDC and neural tissue both in the central and the peripheral nervous system. In this review we assess the feasibility of in-vivo iDC delivery as a form of neural modulation. We present the current understanding of DC/neural interaction. We explore the different design methodologies and technologies that attempt to safely deliver iDC to neural tissue and assess the scope of application for direct current modulation as a form of neuroprosthetic treatment in disease. Finally, we examine the safety implications of long duration iDC delivery. We conclude that DC-based neural implants are a promising new modulation technology that could benefit from further chronic safety assessments and a better understanding of the basic biological and biophysical mechanisms that underpin DC-mediated neural modulation.

Modulations of dendritic Ca2+ spike with weak electric fields in layer 5 pyramidal cells

Weak electric fields (EFs) modulate input/output function of pyramidal cells. Dendritic Ca²⁺ spike is an important cellular mechanism for coupling synaptic inputs from different cortical layers, which plays a critical role in neuronal computation. This study aims to understand the effects of weak EFs on Ca²⁺ spikes initiated in the distal dendrites. We use a computational model to simulate dendritic Ca²⁺ spikes and backpropagating action potentials (APs) in layer 5 pyramidal cells. We apply uniform EFs (less than 20 mV/mm) to the model and examine how they affect the threshold for activation of Ca²⁺ spikes. We show that the effects of weak field on synaptically evoked Ca²⁺ spikes depend on the timing of synaptic inputs. When distal inputs coincide with the onset of EFs within a time window of several milliseconds, field-induced depolarization facilitates the initiation of Ca²⁺ spikes, while field-induced hyperpolarization suppresses dendritic APs. Sustained field-induced depolarization leads to the inactivation of Ca²⁺ channels and increases the threshold of Ca²⁺ spike. Sustained field-induced hyperpolarization de-inactivates Ca²⁺ channels and reduces the threshold of Ca²⁺ spike. By altering the threshold of backpropagation activated Ca²⁺ firing, field-induced depolarization increases the degree of coupling between inputs of the soma and distal dendrites, while field-induced hyperpolarization results in a decrease of coupling. The modulatory effects of weak EF are governed by the field direction with respect to the cell. Our study explains a fundamental link between field-induced polarization, dendritic Ca²⁺ spike, and somato-dendritic coupling. The findings are crucial to interpret how weak EFs achieve specific modulation of cellular activity.

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.

Mean field phase synchronization between chimera states

We study two-layer networks of identical phase oscillators. Each individual layer is a ring network for which a non-local intra-layer coupling leads to the formation of a chimera state. The number of oscillators and their natural frequencies is in general different across the layers. We couple the phases of individual oscillators in one layer to the phase of the mean field of the other layer. This coupling from the mean field to individual oscillators is done in both directions. For a sufficient strength of this inter-layer coupling, the phases of the mean fields lock across the two layers. In contrast, both layers continue to exhibit chimera states with no locking between the phases of individual oscillators across layers, and the two mean field amplitudes remain uncorrelated. Hence, the networks' mean fields show phase synchronization which is analogous to the one between low-dimensional chaotic oscillators. The required coupling strength to achieve this mean field phase synchronization increases with the mismatches in the network sizes and the oscillators' natural frequencies.

Differential polarization of cortical pyramidal neuron dendrites through weak extracellular fields

The rise of transcranial current stimulation (tCS) techniques have sparked an increasing interest in the effects of weak extracellular electric fields on neural activity. These fields modulate ongoing neural activity through polarization of the neuronal membrane. While the somatic polarization has been investigated experimentally, the frequency-dependent polarization of the dendritic trees in the presence of alternating (AC) fields has received little attention yet. Using a biophysically detailed model with experimentally constrained active conductances, we analyze the subthreshold response of cortical pyramidal cells to weak AC fields, as induced during tCS. We observe a strong frequency resonance around 10-20 Hz in the apical dendrites sensitivity to polarize in response to electric fields but not in the basal dendrites nor the soma. To disentangle the relative roles of the cell morphology and active and passive membrane properties in this resonance, we perform a thorough analysis using simplified models, e.g. a passive pyramidal neuron model, simple passive cables and reconstructed cell model with simplified ion channels. We attribute the origin of the resonance in the apical dendrites to (i) a locally increased sensitivity due to the morphology and to (ii) the high density of h-type channels. Our systematic study provides an improved understanding of the subthreshold response of cortical cells to weak electric fields and, importantly, allows for an improved design of tCS stimuli.