Biophysically realistic neuron models for simulation of cortical stimulation

Enabling Electric Field Modeling of Microscopically Realistic Brain

Across all domains of brain stimulation (neuromodulation), conventional analysis of neuron activation involves two discrete steps: i) prediction of macroscopic electric field, ignoring presence of cells and; ii) prediction of cell activation from tissue electric fields. The first step assumes that current flow is not distorted by the dense tortuous network of cell structures. The deficiencies of this assumption have long been recognized, but - except for trivial geometries - ignored, because it presented intractable computation hurdles. This study introduces a novel approach for analyzing electric fields within a microscopically realistic brain volume. Our pipeline overcomes the technical intractability that prevented such analysis while also showing significant implications for brain stimulation. Contrary to the standard finite element method (FEM), we suggest using a nested iterative boundary element method (BEM) coupled with the fast multipole method (FMM). This approach allows for solving problems with multiple length scales more efficiently. A target application is a subvolume of the L2/3 P36 mouse primary visual cortex containing approximately 400 detailed densely packed neuronal cells at a resolution of 100 nm, which is obtained from scanning electron microscopy data. Our immediate result is a reduction of the stimulation field strength necessary for neuron activation by a factor of 0.85-0.55 (by 15%-45%) as compared to macroscopic predictions. This is in line with modern experimental data stating that existing macroscopic theories substantially overestimate electric field levels necessary for brain stimulation.

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.

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.

µ-rhythm phase from somatosensory but not motor cortex correlates with corticospinal excitability in EEG-triggered TMS

BACKGROUND

Sensorimotor µ-rhythm phase is correlated with corticospinal excitability. Transcranial magnetic stimulation (TMS) of motor cortex results in larger motor evoked potentials (MEPs) during the negative peak of the EEG oscillation as extracted with a surface Laplacian. However, the anatomical source of the relevant oscillation is not clear and demonstration of the relationship is sensitive to the choice of EEG montage.

OBJECTIVE/HYPOTHESIS

Here, we compared two EEG montages preferentially sensitive to oscillations originating from the crown of precentral gyrus (dorsal premotor cortex) vs. postcentral gyrus (secondary somatosensory cortex). We hypothesized that the EEG signal from precentral gyrus would correlate more strongly with MEP amplitude, given that the corticospinal neurons are located in the anterior wall of the sulcus and the corticospinal tract has input from premotor cortex.

NEW METHOD

Real-time EEG-triggered TMS of motor cortex was applied in 6 different conditions in randomly interleaved order, 3 phase conditions (positive peak, negative peak, random phase of the ongoing µ-oscillation), and each phase condition for 2 different EEG montages corresponding to oscillations preferentially originating in precentral gyrus (premotor cortex) vs. postcentral gyrus (somatosensory cortex), extracted using FCC3h vs. C3 centered EEG montages.

RESULTS

The negative vs. positive peak of sensorimotor µ-rhythm as extracted from the C3 montage (postcentral gyrus, somatosensory cortex) correlated with states of high vs. low corticospinal excitability (p < 0.001), replicating previous findings. However, no significant correlation was found for sensorimotor µ-rhythm as extracted from the neighboring FCC3 montage (precentral gyrus, premotor cortex). This implies that EEG-signals from the somatosensory cortex are better predictors of corticospinal excitability than EEG-signals from the motor areas.

CONCLUSIONS

The extraction of a brain oscillation whose phase corresponds to corticospinal excitability is highly sensitive to the selected EEG montage and the location of the EEG sensors on the scalp. Here, the cortical source of EEG oscillations predicting response amplitude does not correspond to the cortical target of the stimulation, indicating that even in this simple case, a specific neuronal pathway from somatosensory cortex to primary motor cortex is involved.

