Biophysically realistic neuron models for simulation of cortical stimulation

Bridging macroscopic and microscopic modeling of electric field by brain stimulation

Background

Modeling the electric field (E-field) on the microscopic scale improves our understanding of brain stimulation modalities and modeling methods but requires careful consideration of the conductivity values and correction of the field amplitudes to match conventional models on the macroscopic scale.

Objective

We analyze the correction step and discuss its relevance and implications for E-field modeling efforts bridging the macroscopic and microscopic scales.

Methods

We provide the theoretical framework for comparing microscopic and macroscopic models and describe approaches for effectively and efficiently matching the E-field amplitude and tissue conductivity.

Results

Consistent results can be obtained for brain stimulation models on different scales with appropriately selected conductivity and E-field amplitudes.

Conclusion

Microscopic E-field models enable numerical estimation of conductivity of macroscopic homogenous neural tissue from microscopically realistic brain samples and exploration of the effect of microscopic E-field perturbations on neural activation threshold by brain stimulation, therefore improving modeling accuracy.

Inkjet-printed transparent electrodes: Design, characterization, and initial in vivo evaluation for brain stimulation

Electrical stimulation is a powerful tool for investigating and modulating brain activity, as well as for treating neurological disorders. However, understanding the precise effects of electrical stimulation on neural activity has been hindered by limitations in recording neuronal responses near the stimulating electrode, such as stimulation artifacts in electrophysiology or obstruction of the field of view in imaging. In this study, we introduce a novel stimulation device fabricated from conductive polymers that is transparent and therefore compatible with optical imaging techniques. The device is manufactured using a combination of microfabrication and inkjet printing techniques and is flexible, allowing better adherence to the brain's natural curvature. We characterized the electrical and optical properties of the electrodes, focusing on the trade-off between the maximum current that can be delivered and optical transmittance. We found that a 1 mm diameter, 350 nm thick PEDOT:PSS electrode could be used to apply a maximum current of 130 μA while maintaining 84% transmittance (approximately 50% under 2-photon imaging conditions). We then evaluated the electrode performance in the brain of an anesthetized mouse by measuring the electric field with a nearby recording electrode and found values up to 30 V/m. Finally, we combined experimental data with a finite-element model of the in vivo experimental setup to estimate the distribution of the electric field underneath the electrode in the mouse brain. Our findings indicate that the device can generate an electric field as high as 300 V/m directly beneath the electrode, demonstrating its potential for studying and manipulating neural activity using a range of electrical stimulation techniques relevant to human applications. Overall, this work presents a promising approach for developing versatile new tools to apply and study electrical brain stimulation.

Preclinical insights into gamma-tACS: foundations for clinical translation in neurodegenerative diseases

Gamma transcranial alternating current stimulation (gamma-tACS) represents a novel neuromodulation technique with promising therapeutic applications across neurodegenerative diseases. This mini-review consolidates recent preclinical and clinical findings, examining the mechanisms by which gamma-tACS influences neural oscillations, enhances synaptic plasticity, and modulates neuroimmune responses. Preclinical studies have demonstrated the capacity of gamma-tACS to synchronize neuronal firing, support long-term neuroplasticity, and reduce markers of neuroinflammation, suggesting its potential to counteract neurodegenerative processes. Early clinical studies indicate that gamma-tACS may improve cognitive functions and network connectivity, underscoring its ability to restore disrupted oscillatory patterns central to cognitive performance. Given the intricate and multifactorial nature of gamma oscillations, the development of tailored, optimized tACS protocols informed by extensive animal research is crucial. Overall, gamma-tACS presents a promising avenue for advancing treatments that support cognitive resilience in a range of neurodegenerative conditions.

Analyzing the brain's dynamic response to targeted stimulation using generative modeling

Generative models of brain activity have been instrumental in testing hypothesized mechanisms underlying brain dynamics against experimental datasets. Beyond capturing the key mechanisms underlying spontaneous brain dynamics, these models hold an exciting potential for understanding the mechanisms underlying the dynamics evoked by targeted brain stimulation techniques. This paper delves into this emerging application, using concepts from dynamical systems theory to argue that the stimulus-evoked dynamics in such experiments may be shaped by new types of mechanisms distinct from those that dominate spontaneous dynamics. We review and discuss (a) the targeted experimental techniques across spatial scales that can both perturb the brain to novel states and resolve its relaxation trajectory back to spontaneous dynamics and (b) how we can understand these dynamics in terms of mechanisms using physiological, phenomenological, and data-driven models. A tight integration of targeted stimulation experiments with generative quantitative modeling provides an important opportunity to uncover novel mechanisms of brain dynamics that are difficult to detect in spontaneous settings.

Subthreshold electric fields bidirectionally modulate neurotransmitter release through axon polarization

Subthreshold electric fields modulate brain activity and demonstrate potential in several therapeutic applications. Electric fields are known to generate heterogenous membrane polarization within neurons due to their complex morphologies. While the effects of somatic and dendritic polarization in postsynaptic neurons have been characterized, the functional consequences of axonal polarization on neurotransmitter release from the presynapse are unknown. Here, we combined noninvasive optogenetic indicators of voltage, calcium and neurotransmitter release to study the subcellular response within single neurons to subthreshold electric fields. We first captured the detailed spatiotemporal polarization profile produced by uniform electric fields within individual neurons. Small polarization of presynaptic boutons produces rapid and powerful modulation of neurotransmitter release, with the direction - facilitation or inhibition - depending on the direction of polarization. We determined that subthreshold electric fields drive this effect by rapidly altering the number of synaptic vesicles participating in neurotransmission, producing effects which resemble short-term plasticity akin to presynaptic homeostatic plasticity. These results provide key insights into the mechanisms of subthreshold electric fields at the cellular level.

Abstract Figure

Magnetic activation of electrically active cells

Magnetic control of cell activity has applications ranging from non-invasive neurostimulation to remote activation of cell-based therapies. Unlike other methods of regulating cell activity like heat and light, which are based on known receptors or proteins, no magnetically gated channel has been identified to date. As a result, effective approaches for magnetic control of cell activity are based on strong alternating magnetic fields able to induce electric fields or materials that convert magnetic energy into electrical, thermal, or mechanical energy to stimulate cells. In our investigations of magnetic cell responses, we found that a spiking HEK cell line with no other co-factors responds to a magnetic field that reaches a maximum of 500 mT within 200 ms using a permanent magnet. The response is rare, approximately 1 in 50 cells, but is fast and reproducible, generating an action potential within 200 ms of magnetic field stimulation. The magnetic field stimulation is over 10,000 times slower than the magnetic fields used in transcranial magnetic stimulation (TMS) and the induced electric field is more than an order of magnitude lower than necessary for neuromodulation, suggesting that induced electric currents do not drive the cell response. Instead, our calculation suggests that this response depends on mechanoreception pathways activated by the magnetic torque of TRP-associated lipid rafts. Despite the relatively rare response to magnetic stimulation, when cells form gap junctions, the magnetic stimulation can propagate to nearby cells, causing tissue-level responses. As an example, we co-cultured spiking HEK cells with beta-pancreatic MIN6 cells and found that this co-culture responds to magnetic fields by increasing insulin production. Together, these results point toward a method for the magnetic control of biological activity without the need for a material co-factor such as synthetic nanoparticles. By better understanding this mechanism and enriching for magneto-sensitivity it may be possible to adapt this approach to the rapidly expanding tool kit for wireless cell activity regulation.

