Cortical neuron activation induced by electromagnetic stimulation: a quantitative analysis via modelling and simulation

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

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

Electric field effects on neuronal input-output relationship by regulating NMDA spikes

Evidence shows that the dendritic polarization induced by weak electrical field (EF) can affect the neuronal input-output function via modulating dendritic integration of AMPA synapses, indicating that the supralinear dendritic integration of NMDA synapses can also be influenced by dendritic polarization. However, it remains unknown how dendritic polarization affects NMDA-type dendritic integration, and then contributes to neuronal input-output relationship. Here, we used a computational model of pyramidal neuron with inhomogeneous extracellular potentials to characterize the relationship among EF, dendritic integration, and somatic output. Basing on singular perturbation we analyzed the subthreshold dynamics of membrane potentials in response to NMDA synapses, and found that the equilibrium mapping of a fast subsystem can characterize the asymptotic subthreshold input-output (sI/O) relationship for EF-regulated supralinear dendritic integration, allowing us to predict the tendency of EF-regulated dendritic integration by showing the variation of equilibrium mapping under EF stimulation. EF-induced depolarization at distal dendrites receiving synapses plays a crucial role in shifting the steep change of sI/O left by facilitating dendritic NMDA spike generation and in decreasing the plateau of sI/O via reducing driving force. And more effective EF modulation appears at sparsely activated NMDA receptors compared with clustered synaptic inputs. During the action potential (AP) generation, the respective contribution of EF-regulated dendritic integration and EF-induced somatic polarization was identified to show their synergetic or antagonistic effect on AP generation, depending on neuronal excitability. These results provided insight in understanding the modulation effect of EF on neuronal computation, which is important for optimizing noninvasive brain stimulation.

Supplementary Information

The online version contains supplementary material available at 10.1007/s11571-022-09922-y.

A Review of Formulations, Boundary Value Problems and Solutions for Numerical Computation of Transcranial Magnetic Stimulation Fields

Since the inception of the transcranial magnetic stimulation (TMS) technique, it has become imperative to numerically compute the distribution of the electric field induced in the brain. Various models of the coil-brain system have been proposed for this purpose. These models yield a set of formulations and boundary conditions that can be employed to calculate the induced electric field. However, the literature on TMS simulation presents several of these formulations, leading to potential confusion regarding the interpretation and contribution of each source of electric field. The present study undertakes an extensive compilation of widely utilized formulations, boundary value problems and numerical solutions employed in TMS fields simulations, analyzing the advantages and disadvantages associated with each used formulation and numerical method. Additionally, it explores the implementation strategies employed for their numerical computation. Furthermore, this work provides numerical expressions that can be utilized for the numerical computation of TMS fields using the finite difference and finite element methods. Notably, some of these expressions are deduced within the present study. Finally, an overview of some of the most significant results obtained from numerical computation of TMS fields is presented. The aim of this work is to serve as a guide for future research endeavors concerning the numerical simulation of TMS.

Cortical inhibition and facilitation are mediated by distinct physiological processes

A complex interaction of inhibitory and facilitatory interneuronal processes may underlie development of cortical excitability in the human motor cortex. To determine whether distinct interneuronal processes mediated cortical excitability, threshold tracking transcranial magnetic stimulation was utilised to assess cortical excitability, with figure-of-eight coil oriented in posterior-anterior (PA), anterior-posterior (AP) and latero-medial (LM) directions. Motor evoked potential (MEP) responses were recorded over the contralateral abductor pollicis brevis. Resting motor threshold (RMT), short interval intracortical inhibition (SICI), short interval intracortical facilitation (SICF) and intracortical facilitation were recorded. Significant effects of coil orientation were evident on SICI (F = 8.560, P = 0.002) and SICF (F = 7.132, P = 0.003). SICI was greater when recorded with PA (9.7 ± 10.9%, P = 0.029) and AP (13.1 ± 7.0%, P = 0.003) compared to LM (5.2 ± 7.3%) directed currents. SICF was significantly greater with PA (-14.7 ± 8.1%, P = 0.016) and LM (-14.7 ± 8.8%, P = 0.005) compared to AP (-9.1 ± 7.2%) coil orientations. SICI recorded with LM and PA coil orientations were correlated (R = 0.7, P = 0.002), as was SICF recorded with AP vs LM (R = 0.60, P = 0.019) and LM vs PA (R = 0.69, P = 0.002) coil orientations. RMT was significantly smaller with PA compared to AP (P < 0.001) and LM (P = 0.018) stimulation. Recruitment of distinct interneuronal processes with variable cortical orientation and thresholds underlies short interval intracortical inhibition and facilitation.