The Long-Term Stability of Intracortical Microstimulation and the Foreign Body Response Are Layer Dependent

Intracortical microstimulation (ICMS) of the somatosensory cortex (S1) can restore sensory function in patients with paralysis. Studies assessing the stability of ICMS have reported heterogeneous responses across electrodes and over time, potentially hindering the implementation and translatability of these technologies. The foreign body response (FBR) and the encapsulating glial scar have been associated with a decay in chronic performance of implanted electrodes. Moreover, the morphology, intrinsic properties, and function of cells vary across cortical layers, each potentially affecting the sensitivity to ICMS as well as the degree of the FBR across cortical depth. However, layer-by-layer comparisons of the long-term stability of ICMS as well as the extent of the astrocytic glial scar change across cortical layers have not been well explored. Here, we implanted silicon microelectrodes with electrode sites spanning all the layers of S1 in rats. Using a behavioral paradigm, we obtained ICMS detection thresholds from all cortical layers for up to 40 weeks. Our results showed that the sensitivity and long-term performance of ICMS is indeed layer dependent. Overall, detection thresholds decreased during the first 7 weeks post-implantation (WPI). This was followed by a period in which thresholds remained stable or increased depending on the interfacing layer: thresholds in L1 and L6 exhibited the most consistent increases over time, while those in L4 and L5 remained the most stable. Furthermore, histological investigation of the tissue surrounding the electrode showed a biological response of microglia and macrophages which peaked at L1, while the area of the astrocytic glial scar peaked at L2/3. Interestingly, the biological response of these FBR markers is less exacerbated at L4 and L5, suggesting a potential link between the FBR and the long-term stability of ICMS. These findings suggest that interfacing depth can play an important role in the design of chronically stable implantable microelectrodes.

Short periods of bipolar anodal TDCS induce no instantaneous dose-dependent increase in cerebral blood flow in the targeted human motor cortex

Anodal transcranial direct current stimulation (aTDCS) of primary motor hand area (M1-HAND) can enhance corticomotor excitability, but it is still unknown which current intensity produces the strongest effect on intrinsic neural firing rates and synaptic activity. Magnetic resonance imaging (MRI) combined with pseudo-continuous Arterial Spin Labeling (pcASL MRI) can map regional cortical blood flow (rCBF). The measured rCBF signal is sensitive to regional changes in neuronal activity due to neurovascular coupling. Therefore, concurrent TDCS and pcASL MRI may reveal the relationship between current intensity and TDCS-induced changes in overall firing rates and synaptic activity in the cortical target. Here we employed pcASL MRI to map acute rCBF changes during short-duration aTDCS of left M1-HAND. Using the rCBF response as a proxy for regional neuronal activity, we investigated if short-duration aTDCS produces an instantaneous dose-dependent rCBF increase in the targeted M1-HAND that may be useful for individual dosing. Nine healthy right-handed participants received 30 s of aTDCS at 0.5, 1.0, 1.5, and 2.0 mA with the anode placed over left M1-HAND and cathode over the right supraorbital region. Concurrent pcASL MRI at 3 T probed TDCS-related rCBF changes in the targeted M1-HAND. Movement-induced rCBF changes were also assessed. Apart from a subtle increase in rCBF at 0.5 mA, short-duration aTDCS did not modulate rCBF in the M1-HAND relative to no-stimulation periods. None of the participants showed a dose-dependent increase in rCBF during aTDCS, even after accounting for individual differences in TDCS-induced electrical field strength. In contrast, finger movements led to robust activation of left M1-HAND before and after aTDCS. Short-duration bipolar aTDCS does not produce consistant instantaneous dose-dependent rCBF increases in the targeted M1-HAND at conventional intensity ranges. Therefore, the regional hemodynamic response profile to short-duration aTDCS may not be suited to inform individual dosing of TDCS intensity.

In silico assessment of electrophysiological neuronal recordings mediated by magnetoelectric nanoparticles

Magnetoelectric materials hold untapped potential to revolutionize biomedical technologies. Sensing of biophysical processes in the brain is a particularly attractive application, with the prospect of using magnetoelectric nanoparticles (MENPs) as injectable agents for rapid brain-wide modulation and recording. Recent studies have demonstrated wireless brain stimulation in vivo using MENPs synthesized from cobalt ferrite (CFO) cores coated with piezoelectric barium titanate (BTO) shells. CFO–BTO core–shell MENPs have a relatively high magnetoelectric coefficient and have been proposed for direct magnetic particle imaging (MPI) of brain electrophysiology. However, the feasibility of acquiring such readouts has not been demonstrated or methodically quantified. Here we present the results of implementing a strain-based finite element magnetoelectric model of CFO–BTO core–shell MENPs and apply the model to quantify magnetization in response to neural electric fields. We use the model to determine optimal MENPs-mediated electrophysiological readouts both at the single neuron level and for MENPs diffusing in bulk neural tissue for in vivo scenarios. Our results lay the groundwork for MENP recording of electrophysiological signals and provide a broad analytical infrastructure to validate MENPs for biomedical applications.