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

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

Repeated tDCS at clinically-relevant field intensity can boost concurrent motor learning in rats

Electric fields used in clinical trials with transcranial direct current stimulation (tDCS) are small, with magnitudes that have yet to demonstrate measurable effects in preclinical animal models. We hypothesized that weak stimulation will nevertheless produce sizable effects, provided that it is applied concurrently with behavioral training, and repeated over multiple sessions. We tested this here in a rodent model of dexterous motor-skill learning. We developed a preparation that allows concurrent stimulation during the performance of a pellet-reaching task in freely behaving rats. The task was automated to minimize experimenter bias. We measured field magnitudes intracranially to calibrate the stimulation current. In this study, only male rats were used. Animals were trained for 20 min with concurrent epicranial tDCS over 10 daily sessions. Behavior was recorded with high-speed video to quantify reaching dynamics. We also measured motor-evoked potentials (MEPs) bilaterally with epidural microstimulation. The new electrode montage enabled stable stimulation over 10 sessions with a field intensity of 2V/m at the motor cortex. The number of successful reaches improved across days of training, and the rate of learning was higher in the anodal group as compared to sham-control animals (F(1)=7.12, p=0.008, N=24). MEPs were not systematically affected by tDCS. Posthoc analysis suggests that tDCS modulated motor learning only for right-pawed animals, improving success of reaching, but limiting stereotypy in these animals. Repeated and concurrent anodal tDCS can boost motor-skill learning at clinically-relevant field intensities. In this animal model the effect interacted with paw preference and was not associated with corticospinal excitability.

Finite Element Modelling for Biophysical Models of Nervous System Stimulation: Best Practices for Multiscale Adaptive Meshing

This paper presents methods for FEM modelling the peripheral and central nervous systems with considerations for meshing and computational constraints. FEM models in this context are convenient for testing hypothesises about the effects of different stimulation parameters and exploring different electrode designs before moving to in vitro and in vivo experiments. The methods presented in this paper are motivated by assessing differentiation errors from different mesh sizes and the transitions between different materials in the model. We aim to support the development of transparent and reproducible modelling experiments. Accurate and reproducible models are essential, given the importance of the applications in which these models are used. However, a dearth of literature is devoted to promoting best practices in finite element modelling for biophysical models. We evaluate the impact of differentiation errors on calculating the Activating Function and predicting action potentials in a Hodgkin-Huxley (H-H) axon model. We found that poor spatial discretisation facilitates the generation of double-derivative noise. However, it does not generate false predictions of action potentials on the H-H model. Activation thresholds were higher (57.5 mA) for coarser meshes than Fine and Extremely Fine (55 mA). Implementing Multiscale meshes with the finest refined sizes reduced material transition discontinuities reflected in the activating function calculation. Our findings support using the finest spatial discretisations possible within computational constraints, which may rely on adaptive meshing techniques. We advocate coupling the extracellular field to H-H-based axons to further limit potential error sources.

Enabling electric field model of microscopically realistic brain

BACKGROUND

Modeling brain stimulation at the microscopic scale may reveal new paradigms for various stimulation modalities.

OBJECTIVE

We present the largest map to date of extracellular electric field distributions within a layer L2/L3 mouse primary visual cortex brain sample. This was enabled by the automated analysis of serial section electron microscopy images with improved handling of image defects, covering a volume of 250 × 140 × 90 μm³.

METHODS

The map was obtained by applying a uniform brain stimulation electric field at three different polarizations and accurately computing microscopic field perturbations using the boundary element fast multipole method. We used the map to identify the effect of microscopic field perturbations on the activation thresholds of individual neurons. Previous relevant studies modeled a macroscopically homogeneous cortical volume.

RESULT

Our result shows that the microscopic field perturbations - an 'electric field spatial noise' with a mean value of zero - only modestly influence the macroscopically predicted stimulation field strengths necessary for neuronal activation. The thresholds do not change by more than 10 % on average.

CONCLUSION

Under the stated limitations and assumptions of our method, this result essentially justifies the conventional theory of "invisible" neurons embedded in a macroscopic brain model for transcranial magnetic and transcranial electrical stimulation. However, our result is solely sample-specific and is only relevant to this relatively small sample with 396 neurons. It largely neglects the effect of the microcapillary network. Furthermore, we only considered the uniform impressed field and a single-pulse stimulation time course.

Circuits and mechanisms for TMS-induced corticospinal waves: Connecting sensitivity analysis to the network graph

Transcranial magnetic stimulation (TMS) is a non-invasive, FDA-cleared treatment for neuropsychiatric disorders with broad potential for new applications, but the neural circuits that are engaged during TMS are still poorly understood. Recordings of neural activity from the corticospinal tract provide a direct readout of the response of motor cortex to TMS, and therefore a new opportunity to model neural circuit dynamics. The study goal was to use epidural recordings from the cervical spine of human subjects to develop a computational model of a motor cortical macrocolumn through which the mechanisms underlying the response to TMS, including direct and indirect waves, could be investigated. An in-depth sensitivity analysis was conducted to identify important pathways, and machine learning was used to identify common circuit features among these pathways. Sensitivity analysis identified neuron types that preferentially contributed to single corticospinal waves. Single wave preference could be predicted using the average connection probability of all possible paths between the activated neuron type and L5 pyramidal tract neurons (PTNs). For these activations, the total conduction delay of the shortest path to L5 PTNs determined the latency of the corticospinal wave. Finally, there were multiple neuron type activations that could preferentially modulate a particular corticospinal wave. The results support the hypothesis that different pathways of circuit activation contribute to different corticospinal waves with participation of both excitatory and inhibitory neurons. Moreover, activation of both afferents to the motor cortex as well as specific neuron types within the motor cortex initiated different I-waves, and the results were interpreted to propose the cortical origins of afferents that may give rise to certain I-waves. The methodology provides a workflow for performing computationally tractable sensitivity analyses on complex models and relating the results to the network structure to both identify and understand mechanisms underlying the response to acute stimulation.

Enabling Electric Field Model of Microscopically Realistic Brain

Modeling brain stimulation at the microscopic scale may reveal new paradigms for various stimulation modalities. We present the largest map to date of extracellular electric field distributions within a layer L2/L3 mouse primary visual cortex brain sample. This was enabled by the automated analysis of serial section electron microscopy images with improved handling of image defects, covering a volume of 250 × 140 × 90 μm 3 . The map was obtained by applying a uniform brain stimulation electric field at three different polarizations and accurately computing microscopic field perturbations using the boundary element fast multipole method. We used the map to identify the effect of microscopic field perturbations on the activation thresholds of individual neurons. Previous relevant studies modeled a macroscopically homogeneous cortical volume. Our result shows that the microscopic field perturbations - an 'electric field spatial noise' with a mean value of zero - only modestly influence the macroscopically predicted stimulation field strengths necessary for neuronal activation. The thresholds do not change by more than 10% on average. Under the stated limitations and assumptions of our method, this result justifies the conventional theory of "invisible" neurons embedded in a macroscopic brain model for transcranial magnetic and transcranial electrical stimulation. However, our result is solely sample-specific and largely neglects the effect of the microcapillary network. Furthermore, we only considered the uniform impressed field and a single- pulse stimulation time course.

