Responses of model cortical neurons to temporal interference stimulation and related transcranial alternating current stimulation modalities

Spatially Selective Retinal Ganglion Cell Activation Using Low Invasive Extraocular Temporal Interference Stimulation

Conventional retinal implants involve complex surgical procedures and require invasive implantation. Temporal Interference Stimulation (TIS) has achieved noninvasive and focused stimulation of deep brain regions by delivering high-frequency currents with small frequency differences on multiple electrodes. In this study, we conducted in silico investigations to evaluate extraocular TIS's potential as a novel visual restoration approach. Different from the previously published retinal TIS model, the new model of extraocular TIS incorporated a biophysically detailed retinal ganglion cell (RGC) population, enabling a more accurate simulation of retinal outputs under electrical stimulation. Using this improved model, we made the following major discoveries: (1) the maximum value of TIS envelope electric potential ([Formula: see text] showed a strong correlation with TIS-induced RGC activation; (2) the preferred stimulating/return electrode (SE/RE) locations to achieve focalized TIS were predicted; (3) the performance of extraocular TIS was better than same-frequency sinusoidal stimulation (SSS) in terms of lower RGC threshold and more focused RGC activation; (4) the optimal stimulation parameters to achieve lower threshold and focused activation were identified; and (5) spatial selectivity of TIS could be improved by integrating current steering strategy and reducing electrode size. This study provides insights into the feasibility and effectiveness of a low-invasive stimulation approach in enhancing vision restoration.

Nonlinearities and timescales in neural models of temporal interference stimulation

In temporal interference (TI) stimulation, neuronal cells react to two interfering sinusoidal electric fields with a slightly different frequency (f 1 ${f}_{1}$ ,f 2 ${f}_{2}$ in the range of about 1-4 kHz,∣ f 1 - f 2 ∣ $| {f}_{1}-{f}_{2}| $ in the range of about 1-100 Hz). It has been previously observed that for the same input intensity, the neurons do not react to a purely sinusoidal signal atf 1 ${f}_{1}$ orf 2 ${f}_{2}$ . This study seeks a better understanding of the largely unknown mechanisms underlying TI neuromodulation. To this end, single-compartment models are used to simulate computationally the response of neurons to the sinusoidal and TI waveform. This study compares five different neuron models: Hodgkin-Huxley (HH), Frankenhaeuser-Huxley (FH), along with leaky, exponential, and adaptive-exponential integrate-and-fire (IF). It was found that IF models do not entirely reflect the experimental behavior while the HH and FH model did qualitatively replicate the observed neural responses. Changing the time constants and steady state values of the ion gates in the FH model alters the response to both the sinusoidal and TI signal, possibly reducing the firing threshold of the sinusoidal input below that of the TI input. The results show that in the modified (simplified) model, TI stimulation is not qualitatively impacted by nonlinearities in the current-voltage relation. In contrast, ion channels have a significant impact on the neuronal response. This paper offers insights into neuronal biophysics and computational models of TI stimulation.

Transcranial temporal interference stimulation (tTIS) influences event-related alpha activity during mental rotation

Non-invasive brain stimulation techniques offer therapeutic potential for neurological and psychiatric disorders. However, current methods are often limited in their stimulation depth. The novel transcranial temporal interference stimulation (tTIS) aims to overcome this limitation by non-invasively targeting deeper brain regions. In this study, we aimed to evaluate the efficacy of tTIS in modulating alpha activity during a mental rotation task. The effects of tTIS were compared with transcranial alternating current stimulation (tACS) and a sham control. Participants were randomly assigned to a tTIS, tACS, or sham group. They performed alternating blocks of resting and mental rotation tasks before, during, and after stimulation. During the stimulation blocks, participants received 20 min of stimulation adjusted to their individual alpha frequency (IAF). We assessed shifts in resting state alpha power, event-related desynchronization (ERD) of alpha activity during mental rotation, as well as resulting improvements in behavioral performance. Our results indicate tTIS and tACS to be effective in modulating cortical alpha activity during mental rotation, leading to an increase in ERD from pre- to poststimulation as well as compared to sham stimulation. However, this increase in ERD was not correlated with enhanced mental rotation performance, and resting state alpha power remained unchanged. Our findings underscore the complex nature of tTIS and tACS efficacy, indicating that stimulation effects are more observable during active cognitive tasks, while their impacts are less pronounced on resting neuronal systems.