Brain stimulation competes with ongoing oscillations for control of spike timing in the primate brain

Transcranial alternating current stimulation (tACS) is a popular method for modulating brain activity noninvasively. In particular, tACS is often used as a targeted intervention that enhances a neural oscillation at a specific frequency to affect a particular behavior. However, these interventions often yield highly variable results. Here, we provide a potential explanation for this variability: tACS competes with the brain's ongoing oscillations. Using neural recordings from alert nonhuman primates, we find that when neural firing is independent of ongoing brain oscillations, tACS readily entrains spiking activity, but when neurons are strongly entrained to ongoing oscillations, tACS often causes a decrease in entrainment instead. Consequently, tACS can yield categorically different results on neural activity, even when the stimulation protocol is fixed. Mathematical analysis suggests that this competition is likely to occur under many experimental conditions. Attempting to impose an external rhythm on the brain may therefore often yield precisely the opposite effect.

The science and engineering behind sensitized brain-controlled bionic hands

Advances in our understanding of brain function, along with the development of neural interfaces that allow for the monitoring and activation of neurons, have paved the way for brain-machine interfaces (BMIs), which harness neural signals to reanimate the limbs via electrical activation of the muscles or to control extracorporeal devices, thereby bypassing the muscles and senses altogether. BMIs consist of reading out motor intent from the neuronal responses monitored in motor regions of the brain and executing intended movements with bionic limbs, reanimated limbs, or exoskeletons. BMIs also allow for the restoration of the sense of touch by electrically activating neurons in somatosensory regions of the brain, thereby evoking vivid tactile sensations and conveying feedback about object interactions. In this review, we discuss the neural mechanisms of motor control and somatosensation in able-bodied individuals and describe approaches to use neuronal responses as control signals for movement restoration and to activate residual sensory pathways to restore touch. Although the focus of the review is on intracortical approaches, we also describe alternative signal sources for control and noninvasive strategies for sensory restoration.

Intracortical microstimulation pulse waveform and frequency recruits distinct spatiotemporal patterns of cortical neuron and neuropil activation

OBJECTIVE

Neural prosthetics often use intracortical microstimulation (ICMS) for sensory restoration. To restore natural and functional feedback, we must first understand how stimulation parameters influence the recruitment of neural populations. ICMS waveform asymmetry modulates the spatial activation of neurons around an electrode at 10 Hz; however, it is unclear how asymmetry may differentially modulate population activity at frequencies typically employed in the clinic (e.g. 100 Hz). We hypothesized that stimulation waveform asymmetry would differentially modulate preferential activation of certain neural populations, and the differential population activity would be frequency-dependent.

APPROACH

We quantified how asymmetric stimulation waveforms delivered at 10 Hz or 100 Hz for 30s modulated spatiotemporal activity of cortical layer II/III pyramidal neurons using in vivo two-photon and mesoscale calcium imaging in anesthetized mice. Asymmetry is defined in terms of the ratio of the duration of the leading phase to the duration of the return phase of charge-balanced cathodal- and anodal-first waveforms (i.e. longer leading phase relative to return has larger asymmetry).

MAIN RESULTS

Neurons within 40-60µm of the electrode display stable stimulation-induced activity indicative of direct activation, which was independent of waveform asymmetry. The stability of 72% of activated neurons and the preferential activation of 20-90 % of neurons depended on waveform asymmetry. Additionally, this asymmetry-dependent activation of different neural populations was associated with differential progression of population activity. Specifically, neural activity tended to increase over time during 10 hz stimulation for some waveforms, whereas activity remained at the same level throughout stimulation for other waveforms. During 100 Hz stimulation, neural activity decreased over time for all waveforms, but decreased more for the waveforms that resulted in increasing neural activity during 10 Hz stimulation.

SIGNIFICANCE

These data demonstrate that at frequencies commonly used for sensory restoration, stimulation waveform alters the pattern of activation of different but overlapping populations of excitatory neurons. The impact of these waveform specific responses on the activation of different subtypes of neurons as well as sensory perception merits further investigation.

