Effects of transcranial alternating current stimulation on spiking activity in computational models of single neocortical neurons

Computational Models of High-Definition Electroconvulsive Therapy for Focal or Multitargeting Treatment

ABSTRACT

Attempts to dissociate electroconvulsive therapy (ECT) therapeutic efficacy from cognitive side effects of ECT include modifying electrode placement, but traditional electrode placements employing 2 large electrodes are inherently nonfocal, limiting the ability to selectively engage targets associated with clinical benefit while avoiding nontargets associated with adverse side effects. Limited focality represents a technical limitation of conventional ECT, and there is growing evidence that the spatial distribution of the ECT electric fields induced in the brain drives efficacy and side effects. Computational models can be used to predict brain current flow patterns for existing and novel ECT montages. Using finite element method simulations (under quasi-static, nonadaptive assumptions, 800-mA total current), the electric fields generated in the superficial cortex and subcortical structures were predicted for the following traditional ECT montages (bilateral temporal, bifrontal, right unilateral) and experimental montages (focal electrically administered seizure therapy, lateralized high-definition [HD]-ECT, unilateral 4 × 1-ring HD-ECT, bilateral 4 × 1-ring HD-ECT, and a multipolar HD-ECT). Peak brain current density in regions of interest was quantified. Conventional montages (bilateral bifrontal, right unilateral) each produce distinct but diffuse and deep current flow. Focal electrically administered seizure therapy and lateralized HD-ECT produce unique, lateralized current flow, also impacting specific deep regions. A 4 × 1-ring HD-ECT restricts current flow to 1 (unilateral) or 2 (bilateral) cortical regions. Multipolar HD-ECT shows optimization to a specific target set. Future clinical trials are needed to determine whether enhanced control over current distribution is achieved with these experimental montages, and the resultant seizures, improve the risk/benefit ratio of ECT.

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.

The phase of tACS-entrained pre-SMA beta oscillations modulates motor inhibition

Inhibitory control has been linked to beta oscillations in the fronto-basal ganglia network. Here we aim to investigate the functional role of the phase of this oscillatory beta rhythm for successful motor inhibition. We applied 20 Hz transcranial alternating current stimulation (tACS) to the pre-supplementary motor area (pre-SMA) while presenting stop signals at 4 (Experiment 1) and 8 (Experiment 2) equidistant phases of the tACS entrained beta oscillations. Participants showed better inhibitory performance when stop signals were presented at the trough of the beta oscillation whereas their inhibitory control performance decreased with stop signals being presented at the oscillatory beta peak. These results are consistent with the communication through coherence theory, in which postsynaptic effects are thought to be greater when an input arrives at an optimal phase within the oscillatory cycle of the target neuronal population. The current study provides mechanistic insights into the neural communication principles underlying successful motor inhibition and may have implications for phase-specific interventions aimed at treating inhibitory control disorders such as PD or OCD.

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.

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.

Induced neural phase precession through exogenous electric fields

The gradual shifting of preferred neural spiking relative to local field potentials (LFPs), known as phase precession, plays a prominent role in neural coding. Correlations between the phase precession and behavior have been observed throughout various brain regions. As such, phase precession is suggested to be a global neural mechanism that promotes local neuroplasticity. However, causal evidence and neuroplastic mechanisms of phase precession are lacking so far. Here we show a causal link between LFP dynamics and phase precession. In three experiments, we modulated LFPs in humans, a non-human primate, and computational models using alternating current stimulation. We show that continuous stimulation of motor cortex oscillations in humans lead to a gradual phase shift of maximal corticospinal excitability by ~90°. Further, exogenous alternating current stimulation induced phase precession in a subset of entrained neurons (~30%) in the non-human primate. Multiscale modeling of realistic neural circuits suggests that alternating current stimulation-induced phase precession is driven by NMDA-mediated synaptic plasticity. Altogether, the three experiments provide mechanistic and causal evidence for phase precession as a global neocortical process. Alternating current-induced phase precession and consequently synaptic plasticity is crucial for the development of novel therapeutic neuromodulation methods.

