The "quasi-uniform" assumption in animal and computational models of non-invasive electrical stimulation

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

ABSTRACT

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

How conductivity boundaries influence the electric field induced by transcranial magnetic stimulation in in vitro experiments

BACKGROUND

Although transcranial magnetic stimulation (TMS) has become a valuable method for non-invasive brain stimulation, the cellular basis of TMS activation of neurons is still not fully understood. In vitro preparations have been used to understand the biophysical mechanisms of TMS, but in many cases these studies have encountered substantial difficulties in activating neurons.

OBJECTIVE/HYPOTHESIS

The hypothesis of this work is that conductivity boundaries can have large effects on the electric field in commonly used in vitro preparations. Our goal was to analyze the resulting difficulties in in vitro TMS using a simulation study, using a charge-based boundary element model.

METHODS

We decomposed the total electric field into the sum of the primary electric field, which only depends on coil geometry and current, and the secondary electric field arising from conductivity boundaries, which strongly depends on tissue and chamber geometry. We investigated the effect of the conductivity boundaries on the electric field strength for a variety of in vitro experimental settings to determine the sources of difficulty.

RESULTS

We showed that conductivity boundaries can have large effects on the electric field in in vitro preparations. Depending on the geometry of the air-saline and the saline-tissue interfaces, the secondary electric field can significantly enhance, or attenuate the primary electric field, resulting in a much stronger or weaker total electric field inside the tissue; we showed this using a realistic preparation. Submerged chambers are generally much more efficient than interface chambers since the secondary field due to the thin film of saline covering the tissue in the interface chamber opposes the primary field and significantly reduces the total field in the tissue placed in the interface chamber. The relative dimensions of the chamber and the TMS coil critically determine the total field; the popular setup with a large coil and a small chamber is particularly sub-optimal because the secondary field due to the air-chamber boundary opposes the primary field, thereby attenuating the total field. The form factor (length vs width) of the tissue in the direction of the induced field can be important since a relatively narrow tissue enhances the total field at the saline-tissue boundary.

CONCLUSIONS

Overall, we found that the total electric field in the tissue is higher in submerged chambers, higher if the chamber size is larger than the coil and if the shorter tissue dimension is in the direction of the electric field. Decomposing the total field into the primary and secondary fields is useful for designing in vitro experiments and interpreting the results.

Quasistatic approximation in neuromodulation

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

Frequency-domain analysis of membrane polarization in two-compartment model neurons with weak alternating electric fields

Transcranial alternating current stimulation (tACS) is widely used in studying brain functions and the treatment of neuropsychiatric diseases in a frequency-specific manner. However, how tACS works on neuronal activity has been poorly understood. In this paper, we use linear system analysis to investigate how weak alternating electric fields (EFs) affect the membrane polarization of neurons in the frequency domain. Two biophysically realistic conductance-based two-compartment models of cortical pyramidal neurons are developed to simulate subthreshold membrane polarization with weak alternating EFs. We linearize the original nonlinear models at the stable equilibrium points and further simplify them to the two- or three-dimensional linear systems. Thus, we calculate the transfer functions of the low-dimensional linear models to model neuronal polarization patterns. Based on the transfer functions, we compute the amplitude- and phase-frequency characteristics to describe the relationship between weak EFs and membrane polarization. We also computed the parameters (gain, zeros, and poles) and structures (the number of zeros and poles) of transfer functions to reveal how neuronal intrinsic properties affect the parameters and structure of transfer functions and thus the frequency-dependent membrane polarization with alternating EFs. We find that the amplitude and phase of membrane polarization both strongly depended on EF frequency, and these frequency responses are modulated by the intrinsic properties of neurons. The compartment geometry, internal coupling conductance, and ionic currents (except Ih) affect the frequency-dependent polarization by mainly changing the gain and pole of transfer functions. Larger gain contributes to larger amplitude-frequency characteristics. The closer the pole is to the imaginary axis, the lower phase-frequency characteristics. However, Ih changes the structure of transfer function in the dendrite by introducing a new pair of zero-pole points, which decrease the amplitude at low frequencies and thus lead to a visible resonance. These results highlight the effects of passive properties and active ion currents on subthreshold membrane polarization with alternating EFs in the frequency domain, which provide an explainable connection of how intrinsic properties of neurons modulate the neuronal input-output functions with weak EF stimulation.

Transcranial electric stimulation modulates firing rate at clinically relevant intensities

BACKGROUND

Notwithstanding advances with low-intensity transcranial electrical stimulation (tES), there remain questions about the efficacy of clinically realistic electric fields on neuronal function.

OBJECTIVE

To measure electric fields magnitude and their effects on neuronal firing rate of hippocampal neurons in freely moving rats, and to establish calibrated computational models of current flow.

METHODS

Current flow models were calibrated on electric field measures in the motor cortex (n = 2 anesthetized rats) and hippocampus. A Neuropixels 2.0 probe with 384 channels was used in an in-vivo rat model of tES (n = 4 freely moving and 2 urethane anesthetized rats) to detect effects of weak fields on neuronal firing rate. High-density field mapping and computational models verified field intensity (1 V/m in hippocampus per 50 μA of applied skull currents).

RESULTS

Electric fields of as low as 0.35 V/m (0.25-0.47) acutely modulated average firing rate in the hippocampus. At these intensities, firing rate effects increased monotonically with electric field intensity at a rate of 11.5 % per V/m (7.2-18.3). For the majority of excitatory neurons, firing increased for soma-depolarizing stimulation and diminished for soma-hyperpolarizing stimulation. While more diverse, the response of inhibitory neurons followed a similar pattern on average, likely as a result of excitatory drive.

CONCLUSION

In awake animals, electric fields modulate spiking rate above levels previously observed in vitro. Firing rate effects are likely mediated by somatic polarization of pyramidal neurons. We recommend that all future rodent experiments directly measure electric fields to insure rigor and reproducibility.

Quasistatic approximation in neuromodulation

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

Transcranial electric stimulation modulates firing rate at clinically relevant intensities

Notwithstanding advances with low-intensity transcranial electrical stimulation (TES), there remain questions about the efficacy of clinically realistic electric fields on neuronal function. We used Neuropixels 2.0 probe with 384 channels in an in-vivo rat model of TES to detect effects of weak fields on neuronal firing rate. High-density field mapping and computational models verified field intensity (1 V/m in hippocampus per 50 μA of applied skull currents). We demonstrate that electric fields below 0.5 V/m acutely modulate firing rate in 5% of neurons recorded in the hippocampus. At these intensities, average firing rate effects increased monotonically with electric field intensity at a rate of 7 % per V/m. For the majority of excitatory neurons, firing increased for cathodal stimulation and diminished for anodal stimulation. While more diverse, the response of inhibitory neurons followed a similar pattern on average, likely as a result of excitatory drive. Our results indicate that responses to TES at clinically relevant intensities are driven by a fraction of high-responder excitatory neurons, with polarity-specific effects. We conclude that transcranial electric stimulation is an effective neuromodulator at clinically realistic intensities.

Cerebellar Modulation of Sensorimotor Associative Plasticity Is Impaired in Cervical Dystonia

BACKGROUND

In recent years, cervical dystonia (CD) has been recognized as a network disorder that involves not only the basal ganglia but other brain regions, such as the primary motor and somatosensory cortex, brainstem, and cerebellum. So far, the role of the cerebellum in the pathophysiology of dystonia is only poorly understood.

OBJECTIVE

The objective of this study was to investigate the role of the cerebellum on sensorimotor associative plasticity in patients with CD.

