Differential polarization of cortical pyramidal neuron dendrites through weak extracellular fields

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.

Cell-class-specific electric field entrainment of neural activity

Electric fields affect the activity of neurons and brain circuits, yet how this happens at the cellular level remains enigmatic. Lack of understanding of how to stimulate the brain to promote or suppress specific activity significantly limits basic research and clinical applications. Here, we study how electric fields impact subthreshold and spiking properties of major cortical neuronal classes. We find that neurons in the rodent and human cortex exhibit strong, cell-class-dependent entrainment that depends on stimulation frequency. Excitatory pyramidal neurons, with their slower spike rate, entrain to both slow and fast electric fields, while inhibitory classes like Pvalb and Sst (with their fast spiking) predominantly phase-lock to fast fields. We show that this spike-field entrainment is the result of two effects: non-specific membrane polarization occurring across classes and class-specific excitability properties. Importantly, these properties are present across cortical areas and species. These findings allow for the design of selective and class-specific neuromodulation.

intensity- and frequency-specific effects of transcranial alternating current stimulation are explained by network dynamics

Objective. Transcranial alternating current stimulation (tACS) can be used to non-invasively entrain neural activity and thereby cause changes in local neural oscillatory power. Despite its increased use in cognitive and clinical neuroscience, the fundamental mechanisms of tACS are still not fully understood.Approach. We developed a computational neuronal network model of two-compartment pyramidal neurons (PY) and inhibitory interneurons, which mimic the local cortical circuits. We modeled tACS with electric field strengths that are achievable in human applications. We then simulated intrinsic network activity and measured neural entrainment to investigate how tACS modulates ongoing endogenous oscillations.Main results. The intensity-specific effects of tACS are non-linear. At low intensities (<0.3 mV mm-1), tACS desynchronizes neural firing relative to the endogenous oscillations. At higher intensities (>0.3 mV mm-1), neurons are entrained to the exogenous electric field. We then further explore the stimulation parameter space and find that the entrainment of ongoing cortical oscillations also depends on stimulation frequency by following an Arnold tongue. Moreover, neuronal networks can amplify the tACS-induced entrainment via synaptic coupling and network effects. Our model shows that PY are directly entrained by the exogenous electric field and drive the inhibitory neurons.Significance. The results presented in this study provide a mechanistic framework for understanding the intensity- and frequency-specific effects of oscillating electric fields on neuronal networks. This is crucial for rational parameter selection for tACS in cognitive studies and clinical applications.

Cell class-specific electric field entrainment of neural activity

Electric fields affect the activity of neurons and brain circuits, yet how this interaction happens at the cellular level remains enigmatic. Lack of understanding on how to stimulate the human brain to promote or suppress specific activity patterns significantly limits basic research and clinical applications. Here we study how electric fields impact the subthreshold and spiking properties of major cortical neuronal classes. We find that cortical neurons in rodent neocortex and hippocampus as well as human cortex exhibit strong and cell class-dependent entrainment that depends on the stimulation frequency. Excitatory pyramidal neurons with their typically slower spike rate entrain to slow and fast electric fields, while inhibitory classes like Pvalb and SST with their fast spiking predominantly phase lock to fast fields. We show this spike-field entrainment is the result of two effects: non-specific membrane polarization occurring across classes and class-specific excitability properties. Importantly, these properties of spike-field and class-specific entrainment are present in cells across cortical areas and species (mouse and human). These findings open the door to the design of selective and class-specific neuromodulation technologies.

Cognitive and Neuropathophysiological Outcomes of Gamma-tACS in Dementia: A Systematic Review

Despite the numerous pharmacological interventions targeting dementia, no disease-modifying therapy is available, and the prognosis remains unfavorable. A promising perspective involves tackling high-frequency gamma-band (> 30 Hz) oscillations involved in hippocampal-mediated memory processes, which are impaired from the early stages of typical Alzheimer's Disease (AD). Particularly, the positive effects of gamma-band entrainment on mouse models of AD have prompted researchers to translate such findings into humans using transcranial alternating current stimulation (tACS), a methodology that allows the entrainment of endogenous cortical oscillations in a frequency-specific manner. This systematic review examines the state-of-the-art on the use of gamma-tACS in Mild Cognitive Impairment (MCI) and dementia patients to shed light on its feasibility, therapeutic impact, and clinical effectiveness. A systematic search from two databases yielded 499 records resulting in 10 included studies and a total of 273 patients. The results were arranged in single-session and multi-session protocols. Most of the studies demonstrated cognitive improvement following gamma-tACS, and some studies showed promising effects of gamma-tACS on neuropathological markers, suggesting the feasibility of gamma-tACS in these patients anyhow far from the strong evidence available for mouse models. Nonetheless, the small number of studies and their wide variability in terms of aims, parameters, and measures, make it difficult to draw firm conclusions. We discuss results and methodological limitations of the studies, proposing possible solutions and future avenues to improve research on the effects of gamma-tACS on dementia.