Cell-specific effects of temporal interference stimulation on cortical function

Temporal interference (TI) stimulation is a popular non-invasive neurostimulation technique that utilizes the following salient neural behavior: pure sinusoid (generated in off-target brain regions) appears to cause no stimulation, whereas modulated sinusoid (generated in target brain regions) does. To understand its effects and mechanisms, we examine responses of different cell types, excitatory pyramidal (Pyr) and inhibitory parvalbumin-expressing (PV) neurons, to pure and modulated sinusoids, in intact network as well as in isolation. In intact network, we present data showing that PV neurons are much less likely than Pyr neurons to exhibit TI stimulation. Remarkably, in isolation, our data shows that almost all Pyr neurons stop exhibiting TI stimulation. We conclude that TI stimulation is largely a network phenomenon. Indeed, PV neurons actively inhibit Pyr neurons in the off-target regions due to pure sinusoids (in off-target regions) generating much higher PV firing rates than modulated sinusoids in the target regions. Additionally, we use computational studies to support and extend our experimental observations.

Prediction of hippocampal electric field in time series induced by TI-DMS with temporal convolutional network

Temporal interference deep-brain magnetic stimulation (TI-DMS) induces rhythmic electric field (EF) in the hippocampus to normalize cognitive function. The rhythmic time series of the hippocampal EF is essential for the assessment of TI-DMS. However, the finite element method (FEM) takes several hours to obtain the time series of EF. In order to reduce the time cost, the temporal convolutional network (TCN) model is adopted to predict the time series of hippocampal EF induced by TI-DMS. It takes coil configuration and loaded current as input and predicts the time series of maximum and mean values of the left and right hippocampal EF. The prediction takes only a few seconds. The model parameter combination of kernel size and layers is selected optimally by cross-validation method. The experimental results for multiple subjects show that the R2 of all the time series predicted by the model exceed 0.98. And the prediction accuracy is even higher as the input parameters approach the training set. These results demonstrate that the adopted model can quickly predict the time series of hippocampal EF induced by TI-DMS with relatively high accuracy, which is beneficial for future clinical applications.

Quasistatic approximation in neuromodulation

We define and explain the quasistatic approximation (QSA) as applied to field modeling for electrical and magnetic stimulation. Neuromodulation analysis pipelines include discrete stages, and QSA is applied specifically when calculating the electric and magnetic fields generated in tissues by a given stimulation dose. QSA simplifies the modeling equations to support tractable analysis, enhanced understanding, and computational efficiency. The application of QSA in neuromodulation is based on four underlying assumptions: (A1) no wave propagation or self-induction in tissue, (A2) linear tissue properties, (A3) purely resistive tissue, and (A4) non-dispersive tissue. As a consequence of these assumptions, each tissue is assigned a fixed conductivity, and the simplified equations (e.g. Laplace's equation) are solved for the spatial distribution of the field, which is separated from the field's temporal waveform. Recognizing that electrical tissue properties may be more complex, we explain how QSA can be embedded in parallel or iterative pipelines to model frequency dependence or nonlinearity of conductivity. We survey the history and validity of QSA across specific applications, such as microstimulation, deep brain stimulation, spinal cord stimulation, transcranial electrical stimulation, and transcranial magnetic stimulation. The precise definition and explanation of QSA in neuromodulation are essential for rigor when using QSA models or testing their limits.