METHODS

Sixteen patients with CD and 13 healthy subjects received cerebellar transcranial direct current stimulation (ctDCS) followed by a paired associative stimulation (PAS) protocol based on transcranial magnetic stimulation that induces sensorimotor associative plasticity. Across three sessions the participants received excitatory anodal, inhibitory cathodal, and sham ctDCS in a double-blind crossover design. Before and after the intervention, motor cortical excitability and motor symptom severity were assessed.

RESULTS

PAS induced an increase in motor cortical excitability in both healthy control subjects and patients with CD. In healthy subjects this effect was attenuated by both anodal and cathodal ctDCS with a stronger effect of cathodal stimulation. In patients with CD, anodal stimulation suppressed the PAS effect, whereas cathodal stimulation had no influence on PAS. Motor symptom severity was unchanged after the intervention.

CONCLUSIONS

Cerebellar modulation with cathodal ctDCS had no effect on sensorimotor associative plasticity in patients with CD, in contrast with the net inhibitory effect in healthy subjects. This is further evidence that the cerebello-thalamo-cortical network plays a role in the pathophysiology of dystonia. © 2023 The Authors. Movement Disorders published by Wiley Periodicals LLC on behalf of International Parkinson and Movement Disorder Society.

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.

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.

A systematic review of computational models for the design of spinal cord stimulation therapies: from neural circuits to patient-specific simulations

Seventy years ago, Hodgkin and Huxley published the first mathematical model to describe action potential generation, laying the foundation for modern computational neuroscience. Since then, the field has evolved enormously, with studies spanning from basic neuroscience to clinical applications for neuromodulation. Computer models of neuromodulation have evolved in complexity and personalization, advancing clinical practice and novel neurostimulation therapies, such as spinal cord stimulation. Spinal cord stimulation is a therapy widely used to treat chronic pain, with rapidly expanding indications, such as restoring motor function. In general, simulations contributed dramatically to improve lead designs, stimulation configurations, waveform parameters and programming procedures and provided insight into potential mechanisms of action of electrical stimulation. Although the implementation of neural models are relentlessly increasing in number and complexity, it is reasonable to ask whether this observed increase in complexity is necessary for improved accuracy and, ultimately, for clinical efficacy. With this aim, we performed a systematic literature review and a qualitative meta-synthesis of the evolution of computational models, with a focus on complexity, personalization and the use of medical imaging to capture realistic anatomy. Our review showed that increased model complexity and personalization improved both mechanistic and translational studies. More specifically, the use of medical imaging enabled the development of patient-specific models that can help to transform clinical practice in spinal cord stimulation. Finally, we combined our results to provide clear guidelines for standardization and expansion of computational models for spinal cord stimulation.

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.

Computation of group-level electric field in lower limb motor area for different tDCS montages

OBJECTIVE

Transcranial direct current stimulation (tDCS) injects a weak electric current into the brain via electrodes attached to the scalp to modulate cortical excitability. tDCS is used to rebalance brain activity between affected and unaffected hemispheres in rehabilitation. However, a systematic quantitative evaluation of tDCS montage is not reported for the lower limbs. In this study, we computationally investigated the generated electric field intensity, polarity, and co-stimulation of cortical areas for lower limb targeting using high-resolution head models.

METHODS

Volume conductor models have thus been employed to estimate the electric field in the brain. A total of 18 head models of healthy subjects were used to calculate the group-level electric fields generated from four montages of tDCS for modulation of lower limbs.

RESULTS

C1-C2 montage delivered higher electric field intensities while reaching deeper regions of the lower-limb motor area. It produced a uniform polarization on the same hemisphere target with comparable intensities between hemispheres but with higher variability.

CONCLUSIONS

Proper montage selection allows reaching deeper regions of the lower-limb motor area with uniform polarization.

SIGNIFICANCE

First systematic computational study providing support to tDCS experimental studies using montages for the lower limb while considering polarity factor for balancing brain activity.

Quasi-static pipeline in electroconvulsive therapy computational modeling

BACKGROUND

Computational models of current flow during Electroconvulsive Therapy (ECT) rely on the quasi-static assumption, yet tissue impedance during ECT may be frequency specific and change adaptively to local electric field intensity.

OBJECTIVES

We systematically consider the application of the quasi-static pipeline to ECT under conditions where 1) static impedance is measured before ECT and 2) during ECT when dynamic impedance is measured. We propose an update to ECT modeling accounting for frequency-dependent impedance.

METHODS

The frequency content on an ECT device output is analyzed. The ECT electrode-body impedance under low-current conditions is measured with an impedance analyzer. A framework for ECT modeling under quasi-static conditions based on a single device-specific frequency (e.g., 1 kHz) is proposed.

RESULTS

Impedance using ECT electrodes under low-current is frequency dependent and subject specific, and can be approximated at >100 Hz with a subject-specific lumped parameter circuit model but at <100 Hz increased non-linearly. The ECT device uses a 2 μA 800 Hz test signal and reports a static impedance that approximate 1 kHz impedance. Combined with prior evidence suggesting that conductivity does not vary significantly across ECT output frequencies at high-currents (800-900 mA), we update the adaptive pipeline for ECT modeling centered at 1 kHz frequency. Based on individual MRI and adaptive skin properties, models match static impedance (at 2 μA) and dynamic impedance (at 900 mA) of four ECT subjects.

CONCLUSIONS

By considering ECT modeling at a single representative frequency, ECT adaptive and non-adaptive modeling can be rationalized under a quasi-static pipeline.

A microfluidic perspective on conventional in vitro transcranial direct current stimulation methods

Transcranial direct current stimulation (tDCS) is a promising non-invasive brain stimulation method to treat neurological and psychiatric diseases. However, its underlying neural mechanisms warrant further investigation. Indeed, dose-response interrelations are poorly understood. Placing explanted brain tissue, mostly from mice or rats, into a uniform direct current electric field (dcEF) is a well-established in vitro system to elucidate the neural mechanism of tDCS. Nevertheless, we will show that generating a defined, uniform, and constant dcEF throughout a brain slice is challenging. This article critically reviews the methods used to generate and calibrate a uniform dcEF. We use finite element analysis (FEA) to evaluate the widely used parallel electrode configuration and show that it may not reliably generate uniform dcEF within a brain slice inside an open interface or submerged chamber. Moreover, equivalent circuit analysis and measurements inside a testing chamber suggest that calibrating the dcEF intensity with two recording electrodes can inaccurately capture the true EF magnitude in the targeted tissue when specific criteria are not met. Finally, we outline why microfluidic chambers are an effective and calibration-free approach of generating spatiotemporally uniform dcEF for DCS in vitro studies, facilitating accurate and fine-scale dcEF adjustments. We are convinced that improving the precision and addressing the limitations of current experimental platforms will substantially improve the reproducibility of in vitro experimental results. A better mechanistic understanding of dose-response relations will ultimately facilitate more effective non-invasive stimulation therapies in patients.

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.

Neurocapillary-Modulation

OBJECTIVES

We consider two consequences of brain capillary ultrastructure in neuromodulation. First, blood-brain barrier (BBB) polarization as a consequence of current crossing between interstitial space and the blood. Second, interstitial current flow distortion around capillaries impacting neuronal stimulation.

MATERIALS AND METHODS

We developed computational models of BBB ultrastructure morphologies to first assess electric field amplification at the BBB (principle 1) and neuron polarization amplification by the presence of capillaries (principle 2). We adapt neuron cable theory to develop an analytical solution for maximum BBB polarization sensitivity.