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.

State of the Art and Current Challenges on Electroactive Biomaterials and Strategies for Neural Tissue Regeneration

The loss or failure of an organ/tissue stands as one of the healthcare system's most prevalent, devastating, and costly challenges. Strategies for neural tissue repair and regeneration have received significant attention due to their particularly strong impact on patients' well-being. Many research efforts are dedicated not only to control the disease symptoms but also to find solutions to repair the damaged tissues. Neural tissue engineering (TE) plays a key role in addressing this problem and significant efforts are being carried out to develop strategies for neural repair treatment. In the last years, active materials allowing to tune cell-materials interaction are being increasingly used, representing a recent paradigm in TE applications. Among the most important stimuli influencing cell behavior are the electrical and mechanical ones. In this way, materials with the ability to provide this kind of stimuli to the neural cells seem to be appropriate to support neural TE. In this scope, this review summarizes the different biomaterials types used for neural TE, highlighting the relevance of using active biomaterials and electrical stimulation. Furthermore, this review provides not only a compilation of the most relevant studies and results but also strategies for novel and more biomimetic approaches for neural TE.

Less might be more: 1 mA but not 1.5 mA of tDCS improves tactile orientation discrimination

Background

Transcranial direct current stimulation (tDCS) is a frequently used brain stimulation method; however, studies on tactile perception using tDCS are inconsistent, which might be explained by the variations in endogenous and exogenous parameters that influence tDCS.

Objectives

We aimed to investigate the effect of one of these endogenous parameters-the tDCS amplitude-on tactile perception.

Methods

We conducted this experiment on 28 undergraduates/graduates aged 18-36 years. In separate sessions, participants received 20 min of 1 mA or 1.5 mA current tDCS in a counterbalanced order. Half of the participants received anodal tDCS of the left SI coupled with cathodal tDCS of the right SI, and this montage was reversed for the other half. Pre- and post-tDCS tactile discrimination performance was assessed using the Grating Orientation Task (GOT). In this task, plastic domes with gratings of different widths cut into their surfaces are placed on the fingertip, and participants have to rate the orientation of the gratings.

Results

Linear modeling with amplitude, dome, and session as within factors and montage as between factors revealed the following: significant main effects of grating width, montage, and session and a marginally significant interaction effect of session and amplitude. Posthoc t-tests indicated that performance in GOT improved after 1 mA but not 1.5 mA tDCS independent of the montage pattern of the electrodes.

Conclusion

Increasing the stimulation amplitude from 1 mA to 1.5 mA does not facilitate the tDCS effect on GOT performance. On the contrary, the effect seemed more robust for the lower-current amplitude.

Transcranial magnetic stimulation in non-human primates: A systematic review

Transcranial magnetic stimulation (TMS) is widely employed as a tool to investigate and treat brain diseases. However, little is known about the direct effects of TMS on the brain. Non-human primates (NHPs) are a valuable translational model to investigate how TMS affects brain circuits given their neurophysiological similarity with humans and their capacity to perform complex tasks that approach human behavior. This systematic review aimed to identify studies using TMS in NHPs as well as to assess their methodological quality through a modified reference checklist. The results show high heterogeneity and superficiality in the studies regarding the report of the TMS parameters, which have not improved over the years. This checklist can be used for future TMS studies with NHPs to ensure transparency and critical appraisal. The use of the checklist would improve methodological soundness and interpretation of the studies, facilitating the translation of the findings to humans. The review also discusses how advancements in the field can elucidate the effects of TMS in the brain.

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.

Neurocognitive, physiological, and biophysical effects of transcranial alternating current stimulation

Transcranial alternating current stimulation (tACS) can modulate human neural activity and behavior. Accordingly, tACS has vast potential for cognitive research and brain disorder therapies. The stimulation generates oscillating electric fields in the brain that can bias neural spike timing, causing changes in local neural oscillatory power and cross-frequency and cross-area coherence. tACS affects cognitive performance by modulating underlying single or nested brain rhythms, local or distal synchronization, and metabolic activity. Clinically, stimulation tailored to abnormal neural oscillations shows promising results in alleviating psychiatric and neurological symptoms. We summarize the findings of tACS mechanisms, its use for cognitive applications, and novel developments for personalized stimulation.