Temporal interference stimulation disrupts spike timing in the primate brain

Electrical stimulation can regulate brain activity, producing clear clinical benefits, but focal and effective neuromodulation often requires surgically implanted electrodes. Recent studies argue that temporal interference (TI) stimulation may provide similar outcomes non-invasively. During TI, scalp electrodes generate multiple electrical fields in the brain, modulating neural activity only at their intersection. Despite considerable enthusiasm for this approach, little empirical evidence demonstrates its effectiveness, especially under conditions suitable for human use. Here, using single-neuron recordings in non-human primates, we establish that TI reliably alters the timing, but not the rate, of spiking activity. However, we show that TI requires strategies-high carrier frequencies, multiple electrodes, and amplitude-modulated waveforms-that also limit its effectiveness. Combined, these factors make TI 80 % weaker than other forms of non-invasive brain stimulation. Although unlikely to cause widespread neuronal entrainment, TI may be ideal for disrupting pathological oscillatory activity, a hallmark of many neurological disorders.

Quasistatic approximation in neuromodulation

We define and explain the quasistatic approximation (QSA) as applied to field modeling for electrical and magnetic stimulation. Neuromodulation analysis pipelines include discrete stages, and QSA is applied specifically when calculating the electric and magnetic fields generated in tissues by a given stimulation dose. QSA simplifies the modeling equations to support tractable analysis, enhanced understanding, and computational efficiency. The application of QSA in neuro-modulation is based on four underlying assumptions: (A1) no wave propagation or self-induction in tissue, (A2) linear tissue properties, (A3) purely resistive tissue, and (A4) non-dispersive tissue. As a consequence of these assumptions, each tissue is assigned a fixed conductivity, and the simplified equations (e.g., Laplace's equation) are solved for the spatial distribution of the field, which is separated from the field's temporal waveform. Recognizing that electrical tissue properties may be more complex, we explain how QSA can be embedded in parallel or iterative pipelines to model frequency dependence or nonlinearity of conductivity. We survey the history and validity of QSA across specific applications, such as microstimulation, deep brain stimulation, spinal cord stimulation, transcranial electrical stimulation, and transcranial magnetic stimulation. The precise definition and explanation of QSA in neuromodulation are essential for rigor when using QSA models or testing their limits.

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.

Pulse-width modulated temporal interference (PWM-TI) brain stimulation

BACKGROUND

Electrical stimulation involving temporal interference of two different kHz frequency sinusoidal electric fields (temporal interference (TI)) enables non-invasive deep brain stimulation, by creating an electric field that is amplitude modulated at the slow difference frequency (within the neural range), at the target brain region.

OBJECTIVE

Here, we investigate temporal interference neural stimulation using square, rather than sinusoidal, electric fields that create an electric field that is pulse-width, but not amplitude, modulated at the difference frequency (pulse-width modulated temporal interference, (PWM-TI)).

METHODS/RESULTS

We show, using ex-vivo single-cell recordings and in-vivo calcium imaging, that PWM-TI effectively stimulates neural activity at the difference frequency at a similar efficiency to traditional TI. We then demonstrate, using computational modelling, that the PWM stimulation waveform induces amplitude-modulated membrane potential depolarization due to the membrane's intrinsic low-pass filtering property.

CONCLUSIONS

PWM-TI can effectively drive neural activity at the difference frequency. The PWM-TI mechanism involves converting an envelope amplitude-fixed PWM field to an amplitude-modulated membrane potential via the low-pass filtering of the passive neural membrane. Unveiling the biophysics underpinning the neural response to complex electric fields may facilitate the development of new brain stimulation strategies with improved precision and efficiency.

Noninvasive theta-burst stimulation of the human striatum enhances striatal activity and motor skill learning

The stimulation of deep brain structures has thus far only been possible with invasive methods. Transcranial electrical temporal interference stimulation (tTIS) is a novel, noninvasive technology that might overcome this limitation. The initial proof-of-concept was obtained through modeling, physics experiments and rodent models. Here we show successful noninvasive neuromodulation of the striatum via tTIS in humans using computational modeling, functional magnetic resonance imaging studies and behavioral evaluations. Theta-burst patterned striatal tTIS increased activity in the striatum and associated motor network. Furthermore, striatal tTIS enhanced motor performance, especially in healthy older participants as they have lower natural learning skills than younger subjects. These findings place tTIS as an exciting new method to target deep brain structures in humans noninvasively, thus enhancing our understanding of their functional role. Moreover, our results lay the groundwork for innovative, noninvasive treatment strategies for brain disorders in which deep striatal structures play key pathophysiological roles.

