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.

Reduced Auditory Perception and Brain Response with Quiet TMS Coil.

BACKGROUND: Electromagnetic forces in transcranial magnetic stimulation (TMS) coils generate a loud clicking sound that produces confounding auditory activation and is potentially hazardous to hearing. To reduce this noise while maintaining stimulation efficiency similar to conventional TMS coils, we previously developed a quiet TMS double containment coil (qTMS-DCC). OBJECTIVE: To compare the stimulation strength, perceived loudness, and EEG response between qTMS-DCC and a commercial TMS coil. METHODS: Nine healthy volunteers participated in a within-subject study design. The resting motor thresholds (RMTs) for qTMS-DCC and MagVenture Cool-B65 were measured. Psychoacoustic titration matched the Cool-B65 loudness to qTMS-DCC pulsed at 80, 100, and 120% RMT. Event-related potentials (ERPs) were recorded for both coils. The psychoacoustic titration and ERPs were acquired with the coils both on and 6 cm off the scalp, the latter isolating the effects of airborne auditory stimulation from body sound and electromagnetic stimulation. The ERP comparisons focused on a centro-frontal region that encompassed peak responses in the global signal. RESULTS: RMT did not differ significantly between the coils, with or without the EEG cap on the head. qTMS-DCC was perceived to be substantially quieter than Cool-B65. For example, qTMS-DCC at 100% coil-specific RMT sounded like Cool-B65 at 34% RMT. The general ERP waveform and topography were similar between the two coils, as were early-latency components, indicating comparable electromagnetic brain stimulation in the on-scalp condition. qTMS-DCC had a significantly smaller P180 component in both on-scalp and off-scalp conditions, supporting reduced auditory activation. CONCLUSIONS: The stimulation efficiency of qTMS-DCC matched Cool-B65, while having substantially lower perceived loudness and auditory-evoked potentials. Highlights: qTMS coil is subjectively and objectively quieter than conventional Cool-B65 coilqTMS coil at 100% motor threshold was as loud as Cool-B65 at 34% motor thresholdAttenuated coil noise reduced auditory N100 and P180 evoked response componentsqTMS coil enables reduction of auditory activation without masking.

Abnormalities of cortical stimulation strength-duration time constant in amyotrophic lateral sclerosis.

OBJECTIVES: Strength-duration time constant (SDTC) may now be determined for cortical motor neurones, with activity mediated by transient Na+ conductances. The present study determined whether cortical SDTC is abnormal and linked to the pathogenesis of amyotrophic lateral sclerosis. METHODS: Cortical SDTC and rheobase were estimated from 17 ALS patients using a controllable pulse parameter transcranial magnetic stimulation (cTMS) device. Resting motor thresholds (RMTs) were determined at pulse widths (PW) of 30, 45, 60, 90 and 120 µs and M-ratio of 0.1, using a figure-of-eight coil applied to the primary motor cortex. RESULTS: SDTC was significantly reduced in ALS patients (150.58 ± 9.98 µs; controls 205.94 ± 13.7 µs, P < 0.01). The reduced SDTC correlated with a rate of disease progression (Rho = -0.440, P < 0.05), ALS functional rating score (ALSFRS-R) score (Rho = 0.446, P < 0.05), and disease duration (R = 0.428, P < 0.05). The degree of change in SDTC was greater in patients with cognitive abnormalities as manifested by an abnormal total Edinburgh Cognitive ALS Screen score (140.5 ± 28.7 µs, P < 0.001) and ALS-specific subscore (141.7 ± 33.2 µs, P = 0.003). CONCLUSIONS: Cortical SDTC reduction was associated with a more aggressive ALS phenotype, or with more prominent cognitive impairment. SIGNIFICANCE: An increase in transient Na+ conductances may account for the reduction in SDTC, linked to the pathogenesis of ALS.

Scalp surface estimation and head registration using sparse sampling and 3D statistical models.