RESULTS

Electrical current crosses between the brain parenchyma (interstitial space) and capillaries, producing BBB electric fields (EBBB) that are >400x of the average parenchyma electric field (ĒBRAIN), which in turn modulates transport across the BBB. Specifically, for a BBB space constant (λBBB) and wall thickness (dth-BBB), the analytical solution for maximal BBB electric field (EABBB) is given as: (ĒBRAIN × λBBB)/dth-BBB. Electrical current in the brain parenchyma is distorted around brain capillaries, amplifying neuronal polarization. Specifically, capillary ultrastructure produces ∼50% modulation of the ĒBRAIN over the ∼40 μm inter-capillary distance. The divergence of EBRAIN (Activating function) is thus ∼100 kV/m2 per unit ĒBRAIN.

CONCLUSIONS

BBB stimulation by principle 1 suggests novel therapeutic strategies such as boosting metabolic capacity or interstitial fluid clearance. Whereas the spatial profile of EBRAIN is traditionally assumed to depend only on macroscopic anatomy, principle 2 suggests a central role for local capillary ultrastructure-which impact forms of neuromodulation including deep brain stimulation (DBS), spinal cord stimulation (SCS), transcranial magnetic stimulation (TMS), electroconvulsive therapy (ECT), and transcranial electrical stimulation (tES)/transcranial direct current stimulation (tDCS).

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.

Transcranial direct current stimulation of cerebellum alters spiking precision in cerebellar cortex: A modeling study of cellular responses

Transcranial direct current stimulation (tDCS) of the cerebellum has rapidly raised interest but the effects of tDCS on cerebellar neurons remain unclear. Assessing the cellular response to tDCS is challenging because of the uneven, highly stratified cytoarchitecture of the cerebellum, within which cellular morphologies, physiological properties, and function vary largely across several types of neurons. In this study, we combine MRI-based segmentation of the cerebellum and a finite element model of the tDCS-induced electric field (EF) inside the cerebellum to determine the field imposed on the cerebellar neurons throughout the region. We then pair the EF with multicompartment models of the Purkinje cell (PC), deep cerebellar neuron (DCN), and granule cell (GrC) and quantify the acute response of these neurons under various orientations, physiological conditions, and sequences of presynaptic stimuli. We show that cerebellar tDCS significantly modulates the postsynaptic spiking precision of the PC, which is expressed as a change in the spike count and timing in response to presynaptic stimuli. tDCS has modest effects, instead, on the PC tonic firing at rest and on the postsynaptic activity of DCN and GrC. In Purkinje cells, anodal tDCS shortens the repolarization phase following complex spikes (-14.7 ± 6.5% of baseline value, mean ± S.D.; max: -22.7%) and promotes burstiness with longer bursts compared to resting conditions. Cathodal tDCS, instead, promotes irregular spiking by enhancing somatic excitability and significantly prolongs the repolarization after complex spikes compared to baseline (+37.0 ± 28.9%, mean ± S.D.; max: +84.3%). tDCS-induced changes to the repolarization phase and firing pattern exceed 10% of the baseline values in Purkinje cells covering up to 20% of the cerebellar cortex, with the effects being distributed along the EF direction and concentrated in the area under the electrode over the cerebellum. Altogether, the acute effects of tDCS on cerebellum mainly focus on Purkinje cells and modulate the precision of the response to synaptic stimuli, thus having the largest impact when the cerebellar cortex is active. Since the spatiotemporal precision of the PC spiking is critical to learning and coordination, our results suggest cerebellar tDCS as a viable therapeutic option for disorders involving cerebellar hyperactivity such as ataxia.

Transcranial direct current stimulation (tDCS) of the cerebellum is gaining momentum as a neuromodulation tool for the treatment of neurological diseases like movement disorders. Nonetheless, the response of cells in the cerebellum to tDCS is unclear and hardly generalizes from our understanding of tDCS of the cerebral cortex. We use computational models to investigate the response of several types of cerebellar neurons to the electric field induced by tDCS and show that, differently from the cerebral cortex, tDCS has significant acute effects on the cerebellar cortex. These effects (i) primarily alter the way Purkinje cells encode synaptic stimuli from the molecular layer and (ii) can help hyperactive cells regain postsynaptic spiking precision. Since the spatiotemporal precision of the Purkinje cell spiking is critical to learning and coordination, the study shows how tDCS can operate at the cellular level to treat movement disorders like tremor and ataxia.

High-resolution computational modeling of the current flow in the outer ear during transcutaneous auricular Vagus Nerve Stimulation (taVNS)

BACKGROUND

Transcutaneous auricular Vagus Nerve Stimulation (taVNS) applies low-intensity electrical current to the ear with the intention of activating the auricular branch of the Vagus nerve. The sensitivity and selectivity of stimulation applied to the ear depends on current flow pattern produced by a given electrode montage (size and placement).

OBJECTIVE

We compare different electrodes designs for taVNS considering both the predicted peak electric fields (sensitivity) and their spatial distribution (selectivity).

METHODS

Based on optimized high-resolution (0.47 mm) T1 and T2 weighted MRI, we developed an anatomical model of the left ear and the surrounding head tissues including brain, CSF/meninges, skull, muscle, blood vessels, fat, cartilage, and skin. The ear was further segmented into 6 regions of interest (ROI) based on various nerve densities: cavum concha, cymba concha, crus of helix, tragus, antitragus, and earlobe. A range of taVNS electrode montages were reproduced spanning varied electrodes sizes and placements over the tragus, cymba concha, earlobe, cavum concha, and crus of helix. Electric field across the ear (from superficial skin to cartilage) for each montage at 1 mA or 2 mA taVNS, assuming an activation threshold of 6.15 V/m, 12.3 V/m or 24.6 V/m was predicted using a Finite element method (FEM). Finally, considering every ROI, we calculated the sensitivity and selectivity of each montage.

RESULTS

Current flow patterns through the ear were highly specific to the electrode montage. Electric field was maximal at the ear regions directly under the electrodes, and for a given total current, increases with decreasing electrode size. Depending on the applied current and nerves threshold, activation may also occur in the regions between multiple anterior surface electrodes. Each considered montage was selective for one or two regions of interest. For example, electrodes across the tragus restricted significant electric field to the tragus. Stimulation across the earlobe restricted significant electric field to the earlobe and the antitragus. Because of this relative selectivity, use of control ear montages in experimental studies, support testing of targeting. Relative targeting was robust across assumptions of activation threshold and tissue properties.

DISCUSSION

Computational models provide additional insight on how details in electrode shape and placement impact sensitivity (how much current is needed) and selectivity (spatial distribution), thereby supporting analysis of existing approaches and optimization of new devices. Our result suggest taVNS current patterns and relative target are robust across individuals, though (variance in) axon morphology was not represented.

Inducing neuroplasticity through intracranial θ-burst stimulation in the human sensorimotor cortex

The progress of therapeutic neuromodulation greatly depends on improving stimulation parameters to most efficiently induce neuroplasticity effects. Intermittent θ-burst stimulation (iTBS), a form of electrical stimulation that mimics natural brain activity patterns, has proved to efficiently induce such effects in animal studies and rhythmic transcranial magnetic stimulation studies in humans. However, little is known about the potential neuroplasticity effects of iTBS applied through intracranial electrodes in humans. This study characterizes the physiological effects of intracranial iTBS in humans and compare them with α-frequency stimulation, another frequently used neuromodulatory pattern. We applied these two stimulation patterns to well-defined regions in the sensorimotor cortex, which elicited contralateral hand muscle contractions during clinical mapping, in patients with epilepsy implanted with intracranial electrodes. Treatment effects were evaluated using oscillatory coherence across areas connected to the treatment site, as defined with corticocortical-evoked potentials. Our results show that iTBS increases coherence in the β-frequency band within the sensorimotor network indicating a potential neuroplasticity effect. The effect is specific to the sensorimotor system, the β band, and the stimulation pattern and outlasted the stimulation period by ∼3 min. The effect occurred in four out of seven subjects depending on the buildup of the effect during iTBS treatment and other patterns of oscillatory activity related to ceiling effects within the β band and to preexistent coherence within the α band. By characterizing the neurophysiological effects of iTBS within well-defined cortical networks, we hope to provide an electrophysiological framework that allows clinicians/researchers to optimize brain stimulation protocols which may have translational value.NEW & NOTEWORTHY θ-Burst stimulation (TBS) protocols in transcranial magnetic stimulation studies have shown improved treatment efficacy in a variety of neuropsychiatric disorders. The optimal protocol to induce neuroplasticity in invasive direct electrical stimulation approaches is not known. We report that intracranial TBS applied in human sensorimotor cortex increases local coherence of preexistent β rhythms. The effect is specific to the stimulation frequency and the stimulated network and outlasts the stimulation period by ∼3 min.