Significance statement

This study is arguably the first attempt to model brain stimulation at the microscopic scale, enabled by automated analysis of modern scanning electron microscopy images of the brain. It concentrates on modeling microscopic perturbations of the extracellular electric field caused by the physical cell structure and is applicable to any type of brain stimulation.

Data availability statement

Post-processed cell CAD models (383, stl format), microcapillary CAD models (34, stl format), post-processed neuron morphologies (267, swc format), extracellular electric field and potential distributions at different polarizations (267x3, MATLAB format), *.ses projects files for biophysical modeling with Neuron software (267x2, Neuron format), and computed neuron activating thresholds at different conditions (267x8, Excel tables, without the sample polarization correction from Section 2.8) are made available online through BossDB , a volumetric open-source database for 3D and 4D neuroscience data.

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.

A survey on integral equations for bioelectric modeling

Bioelectric modeling problems, such as electroencephalography, magnetoencephalography, transcranial electrical stimulation, deep brain stimulation, and transcranial magnetic stimulation, among others, can be approached through the formulation and resolution of integral equations of theboundary element method(BEM). Recently, it has been realized that thecharge-based formulationof the BEM is naturally well-suited for the application of thefast multipole method(FMM). The FMM is a powerful algorithm for the computation of many-body interactions and is widely applied in electromagnetic modeling problems. With the introduction of BEM-FMM in the context of bioelectromagnetism, the BEM can now compete with thefinite element method(FEM) in a number of application cases. This survey has two goals: first, to give a modern account of the main BEM formulations in the literature and their integration with FMM, directed to general researchers involved in development of BEM software for bioelectromagnetic applications. Second, to survey different techniques and available software, and to contrast different BEM and FEM approaches. As a new contribution, we showcase that the charge-based formulation is dual to the more common surface potential formulation.

Ultra-high frequency repetitive TMS at subthreshold intensity induces suprathreshold motor response via temporal summation

Objective.The transcranial magnetic stimulation (TMS) coil induces an electric field that diminishes rapidly upon entering the brain. This presents a challenge in achieving focal stimulation of a deep brain structure. Neuronal elements, including axons, dendrites, and cell bodies, exhibit specific time constants. When exposed to repetitive TMS pulses at a high frequency, there is a cumulative effect on neuronal membrane potentials, resulting in temporal summation. This study aims to determine whether TMS pulse train at high-frequency and subthreshold intensity could induce a suprathreshold response.Approach.As a proof of concept, we developed a TMS machine in-house that could consistently output pulses up to 250 Hz, and performed experiments on 22 awake rats to test whether temporal summation was detectable under pulse trains at 100, 166, or 250 Hz.Main results.Results revealed that TMS pulses at 55% maximum stimulator output (MSO, peak dI/dt= 68.5 A/μs at 100% MSO, pulse width = 48μs) did not induce motor responses with either single pulses or pulse trains. Similarly, a single TMS pulse at 65% MSO failed to evoke a motor response in rats; however, a train of TMS pulses at frequencies of 166 and 250 Hz, but not at 100 Hz, successfully triggered motor responses and MEP signals, suggesting a temporal summation effect dependent on both pulse intensities and pulse train frequencies.Significance.We propose that the temporal summation effect can be leveraged to design the next-generation focal TMS system: by sequentially driving multiple coils at high-frequency and subthreshold intensity, areas with the most significant overlapping E-fields undergo maximal temporal summation effects, resulting in a suprathreshold response.

Multi-scale modelling of location- and frequency-dependent synaptic plasticity induced by transcranial magnetic stimulation in the dendrites of pyramidal neurons

Background

Repetitive transcranial magnetic stimulation (rTMS) induces long-term changes of synapses, but the mechanisms behind these modifications are not fully understood. Although there has been progress in the development of multi-scale modeling tools, no comprehensive module for simulating rTMS-induced synaptic plasticity in biophysically realistic neurons exists..

Objective

We developed a modelling framework that allows the replication and detailed prediction of long-term changes of excitatory synapses in neurons stimulated by rTMS.

Methods

We implemented a voltage-dependent plasticity model that has been previously established for simulating frequency-, time-, and compartment-dependent spatio-temporal changes of excitatory synapses in neuronal dendrites. The plasticity model can be incorporated into biophysical neuronal models and coupled to electrical field simulations.

Results

We show that the plasticity modelling framework replicates long-term potentiation (LTP)-like plasticity in hippocampal CA1 pyramidal cells evoked by 10-Hz repetitive magnetic stimulation (rMS). This plasticity was strongly distance dependent and concentrated at the proximal synapses of the neuron. We predicted a decrease in the plasticity amplitude for 5 Hz and 1 Hz protocols with decreasing frequency. Finally, we successfully modelled plasticity in distal synapses upon local electrical theta-burst stimulation (TBS) and predicted proximal and distal plasticity for rMS TBS. Notably, the rMS TBS-evoked synaptic plasticity exhibited robust facilitation by dendritic spikes and low sensitivity to inhibitory suppression.

Conclusion

The plasticity modelling framework enables precise simulations of LTP-like cellular effects with high spatio-temporal resolution, enhancing the efficiency of parameter screening and the development of plasticity-inducing rTMS protocols.

Coil Orientation and Stimulation Threshold in Transcranial Magnetic Stimulation (TMS)

Transcranial Magnetic Stimulation (TMS) is used to treat mental disorders and explore brain function via applied electromagnetic fields generated by a high current coil placed on the subject's scalp. While TMS has been in clinical use for decades, and continues to be a rapidly expanding therapeutic modality, there are still many unknowns regarding how stimulation parameters may affect treatment efficacy and how they may be optimized. One key parameter that is readily accessible is coil orientation and its effects on TMS stimulation threshold. In this work, a multi-scale modeling approach addressed the effects of coil orientation on the TMS stimulation threshold for neuronal activation with several TMS coil current pulse shapes and widths. The modeling tool that was used incorporated an anatomically realistic macro scale model of the human brain cortex, and a micro scale neuronal model based on a representative layer 5 pyramidal brain cell. Simulations were performed for the left primary motor cortical area. Coil orientations associated with a minimum stimulation threshold for various current pulses were identified and then validated using data collected and published by another research team. This multi-scale modeling approach is versatile and can potentially be used for various current pulses and TMS coil locations to predict and map optimum TMS coil orientations for a wide range of treatment applications.