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.

Entrainment of cerebellar purkinje cells with directional AC electric fields in anesthetized rats

BACKGROUND

Transcranial electrical stimulation (tES) shows promise to treat neurological disorders. Knowledge of how the orthogonal components of the electric field (E-field) alter neuronal activity is required for strategic placement of transcranial electrodes. Yet, essentially no information exists on this relationship for mammalian cerebellum in vivo, despite the cerebellum being a target for clinical tES studies.

OBJECTIVE

To characterize how cerebellar Purkinje cell (PC) activity varies with the intensity, frequency, and direction of applied AC and DC E-fields.

METHODS

Extracellular recordings were obtained from vermis lobule 7 PCs in anesthetized rats. AC (2-100 Hz) or DC E-fields were generated in a range of intensities (0.75-30 mV/mm) in three orthogonal directions. Field-evoked PC simple spike activity was characterized in terms of firing rate modulation and phase-locking as a function of these parameters. t-tests were used for statistical comparisons.

RESULTS

The effect of applied E-fields was direction and intensity dependent, with rostrocaudally directed fields causing stronger modulations than dorsoventral fields and mediolaterally directed ones causing little to no effect, on average. The directionality dependent modulation suggests that PC is the primary cell type affected the most by electric stimulation, and this effect was probably given rise by a large dendritic tree and a soma. AC stimulation entrained activity in a frequency dependent manner, with stronger phase-locking to the stimulus cycle at higher frequencies. DC fields produced a modulation consisting of strong transients at current onset and offset with an intervening plateau.

CONCLUSION

Orientation of the exogenous E-field critically determines the modulation depth of cerebellar cortical output. With properly oriented fields, PC simple spike activity can strongly be entrained by AC fields, overriding the spontaneous firing pattern.

Dose-dependent effects of transcranial alternating current stimulation on spike timing in awake nonhuman primates

Weak extracellular electric fields can influence spike timing in neural networks. Approaches to noninvasively impose these fields on the brain have high therapeutic potential in neurology and psychiatry. Transcranial alternating current stimulation (TACS) is hypothesized to affect spike timing and cause neural entrainment. However, the conditions under which these effects occur in vivo are unknown. Here, we recorded single-unit activity in the neocortex in awake nonhuman primates during TACS and found dose-dependent neural entrainment to the stimulation waveform. Cluster analysis of changes in interspike intervals identified two main types of neural responses to TACS-increased burstiness and phase entrainment. Our results uncover key mechanisms of TACS and show that the stimulation affects spike timing in the awake primate brain at intensities feasible in humans. Thus, novel TACS protocols tailored to ongoing brain activity may be a tool to normalize spike timing in maladaptive brain networks and neurological disease.

Biophysically grounded mean-field models of neural populations under electrical stimulation

Electrical stimulation of neural systems is a key tool for understanding neural dynamics and ultimately for developing clinical treatments. Many applications of electrical stimulation affect large populations of neurons. However, computational models of large networks of spiking neurons are inherently hard to simulate and analyze. We evaluate a reduced mean-field model of excitatory and inhibitory adaptive exponential integrate-and-fire (AdEx) neurons which can be used to efficiently study the effects of electrical stimulation on large neural populations. The rich dynamical properties of this basic cortical model are described in detail and validated using large network simulations. Bifurcation diagrams reflecting the network's state reveal asynchronous up- and down-states, bistable regimes, and oscillatory regions corresponding to fast excitation-inhibition and slow excitation-adaptation feedback loops. The biophysical parameters of the AdEx neuron can be coupled to an electric field with realistic field strengths which then can be propagated up to the population description. We show how on the edge of bifurcation, direct electrical inputs cause network state transitions, such as turning on and off oscillations of the population rate. Oscillatory input can frequency-entrain and phase-lock endogenous oscillations. Relatively weak electric field strengths on the order of 1 V/m are able to produce these effects, indicating that field effects are strongly amplified in the network. The effects of time-varying external stimulation are well-predicted by the mean-field model, further underpinning the utility of low-dimensional neural mass models.

Direct current stimulation boosts hebbian plasticity in vitro

BACKGROUND

There is evidence that transcranial direct current stimulation (tDCS) can improve learning performance. Arguably, this effect is related to long term potentiation (LTP), but the precise biophysical mechanisms remain unknown.