Registering the head and estimating the scalp surface are important for various biomedical procedures, including those using neuronavigation to localize brain stimulation or recording. However, neuronavigation systems rely on manually-identified fiducial head targets and often require a patient-specific MRI for accurate registration, limiting adoption. We propose a practical technique capable of inferring the scalp shape and use it to accurately register the subject's head. Our method does not require anatomical landmark annotation or an individual MRI scan, yet achieves accurate registration of the subject's head and estimation of its surface. The scalp shape is estimated from surface samples easily acquired using existing pointer tools, and registration exploits statistical head model priors. Our method allows for the acquisition of non-trivial shapes from a limited number of data points while leveraging their object class priors, surpassing the accuracy of common reconstruction and registration methods using the same tools. The proposed approach is evaluated in a virtual study with head MRI data from 1152 subjects, achieving an average reconstruction root-mean-square error of 2.95 mm, which outperforms a common neuronavigation technique by 2.70 mm. We also characterize the error under different conditions and provide guidelines for efficient sampling. Furthermore, we demonstrate and validate the proposed method on data from 50 subjects collected with conventional neuronavigation tools and setup, obtaining an average root-mean-square error of 2.89 mm; adding landmark-based registration improves this error to 2.63 mm. The simulation and experimental results support the proposed method's effectiveness with or without landmark annotation, highlighting its broad applicability.

A semi-automated pipeline for finite element modeling of electric field induced in nonhuman primates by transcranial magnetic stimulation.

BACKGROUND: Transcranial magnetic stimulation (TMS) is used to treat a range of brain disorders by inducing an electric field (E-field) in the brain. However, the precise neural effects of TMS are not well understood. Nonhuman primates (NHPs) are used to model the impact of TMS on neural activity, but a systematic method of quantifying the induced E-field in the cortex of NHPs has not been developed. NEW METHOD: The pipeline uses statistical parametric mapping (SPM) to automatically segment a structural MRI image of a rhesus macaque into five tissue compartments. Manual corrections are necessary around implants. The segmented tissues are tessellated into 3D meshes used in finite element method (FEM) software to compute the TMS induced E-field in the brain. The gray matter can be further segmented into cortical laminae using a volume preserving method for defining layers. RESULTS: Models of three NHPs were generated with TMS coils placed over the precentral gyrus. Two coil configurations, active and sham, were simulated and compared. The results demonstrated a large difference in E-fields at the target. Additionally, the simulations were calculated using two different E-field solvers and were found to not significantly differ. COMPARISON WITH EXISTING METHODS: Current methods segment NHP tissues manually or use automated methods for only the brain tissue. Existing methods also do not stratify the gray matter into layers. CONCLUSION: The pipeline calculates the induced E-field in NHP models by TMS and can be used to plan implant surgeries and determine approximate E-field values around neuron recording sites.

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.

Transcranial magnetic stimulation input-output curve slope differences suggest variation in recruitment across muscle representations in primary motor cortex.

Measurement of the input-output (IO) curves of motor evoked potentials (MEPs) elicited by transcranial magnetic stimulation (TMS) can be used to assess corticospinal excitability and motor recruitment. While IO curves have been used to study disease and pharmacology, few studies have compared the IO curves across the body. This study sought to characterize IO curve parameters across the dominant and non-dominant sides of upper and lower limbs in healthy participants. Laterality preferences were assessed in eight healthy participants and IO curves were measured bilaterally for the first dorsal interosseous (FDI), biceps brachii (BB), and tibialis anterior (TA) muscles. Results show that FDI has lower motor threshold than BB which is, in turn, lower than TA. In addition, both BB and TA have markedly shallower logarithmic IO curve slopes from small to large MEP responses than FDI. After normalizing these slopes by their midpoints to account for differences in motor thresholds, which could result from geometric factors such as the target depth, large differences in logarithmic slopes remain present between all three muscles. The differences in slopes between the muscles could not be explained by differences in normalized IO curve spreads, which relate to the extent of the cortical representation and were comparable across the muscles. The IO curve differences therefore suggest muscle-dependent variations in TMS-evoked recruitment across the primary motor cortex, which should be considered when utilizing TMS-evoked MEPs to study disease states and treatment effects.