Investigating the neural mechanisms of transcranial direct current stimulation effects on human cognition: current issues and potential solutions

Transcranial direct current stimulation (tDCS) has been studied extensively for its potential to enhance human cognitive functions in healthy individuals and to treat cognitive impairment in various clinical populations. However, little is known about how tDCS modulates the neural networks supporting cognition and the complex interplay with mediating factors that may explain the frequently observed variability of stimulation effects within and between studies. Moreover, research in this field has been characterized by substantial methodological variability, frequent lack of rigorous experimental control and small sample sizes, thereby limiting the generalizability of findings and translational potential of tDCS. The present manuscript aims to delineate how these important issues can be addressed within a neuroimaging context, to reveal the neural underpinnings, predictors and mediators of tDCS-induced behavioral modulation. We will focus on functional magnetic resonance imaging (fMRI), because it allows the investigation of tDCS effects with excellent spatial precision and sufficient temporal resolution across the entire brain. Moreover, high resolution structural imaging data can be acquired for precise localization of stimulation effects, verification of electrode positions on the scalp and realistic current modeling based on individual head and brain anatomy. However, the general principles outlined in this review will also be applicable to other imaging modalities. Following an introduction to the overall state-of-the-art in this field, we will discuss in more detail the underlying causes of variability in previous tDCS studies. Moreover, we will elaborate on design considerations for tDCS-fMRI studies, optimization of tDCS and imaging protocols and how to assure high-level experimental control. Two additional sections address the pressing need for more systematic investigation of tDCS effects across the healthy human lifespan and implications for tDCS studies in age-associated disease, and potential benefits of establishing large-scale, multidisciplinary consortia for more coordinated tDCS research in the future. We hope that this review will contribute to more coordinated, methodologically sound, transparent and reproducible research in this field. Ultimately, our aim is to facilitate a better understanding of the underlying mechanisms by which tDCS modulates human cognitive functions and more effective and individually tailored translational and clinical applications of this technique in the future.

Electrode positioning errors reduce current dose for focal tDCS set-ups: Evidence from individualized electric field mapping

OBJECTIVE

Electrode positioning errors contribute to variability of transcranial direct current stimulation (tDCS) effects. We investigated the impact of electrode positioning errors on current flow for tDCS set-ups with different focality.

METHODS

Deviations from planned electrode positions were determined using data acquired in an experimental study (N = 240 datasets) that administered conventional and focal tDCS during magnetic resonance imaging (MRI). Comparison of individualized electric field modeling for planned and empirically derived "actual" electrode positions was conducted to quantify the impact of positioning errors on the electric field dose in target regions for tDCS.

RESULTS

Planned electrode positions resulted in higher current dose in the target regions for focal compared to conventional montages (7-12%). Deviations from planned positions significantly reduced current flow in the target regions, selectively for focal set-ups (26-30%). Dose reductions were significantly larger for focal compared to conventional set-ups (29-43%).

CONCLUSIONS

Precise positioning is crucial when using focal tDCS set-ups to avoid significant reductions of current dose in the intended target regions.

SIGNIFICANCE

Our results highlight the urgent need to routinely implement methods for improving electrode positioning, minimization of electrode drift, verification of electrode positions before and/or after tDCS and also to consider positioning errors when investigating dose-response relationships, especially for focal set-ups.

Axon morphology and intrinsic cellular properties determine repetitive transcranial magnetic stimulation threshold for plasticity

Introduction

Repetitive transcranial magnetic stimulation (rTMS) is a widely used therapeutic tool in neurology and psychiatry, but its cellular and molecular mechanisms are not fully understood. Standardizing stimulus parameters, specifically electric field strength, is crucial in experimental and clinical settings. It enables meaningful comparisons across studies and facilitates the translation of findings into clinical practice. However, the impact of biophysical properties inherent to the stimulated neurons and networks on the outcome of rTMS protocols remains not well understood. Consequently, achieving standardization of biological effects across different brain regions and subjects poses a significant challenge.

Methods

This study compared the effects of 10 Hz repetitive magnetic stimulation (rMS) in entorhino-hippocampal tissue cultures from mice and rats, providing insights into the impact of the same stimulation protocol on similar neuronal networks under standardized conditions.

Results

We observed the previously described plastic changes in excitatory and inhibitory synaptic strength of CA1 pyramidal neurons in both mouse and rat tissue cultures, but a higher stimulation intensity was required for the induction of rMS-induced synaptic plasticity in rat tissue cultures. Through systematic comparison of neuronal structural and functional properties and computational modeling, we found that morphological parameters of CA1 pyramidal neurons alone are insufficient to explain the observed differences between the groups. Although morphologies of mouse and rat CA1 neurons showed no significant differences, simulations confirmed that axon morphologies significantly influence individual cell activation thresholds. Notably, differences in intrinsic cellular properties were sufficient to account for the 10% higher intensity required for the induction of synaptic plasticity in the rat tissue cultures.

Conclusion

These findings demonstrate the critical importance of axon morphology and intrinsic cellular properties in predicting the plasticity effects of rTMS, carrying valuable implications for the development of computer models aimed at predicting and standardizing the biological effects of rTMS.

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.

Energy controls wave propagation in a neural network with spatial stimuli

Nervous system has distinct anisotropy and some intrinsic biophysical properties enable neurons present various firing modes in neural activities. In presence of realistic electromagnetic fields, non-uniform radiation activates these neurons with energy diversity. By using a feasible model, energy function is obtained to predict the growth of synaptic connections of these neurons. Distribution of average value of the Hamilton energy function vs. intensity of noisy disturbance can predict the occurrence of coherence resonance, which the neural activities show high regularity by applying noisy disturbance with moderate intensity. From physical viewpoint, the average energy value has similar role average power for the neuron. Non-uniform spatial disturbance is applied and energy is injected into the neural network, statistical synchronization factor is calculated to predict the network synchronization stability and wave propagation. The intensity for field coupling is adaptively controlled by energy diversity between adjacent neurons. Local energy balance will terminate further growth of the coupling intensity; otherwise, heterogeneity is formed in the network due to energy diversity. Furthermore, memristive channel current is introduced into the neuron model for perceiving the effect of electromagnetic induction and radiation, and a memristive neuron is obtained. The circuit implement of memristive circuit depends on the connection to a magnetic flux-controlled memristor into the mentioned neural circuit in an additive branch circuit. The connection and activation of this memristive neural network are controlled under external spatial electromagnetic radiation by capturing enough field energy. Continuous energy collection and exchange generate energy diversity and synaptic connection is created to regulate the synchronous firing patterns and energy balance.

Neural mechanisms of the temporal response of cortical neurons to intracortical microstimulation

BACKGROUND

Intracortical microstimulation (ICMS) is used to map neuronal circuitry in the brain and restore lost sensory function, including vision, hearing, and somatosensation. The temporal response of cortical neurons to single pulse ICMS is remarkably stereotyped and comprises short latency excitation followed by prolonged inhibition and, in some cases, rebound excitation. However, the neural origin of the different response components to ICMS are poorly understood, and the interactions between the three response components during trains of ICMS pulses remains unclear.

OBJECTIVE

We used computational modeling to determine the mechanisms contributing to the temporal response to ICMS in model cortical neurons.

METHODS

We implemented a biophysically based computational model of a cortical column comprising neurons with realistic morphology and synapses and quantified the temporal response of cortical neurons to different ICMS protocols. We characterized the temporal responses to single pulse ICMS across stimulation intensities and inhibitory (GABA-B/GABA-A) synaptic strengths. To probe interactions between response components, we quantified the response to paired pulse ICMS at different inter-pulse intervals and the response to short trains at different stimulation frequencies. Finally, we evaluated the performance of biomimetic ICMS trains in evoking sustained neural responses.