Adaptive current-flow models of ECT: Explaining individual static impedance, dynamic impedance, and brain current density

BACKGROUND

Improvements in electroconvulsive therapy (ECT) outcomes have followed refinement in device electrical output and electrode montage. The physical properties of the ECT stimulus, together with those of the patient's head, determine the impedances measured by the device and govern current delivery to the brain and ECT outcomes.

OBJECTIVE

However, the precise relations among physical properties of the stimulus, patient head anatomy, and patient-specific impedance to the passage of current are long-standing questions in ECT research and practice. To this end, we develop a computational framework based on diverse clinical data sets.

METHODS

We developed anatomical MRI-derived models of transcranial electrical stimulation (tES) that included changes in tissue conductivity due to local electrical current flow. These "adaptive" models simulate ECT both during therapeutic stimulation using high current (∼1 A) and when dynamic impedance is measured, as well as prior to stimulation when low current (∼1 mA) is used to measure static impedance. We modeled two scalp layers: a superficial scalp layer with adaptive conductivity that increases with electric field up to a subject-specific maximum (σ_SS¯), and a deep scalp layer with a subject-specific fixed conductivity (σ_DS).

RESULTS

We demonstrated that variation in these scalp parameters may explain clinical data on subject-specific static impedance and dynamic impedance, their imperfect correlation across subjects, their relationships to seizure threshold, and the role of head anatomy. Adaptive tES models demonstrated that current flow changes local tissue conductivity which in turn shapes current delivery to the brain in a manner not accounted for in fixed tissue conductivity models.

CONCLUSIONS

Our predictions that variation in individual skin properties, rather than other aspects of anatomy, largely govern the relationship between static impedance, dynamic impedance, and ECT current delivery to the brain, themselves depend on assumptions about tissue properties. Broadly, our novel modeling pipeline opens the door to explore how adaptive-scalp conductivity may impact transcutaneous electrical stimulation (tES).

Multiscale Computational Model Reveals Nerve Response in a Mouse Model for Temporal Interference Brain Stimulation

There has been a growing interest in the non-invasive stimulation of specific brain tissues, while reducing unintended stimulation in surrounding regions, for the medical treatment of brain disorders. Traditional methods for non-invasive brain stimulation, such as transcranial direct current stimulation (tDCS) or transcranial magnetic stimulation (TMS), can stimulate brain regions, but they also simultaneously stimulate the brain and non-brain regions that lie between the target and the stimulation site of the source. Temporal interference (TI) stimulation has been suggested to selectively stimulate brain regions by superposing two alternating currents with slightly different frequencies injected through electrodes attached to the scalp. Previous studies have reported promising results for TI applied to the motor area in mice, but the mechanisms are yet to be clarified. As computational techniques can help reveal different aspects of TI, in this study, we computationally investigated TI stimulation using a multiscale model that computes the generated interference current pattern effects in a neural cortical model of a mouse head. The results indicated that the threshold increased with the carrier frequency and that the beat frequency did not influence the threshold. It was also found that the intensity ratio between the alternating currents changed the location of the responding nerve, which is in agreement with previous experiments. Moreover, particular characteristics of the envelope were investigated to predict the stimulation region intuitively. It was found that regions with high modulation depth (| maximum| − | minimum| values of the envelope) and low minimum envelope (near zero) corresponded with the activation region obtained via neural computation.

Investigating the feasibility of cerebellar transcranial direct current stimulation to facilitate post-stroke overground gait performance in chronic stroke: a partial least-squares regression approach

Background

Investigation of lobule-specific electric field effects of cerebellar transcranial direct current stimulation (ctDCS) on overground gait performance has not been performed, so this study aimed to investigate the feasibility of two lobule-specific bilateral ctDCS montages to facilitate overground walking in chronic stroke.

Methods

Ten chronic post-stroke male subjects participated in this repeated-measure single-blind crossover study, where we evaluated the single-session effects of two bilateral ctDCS montages that applied 2 mA via 3.14 cm² disc electrodes for 15 min targeting (a) dentate nuclei (also, anterior and posterior lobes), and (b) lower-limb representations (lobules VIIb-IX). A two-sided Wilcoxon rank-sum test was performed at a 5% significance level on the percent normalized change measures in the overground gait performance. Partial least squares regression (PLSR) analysis was performed on the quantitative gait parameters as response variables to the mean lobular electric field strength as the predictors. Clinical assessments were performed with the Ten-Meter walk test (TMWT), Timed Up & Go (TUG), and the Berg Balance Scale based on minimal clinically important differences (MCID).

Results

The ctDCS montage specific effect was found significant using a two-sided Wilcoxon rank-sum test at a 5% significance level for 'Step Time Affected Leg' (p = 0.0257) and '%Stance Time Unaffected Leg' (p = 0.0376). The changes in the quantitative gait parameters were found to be correlated to the mean electric field strength in the lobules based on PLSR analysis (R² statistic = 0.6574). Here, the mean electric field strength at the cerebellar lobules, Vermis VIIIb, Ipsi-lesional IX, Vermis IX, Ipsi-lesional X, had the most loading and were positively related to the 'Step Time Affected Leg' and '%Stance Time Unaffected Leg,' and negatively related to the '%Swing Time Unaffected Leg,' '%Single Support Time Affected Leg.' Clinical assessments found similar improvement in the TMWT (MCID: 0.10 m/s), TUG (MCID: 8 s), and BBS score (MCID: 12.5 points) for both the ctDCS montages.

Conclusion

Our feasibility study found an association between the lobular mean electric field strength and the changes in the quantitative gait parameters following a single ctDCS session in chronic stroke. Both the ctDCS montages improved the clinical outcome measures that should be investigated with a larger sample size for clinical validation.

Trial registration: Being retrospectively registered.

Limited Sensitivity of Hippocampal Synaptic Function or Network Oscillations to Unmodulated Kilohertz Electric Fields

Understanding the cellular mechanisms of kilohertz (kHz) electrical stimulation is of broad interest in neuromodulation including forms of transcranial electrical stimulation, interferential stimulation, and high-rate spinal cord stimulation (SCS). Yet, the well-established low-pass filtering by neuronal membranes suggests minimal neuronal polarization in respond to charge-balanced kHz stimulation. The hippocampal brain slice model is among the most studied systems in neuroscience and exhaustively characterized in screening the effects of electrical stimulation. High-frequency electric fields of varied amplitudes (1–150 V/m), waveforms (sinusoidal, symmetrical pule, asymmetrical pulse) and frequencies (1 and10 kHz) were tested. Changes in single or paired-pulse field EPSPs (fEPSP) in CA1 were measured in response to radial-directed and tangential-directed electric fields, with brief (30 s) or long (30 min) application times. The effects of kHz stimulation on ongoing endogenous network activity were tested in carbachol-induced γ oscillation of CA3a and CA3c. Across 23 conditions evaluated, no significant changes in fEPSP were resolved, while responses were detected for within-slice control direct current (DC) fields; 1-kHz sinusoidal and pulse stimulation (≥60 V/m), but not 10 kHz, induced changes in oscillating neuronal network. We thus report no responses to low-amplitude 1-kHz or any 10-kHz fields, suggesting that any brain sensitivity to these fields is via yet to be-determined mechanism(s) of action which were not identified in our experimental preparation.