HYPOTHESIS

We propose that direct current stimulation (DCS) causes small changes in postsynaptic membrane potential during ongoing endogenous synaptic activity. The altered voltage dynamics in the postsynaptic neuron then modify synaptic strength via the machinery of endogenous voltage-dependent Hebbian plasticity. This hypothesis predicts that DCS should exhibit Hebbian properties, namely pathway specificity and associativity.

METHODS

We studied the effects of DCS applied during the induction of LTP in the CA1 region of rat hippocampal slices and using a biophysical computational model.

RESULTS

DCS enhanced LTP, but only at synapses that were undergoing plasticity, confirming that DCS respects Hebbian pathway specificity. When different synaptic pathways cooperated to produce LTP, DCS enhanced this cooperation, boosting Hebbian associativity. Further slice experiments and computer simulations support a model where polarization of postsynaptic pyramidal neurons drives these plasticity effects through endogenous Hebbian mechanisms. The model is able to reconcile several experimental results by capturing the complex interaction between the induced electric field, neuron morphology, and endogenous neural activity.

CONCLUSIONS

These results suggest that tDCS can enhance associative learning. We propose that clinical tDCS should be applied during tasks that induce Hebbian plasticity to harness this phenomenon, and that the effects should be task specific through their interaction with endogenous plasticity mechanisms. Models that incorporate brain state and plasticity mechanisms may help to improve prediction of tDCS outcomes.

Astroglial Isopotentiality and Calcium-Associated Biomagnetic Field Effects on Cortical Neuronal Coupling

Synaptic neurotransmission is necessary but does not sufficiently explain superior cognitive faculties. Growing evidence has shown that neuron-astroglial chemical crosstalk plays a critical role in the processing of information, computation, and memory. In addition to chemical and electrical communication among neurons and between neurons and astrocytes, other nonsynaptic mechanisms called ephaptic interactions can contribute to the neuronal synchronization from different brain regions involved in the processing of information. New research on brain astrocytes has clearly shown that the membrane potential of these cells remains very stable among neighboring and distant astrocytes due to the marked bioelectric coupling between them through gap junctions. This finding raises the possibility that the neocortical astroglial network exerts a guiding template modulating the excitability and synchronization of trillions of neurons by astroglial Ca²⁺-associated bioelectromagnetic interactions. We propose that bioelectric and biomagnetic fields of the astroglial network equalize extracellular local field potentials (LFPs) and associated local magnetic field potentials (LMFPs) in the cortical layers of the brain areas involved in the processing of information, contributing to the adequate and coherent integration of external and internal signals. This article reviews the current knowledge of ephaptic interactions in the cerebral cortex and proposes that the isopotentiality of cortical astrocytes is a prerequisite for the maintenance of the bioelectromagnetic crosstalk between neurons and astrocytes in the neocortex.

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.

Beyond the target area: an integrative view of tDCS-induced motor cortex modulation in patients and athletes

Transcranial Direct Current Stimulation (tDCS) is a non-invasive technique used to modulate neural tissue. Neuromodulation apparently improves cognitive functions in several neurologic diseases treatment and sports performance. In this study, we present a comprehensive, integrative review of tDCS for motor rehabilitation and motor learning in healthy individuals, athletes and multiple neurologic and neuropsychiatric conditions. We also report on neuromodulation mechanisms, main applications, current knowledge including areas such as language, embodied cognition, functional and social aspects, and future directions. We present the use and perspectives of new developments in tDCS technology, namely high-definition tDCS (HD-tDCS) which promises to overcome one of the main tDCS limitation (i.e., low focality) and its application for neurological disease, pain relief, and motor learning/rehabilitation. Finally, we provided information regarding the Transcutaneous Spinal Direct Current Stimulation (tsDCS) in clinical applications, Cerebellar tDCS (ctDCS) and its influence on motor learning, and TMS combined with electroencephalography (EEG) as a tool to evaluate tDCS effects on brain function.