RESULTS

Single pulse ICMS evoked short latency excitation followed by a period of inhibition, but model neurons did not exhibit post-inhibitory excitation. The strength of short latency excitation increased and the duration of inhibition increased with increased stimulation amplitude. Prolonged inhibition resulted from both after-hyperpolarization currents and GABA-B synaptic transmission. During the paired pulse protocol, the strength of short latency excitation evoked by a test pulse decreased marginally compared to those evoked by a single pulse for interpulse intervals (IPI) < 100 m s. Further, the duration of inhibition evoked by the test pulse was prolonged compared to single pulse for IPIs <50 m s and was not predicted by linear superposition of individual inhibitory responses. For IPIs>50 m s, the duration of inhibition evoked by the test pulse was comparable to those evoked by a single pulse. Short ICMS trains evoked repetitive excitatory responses against a background of inhibition. However, the strength of the repetitive excitatory response declined during ICMS at higher frequencies. Further, the duration of inhibition at the cessation of ICMS at higher frequencies was prolonged compared to the duration following a single pulse. Biomimetic pulse trains evoked comparable neural response between the onset and offset phases despite the presence of stimulation induced inhibition.

CONCLUSIONS

The cortical column model replicated the short latency excitation and long-lasting inhibitory components of the stereotyped neural response documented in experimental studies of ICMS. Both cellular and synaptic mechanisms influenced the response components generated by ICMS. The non-linear interactions between response components resulted in dynamic ICMS-evoked neural activity and may play an important role in mediating the ICMS-induced precepts.

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.

Simulation study on high spatio-temporal resolution acousto-electrophysiological neuroimaging

Objective.Acousto-electrophysiological neuroimaging (AENI) is a technique hypothesized to record electrophysiological activity of the brain with millimeter spatial and sub-millisecond temporal resolution. This improvement is obtained by tagging areas with focused ultrasound (fUS). Due to mechanical vibration with respect to the measuring electrodes, the electrical activity of the marked region will be modulated onto the ultrasonic frequency. The region's electrical activity can subsequently be retrieved via demodulation of the measured signal. In this study, the feasibility of this hypothesized technique is tested.Approach.This is done by calculating the forward electroencephalography response under quasi-static assumptions. The head is simplified as a set of concentric spheres. Two sizes are evaluated representing human and mouse brains. Moreover, feasibility is assessed for wet and dry transcranial, and for cortically placed electrodes. The activity sources are modeled by dipoles, with their current intensity profile drawn from a power-law power spectral density.Results.It is shown that mechanical vibration modulates the endogenous activity onto the ultrasonic frequency. The signal strength depends non-linearly on the alignment between dipole orientation, vibration direction and recording point. The strongest signal is measured when these three dependencies are perfectly aligned. The signal strengths are in the pV-range for a dipole moment of 5 nAm and ultrasonic pressures within Food and Drug Administration (FDA)-limits. The endogenous activity can then be accurately reconstructed via demodulation. Two interference types are investigated: vibrational and static. Depending on the vibrational interference, it is shown that millimeter resolution signal detection is possible also for deep brain regions. Subsequently, successful demodulation depends on the static interference, that at MHz-range has to be sub-picovolt.Significance.Our results show that mechanical vibration is a possible underlying mechanism of acousto-electrophyisological neuroimaging. This paper is a first step towards improved understanding of the conditions under which AENI is feasible.

Estimations of Charge Deposition Onto Convoluted Axon Surfaces Within Extracellular Electric Fields

OBJECTIVE

Biophysical models of neural stimulation are a valuable approach to explaining the mechanisms of neuronal recruitment via applied extracellular electric fields. Typically, the applied electric field is estimated via a macroscopic finite element method solution and then applied to cable models as an extracellular voltage source. However, the field resolution is limited by the finite element size (typically 10's-100's of times greater than average neuronal cross-section). As a result, induced charges deposited onto anatomically realistic curved membrane interfaces are not taken into consideration. However, these details may alter estimates of the applied electric field and predictions of neural tissue activation.

METHODS

To estimate microscopic variations of the electric field, data for intra-axonal space segmented from 3D scanning electron microscopy of the mouse brain genu of corpus callosum were used. The boundary element fast multipole method was applied to accurately compute the extracellular solution. Neuronal recruitment was then estimated via an activating function.

RESULTS

Taking the physical structure of the arbor into account generally predicts higher values of the activating function. The relative integral 2-norm difference is 90% on average when the entire axonal arbor is present. A large fraction of this difference might be due to the axonal body itself. When an isolated physical axon is considered with all other axons removed, the relative integral 2-norm difference between the single-axon solution and the complete solution is 25% on average.

CONCLUSION

Our result may provide an explanation as to why Deep Brain Stimulation experiments typically predict lower activation thresholds than commonly used FEM/Cable model approaches to predicting neuronal responses to extracellular electrical stimulation.

SIGNIFICANCE

These results may change methods for bi-domain neural modeling and neural excitation.

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.

Model-based analysis of subthreshold mechanisms of spinal cord stimulation for pain

Objective.Spinal cord stimulation (SCS) is a common treatment for chronic pain. For decades, SCS maximized overlap between stimulation-induced paresthesias and the patient's painful areas. Recently developed SCS paradigms relieve pain at sub-perceptible amplitudes, yet little is known about the neural response to these new waveforms or their analgesic mechanisms of action. Therefore, in this study, we investigated the neural response to multiple forms of paresthesia-free SCS.Approach.We used computational modeling to investigate the neurophysiological effects and the plausibility of commonly proposed mechanisms of three paresthesia-free SCS paradigms: burst, 1 kHz, and 10 kHz SCS. Specifically, in C- and Aβ-fibers, we investigated the effects of different SCS waveforms on spike timing and activation thresholds, as well as how stochastic ion channel gating affects the response of dorsal column axons. Finally, we characterized membrane polarization of superficial dorsal horn neurons.Main results.We found that none of the SCS waveforms activate nor modulate spike timing in C-fibers. Spike timing was modulated in Aβ-fibers only at suprathreshold amplitudes. Ion channel stochasticity had little effect on Aβ-fiber activation thresholds but produced heterogeneous spike timings at suprathreshold amplitudes. Finally, local cells were preferentially polarized in their axon terminals, and the magnitude of this polarization was dependent on cellular morphology and position relative to the stimulation electrodes.Significance.Overall, the mechanisms of action of subparesthetic SCS remain unclear. Our results suggest that no SCS waveforms directly activate C-fibers, and modulation of spike timing is unlikely at subthreshold amplitudes. We conclude that potential subthreshold neuromodulatory effects of SCS on local cells are likely to be presynaptic in nature, as axons are preferentially depolarized during SCS.

Repetitive transcranial magnetic stimulation (rTMS) triggers dose-dependent homeostatic rewiring in recurrent neuronal networks

Repetitive transcranial magnetic stimulation (rTMS) is a non-invasive brain stimulation technique used to induce neuronal plasticity in healthy individuals and patients. Designing effective and reproducible rTMS protocols poses a major challenge in the field as the underlying biomechanisms of long-term effects remain elusive. Current clinical protocol designs are often based on studies reporting rTMS-induced long-term potentiation or depression of synaptic transmission. Herein, we employed computational modeling to explore the effects of rTMS on long-term structural plasticity and changes in network connectivity. We simulated a recurrent neuronal network with homeostatic structural plasticity among excitatory neurons, and demonstrated that this mechanism was sensitive to specific parameters of the stimulation protocol (i.e., frequency, intensity, and duration of stimulation). Particularly, the feedback-inhibition initiated by network stimulation influenced the net stimulation outcome and hindered the rTMS-induced structural reorganization, highlighting the role of inhibitory networks. These findings suggest a novel mechanism for the lasting effects of rTMS, i.e., rTMS-induced homeostatic structural plasticity, and highlight the importance of network inhibition in careful protocol design, standardization, and optimization of stimulation.