Temporal interference stimulation targets deep brain regions by modulating neural oscillations

BACKGROUND

Temporal interference (TI) stimulation of the brain generates amplitude-modulated electric fields oscillating in the kHz range with the goal of non-invasive targeted deep brain stimulation. Yet, the current intensities required in human (sensitivity) to modulate deep brain activity and if superficial brain region are spared (selectivity) at these intensities remains unclear.

OBJECTIVE

We developed an experimentally constrained theory for TI sensitivity to kHz electric field given the attenuation by membrane low-pass filtering property, and for TI selectivity to deep structures given the distribution of modulated and unmodulated electric fields in brain.

METHODS

The electric field threshold to modulate carbachol-induced gamma oscillations in rat hippocampal slices was determined for unmodulated 0.05-2 kHz sine waveforms, and 5 Hz amplitude-modulated waveforms with 0.1-2 kHz carrier frequencies. The neuronal effects are replicated with a computational network model to explore the underlying mechanisms, and then coupled to a validated current-flow model of the human head.

RESULTS

Amplitude-modulated electric fields are stronger in deep brain regions, while unmodulated electric fields are maximal at the cortical regions. Both experiment and model confirmed the hypothesis that spatial selectivity of temporal interference stimulation depends on the phasic modulation of neural oscillations only in deep brain regions. Adaptation mechanism (e.g. GABA_b) enhanced sensitivity to amplitude modulated waveform in contrast to unmodulated kHz and produced selectivity in modulating gamma oscillation (i.e. Higher gamma modulation in amplitude modulated vs unmodulated kHz stimulation). Selection of carrier frequency strongly affected sensitivity to amplitude modulation stimulation. Amplitude modulated stimulation with 100 Hz carrier frequency required ∼5 V/m (corresponding to ∼13 mA at the scalp surface), whereas, 1 kHz carrier frequency ∼60 V/m (∼160 mA) and 2 kHz carrier frequency ∼80 V/m (∼220 mA) to significantly modulate gamma oscillation. Sensitivity is increased (scalp current required decreased) for theoretical neuronal membranes with faster time constants.

CONCLUSION

The TI sensitivity (current required at the scalp) depends on the neuronal membrane time-constant (e.g. axons) approaching the kHz carrier frequency. TI selectivity is governed by network adaption (e.g. GABA_b) that is faster than the amplitude-modulation frequency. Thus, we show neuronal and network oscillations time-constants determine the scalp current required and the selectivity achievable with TI in humans.

Impact of brain atrophy on tDCS and HD-tDCS current flow: a modeling study in three variants of primary progressive aphasia

BACKGROUND

During transcranial direct current stimulation (tDCS), the amount and distribution of current that reaches the brain depends on individual anatomy. Many progressive neurodegenerative diseases are associated with cortical atrophy, but the importance of individual brain atrophy during tDCS in patients with progressive atrophy, including primary progressive aphasia (PPA), remains unclear.

OBJECTIVE

In the present study, we addressed the question whether brain anatomy in patients with distinct cortical atrophy patterns would impact brain current intensity and distribution during tDCS over the left IFG.

METHOD

We developed state-of-the-art, gyri-precise models of three subjects, each representing a variant of primary progressive aphasia: non-fluent variant PPA (nfvPPA), semantic variant PPA (svPPA), and logopenic variant PPA (lvPPA). We considered two exemplary montages over the left inferior frontal gyrus (IFG): a conventional pad montage (anode over F7, cathode over the right cheek) and a 4 × 1 high-definition tDCS montage. We further considered whether local anatomical features, specifically distance of the cortex to skull, can directly predict local electric field intensity.

RESULTS

We found that the differences in brain current flow across the three PPA variants fall within the distribution of anatomically typical adults. While clustering of electric fields was often around individual gyri or sulci, the minimal distance from the gyri/sulci to skull was not correlated with electric field intensity.

CONCLUSION

Limited to the conditions and assumptions considered here, this argues against a specific need to adjust the tDCS montage for these patients any more than might be considered useful in anatomically typical adults. Therefore, local atrophy does not, in isolation, reliably predict local electric field. Rather, our results are consistent with holistic head anatomy influencing brain current flow, with tDCS producing diffuse and individualized brain current flow patterns and HD-tDCS producing targeted brain current flow across individuals.

Significant group-level hotspots found in deep brain regions during transcranial direct current stimulation (tDCS): A computational analysis of electric fields

OBJECTIVE

Transcranial direct current stimulation (tDCS) is a neuromodulation scheme that delivers a small current via electrodes placed on the scalp. The target is generally assumed to be under the electrode, but deep brain regions could also be involved due to the large current spread between the electrodes. This study aims to computationally evaluate if group-level hotspots exist in deep brain regions for different electrode montages.

METHODS

We computed the tDCS-generated electric fields (EFs) in a group of subjects using interindividual registration methods that permitted the projection of EFs from individual realistic head models (n = 18) to a standard deep brain region.

RESULTS

The spatial distribution and peak values (standard deviation of 14%) of EFs varied significantly. Nevertheless, group-level EF hotspots appeared in deep brain regions. The caudate had the highest field peaks in particular for F3-F4 montage (70% of maximum cortical EF), while other regions reach field peaks of 50%.

CONCLUSIONS

tDCS at deeper regions may include not only modulation via underlying cortical or subcortical circuits but also modulation of deep brain regions.

SIGNIFICANCE

The presented EF atlas in deep brain regions can be used to explain tDCS mechanism or select the most appropriate tDCS montage.

Simulation of transcranial magnetic stimulation in head model with morphologically-realistic cortical neurons

BACKGROUND

Transcranial magnetic stimulation (TMS) enables non-invasive modulation of brain activity with both clinical and research applications, but fundamental questions remain about the neural types and elements TMS activates and how stimulation parameters affect the neural response.

OBJECTIVE

To develop a multi-scale computational model to quantify the effect of TMS parameters on the direct response of individual neurons.

METHODS

We integrated morphologically-realistic neuronal models with TMS-induced electric fields computed in a finite element model of a human head to quantify the cortical response to TMS with several combinations of pulse waveforms and current directions.

RESULTS

TMS activated with lowest intensity intracortical axonal terminations in the superficial gyral crown and lip regions. Layer 5 pyramidal cells had the lowest thresholds, but layer 2/3 pyramidal cells and inhibitory basket cells were also activated at most intensities. Direct activation of layers 1 and 6 was unlikely. Neural activation was largely driven by the field magnitude, rather than the field component normal to the cortical surface. Varying the induced current direction caused a waveform-dependent shift in the activation site and provided a potential mechanism for experimentally observed differences in thresholds and latencies of muscle responses.

CONCLUSIONS

This biophysically-based simulation provides a novel method to elucidate mechanisms and inform parameter selection of TMS and other cortical stimulation modalities. It also serves as a foundation for more detailed network models of the response to TMS, which may include endogenous activity, synaptic connectivity, inputs from intrinsic and extrinsic axonal projections, and corticofugal axons in white matter.