Distinct Montages of Slow Oscillatory Transcranial Direct Current Stimulation (so-tDCS) Constitute Different Mechanisms during Quiet Wakefulness

Slow oscillatory- (so-) tDCS has been applied in many sleep studies aimed to modulate brain rhythms of slow wave sleep and memory consolidation. Yet, so-tDCS may also modify coupled oscillatory networks. Efficacy of weak electric brain stimulation is however variable and dependent upon the brain state at the time of stimulation (subject and/or task-related) as well as on stimulation parameters (e.g., electrode placement and applied current. Anodal so-tDCS was applied during wakefulness with eyes-closed to examine efficacy when deviating from the dominant brain rhythm. Additionally, montages of different electrodes size and applied current strength were used. During a period of quiet wakefulness bilateral frontolateral stimulation (F3, F4; return electrodes at ipsilateral mastoids) was applied to two groups: ‘Group small’ (n = 16, f:8; small electrodes: 0.50 cm²; maximal current per electrode pair: 0.26 mA) and ‘Group Large’ (n = 16, f:8; 35 cm²; 0.35 mA). Anodal so-tDCS (0.75 Hz) was applied in five blocks of 5 min epochs with 1 min stimulation-free epochs between the blocks. A finger sequence tapping task (FSTT) was used to induce comparable cortical activity across sessions and subject groups. So-tDCS resulted in a suppression of alpha power over the parietal cortex. Interestingly, in Group Small alpha suppression occurred over the standard band (8–12 Hz), whereas for Group Large power of individual alpha frequency was suppressed. Group Small also revealed a decrease in FSTT performance at retest after stimulation. It is essential to include concordant measures of behavioral and brain activity to help understand variability and poor reproducibility in oscillatory-tDCS studies.

Comparative modeling of transcranial magnetic and electric stimulation in mouse, monkey, and human

Transcranial magnetic stimulation (TMS) and transcranial electric stimulation (TES) are increasingly popular methods to noninvasively affect brain activity. However, their mechanism of action and dose-response characteristics remain under active investigation. Translational studies in animals play a pivotal role in these efforts due to a larger neuroscientific toolset enabled by invasive recordings. In order to translate knowledge gained in animal studies to humans, it is crucial to generate comparable stimulation conditions with respect to the induced electric field in the brain. Here, we conduct a finite element method (FEM) modeling study of TMS and TES electric fields in a mouse, capuchin and macaque monkeys, and a human model. We systematically evaluate the induced electric fields and analyze their relationship to head and brain anatomy. We find that with increasing head size, TMS-induced electric field strength first increases and then decreases according to a two-term exponential function. TES-induced electric field strength strongly decreases from smaller to larger specimen with up to 100x fold differences across species. Our results can serve as a basis to compare and match stimulation parameters across studies in animals and humans.

Weak electric fields promote resonance in neuronal spiking activity: Analytical results from two-compartment cell and network models

Transcranial brain stimulation and evidence of ephaptic coupling have sparked strong interests in understanding the effects of weak electric fields on the dynamics of neuronal populations. While their influence on the subthreshold membrane voltage can be biophysically well explained using spatially extended neuron models, mechanistic analyses of neuronal spiking and network activity have remained a methodological challenge. More generally, this challenge applies to phenomena for which single-compartment (point) neuron models are oversimplified. Here we employ a pyramidal neuron model that comprises two compartments, allowing to distinguish basal-somatic from apical dendritic inputs and accounting for an extracellular field in a biophysically minimalistic way. Using an analytical approach we fit its parameters to reproduce the response properties of a canonical, spatial model neuron and dissect the stochastic spiking dynamics of single cells and large networks. We show that oscillatory weak fields effectively mimic anti-correlated inputs at the soma and dendrite and strongly modulate neuronal spiking activity in a rather narrow frequency band. This effect carries over to coupled populations of pyramidal cells and inhibitory interneurons, boosting network-induced resonance in the beta and gamma frequency bands. Our work contributes a useful theoretical framework for mechanistic analyses of population dynamics going beyond point neuron models, and provides insights on modulation effects of extracellular fields due to the morphology of pyramidal cells.

The elongated spatial structure of pyramidal neurons, which possess large apical dendrites, plays an important role for the integration of synaptic inputs and mediates sensitivity to weak extracellular electric fields. Modeling studies at the population level greatly contribute to our mechanistic understanding but face a methodological challenge because morphologically detailed neuron models are too complex for use in noisy, in-vivo like conditions and large networks in particular. Here we present an analytical approach based on a two-compartment spiking neuron model that can distinguish synaptic inputs at the apical dendrite from those at the somatic region and accounts for an extracellular field in a biophysically minimalistic way. We devised efficient methods to approximate the responses of a spatially more detailed pyramidal neuron model, and to study the spiking dynamics of single neurons and sparsely coupled large networks in the presence of fluctuating inputs. Using these methods we focused on how responses are affected by oscillatory weak fields. Our results suggest that ephaptic coupling may play a mechanistic role for oscillations of population activity and indicate the potential to entrain networks by weak electric stimulation.

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.

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.