Neural Recruitment During Conventional, Burst, and 10-kHz Spinal Cord Stimulation for Pain

Spinal cord stimulation (SCS) is a popular neurostimulation therapy for severe chronic pain. To improve stimulation efficacy, multiple modes are now used clinically, including conventional, burst, and 10-kHz SCS. Clinical observations have produced speculation that these modes target different neural elements and/or work via distinct mechanisms of action. However, in humans, these hypotheses cannot be conclusively answered via experimental methods. Therefore, we utilized computational modeling to assess the response of primary afferents, interneurons, and projection neurons to conventional, burst, and 10-kHz SCS. We found that local cell thresholds were always higher than afferent thresholds, arguing against direct recruitment of these local cells. Furthermore, although we observed relative threshold differences between conventional, burst, and 10-kHz SCS, the recruitment order was the same. Finally, contrary to previous reports, axon collateralization produced complex changes in activation thresholds of primary afferents. These results motivate future work to contextualize clinical observations across SCS paradigms. PERSPECTIVE: This article presents the first computational modeling study to investigate neural recruitment during conventional, burst, and 10-kilohertz spinal cord stimulation for chronic pain within a single modeling framework. The results provide insight into these treatments' unknown mechanisms of action and offer context to interpreting clinical observations.

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

Neural oscillations are a key mechanism for information transfer in brain circuits. Rhythmic fluctuations of local field potentials control spike timing through cyclic membrane de- and hyperpolarization. Transcranial alternating current stimulation (tACS) is a non-invasive neuromodulation method which can directly interact with brain oscillatory activity by imposing an oscillating electric field on neurons. Despite its increasing use, the basic mechanisms of tACS are still not fully understood. Here, we investigate in a computational study the effects of tACS on morphologically realistic neurons with ongoing spiking activity. We characterize the membrane polarization as a function of electric field strength and subsequent effects on spiking activity in a set of 25 neurons from different neocortical layers. We find that tACS does not affect the firing rate of investigated neurons for electric field strengths applicable to human studies. However, we find that the applied electric fields entrain the spiking activity of large pyramidal neurons and large basket neurons at < 1 mV/mm field strengths. Our model results are in line with recent experimental studies and can provide a mechanistic framework to understand the effects of oscillating electric fields on single neuron activity. They highlight the importance of neuron morphology and biophysics in responsiveness to electrical stimulation.

Stoney vs. Histed: Quantifying the spatial effects of intracortical microstimulation

BACKGROUND

Intracortical microstimulation (ICMS) is used to map neural circuits and restore lost sensory modalities such as vision, hearing, and somatosensation. The spatial effects of ICMS remain controversial: Stoney and colleagues proposed that the volume of somatic activation increased with stimulation intensity, while Histed et al., suggested activation density, but not somatic activation volume, increases with stimulation intensity.

OBJECTIVE

We used computational modeling to quantify the spatial effects of ICMS intensity and unify the apparently paradoxical findings of Histed and Stoney.

METHODS

We implemented a biophysically-based computational model of a cortical column comprising neurons with realistic morphology and representative synapses. We quantified the spatial effects of single pulses and short trains of ICMS, including the volume of activated neurons and the density of activated neurons as a function of stimulation intensity.

RESULTS

At all amplitudes, the dominant mode of somatic activation was by antidromic propagation to the soma following axonal activation, rather than via transsynaptic activation. There were no occurrences of direct activation of somata or dendrites. The volume over which antidromic action potentials were initiated grew with stimulation amplitude, while the volume of somatic activation increased marginally. However, the density of somatic activation within the activated volume increased with stimulation amplitude.

CONCLUSIONS

The results resolve the apparent paradox between Stoney and Histed's results by demonstrating that the volume over which action potentials are initiated grows with ICMS amplitude, consistent with Stoney. However, the volume occupied by the activated somata remains approximately constant, while the density of activated neurons within that volume increase, consistent with Histed.