The Quasi-uniform assumption for Spinal Cord Stimulation translational research

BACKGROUND

Quasi-uniform assumption is a general theory that postulates local electric field predicts neuronal activation. Computational current flow model of spinal cord stimulation (SCS) of humans and animal models inform how the quasi-uniform assumption can support scaling neuromodulation dose between humans and translational animal.

NEW METHOD

Here we developed finite element models of cat and rat SCS, and brain slice, alongside SCS models. Boundary conditions related to species specific electrode dimensions applied, and electric fields per unit current (mA) predicted.

RESULTS

Clinically and across animal, electric fields change abruptly over small distance compared to the neuronal morphology, such that each neuron is exposed to multiple electric fields. Per unit current, electric fields generally decrease with body mass, but not necessarily and proportionally across tissues. Peak electric field in dorsal column rat and cat were ∼17x and ∼1x of clinical values, for scaled electrodes and equal current. Within the spinal cord, the electric field for rat, cat, and human decreased to 50% of peak value caudo-rostrally (C5-C6) at 0.48 mm, 3.2 mm, and 8 mm, and mediolaterally at 0.14 mm, 2.3 mm, and 3.1 mm. Because these space constants are different, electric field across species cannot be matched without selecting a region of interest (ROI).

COMPARISON WITH EXISTING METHOD

This is the first computational model to support scaling neuromodulation dose between humans and translational animal.

CONCLUSIONS

Inter-species reproduction of the electric field profile across the entire surface of neuron populations is intractable. Approximating quasi-uniform electric field in a ROI is a rational step to translational scaling.

Coupling Magnetically Induced Electric Fields to Neurons: Longitudinal and Transverse Activation

We present a theory and computational models to couple the electric field induced by magnetic stimulation to neuronal membranes. Based on the characteristics of magnetically induced electric fields and the modified cable equation that we developed previously, quasipotentials are derived as a simple and accurate approximation for coupling of the electric fields to neurons. The conventional and modified cable equations are used to simulate magnetic stimulation of long peripheral nerves by circular and figure-8 coils. Activation thresholds are obtained over a range of lateral and vertical coil positions for two nonlinear membrane models representing unmyelinated and myelinated straight axons and also for undulating myelinated axons. For unmyelinated straight axons, the thresholds obtained with the modified cable equation are significantly lower due to transverse polarization, and the spatial distributions of thresholds as a function of coil position differ significantly from predictions by the activating function. However, the activation thresholds of unmyelinated axons obtained with either cable equation are very high and beyond the output capabilities of conventional magnetic stimulators. For myelinated axons, threshold values are similar for both cable equations and within the range of magnetic stimulators. Whereas the transverse field contributes negligibly to the activation thresholds of myelinated fibers, axonal undulation can significantly increase or decrease thresholds depending on coil position. The analysis provides a rigorous theoretical foundation and implementation methods for the use of the cable equation to model neuronal response to magnetically induced electric fields. Experimentally observed stimulation with the electric fields perpendicular to the nerve trunk cannot be explained by transverse polarization and is likely due to nerve fiber undulation and other geometrical inhomogeneities.

Effects of Transcranial Direct Current Stimulation With Caffeine Intake on Muscular Strength and Perceived Exertion

Lattari, E, Vieira, LAF, Oliveira, BRR, Unal, G, Bikson, M, de Mello Pedreiro, RC, Marques Neto, SR, Machado, S, and Maranhão-Neto, GA. Effects of transcranial direct current stimulation with caffeine intake on muscular strength and perceived exertion. J Strength Cond Res 33(5): 1237-1243, 2019-The aim of this study was to investigate the acute effects of transcranial direct current stimulation (tDCS) associated with caffeine intake on muscular strength and ratings of perceived exertion (RPE). Fifteen healthy young males recreationally trained (age: 25.3 ± 3.2 years, body mass: 78.0 ± 6.9 kg, height: 174.1 ± 6.1 cm) were recruited. The experimental conditions started with the administration of caffeine (Caff) or placebo (Pla) 1 hour before starting the anodal tDCS (a-tDCS or sham). There was an intake of 5 mg·kg of Caff or 5 mg·kg of Pla. After the intake, a-tDCS or sham was applied in the left dorsolateral prefrontal cortex with intensity of 2 mA and 20 minutes of duration. The experimental conditions were defined as Sham + Pla, a-tDCS + Pla, Sham + Caff, and a-tDCS + Caff. After the conditions, muscular strength and RPE were verified. Muscular strength was determined by volume load performed in bench press exercise. Muscular strength in Sham + Pla condition was lower compared with all others conditions (p < 0.05). The RPE in the Sham + Pla was greater compared with a-tDCS + Caff (p < 0.05). Muscular strength was greater in all experimental conditions, and a-tDCS + Caff had lower RPE compared with placebo. When very little gains in muscle strength are expected, both caffeine and tDCS were effective in increasing muscle strength. Besides, the improvement in RPE of the caffeine associated with a-tDCS could prove advantageous in participants experienced in strength training. In fact, coaches and applied sport scientists quantitating the intensity of training based on RPE.

Computational comparison of conventional and novel electroconvulsive therapy electrode placements for the treatment of depression

BACKGROUND

Electroconvulsive therapy (ECT) is a highly effective treatment for severe psychiatric disorders. Despite its high efficacy, the use of ECT would be greater if the risk of cognitive side effects were reduced. Over the last 20 years, developments in ECT technique, including improvements in the dosing methodology and modification of the stimulus waveform, have allowed for improved treatment methods with reduced adverse cognitive effects. There is increasing evidence that the electrode placement is important for orienting the electrical stimulus and therefore modifying treatment outcomes, with potential for further improvement of the placements currently used in ECT.

OBJECTIVE

We used computational modelling to perform an in-depth examination into regional differences in brain excitation by the ECT stimulus for several lesser known and novel electrode placements, in order to investigate the potential for an electrode placement that may optimise clinical outcomes.

METHODS

High resolution finite element human head models were generated from MRI scans of three subjects. The models were used to compare regional differences in average electric field (EF) magnitude among a total of thirteen bipolar ECT electrode placements, i.e. three conventional placements as well as ten lesser known and novel placements.

RESULTS AND CONCLUSION

In this exploratory study on a systemic comparison of thirteen ECT electrode placements, the EF magnitude at regions of interest (ROIs) was highly dependent upon the position of both electrodes, especially the ROIs close to the cortical surface. Compared to conventional right-unilateral (RUL) ECT using a temporo-parietal placement, fronto-parietal and supraorbito-parietal RUL also robustly stimulated brain regions considered important for efficacy, while sparing regions related to cognitive functions, and may be a preferrable approach to the currently used placement for RUL ECT. The simulations also found that regional average EF magnitude varied between individual subjects, due to factors such as head size, and results also depended on the size of the defined ROI.

Biophysically realistic neuron models for simulation of cortical stimulation

OBJECTIVE

We implemented computational models of human and rat cortical neurons for simulating the neural response to cortical stimulation with electromagnetic fields.

APPROACH

We adapted model neurons from the library of Blue Brain models to reflect biophysical and geometric properties of both adult rat and human cortical neurons and coupled the model neurons to exogenous electric fields (E-fields). The models included 3D reconstructed axonal and dendritic arbors, experimentally-validated electrophysiological behaviors, and multiple, morphological variants within cell types. Using these models, we characterized the single-cell responses to intracortical microstimulation (ICMS) and uniform E-field with dc as well as pulsed currents.

MAIN RESULTS

The strength-duration and current-distance characteristics of the model neurons to ICMS agreed with published experimental results, as did the subthreshold polarization of cell bodies and axon terminals by uniform dc E-fields. For all forms of stimulation, the lowest threshold elements were terminals of the axon collaterals, and the dependence of threshold and polarization on spatial and temporal stimulation parameters was strongly affected by morphological features of the axonal arbor, including myelination, diameter, and branching.