Amplitude-determined seizure-threshold, electric field modeling, and electroconvulsive therapy antidepressant and cognitive outcomes.

Electroconvulsive therapy (ECT) pulse amplitude, which dictates the induced electric field (E-field) magnitude in the brain, is presently fixed at 800 or 900 milliamperes (mA) without clinical or scientific rationale. We have previously demonstrated that increased E-field strength improves ECT's antidepressant effect but worsens cognitive outcomes. Amplitude-determined seizure titration may reduce the E-field variability relative to fixed amplitude ECT. In this investigation, we assessed the relationships among amplitude-determined seizure-threshold (STa), E-field magnitude, and clinical outcomes in older adults (age range 50 to 80 years) with depression. Subjects received brain imaging, depression assessment, and neuropsychological assessment pre-, mid-, and post-ECT. STa was determined during the first treatment with a Soterix Medical 4×1 High Definition ECT Multi-channel Stimulation Interface (Investigation Device Exemption: G200123). Subsequent treatments were completed with right unilateral electrode placement (RUL) and 800 mA. We calculated Ebrain defined as the 90th percentile of E-field magnitude in the whole brain for RUL electrode placement. Twenty-nine subjects were included in the final analyses. Ebrain per unit electrode current, Ebrain/I, was associated with STa. STa was associated with antidepressant outcomes at the mid-ECT assessment and bitemporal electrode placement switch. Ebrain/I was associated with changes in category fluency with a large effect size. The relationship between STa and Ebrain/I extends work from preclinical models and provides a validation step for ECT E-field modeling. ECT with individualized amplitude based on E-field modeling or STa has the potential to enhance neuroscience-based ECT parameter selection and improve clinical outcomes.

Multi-scale model of axonal and dendritic polarization by transcranial direct current stimulation in realistic head geometry.

BACKGROUND: Transcranial direct current stimulation (tDCS) is a non-invasive brain stimulation modality that can alter cortical excitability. However, it remains unclear how the subcellular elements of different neuron types are polarized by specific electric field (E-field) distributions. OBJECTIVE: To quantify neuronal polarization generated by tDCS in a multi-scale computational model. METHODS: We embedded layer-specific, morphologically-realistic cortical neuron models in a finite element model of the E-field in a human head and simulated steady-state polarization generated by conventional primary-motor-cortex-supraorbital (M1-SO) and 4 × 1 high-definition (HD) tDCS. We quantified somatic, axonal, and dendritic polarization of excitatory pyramidal cells in layers 2/3, 5, and 6, as well as inhibitory interneurons in layers 1 and 4 of the hand knob. RESULTS: Axonal and dendritic terminals were polarized more than the soma in all neurons, with peak axonal and dendritic polarization of 0.92 mV and 0.21 mV, respectively, compared to peak somatic polarization of 0.07 mV for 1.8 mA M1-SO stimulation. Both montages generated regions of depolarization and hyperpolarization beneath the M1 anode; M1-SO produced slightly stronger, more diffuse polarization peaking in the central sulcus, while 4 × 1 HD produced higher peak polarization in the gyral crown. The E-field component normal to the cortical surface correlated strongly with pyramidal neuron somatic polarization (R2>0.9), but exhibited weaker correlations with peak pyramidal axonal and dendritic polarization (R2:0.5-0.9) and peak polarization in all subcellular regions of interneurons (R2:0.3-0.6). Simulating polarization by uniform local E-field extracted at the soma approximated the spatial distribution of tDCS polarization but produced large errors in some regions (median absolute percent error: 7.9 %). CONCLUSIONS: Polarization of pre- and postsynaptic compartments of excitatory and inhibitory cortical neurons may play a significant role in tDCS neuromodulation. These effects cannot be predicted from the E-field distribution alone but rather require calculation of the neuronal response.