Effect of Pulse Duration and Direction on Plasticity Induced by 5 Hz Repetitive Transcranial Magnetic Stimulation in Correlation With Neuronal Depolarization

Introduction: High frequency repetitive transcranial magnetic stimulation applied to the motor cortex causes an increase in the amplitude of motor evoked potentials (MEPs) that persists after stimulation. Here, we focus on the aftereffects generated by high frequency controllable pulse TMS (cTMS) with different directions, intensities, and pulse durations.

Objectives: To investigate the influence of pulse duration, direction, and amplitude in correlation to induced depolarization on the excitatory plastic aftereffects of 5 Hz repetitive transcranial magnetic stimulation (rTMS) using bidirectional cTMS pulses.

Methods: We stimulated the hand motor cortex with 5 Hz rTMS applying 1,200 bidirectional pulses with the main component durations of 80, 100, and 120 μs using a controllable pulse stimulator TMS (cTMS). Fourteen healthy subjects were investigated in nine sessions with 80% resting motor threshold (RMT) for posterior-anterior (PA) and 80 and 90% RMT anterior-posterior (AP) induced current direction. We used a model approximating neuronal membranes as a linear first order low-pass filter to estimate the strength–duration time constant and to simulate the membrane polarization produced by each waveform.

Results: PA and AP 5 Hz rTMS at 80% RMT produced no significant excitation. An exploratory analysis indicated that 90% RMT AP stimulation with 100 and 120 μs pulses but not 80 μs pulses led to significant excitation. We found a positive correlation between the plastic outcome of each session and the simulated peak neural membrane depolarization for time constants >100 μs. This correlation was strongest for neural elements that are depolarized by the main phase of the AP pulse, suggesting the effects were dependent on pulse direction.

Conclusions: Among the tested conditions, only 5 Hz rTMS with higher intensity and wider pulses appeared to produce excitatory aftereffects. This correlated with the greater depolarization of neural elements with time constants slower than the directly activated neural elements responsible for producing the motor output (e.g., somatic or dendritic membrane).

Significance: Higher intensities and wider pulses seem to be more efficient in inducing excitation. If confirmed, this observation could lead to better results in future clinical studies performed with wider pulses.

Comparison between the modelled response of primary motor cortex neurons to pulse-width modulated and conventional TMS stimuli

In this study, the neural response to pulse-width modulated (PWM) transcranial magnetic stimulation (TMS) is estimated using a computational neural model which simulates the response of cortical neurons to TMS. The recently introduced programmable TMS uses PWM to approximate conventional resonance-based TMS pulses by fast switching between voltage levels. The effect of such stimulation on the six cortical layers is modelled by estimating the activation threshold of the neurons. Modelling results are compared between the novel device and that of conventional TMS stimuli generated by Magstim stimulators. The neural responses to the PWM pulses and the conventional stimuli show a high correlation, which validates the use of pulse-width modulated pulses in TMS.Clinical Relevance- This computational modelling study demonstrates an equivalent effect of PWM and conventional TMS pulses on the nervous system which paves the way to more flexibility in exploring and choosing stimulation parameters for TMS treatment.

Is electric field strength deterministic in cortical neurons' response to transcranial electrical stimulation?

Transcranial electrical stimulation (tES), which modulates cortical excitability via electric currents, has attracted increasing attention because of its application in treating neurologic and psychiatric disorders. To obtain a better understanding of the brain areas affected and stimulation's cellular effects, a multi-scale model was proposed that combines multi-compartmental neuronal models and a head model. While one multi-scale model of tES that used straight axons reported that the direction of electric field (EF) is a determining factor in a neuronal response, another model of transcranial magnetic stimulation (TMS) that used arborized axons reported that EF magnitude is more crucial than EF direction because of arborized axons' reduced sensitivity to the latter. Our goal was to investigate whether EF magnitude remains a crucial factor in the neuronal response in a multi-scale model of tES into which an arborized axon is integrated. To achieve this goal, we constructed a multi-scale model that integrated three types of neurons and a realistic head model, and then simulated the neuronal response to realistic EF. We found that EF magnitude was correlated with excitation threshold, and thus, it may be one of the determining factors in cortical neurons' response to tES.Clinical Relevance-This multi-scale model based on biophysical and morphological properties and realistic brain geometry may help elucidate tES's neural mechanisms. Moreover, given its clinical applications, this model may help predict a patient's neuronal response to brain stimulation effectively.