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.

Axon morphology and intrinsic cellular properties determine repetitive transcranial magnetic stimulation threshold for plasticity

Repetitive transcranial magnetic stimulation (rTMS) is a widely used therapeutic tool in neurology and psychiatry, but its cellular and molecular mechanisms are not fully understood. Standardizing stimulus parameters, specifically electric field strength and direction, is crucial in experimental and clinical settings. It enables meaningful comparisons across studies and facilitating the translation of findings into clinical practice. However, the impact of biophysical properties inherent to the stimulated neurons and networks on the outcome of rTMS protocols remains not well understood. Consequently, achieving standardization of biological effects across different brain regions and subjects poses a significant challenge. This study compared the effects of 10 Hz repetitive magnetic stimulation (rMS) in entorhino-hippocampal tissue cultures from mice and rats, providing insights into the impact of the same stimulation protocol on similar neuronal networks under standardized conditions. We observed the previously described plastic changes in excitatory and inhibitory synaptic strength of CA1 pyramidal neurons in both mouse and rat tissue cultures, but a higher stimulation intensity was required for the induction of rMS-induced synaptic plasticity in rat tissue cultures. Through systematic comparison of neuronal structural and functional properties and computational modeling, we found that morphological parameters of CA1 pyramidal neurons alone are insufficient to explain the observed differences between the groups. However, axon morphologies of individual cells played a significant role in determining activation thresholds. Notably, differences in intrinsic cellular properties were sufficient to account for the 10 % higher intensity required for the induction of synaptic plasticity in the rat tissue cultures. These findings demonstrate the critical importance of axon morphology and intrinsic cellular properties in predicting the plasticity effects of rTMS, carrying valuable implications for the development of computer models aimed at predicting and standardizing the biological effects of rTMS.

An optimization framework for targeted spinal cord stimulation

Objective. Spinal cord stimulation (SCS) is a common neurostimulation therapy to manage chronic pain. Technological advances have produced new neurostimulation systems with expanded capabilities in an attempt to improve the clinical outcomes associated with SCS. However, these expanded capabilities have dramatically increased the number of possible stimulation parameters and made it intractable to efficiently explore this large parameter space within the context of standard clinical programming procedures. Therefore, in this study, we developed an optimization approach to define the optimal current amplitudes or fractions across individual contacts in an SCS electrode array(s).Approach. We developed an analytic method using the Lagrange multiplier method along with smoothing approximations. To test our optimization framework, we used a hybrid computational modeling approach that consisted of a finite element method model and multi-compartment models of axons and cells within the spinal cord. Moreover, we extended our approach to multi-objective optimization to explore the trade-off between activating regions of interest (ROIs) and regions of avoidance (ROAs).Main results. For simple ROIs, our framework suggested optimized configurations that resembled simple bipolar configurations. However, when we considered multi-objective optimization, our framework suggested nontrivial stimulation configurations that could be selected from Pareto fronts to target multiple ROIs or avoid ROAs.Significance. We developed an optimization framework for targeted SCS. Our method is analytic, which allows for the fast calculation of optimal solutions. For the first time, we provided a multi-objective approach for selective SCS. Through this approach, we were able to show that novel configurations can provide neural recruitment profiles that are not possible with conventional stimulation configurations (e.g. bipolar stimulation). Most importantly, once integrated with computational models that account for sources of interpatient variability (e.g. anatomy, electrode placement), our optimization framework can be utilized to provide stimulation settings tailored to the needs of individual patients.

Identifiability Analysis and Noninvasive Online Estimation of the First-Order Neural Activation Dynamics in the Brain With Closed-Loop Transcranial Magnetic Stimulation

BACKGROUND

Neurons demonstrate very distinct nonlinear activation dynamics, influenced by the neuron type, morphology, ion channel expression, and various other factors. The measurement of the activation dynamics can identify the neural target of stimulation and detect deviations, e.g., for diagnosis. This paper describes a tool for closed-loop sequential parameter estimation (SPE) of the activation dynamics through transcranial magnetic stimulation (TMS). The proposed SPE method operates in real time, selects ideal stimulus parameters, detects and processes the response, and concurrently estimates the input-output (IO) curve and the first-order approximation of the activated neural target.

OBJECTIVE

To develop a method for concurrent SPE of the first-order activation dynamics and IO curve with closed-loop TMS.

METHOD

First, identifiability of an integrated model of the first-order neural activation dynamics and IO curve is assessed, demonstrating that at least two IO curves need to be acquired with different pulse widths. Then, a two-stage SPE method is proposed. It estimates the IO curve by using Fisher information matrix (FIM) optimization in the first stage and subsequently estimates the membrane time constant as well as the coupling gain in the second stage. The procedure continues in a sequential manner until a stopping rule is satisfied.

RESULTS

The results of 73 simulation cases confirm the satisfactory estimation of the membrane time constant and coupling gain with average absolute relative errors (AREs) of 6.2% and 5.3%, respectively, with an average of 344 pulses (172 pulses for each IO curve or pulse width). The method estimates the IO curves' lower and upper plateaus, mid-point, and slope with average AREs of 0.2%, 0.7%, 0.9%, and 14.5%, respectively. The conventional time constant estimation method based on the strength-duration (S-D) curve leads to 33.3% ARE, which is 27.0% larger than 6.2% ARE obtained through the proposed real-time FIM-based SPE method in this paper.

CONCLUSIONS

SPE of the activation dynamics requires acquiring at least two IO curves with different pulse widths, which needs a controllable TMS (cTMS) device with adjustable pulse duration.

SIGNIFICANCE

The proposed SPE method enhances the cTMS functionality, which can contribute novel insights in research and clinical studies.

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.

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.

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.

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.

Relative Contributions of Different Neural Sources to the EEG

Dogma dictates that the EEG signal is generated by postsynaptic currents (PSCs) because there are an enormous number of synapses in the brain, and PSCs have relatively long durations. However, PSCs are not the only potential source of electric fields in the brain. Action potentials, afterpolarizations, and presynaptic activity can also generate electric fields. Experimentally it is exceedingly difficult to delineate the contributions of different sources because they are casually linked. However, using computational modeling, we can interrogate the relative contributions of different neural elements to the EEG. We used a library of neuron models with morphologically realistic axonal arbors to quantify the relative contributions of PSCs, action potentials, and presynaptic activity to the EEG signal. Consistent with prior assertions, PSCs were the largest contributor to the EEG, but action potentials and afterpolarizations can also make appreciable contributions. For a population of neurons generating simultaneous PSCs and action potentials, we found that the action potentials accounted for up to 20% of the source strength while PSCs accounted for the other 80% and presynaptic activity negligibly contributed. Additionally, L5 PCs generated the largest PSC and action potential signals indicating that they the dominant EEG signal generator. Further, action potentials and afterpolarizations were sufficient to generate physiological oscillations, indicating that they are valid source contributors to the EEG. The EEG emerges from a combination of multiple different source, and, while PSCs are the largest contributor, other sources are non-negligible and should be included in modeling, analysis and interpretation of the EEG.