Automatic Neurocranial Landmarks Detection from Visible Facial Landmarks Leveraging 3D Head Priors.

The localization and tracking of neurocranial landmarks is essential in modern medical procedures, e.g., transcranial magnetic stimulation (TMS). However, state-of-the-art treatments still rely on the manual identification of head targets and require setting retroreflective markers for tracking. This limits the applicability and scalability of TMS approaches, making them time-consuming, dependent on expensive hardware, and prone to errors when retroreflective markers drift from their initial position. To overcome these limitations, we propose a scalable method capable of inferring the position of points of interest on the scalp, e.g., the International 10-20 System's neurocranial landmarks. In contrast with existing approaches, our method does not require human intervention or markers; head landmarks are estimated leveraging visible facial landmarks, optional head size measurements, and statistical head model priors. We validate the proposed approach on ground truth data from 1,150 subjects, for which facial 3D and head information is available; our technique achieves a localization RMSE of 2.56 mm on average, which is of the same order as reported by high-end techniques in TMS. Our implementation is available at https://github.com/odedsc/ANLD.

Multi-scale model of axonal and dendritic polarization by transcranial direct current stimulation in realistic head geometry.

Background: Transcranial direct current stimulation (tDCS) is a non-invasive brain stimulation modality that can alter cortical excitability. However, it remains unclear how the subcellular elements of different neuron types are polarized by specific electric field (E-field) distributions. Objective: To quantify neuronal polarization generated by tDCS in a multi-scale computational model. Methods: We embedded layer-specific, morphologically-realistic cortical neuron models in a finite element model of the E-field in a human head and simulated steady-state polarization generated by conventional primary-motor-cortex-supraorbital (M1-SO) and 4×1 high-definition (HD) tDCS. We quantified somatic, axonal, and dendritic polarization of excitatory pyramidal cells in layers 2/3, 5, and 6, as well as inhibitory interneurons in layers 1 and 4 of the hand knob. Results: Axonal and dendritic terminals were polarized more than the soma in all neurons, with peak axonal and dendritic polarization of 0.92 mV and 0.21 mV, respectively, compared to peak somatic polarization of 0.07 mV for 1.8 mA M1-SO stimulation. Both montages generated regions of depolarization and hyperpolarization beneath the M1 anode; M1-SO produced slightly stronger, more diffuse polarization peaking in the central sulcus, while 4×1 HD produced higher peak polarization in the gyral crown. Simulating polarization by uniform local E-field approximated the spatial distribution of tDCS polarization but produced large errors in some regions. Conclusions: Polarization of pre- and postsynaptic compartments of excitatory and inhibitory cortical neurons may play a significant role in tDCS neuromodulation. These effects cannot be predicted from the E-field distribution alone but rather require calculation of the neuronal response.

Three novel methods for determining motor threshold with transcranial magnetic stimulation outperform conventional procedures.