Multi-scale modeling toolbox for single neuron and subcellular activity under Transcranial Magnetic Stimulation

BACKGROUND

Transcranial Magnetic Stimulation (TMS) is a widely used non-invasive brain stimulation method. However, its mechanism of action and the neural response to TMS are still poorly understood. Multi-scale modeling can complement experimental research to study the subcellular neural effects of TMS. At the macroscopic level, sophisticated numerical models exist to estimate the induced electric fields. However, multi-scale computational modeling approaches to predict TMS cellular and subcellular responses, crucial to understanding TMS plasticity inducing protocols, are not available so far.

OBJECTIVE

We develop an open-source multi-scale toolbox Neuron Modeling for TMS (NeMo-TMS) to address this problem.

METHODS

NeMo-TMS generates accurate neuron models from morphological reconstructions, couples them to the external electric fields induced by TMS, and simulates the cellular and subcellular responses of single-pulse and repetitive TMS.

RESULTS

We provide examples showing some of the capabilities of the toolbox.

CONCLUSION

NeMo-TMS toolbox allows researchers a previously not available level of detail and precision in realistically modeling the physical and physiological effects of TMS.

The Role of Electrode-Site Placement in the Long-Term Stability of Intracortical Microstimulation

Intracortical microelectrodes are neuroprosthetic devices used in brain-machine interfaces to both record and stimulate neural activity in the brain. These technologies have been improved by advances in microfabrication, which have led to the creation of subcellular and high-density microelectrodes. The greater number of independent stimulation channels in these devices allows for improved neuromodulation selectivity, compared to single-site microelectrodes. Elements of electrode design such as electrode-site placement can influence the long-term performance of neuroprostheses. Previous studies have shown that electrode-sites placed on the edge of a planar microelectrode have greater chronic recording functionality than sites placed in the center. However, the effect of electrode-site placement on long-term intracortical microstimulation (ICMS) is still unknown. Here, we show that, in rats chronically implanted with custom-made planar silicon microelectrodes, electrode-sites on the tip of the device outperformed those on both the edge and center in terms of the effect per charge delivered, though there is still a slight advantage to using edge sites over center sites for ICMS. Longitudinal analysis of ICMS detection thresholds over a 16-week period revealed that while all sites followed a similar trend over time, the tip and edge sites consistently elicited the behavioral response with less charge compared to center sites. Furthermore, we quantified channel activity over time and found that edge sites remained more active than center sites over time, though the rate of decay of active sites for center and edge sites was comparable. Our results demonstrate that electrode-site placement plays an important role in the long-term stability of intracortical microstimulation and could be a potential factor to consider in the design of future intracortical electrodes.

A probabilistic transcranial magnetic stimulation localization method

Objective.Transcranial magnetic stimulation (TMS) can be used to safely and noninvasively activate brain tissue. However, the characteristic parameters of the neuronal activation have been largely unclear. In this work, we propose a novel neuronal activation model and develop a method to infer its parameters from measured motor evoked potential signals.Approach.The connection between neuronal activation due to an induced electric field and a measured motor threshold is modeled. The posterior distribution of the model parameters are inferred from measurement data using Bayes' formula. The measurements are the active motor thresholds obtained with multiple stimulating coil locations, and the parameters of the model are the location, preferred direction of activation, and threshold electric field value of the activation site. The posterior distribution is sampled using a Markov chain Monte Carlo method. We quantify the plausibility of the model by calculating the marginal likelihood of the measured thresholds. The method is validated with synthetic data and applied to motor threshold measurements from the first dorsal interosseus muscle in five healthy participants.Main results.The method produces a probability distribution for the activation location, from which a minimal volume where the activation occurs with 95% probability can be derived. For eight or nine stimulating coil locations, the smallest such a volume obtained was approximately 100 mm³. The 95% probability volume intersected the pre-central gyral crown and the anterior wall of the central sulcus, and the preferred direction was perpendicular to the central sulcus, both findings being consistent with the literature. Furthermore, it was not possible to rule out if the activation occurred either in the white or grey matter. In one participant, two distinct activations sites were found while others exhibited a unique site.Significance.The method is both generic and robust, and it lays a foundation for a framework that enables accurate analysis and characterization of TMS activation mechanisms.