Induced neural phase precession through exogeneous electric fields

The gradual shifting of preferred neural spiking relative to local field potentials (LFPs), known as phase precession, plays a prominent role in neural coding. Correlations between the phase precession and behavior have been observed throughout various brain regions. As such, phase precession is suggested to be a global neural mechanism that promotes local neuroplasticity. However, causal evidence and neuroplastic mechanisms of phase precession are lacking so far. Here we show a causal link between LFP dynamics and phase precession. In three experiments, we modulated LFPs in humans, a non-human primate, and computational models using alternating current stimulation. We show that continuous stimulation of motor cortex oscillations in humans lead to a gradual phase shift of maximal corticospinal excitability by ~90°. Further, exogenous alternating current stimulation induced phase precession in a subset of entrained neurons (~30%) in the non-human primate. Multiscale modeling of realistic neural circuits suggests that alternating current stimulation-induced phase precession is driven by NMDA-mediated synaptic plasticity. Altogether, the three experiments provide mechanistic and causal evidence for phase precession as a global neocortical process. Alternating current-induced phase precession and consequently synaptic plasticity is crucial for the development of novel therapeutic neuromodulation methods.

Understanding the effects of cortical gyrification in tACS: insights from experiments and computational models

The alpha rhythm is often associated with relaxed wakefulness or idling and is altered by various factors. Abnormalities in the alpha rhythm have been linked to several neurological and psychiatric disorders, including Alzheimer's disease. Transcranial alternating current stimulation (tACS) has been proposed as a potential tool to restore a disrupted alpha rhythm in the brain by stimulating at the individual alpha frequency (IAF), although some research has produced contradictory results. In this study, we applied an IAF-tACS protocol over parieto-occipital areas to a sample of healthy subjects and measured its effects over the power spectra. Additionally, we used computational models to get a deeper understanding of the results observed in the experiment. Both experimental and numerical results showed an increase in alpha power of 8.02% with respect to the sham condition in a widespread set of regions in the cortex, excluding some expected parietal regions. This result could be partially explained by taking into account the orientation of the electric field with respect to the columnar structures of the cortex, showing that the gyrification in parietal regions could generate effects in opposite directions (hyper-/depolarization) at the same time in specific brain regions. Additionally, we used a network model of spiking neuronal populations to explore the effects that these opposite polarities could have on neural activity, and we found that the best predictor of alpha power was the average of the normal components of the electric field. To sum up, our study sheds light on the mechanisms underlying tACS brain activity modulation, using both empirical and computational approaches. Non-invasive brain stimulation techniques hold promise for treating brain disorders, but further research is needed to fully understand and control their effects on brain dynamics and cognition. Our findings contribute to this growing body of research and provide a foundation for future studies aimed at optimizing the use of non-invasive brain stimulation in clinical settings.

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.

Quasi-static approximation error of electric field analysis for transcranial current stimulation

Objective.Numerical modeling of electric fields induced by transcranial alternating current stimulation (tACS) is currently a part of the standard procedure to predict and understand neural response. Quasi-static approximation (QSA) for electric field calculations is generally applied to reduce the computational cost. Here, we aimed to analyze and quantify the validity of the approximation over a broad frequency range.Approach.We performed electromagnetic modeling studies using an anatomical head model and considered approximations assuming either a purely ohmic medium (i.e. static formulation) or a lossy dielectric medium (QS formulation). The results were compared with the solution of Maxwell's equations in the cases of harmonic and pulsed signals. Finally, we analyzed the effect of electrode positioning on these errors.Main results.Our findings demonstrate that the QSA is valid and produces a relative error below 1% up to 1.43 MHz. The largest error is introduced in the static case, where the error is over 1% across the entire considered spectrum and as high as 20% in the brain at 10 Hz. We also highlight the special importance of considering the capacitive effect of tissues for pulsed waveforms, which prevents signal distortion induced by the purely ohmic approximation. At the neuron level, the results point a difference of sense electric field as high as 22% at focusing point, impacting pyramidal cells firing times.Significance.QSA remains valid in the frequency range currently used for tACS. However, neglecting permittivity (static formulation) introduces significant error for both harmonic and non-harmonic signals. It points out that reliable low frequency dielectric data are needed for accurate transcranial current stimulation numerical modeling.