Visualizing interferential stimulation of human brains

Introduction

Transcranial electrical stimulation (TES) is limited in focally stimulating deep-brain regions, even with optimized stimulation montages. Recently, interferential stimulation (IFS), also known as transcranial temporal interference stimulation (TI, TIS, or tTIS), has drawn much attention in the TES community as both computational and experimental studies show that IFS can reach deep-brain areas. However, the underlying electrodynamics of IFS is complicated and difficult to visualize. Existing literature only shows static visualization of the interfered electric field induced by IFS. These could result in a simplified understanding that there is always one static focal spot between the two pairs of stimulation electrodes. This static visualization can be frequently found in the IFS literature. Here, we aimed to systematically visualize the entire dynamics of IFS.

Methods and results

Following the previous study, the lead field was solved for the MNI-152 head, and optimal montages using either two pairs of electrodes or two arrays of electrodes were found to stimulate a deep-brain region close to the left striatum with the highest possible focality. We then visualized the two stimulating electrical currents injected with similar frequencies. We animated the instant electric field vector at the target and one exemplary off-target location both in 3D space and as a 2D Lissajous curve. We finally visualized the distribution of the interfered electric field and the amplitude modulation envelope at an axial slice going through the target location. These two quantities were visualized in two directions: radial-in and posterior-anterior.

Discussion

We hope that with intuitive visualization, this study can contribute as an educational resource to the community's understanding of IFS as a powerful modality for non-invasive focal deep-brain stimulation.

A mini-review: recent advancements in temporal interference stimulation in modulating brain function and behavior

Numerous studies have assessed the effect of Temporal Interference (TI) on human performance. However, a comprehensive literature review has not yet been conducted. Therefore, this review aimed to search PubMed and Web of Science databases for TI-related literature and analyze the findings. We analyzed studies involving preclinical, human, and computer simulations, and then discussed the mechanism and safety of TI. Finally, we identified the gaps and outlined potential future directions. We believe that TI is a promising technology for the treatment of neurological movement disorders, due to its superior focality, steerability, and tolerability compared to traditional electrical stimulation. However, human experiments have yielded fewer and inconsistent results, thus animal and simulation experiments are still required to perfect stimulation protocols for human trials.

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.

Optimized monophasic pulses with equivalent electric field for rapid-rate transcranial magnetic stimulation

Objective.Transcranial magnetic stimulation (TMS) with monophasic pulses achieves greater changes in neuronal excitability but requires higher energy and generates more coil heating than TMS with biphasic pulses, and this limits the use of monophasic pulses in rapid-rate protocols. We sought to design a stimulation waveform that retains the characteristics of monophasic TMS but significantly reduces coil heating, thereby enabling higher pulse rates and increased neuromodulation effectiveness.Approach.A two-step optimization method was developed that uses the temporal relationship between the electric field (E-field) and coil current waveforms. The model-free optimization step reduced the ohmic losses of the coil current and constrained the error of the E-field waveform compared to a template monophasic pulse, with pulse duration as a second constraint. The second, amplitude adjustment step scaled the candidate waveforms based on simulated neural activation to account for differences in stimulation thresholds. The optimized waveforms were implemented to validate the changes in coil heating.Main results.Depending on the pulse duration and E-field matching constraints, the optimized waveforms produced 12%-75% less heating than the original monophasic pulse. The reduction in coil heating was robust across a range of neural models. The changes in the measured ohmic losses of the optimized pulses compared to the original pulse agreed with numeric predictions.Significance.The first step of the optimization approach was independent of any potentially inaccurate or incorrect model and exhibited robust performance by avoiding the highly nonlinear behavior of neural responses, whereas neural simulations were only run once for amplitude scaling in the second step. This significantly reduced computational cost compared to iterative methods using large populations of candidate solutions and more importantly reduced the sensitivity to the choice of neural model. The reduced coil heating and power losses of the optimized pulses can enable rapid-rate monophasic TMS protocols.