SIGNIFICANCE

These results provide key insights into the mechanisms of cortical stimulation. The presented models can be used to study various cortical stimulation modalities while incorporating detailed spatial and temporal features of the applied E-field.

Solenoidal Micromagnetic Stimulation Enables Activation of Axons With Specific Orientation

Electrical stimulation of the central and peripheral nervous systems - such as deep brain stimulation, spinal cord stimulation, and epidural cortical stimulation are common therapeutic options increasingly used to treat a large variety of neurological and psychiatric conditions. Despite their remarkable success, there are limitations which if overcome, could enhance outcomes and potentially reduce common side-effects. Micromagnetic stimulation (μMS) was introduced to address some of these limitations. One of the most remarkable properties is that μMS is theoretically capable of activating neurons with specific axonal orientations. Here, we used computational electromagnetic models of the μMS coils adjacent to neuronal tissue combined with axon cable models to investigate μMS orientation-specific properties. We found a 20-fold reduction in the stimulation threshold of the preferred axonal orientation compared to the orthogonal direction. We also studied the directional specificity of μMS coils by recording the responses evoked in the inferior colliculus of rodents when a pulsed magnetic stimulus was applied to the surface of the dorsal cochlear nucleus. The results confirmed that the neuronal responses were highly sensitive to changes in the μMS coil orientation. Accordingly, our results suggest that μMS has the potential of stimulating target nuclei in the brain without affecting the surrounding white matter tracts.

High-Resolution Multi-Scale Computational Model for Non-Invasive Cervical Vagus Nerve Stimulation

OBJECTIVES

To develop the first high-resolution, multi-scale model of cervical non-invasive vagus nerve stimulation (nVNS) and to predict vagus fiber type activation, given clinically relevant rheobase thresholds.

METHODS

An MRI-derived Finite Element Method (FEM) model was developed to accurately simulate key macroscopic (e.g., skin, soft tissue, muscle) and mesoscopic (cervical enlargement, vertebral arch and foramen, cerebral spinal fluid [CSF], nerve sheath) tissue components to predict extracellular potential, electric field (E-Field), and activating function along the vagus nerve. Microscopic scale biophysical models of axons were developed to compare axons of varying size (Aα-, Aβ- and Aδ-, B-, and C-fibers). Rheobase threshold estimates were based on a step function waveform.

RESULTS

Macro-scale accuracy was found to determine E-Field magnitudes around the vagus nerve, while meso-scale precision determined E-field changes (activating function). Mesoscopic anatomical details that capture vagus nerve passage through a changing tissue environment (e.g., bone to soft tissue) profoundly enhanced predicted axon sensitivity while encapsulation in homogenous tissue (e.g., nerve sheath) dulled axon sensitivity to nVNS.

CONCLUSIONS

These findings indicate that realistic and precise modeling at both macroscopic and mesoscopic scales are needed for quantitative predictions of vagus nerve activation. Based on this approach, we predict conventional cervical nVNS protocols can activate A- and B- but not C-fibers. Our state-of-the-art implementation across scales is equally valuable for models of spinal cord stimulation, cortex/deep brain stimulation, and other peripheral/cranial nerve models.

Ih interacts with somato-dendritic structure to determine frequency response to weak alternating electric field stimulation

Transcranial current stimulation (tCS) modulates brain dynamics using weak electric fields. Given the pathological changes in brain network oscillations in neurological and psychiatric illnesses, using alternating electric field waveforms that engage rhythmic activity has been proposed as a targeted, network-level treatment approach. Previous studies have investigated the effects of electric fields at the neuronal level. However, the biophysical basis of the cellular response to electric fields has remained limited. Here, we characterized the frequency-dependent response of different compartments in a layer V pyramidal neuron to exogenous electric fields to dissect the relative contributions of voltage-gated ion channels and neuronal morphology. Hyperpolarization-activated cation current (I_h) in the distal dendrites was the primary ionic mechanism shaping the model's response to electric field stimulation and caused subthreshold resonance in the tuft at 20 ± 4 Hz. In contrast, subthreshold I_h-mediated resonance in response to local sinusoidal current injection was present in all model compartments at 11 ± 2 Hz. The frequencies of both resonance responses were modulated by I_h conductance density. We found that the difference in resonance frequency between the two stimulation types can be explained by the fact that exogenous electric fields simultaneously polarize the membrane potentials at the distal ends of the neuron (relative to field direction) in opposite directions. Our results highlight the role of I_h in shaping the cellular response to electric field stimulation and suggest that the common model of tCS as a weak somatic current injection fails to capture the cellular effects of electric field stimulation. NEW & NOTEWORTHY Modulation of cortical oscillation by brain stimulation serves as a tool to understand the causal role of network oscillations in behavior and is a potential treatment modality that engages impaired network oscillations in disorders of the central nervous system. To develop targeted stimulation paradigms, cellular-level effects must be understood. We demonstrate that hyperpolarization-activated cation current (I_h) and cell morphology cooperatively shape the response to applied alternating electric fields.

Multi-Scale Computational Models for Electrical Brain Stimulation

Electrical brain stimulation (EBS) is an appealing method to treat neurological disorders. To achieve optimal stimulation effects and a better understanding of the underlying brain mechanisms, neuroscientists have proposed computational modeling studies for a decade. Recently, multi-scale models that combine a volume conductor head model and multi-compartmental models of cortical neurons have been developed to predict stimulation effects on the macroscopic and microscopic levels more precisely. As the need for better computational models continues to increase, we overview here recent multi-scale modeling studies; we focused on approaches that coupled a simplified or high-resolution volume conductor head model and multi-compartmental models of cortical neurons, and constructed realistic fiber models using diffusion tensor imaging (DTI). Further implications for achieving better precision in estimating cellular responses are discussed.

Direct current stimulation boosts synaptic gain and cooperativity in vitro

KEY POINTS

Direct current stimulation (DCS) polarity specifically modulates synaptic efficacy during a continuous train of presynaptic inputs, despite synaptic depression. DCS polarizes afferent axons and postsynaptic neurons, boosting cooperativity between synaptic inputs. Polarization of afferent neurons in upstream brain regions may modulate activity in the target brain region during transcranial DCS (tDCS). A statistical theory of coincident activity predicts that the diffuse and weak profile of current flow can be advantageous in enhancing connectivity between co-active brain regions.

ABSTRACT

Transcranial direct current stimulation (tDCS) produces sustained and diffuse current flow in the brain with effects that are state dependent and outlast stimulation. A mechanistic explanation for tDCS should capture these spatiotemporal features. It remains unclear how sustained DCS affects ongoing synaptic dynamics and how modulation of afferent inputs by diffuse stimulation changes synaptic activity at the target brain region. We tested the effect of acute DCS (10-20 V m^-1 for 3-5 s) on synaptic dynamics with constant rate (5-40 Hz) and Poisson-distributed (4 Hz mean) trains of presynaptic inputs. Across tested frequencies, sustained synaptic activity was modulated by DCS with polarity-specific effects. Synaptic depression attenuates the sensitivity to DCS from 1.1% per V m^-1 to 0.55%. DCS applied during synaptic activity facilitates cumulative neuromodulation, potentially reversing endogenous synaptic depression. We establish these effects are mediated by both postsynaptic membrane polarization and afferent axon fibre polarization, which boosts cooperativity between synaptic inputs. This potentially extends the locus of neuromodulation from the nominal target to afferent brain regions. Based on these results we hypothesized the polarization of afferent neurons in upstream brain regions may modulate activity in the target brain region during tDCS. A multiscale model of transcranial electrical stimulation including a finite element model of brain current flow, numerical simulations of neuronal activity, and a statistical theory of coincident activity predicts that the diffuse and weak profile of current flow can be advantageous. Thus, we propose that specifically because tDCS is diffuse, weak and sustained it can boost connectivity between co-active brain regions.