Objective. Thresholding of neural responses is central to many applications of transcranial magnetic stimulation (TMS), but the stochastic aspect of neuronal activity and motor evoked potentials (MEPs) challenges thresholding techniques. We analyzed existing methods for obtaining TMS motor threshold and their variations, introduced new methods from other fields, and compared their accuracy and speed.Approach. In addition to existing relative-frequency methods, such as the five-out-of-ten method, we examined adaptive methods based on a probabilistic motor threshold model using maximum-likelihood (ML) or maximuma-posteriori(MAP) estimation. To improve the performance of these adaptive estimation methods, we explored variations in the estimation procedure and inclusion of population-level prior information. We adapted a Bayesian estimation method which iteratively incorporated information of the TMS responses into the probability density function. A family of non-parametric stochastic root-finding methods with different convergence criteria and stepping rules were explored as well. The performance of the thresholding methods was evaluated with an independent stochastic MEP model.Main Results. The conventional relative-frequency methods required a large number of stimuli, were inherently biased on the population level, and had wide error distributions for individual subjects. The parametric estimation methods obtained the thresholds much faster and their accuracy depended on the estimation method, with performance significantly improved when population-level prior information was included. Stochastic root-finding methods were comparable to adaptive estimation methods but were much simpler to implement and did not rely on a potentially inaccurate underlying estimation model.Significance. Two-parameter MAP estimation, Bayesian estimation, and stochastic root-finding methods have better error convergence compared to conventional single-parameter ML estimation, and all these methods require significantly fewer TMS pulses for accurate estimation than conventional relative-frequency methods. Stochastic root-finding appears particularly attractive due to the low computational requirements, simplicity of the algorithmic implementation, and independence from potential model flaws in the parametric estimators.

Rapid estimation of cortical neuron activation thresholds by transcranial magnetic stimulation using convolutional neural networks.

BACKGROUND: Transcranial magnetic stimulation (TMS) can modulate neural activity by evoking action potentials in cortical neurons. TMS neural activation can be predicted by coupling subject-specific head models of the TMS-induced electric field (E-field) to populations of biophysically realistic neuron models; however, the significant computational cost associated with these models limits their utility and eventual translation to clinically relevant applications. OBJECTIVE: To develop computationally efficient estimators of the activation thresholds of multi-compartmental cortical neuron models in response to TMS-induced E-field distributions. METHODS: Multi-scale models combining anatomically accurate finite element method (FEM) simulations of the TMS E-field with layer-specific representations of cortical neurons were used to generate a large dataset of activation thresholds. 3D convolutional neural networks (CNNs) were trained on these data to predict thresholds of model neurons given their local E-field distribution. The CNN estimator was compared to an approach using the uniform E-field approximation to estimate thresholds in the non-uniform TMS-induced E-field. RESULTS: The 3D CNNs estimated thresholds with mean absolute percent error (MAPE) on the test dataset below 2.5% and strong correlation between the CNN predicted and actual thresholds for all cell types (R2 > 0.96). The CNNs estimated thresholds with a 2-4 orders of magnitude reduction in the computational cost of the multi-compartmental neuron models. The CNNs were also trained to predict the median threshold of populations of neurons, speeding up computation further. CONCLUSION: 3D CNNs can estimate rapidly and accurately the TMS activation thresholds of biophysically realistic neuron models using sparse samples of the local E-field, enabling simulating responses of large neuron populations or parameter space exploration on a personal computer.

Electroconvulsive Therapy: Mechanisms of Action, Clinical Considerations, and Future Directions.

LEARNING OBJECTIVES: • Outline and discuss the fundamental physiologic, cellular, and molecular mechanisms of ECT to devise strategies to optimize therapeutic outcomes• Summarize the overview of ECT, its efficacy in treating depression, the known effects on cognition, evidence of mechanisms, and future directions. ABSTRACT: Electroconvulsive therapy (ECT) is the most effective treatment for a variety of psychiatric illnesses, including treatment-resistant depression, bipolar depression, mania, catatonia, and clozapine-resistant schizophrenia. ECT is a medical and psychiatric procedure whereby electrical current is delivered to the brain under general anesthesia to induce a generalized seizure. ECT has evolved a great deal since the 1930s. Though it has been optimized for safety and to reduce adverse effects on cognition, issues persist. There is a need to understand fundamental physiologic, cellular, and molecular mechanisms of ECT to devise strategies to optimize therapeutic outcomes. Clinical trials that set out to adjust parameters, electrode placement, adjunctive medications, and patient selection are critical steps towards the goal of improving outcomes with ECT. This narrative review provides an overview of ECT, its efficacy in treating depression, its known effects on cognition, evidence of its mechanisms, and future directions.

Dependence of cortical neuronal strength-duration properties on TMS pulse shape.