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

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

Modeling the Impact of Electrode/Tissue Geometry on Electrical Stimulation in Stereo-EEG

PURPOSE

Electrical stimulation through depth electrodes is used to map function and seizure onset during stereoelectroencephalography in patients undergoing evaluation for epilepsy surgery. Factors such as electrode design, location, and orientation are expected to impact effects of electrical stimulation.

METHODS

We developed a steady-state finite element model of brain tissue including five layers (skull through white matter) and an implanted electrode to explore the impact of electrode design and placement on the activation of brain tissue by electrical stimulation. We calculated electric potentials, current densities, and volume of tissue activated ( Volact ) in response to constant current bipolar stimulation. We modeled two depth electrode designs (3.5- and 4.43-mm intercontact spacing) and varied electrode location and orientation.

RESULTS

The electrode with greater intercontact spacing produced 8% to 23% larger Volact (1% to 16% considering only gray matter). Vertical displacement of the electrodes by half intercontact space increased Volact for upward displacement (6% to 83% for all brain tissue or -5% to 96% gray matter only) and decreased Volact (1% to 16% or 24% to 49% gray matter only) for downward displacement. Rotating the electrode in the tissue by 30° to 60° with respect to the vertical axis increased Volact by 30% to 90% (20%-48% gray matter only).

CONCLUSIONS

Location and orientation of depth electrodes with respect to surrounding brain tissue have a large impact on the amount of tissue activated during electrical stimulation mapping in stereoelectroencephalography. Electrode design has an impact, although modest for commonly used designs. Individualization of stimulation intensity at each location remains critical, especially for avoiding false-negative results.

Multielectrode Cortical Stimulation Selectively Induces Unidirectional Wave Propagation of Excitatory Neuronal Activity in Biophysical Neural Model

Cortical stimulation is emerging as an experimental tool in basic research and a promising therapy for a range of neuropsychiatric conditions. As multielectrode arrays enter clinical practice, the possibility of using spatiotemporal patterns of electrical stimulation to induce desired physiological patterns has become theoretically possible, but in practice can only be implemented by trial-and-error because of a lack of predictive models. Experimental evidence increasingly establishes traveling waves as fundamental to cortical information-processing, but we lack an understanding of how to control wave properties despite rapidly improving technologies. This study uses a hybrid biophysical-anatomical and neural-computational model to predict and understand how a simple pattern of cortical surface stimulation could induce directional traveling waves via asymmetric activation of inhibitory interneurons. We found that pyramidal cells and basket cells are highly activated by the anodal electrode and minimally activated by the cathodal electrodes, while Martinotti cells are moderately activated by both electrodes but exhibit a slight preference for cathodal stimulation. Network model simulations found that this asymmetrical activation results in a traveling wave in superficial excitatory cells that propagates unidirectionally away from the electrode array. Our study reveals how asymmetric electrical stimulation can easily facilitate traveling waves by relying on two distinct types of inhibitory interneuron activity to shape and sustain the spatiotemporal dynamics of endogenous local circuit mechanisms.SIGNIFICANCE STATEMENT Electrical brain stimulation is becoming increasingly useful to probe the workings of brain and to treat a variety of neuropsychiatric disorders. However, stimulation is currently performed in a trial-and-error fashion as there are no methods to predict how different electrode arrangements and stimulation paradigms will affect brain functioning. In this study, we demonstrate a hybrid modeling approach, which makes experimentally testable predictions that bridge the gap between the microscale effects of multielectrode stimulation and the resultant circuit dynamics at the mesoscale. Our results show how custom stimulation paradigms can induce predictable, persistent changes in brain activity, which has the potential to restore normal brain function and become a powerful therapy for neurological and psychiatric conditions.

Comparison between an exact and a heuristic neural mass model with second-order synapses

Neural mass models (NMMs) are designed to reproduce the collective dynamics of neuronal populations. A common framework for NMMs assumes heuristically that the output firing rate of a neural population can be described by a static nonlinear transfer function (NMM1). However, a recent exact mean-field theory for quadratic integrate-and-fire (QIF) neurons challenges this view by showing that the mean firing rate is not a static function of the neuronal state but follows two coupled nonlinear differential equations (NMM2). Here we analyze and compare these two descriptions in the presence of second-order synaptic dynamics. First, we derive the mathematical equivalence between the two models in the infinitely slow synapse limit, i.e., we show that NMM1 is an approximation of NMM2 in this regime. Next, we evaluate the applicability of this limit in the context of realistic physiological parameter values by analyzing the dynamics of models with inhibitory or excitatory synapses. We show that NMM1 fails to reproduce important dynamical features of the exact model, such as the self-sustained oscillations of an inhibitory interneuron QIF network. Furthermore, in the exact model but not in the limit one, stimulation of a pyramidal cell population induces resonant oscillatory activity whose peak frequency and amplitude increase with the self-coupling gain and the external excitatory input. This may play a role in the enhanced response of densely connected networks to weak uniform inputs, such as the electric fields produced by noninvasive brain stimulation.

Repetitive transcranial magnetic stimulation (rTMS) triggers dose-dependent homeostatic rewiring in recurrent neuronal networks

Repetitive transcranial magnetic stimulation (rTMS) is a non-invasive brain stimulation technique used to induce neuronal plasticity in healthy individuals and patients. Designing effective and reproducible rTMS protocols poses a major challenge in the field as the underlying biomechanisms remain elusive. Current clinical protocol designs are often based on studies reporting rTMS-induced long-term potentiation or depression of synaptic transmission. Herein, we employed computational modeling to explore the effects of rTMS on long-term structural plasticity and changes in network connectivity. We simulated a recurrent neuronal network with homeostatic structural plasticity between excitatory neurons, and demonstrated that this mechanism was sensitive to specific parameters of the stimulation protocol (i.e., frequency, intensity, and duration of stimulation). The feedback-inhibition initiated by network stimulation influenced the net stimulation outcome and hindered the rTMS-induced homeostatic structural plasticity, highlighting the role of inhibitory networks. These findings suggest a novel mechanism for the lasting effects of rTMS, i.e., rTMS-induced homeostatic structural plasticity, and highlight the importance of network inhibition in careful protocol design, standardization, and optimization of stimulation.

Spherical harmonics representation of the steady-state membrane potential shift induced by tDCS in realistic neuron models

Objective.We provide a systematic framework for quantifying the effect of externally applied weak electric fields on realistic neuron compartment models as captured by physiologically relevant quantities such as the membrane potential or transmembrane current as a function of the orientation of the field.Approach.We define a response function as the steady-state change of the membrane potential induced by a canonical external field of 1 V m^-1as a function of its orientation. We estimate the function values through simulations employing reconstructions of the rat somatosensory cortex from the Blue Brain Project. The response of different cell types is simulated using the NEURON simulation environment. We represent and analyze the angular response as an expansion in spherical harmonics.Main results.We report membrane perturbation values comparable to those in the literature, extend them to different cell types, and provide their profiles as spherical harmonic coefficients. We show that at rest, responses are dominated by their dipole terms (ℓ=1), in agreement with experimental findings and compartment theory. Indeed, we show analytically that for a passive cell, only the dipole term is nonzero. However, while minor, other terms are relevant for states different from resting. In particular, we show howℓ=0andℓ=2terms can modify the function to induce asymmetries in the response.Significance.This work provides a practical framework for the representation of the effects of weak electric fields on different neuron types and their main regions-an important milestone for developing micro- and mesoscale models and optimizing brain stimulation solutions.