Computational models of Bitemporal, Bifrontal and Right Unilateral ECT predict differential stimulation of brain regions associated with efficacy and cognitive side effects

BACKGROUND

Extensive clinical research has shown that the efficacy and cognitive outcomes of electroconvulsive therapy (ECT) are determined, in part, by the type of electrode placement used. Bitemporal ECT (BT, stimulating electrodes placed bilaterally in the frontotemporal region) is the form of ECT with relatively potent clinical and cognitive side effects. However, the reasons for this are poorly understood.

OBJECTIVE

This study used computational modelling to examine regional differences in brain excitation between BT, Bifrontal (BF) and Right Unilateral (RUL) ECT, currently the most clinically-used ECT placements. Specifically, by comparing similarities and differences in current distribution patterns between BT ECT and the other two placements, the study aimed to create an explanatory model of critical brain sites that mediate antidepressant efficacy and sites associated with cognitive, particularly memory, adverse effects.

METHODS

High resolution finite element human head models were generated from MRI scans of three subjects. The models were used to compare differences in activation between the three ECT placements, using subtraction maps.

RESULTS AND CONCLUSION

In this exploratory study on three realistic head models, Bitemporal ECT resulted in greater direct stimulation of deep midline structures and also left temporal and inferior frontal regions. Interpreted in light of existing knowledge on depressive pathophysiology and cognitive neuroanatomy, it is suggested that the former sites are related to efficacy and the latter to cognitive deficits. We hereby propose an approach using binarised subtraction models that can be used to optimise, and even individualise, ECT therapies.

TDCS modulates cortical excitability in patients with disorders of consciousness

Transcranial direct current stimulation (tDCS)1 has been reported to be a promising technique for consciousness improvement for patients with disorders of consciousness (DOC).2 However, there has been no direct electrophysiological evidence to demonstrate the efficacy of tDCS on patients with DOC. Therefore, we aim to measure the cortical excitability changes induced by tDCS in patients with DOC, to find electrophysiological evidence supporting the therapeutic efficacy of tDCS on patients with DOC. In this study, we enrolled sixteen patients with DOC, including nine vegetative state (VS)3 and seven minimally conscious state (MCS)4 (six females and ten males). TMS-EEG was applied to assess cortical excitability changes after twenty minutes of anodal tDCS of the left dorsolateral prefrontal cortex. Global cerebral excitability were calculated to quantify cortical excitability in the temporal domain: four time intervals (0–100, 100–200, 200–300, 300-400 ms). Then local cerebral excitability in the significantly altered time windows were investigated (frontal, left/right hemispheres, central, and posterior). Compared to baseline and sham stimulation, we found that global cerebral excitability increased in early time windows (0–100 and 100-200 ms) for patients with MCS; for the patients with VS, global cerebral excitability increased in the 0-100 ms interval but decreased in the 300-400 ms interval. The local cerebral excitability was significantly different between MCS and VS. The results indicated that tDCS can effectively modulate the cortical excitability of patients with DOC; and the changes in excitability in temporal and spatial domains are different between patients with MCS and those with VS.

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TDCS was used to alter cerebral excitability in patients of DOC.

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TMS-EEG was used to evaluate cortical excitability changes in patients of DOC.

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TDCS could induce significant cortical excitability changes in patients of DOC.

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TDCS induced different temporal-spatial excitability changes between MCS and VS.

Animal models of transcranial direct current stimulation: Methods and mechanisms

The objective of this review is to summarize the contribution of animal research using direct current stimulation (DCS) to our understanding of the physiological effects of transcranial direct current stimulation (tDCS). We comprehensively address experimental methodology in animal studies, broadly classified as: (1) transcranial stimulation; (2) direct cortical stimulation in vivo and (3) in vitro models. In each case advantages and disadvantages for translational research are discussed including dose translation and the overarching "quasi-uniform" assumption, which underpins translational relevance in all animal models of tDCS. Terminology such as anode, cathode, inward current, outward current, current density, electric field, and uniform are defined. Though we put key animal experiments spanning decades in perspective, our goal is not simply an exhaustive cataloging of relevant animal studies, but rather to put them in context of ongoing efforts to improve tDCS. Cellular targets, including excitatory neuronal somas, dendrites, axons, interneurons, glial cells, and endothelial cells are considered. We emphasize neurons are always depolarized and hyperpolarized such that effects of DCS on neuronal excitability can only be evaluated within subcellular regions of the neuron. Findings from animal studies on the effects of DCS on plasticity (LTP/LTD) and network oscillations are reviewed extensively. Any endogenous phenomena dependent on membrane potential changes are, in theory, susceptible to modulation by DCS. The relevance of morphological changes (galvanotropy) to tDCS is also considered, as we suggest microscopic migration of axon terminals or dendritic spines may be relevant during tDCS. A majority of clinical studies using tDCS employ a simplistic dose strategy where excitability is singularly increased or decreased under the anode and cathode, respectively. We discuss how this strategy, itself based on classic animal studies, cannot account for the complexity of normal and pathological brain function, and how recent studies have already indicated more sophisticated approaches are necessary. One tDCS theory regarding "functional targeting" suggests the specificity of tDCS effects are possible by modulating ongoing function (plasticity). Use of animal models of disease are summarized including pain, movement disorders, stroke, and epilepsy.

Direct Current Stimulation Alters Neuronal Input/Output Function

BACKGROUND

Direct current stimulation (DCS) affects both neuronal firing rate and synaptic efficacy. The neuronal input/output (I/O) function determines the likelihood that a neuron elicits an action potential in response to synaptic input of a given strength. Changes of the neuronal I/O function by DCS may underlie previous observations in animal models and human testing, yet have not been directly assessed.

OBJECTIVE

Test if the neuronal input/output function is affected by DCS METHODS: Using rat hippocampal brain slices and computational modeling, we provide evidence for how DCS modulates the neuronal I/O function.

RESULTS

We show for the first time that DCS modulates the likelihood of neuronal firing for a given and fixed synaptic input. Opposing polarization of soma and dendrite may have a synergistic effect for anodal stimulation, increasing the driving force of synaptic activity while simultaneously increasing spiking probability at the soma. For cathodal stimulation, however, the opposing effects tend to cancel. This results in an asymmetry in the strength of the effects of stimulation for opposite polarities.

CONCLUSIONS

Our results may explain the asymmetries observed in acute and long term effects of transcranial direct current stimulation.

Multilevel computational models for predicting the cellular effects of noninvasive brain stimulation

Since 2000, there has been rapid acceleration in the use of tDCS in both clinical and cognitive neuroscience research, encouraged by the simplicity of the technique (two electrodes and a battery powered stimulator) and the perception that tDCS protocols can be simply designed by placing the anode over the cortex to "excite," and the cathode over cortex to "inhibit." A specific and predictive understanding of tDCS needs experimental data to be placed into a quantitative framework. Biologically constrained computational models provide a useful framework within which to interpret results from empirical studies and generate novel, testable hypotheses. Although not without caveats, computational models provide a tool for exploring cognitive and brain processes, are amenable to quantitative analysis, and can inspire novel empirical work that might be difficult to intuit simply by examining experimental results. We approach modeling the effects of tDCS on neurons from multiple levels: modeling the electric field distribution, modeling single-compartment effects, and finally with multicompartment neuron models.