OBJECTIVE: The aim of present study was to explore the effects of different combinations of transcranial magnetic stimulation (TMS) pulse width and pulse shape on cortical strength-duration time constant (SDTC) and rheobase measurements. METHODS: Resting motor thresholds (RMT) at pulse widths (PW) of 30, 45, 60, 90 and 120 µs and M-ratios of 0.2, 0.1 and 0.025 were determined using figure-of-eight coil with initial posterior-to-anterior induced current. The M-ratio indicates the relative phases of the induced current with lower values signifying a more unidirectional stimulus. Strength-duration time constant (SDTC) and rheobase were estimated for each M-ratio and various PW combinations. Simulations of biophysically realistic cortical neuron models assessed underlying neuronal populations and physiological mechanisms mediating pulse shape effects on strength-duration properties. RESULTS: The M-ratio exerted significant effect on SDTC (F(2,44) = 4.386, P = 0.021), which was longer for M-ratio of 0.2 (243.4 ± 61.2 µs) compared to 0.025 (186.7 ± 52.5 µs, P = 0.034). Rheobase was significantly smaller when assessed with M-ratio 0.2 compared to 0.025 (P = 0.026). SDTC and rheobase values were most consistent with pulse width sets of 30/45/60/90/120 µs, 30/60/90/120 µs, and 30/60/120 µs. Simulation studies indicated that isolated pyramidal neurons in layers 2/3, 5, and large basket-cells in layer 4 exhibited SDTCs comparable to experimental results. Further, simulation studies indicated that reducing transient Na+ channel conductance increased SDTC with larger increases for higher M-ratios. CONCLUSIONS: Cortical strength-duration curve properties vary with pulse shape, and the modulating effect of the hyperpolarising pulse phase on cortical axonal transient Na+ conductances could account for these changes, although a shift in the recruited neuronal populations may contribute as well. SIGNIFICANCE: The dependence of the cortical strength-duration curve properties on the TMS pulse shape and pulse width selection underscores the need for consistent measurement methods across studies and the potential to extract information about pathophysiological processes.

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.

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

Objective.Temporal interference stimulation (TIS) was proposed as a non-invasive, focal, and steerable deep brain stimulation method. However, the mechanisms underlying experimentally-observed suprathreshold TIS effects are unknown, and prior simulation studies had limitations in the representations of the TIS electric field (E-field) and cerebral neurons. We examined the E-field and neural response characteristics for TIS and related transcranial alternating current stimulation modalities.Approach.Using the uniform-field approximation, we simulated a range of stimulation parameters in biophysically realistic model cortical neurons, including different orientations, frequencies, amplitude ratios, amplitude modulation, and phase difference of the E-fields, and obtained thresholds for both activation and conduction block.Main results. For two E-fields with similar amplitudes (representative of E-field distributions at the target region), TIS generated an amplitude-modulated (AM) total E-field. Due to the phase difference of the individual E-fields, the total TIS E-field vector also exhibited rotation where the orientations of the two E-fields were not aligned (generally also at the target region). TIS activation thresholds (75-230 V m-1) were similar to those of high-frequency stimulation with or without modulation and/or rotation. For E-field dominated by the high-frequency carrier and with minimal amplitude modulation and/or rotation (typically outside the target region), TIS was less effective at activation and more effective at block. Unlike AM high-frequency stimulation, TIS generated conduction block with some orientations and amplitude ratios of individual E-fields at very high amplitudes of the total E-field (>1700 V m-1).Significance. The complex 3D properties of the TIS E-fields should be accounted for in computational and experimental studies. The mechanisms of suprathreshold cortical TIS appear to involve neural activity block and periodic activation or onset response, consistent with computational studies of peripheral axons. These phenomena occur at E-field strengths too high to be delivered tolerably through scalp electrodes and may inhibit endogenous activity in off-target regions, suggesting limited significance of suprathreshold TIS.