Slow-oscillatory tACS does not modulate human motor cortical response to repeated plasticity paradigms

Previous history of activity and learning modulates synaptic plasticity and can lead to saturation of synaptic connections. According to the synaptic homeostasis hypothesis, neural oscillations during slow-wave sleep play an important role in restoring plasticity within a functional range. However, it is not known whether slow-wave oscillations—without the concomitant requirement of sleep—play a causal role in human synaptic homeostasis. Here, we aimed to answer this question using transcranial alternating current stimulation (tACS) to induce slow-oscillatory activity in awake human participants. tACS was interleaved between two plasticity-inducing interventions: motor learning, and paired associative stimulation (PAS). The hypothesis tested was that slow-oscillatory tACS would prevent homeostatic interference between motor learning and PAS, and facilitate plasticity from these successive interventions. Thirty-six participants received sham and active fronto-motor tACS in two separate sessions, along with electroencephalography (EEG) recordings, while a further 38 participants received tACS through a control montage. Motor evoked potentials (MEPs) were recorded throughout the session to quantify plasticity changes after the different interventions, and the data were analysed with Bayesian statistics. As expected, there was converging evidence that motor training led to excitatory plasticity. Importantly, we found moderate evidence against an effect of active tACS in restoring PAS plasticity, and no evidence of lasting entrainment of slow oscillations in the EEG. This suggests that, under the conditions tested here, slow-oscillatory tACS does not modulate synaptic homeostasis in the motor system of awake humans.

Enhancement of visual perception by combining transcranial electrical stimulation and visual perceptual training

The visual system remains highly malleable even after its maturity or impairment. Our visual function can be enhanced through many ways, such as transcranial electrical stimulation (tES) and visual perceptual learning (VPL). TES can change visual function rapidly, but its modulation effect is short-lived and unstable. By contrast, VPL can lead to a substantial and long-lasting improvement in visual function, but extensive training is typically required. Theoretically, visual function could be further improved in a shorter time frame by combining tES and VPL than by solely using tES or VPL. Vision enhancement by combining these two methods concurrently is both theoretically and practically significant. In this review, we firstly introduced the basic concept and possible mechanisms of VPL and tES; then we reviewed the current research progress of visual enhancement using the combination of two methods in both general and clinical population; finally, we discussed the limitations and future directions in this field. Our review provides a guide for future research and application of vision enhancement and restoration by combining VPL and tES.

Effects of beta-band and gamma-band rhythmic stimulation on motor inhibition

To investigate whether beta oscillations are causally related to motor inhibition, thirty-six participants underwent two concurrent transcranial alternating current stimulation (tACS) and electroencephalography (EEG) sessions during which either beta (20 Hz) or gamma (70 Hz) stimulation was applied while participants performed a stop-signal task. In addition, we acquired magnetic resonance images to simulate the electric field during tACS. 20 Hz stimulation targeted at the pre-supplementary motor area enhanced inhibition and increased beta oscillatory power around the time of the stop-signal in trials directly following stimulation. The increase in inhibition on stop trials followed a dose-response relationship with the strength of the individually simulated electric field. Computational modeling revealed that 20 and 70 Hz stimulation had opposite effects on the braking process. These results highlight that the effects of tACS are state-dependent and demonstrate that fronto-central beta activity is causally related to successful motor inhibition, supporting its use as a functional biomarker.

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Beta tACS over preSMA improved motor inhibition

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Gamma tACS slowed down the stop process but primarily affected movement execution

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Beta tACS resulted in higher beta spectral power around the time of the stop-signal

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Effects of tACS showed a dose-response relationship with electric field strength