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.

Ideal current dipoles are appropriate source representations for simulating neurons for intracranial recordings

OBJECTIVE

To determine whether dipoles are an appropriate simplified representation of neural sources for stereo-EEG (sEEG).

METHODS

We compared the distributions of voltages generated by a dipole, biophysically realistic cortical neuron models, and extended regions of cortex to determine how well a dipole represented neural sources at different spatial scales and at electrode to neuron distances relevant for sEEG. We also quantified errors introduced by the dipole approximation of neural sources in sEEG source localization using standardized low-resolution electrotomography (sLORETA).

RESULTS

For pyramidal neurons, the coefficient of correlation between voltages generated by a dipole and neuron model were > 0.9 for distances > 1 mm. For small regions of cortex (∼0.1 cm2), the error in voltages between a dipole and region was < 100 µV for all distances. However, larger regions of active cortex (>5 cm2) yielded > 50 µV errors within 1.5 cm of an electrode when compared to single dipoles. Finally, source localization errors were < 5 mm when using dipoles to represent realistic neural sources.

CONCLUSIONS

Single dipoles are an appropriate source model to represent both single neurons and small regions of active cortex, while multiple dipoles are required to represent large regions of cortex.

SIGNIFICANCE

Dipoles are computationally tractable and valid source models for sEEG.

Effects of central nervous system electrical stimulation on non-neuronal cells

Over the past few decades, much progress has been made in the clinical use of electrical stimulation of the central nervous system (CNS) to treat an ever-growing number of conditions from Parkinson's disease (PD) to epilepsy as well as for sensory restoration and many other applications. However, little is known about the effects of microstimulation at the cellular level. Most of the existing research focuses on the effects of electrical stimulation on neurons. Other cells of the CNS such as microglia, astrocytes, oligodendrocytes, and vascular endothelial cells have been understudied in terms of their response to stimulation. The varied and critical functions of these cell types are now beginning to be better understood, and their vital roles in brain function in both health and disease are becoming better appreciated. To shed light on the importance of the way electrical stimulation as distinct from device implantation impacts non-neuronal cell types, this review will first summarize common stimulation modalities from the perspective of device design and stimulation parameters and how these different parameters have an impact on the physiological response. Following this, what is known about the responses of different cell types to different stimulation modalities will be summarized, drawing on findings from both clinical studies as well as clinically relevant animal models and in vitro systems.

Energy efficiency of pulse shaping in electrical stimulation: the interdependence of biophysical effects and circuit design losses

Power efficiency in electrical stimulator circuits is crucial for developing large-scale multichannel applications like bidirectional brain-computer interfaces and neuroprosthetic devices. Many state-of-the-art papers have suggested that some non-rectangular pulse shapes are more energy-efficient for exciting neural excitation than the conventional rectangular shape. However, additional losses in the stimulator circuit, which arise from employing such pulses, were not considered. In this work, we analyze the total energy efficiency of a stimulation system featuring non-rectangular stimuli, taking into account the losses in the stimulator circuit. To this end, activation current thresholds for different pulse shapes and durations in cortical neurons are modeled, and the energy required to generate the pulses from a constant voltage supply is calculated. The proposed calculation reveals an energy increase of 14-51% for non-rectangular pulses compared to the conventional rectangular stimuli, instead of the decrease claimed in previous literature. This result indicates that a rectangular stimulation pulse is more power-efficient than the tested alternative shapes in large-scale multichannel electrical stimulation systems.

A personalizable autonomous neural mass model of epileptic seizures

Work in the last two decades has shown that neural mass models (NMM) can realistically reproduce and explain epileptic seizure transitions as recorded by electrophysiological methods (EEG, SEEG). In previous work, advances were achieved by increasing excitation and heuristically varying network inhibitory coupling parameters in the models. Based on these early studies, we provide a laminar NMM capable of realistically reproducing the electrical activity recorded by SEEG in the epileptogenic zone during interictal to ictal states. With the exception of the external noise input into the pyramidal cell population, the model dynamics are autonomous. By setting the system at a point close to bifurcation, seizure-like transitions are generated, including pre-ictal spikes, low voltage fast activity, and ictal rhythmic activity. A novel element in the model is a physiologically motivated algorithm for chloride dynamics: the gain of GABAergic post-synaptic potentials is modulated by the pathological accumulation of chloride in pyramidal cells due to high inhibitory input and/or dysfunctional chloride transport. In addition, in order to simulate SEEG signals for comparison with real seizure recordings, the NMM is embedded first in a layered model of the neocortex and then in a realistic physical model. We compare modeling results with data from four epilepsy patient cases. By including key pathophysiological mechanisms, the proposed framework captures succinctly the electrophysiological phenomenology observed in ictal states, paving the way for robust personalization methods based on NMMs.

Transcranial magnetic stimulation of the brain: What is stimulated? - A consensus and critical position paper

Transcranial (electro)magnetic stimulation (TMS) is currently the method of choice to non-invasively induce neural activity in the human brain. A single transcranial stimulus induces a time-varying electric field in the brain that may evoke action potentials in cortical neurons. The spatial relationship between the locally induced electric field and the stimulated neurons determines axonal depolarization. The induced electric field is influenced by the conductive properties of the tissue compartments and is strongest in the superficial parts of the targeted cortical gyri and underlying white matter. TMS likely targets axons of both excitatory and inhibitory neurons. The propensity of individual axons to fire an action potential in response to TMS depends on their geometry, myelination and spatial relation to the imposed electric field and the physiological state of the neuron. The latter is determined by its transsynaptic dendritic and somatic inputs, intrinsic membrane potential and firing rate. Modeling work suggests that the primary target of TMS is axonal terminals in the crown top and lip regions of cortical gyri. The induced electric field may additionally excite bends of myelinated axons in the juxtacortical white matter below the gyral crown. Neuronal excitation spreads ortho- and antidromically along the stimulated axons and causes secondary excitation of connected neuronal populations within local intracortical microcircuits in the target area. Axonal and transsynaptic spread of excitation also occurs along cortico-cortical and cortico-subcortical connections, impacting on neuronal activity in the targeted network. Both local and remote neural excitation depend critically on the functional state of the stimulated target area and network. TMS also causes substantial direct co-stimulation of the peripheral nervous system. Peripheral co-excitation propagates centrally in auditory and somatosensory networks, but also produces brain responses in other networks subserving multisensory integration, orienting or arousal. The complexity of the response to TMS warrants cautious interpretation of its physiological and behavioural consequences, and a deeper understanding of the mechanistic underpinnings of TMS will be critical for advancing it as a scientific and therapeutic tool.