Variations of the spontaneous electrical activities of the neuronal networks imposed by the exposure of electromagnetic radiations using computational map-based modeling

The interaction between neurons in a neuronal network develops spontaneous electrical activities. But the effects of electromagnetic radiation on these activities have not yet been well explored. In this study, a ring of three coupled 1-dimensional Rulkov neurons and the generated electromagnetic field (EMF) are considered to investigate how the spontaneous activities might change regarding the EMF exposure. By employing the bifurcation analysis and time series, a comprehensive view of neuronal behavioral changes due to electromagnetic inductions is provided. The main findings of this study are as follows: 1) When a neuronal network is showing a spontaneous chaotic firing manner (without any external stimuli), a generated magnetic field inhibits this type of behavior. In fact, EMF completely eliminated the chaotic intrinsic behaviors of the neuronal loop. 2) When the network is exhibiting regular period-3 spiking patterns, the generated magnetic field changes its firing pattern to chaotic spiking, which is similar to epileptic seizures. 3) With weak synaptic connections, electromagnetic radiation inhibits and suppresses neuronal activities. 4) If the external magnetic flux has a high amplitude, it can change the shape of the induction current according to its shape 5) when there are weak synaptic connections in the network, a high-frequency external magnetic flux engenders high-frequency fluctuations in the membrane voltages. On the whole, electromagnetic radiation changes the pattern of the spontaneous activities of neuronal networks in the brain according to synaptic strengths and initial states of the neurons.

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.

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.

Estimation of the Motor Threshold for Near-Rectangular Stimuli Using the Hodgkin-Huxley Model

The motor threshold measurement is a standard in preintervention probing in TMS experiments. We aim to predict the motor threshold for near-rectangular stimuli to efficiently determine the motor threshold size before any experiments take place. Estimating the behavior of large-scale networks requires dynamically accurate and efficient modeling. We utilized a Hodgkin-Huxley (HH) type model to evaluate motor threshold values and computationally validated its function with known true threshold data from 50 participants trials from state-of-the-art published datasets. For monophasic, bidirectional, and unidirectional rectangular stimuli in posterior-anterior or anterior-posterior directions as generated by the cTMS device, computational modeling of the HH model captured the experimentally measured population-averaged motor threshold values at high precision (maximum error ≤ 8%). The convergence of our biophysically based modeling study with experimental data in humans reveals that the effect of the stimulus shape is strongly correlated with the activation kinetics of the voltage-gated ion channels. The proposed method can reliably predict motor threshold size using the conductance-based neuronal models and could therefore be embedded in new generation neurostimulators. Advancements in neural modeling will make it possible to enhance treatment procedures by reducing the number of delivered magnetic stimuli to participants.

Morphological Influence and Electric Field Direction's Influence on Activation of Cortical Neurons in Electrical Brain Stimulation: a Computational Study

Electrical brain stimulation (EBS) has been actively researched because of its clinical application and usefulness in brain research. However, its effect on individual neurons remains uncertain, as each neuron's response to EBS is highly variable and dependent on its morphology and the axis in which a neuron lies. Hence, our goal was to investigate the way that neuronal morphology affects the cellular response to extracellular stimulation from multiple directions. In this computational study, we observed that the varying neuronal morphology and direction of applied electrical field (EF) had some influence on the excitation threshold, which generates an action potential. Further, change of the excitation threshold depending on EF directions was observed.Clinical Relevance- These findings would help us to understand the variability in the modulatory effects of EBS at the cellular level and would be the basis for understanding the packed fibers' responses to EBS. Ultimately, considering EBS' clinical application, it may also help to predict patient's results from EBS treatment.

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

BACKGROUND

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

OBJECTIVE

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

METHODS

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

RESULTS

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

CONCLUSIONS

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

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

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

Biophysically realistic neuron models for simulation of cortical stimulation

OBJECTIVE

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

APPROACH

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

MAIN RESULTS

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

SIGNIFICANCE

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

Modulations of dendritic Ca2+ spike with weak electric fields in layer 5 pyramidal cells

Weak electric fields (EFs) modulate input/output function of pyramidal cells. Dendritic Ca²⁺ spike is an important cellular mechanism for coupling synaptic inputs from different cortical layers, which plays a critical role in neuronal computation. This study aims to understand the effects of weak EFs on Ca²⁺ spikes initiated in the distal dendrites. We use a computational model to simulate dendritic Ca²⁺ spikes and backpropagating action potentials (APs) in layer 5 pyramidal cells. We apply uniform EFs (less than 20 mV/mm) to the model and examine how they affect the threshold for activation of Ca²⁺ spikes. We show that the effects of weak field on synaptically evoked Ca²⁺ spikes depend on the timing of synaptic inputs. When distal inputs coincide with the onset of EFs within a time window of several milliseconds, field-induced depolarization facilitates the initiation of Ca²⁺ spikes, while field-induced hyperpolarization suppresses dendritic APs. Sustained field-induced depolarization leads to the inactivation of Ca²⁺ channels and increases the threshold of Ca²⁺ spike. Sustained field-induced hyperpolarization de-inactivates Ca²⁺ channels and reduces the threshold of Ca²⁺ spike. By altering the threshold of backpropagation activated Ca²⁺ firing, field-induced depolarization increases the degree of coupling between inputs of the soma and distal dendrites, while field-induced hyperpolarization results in a decrease of coupling. The modulatory effects of weak EF are governed by the field direction with respect to the cell. Our study explains a fundamental link between field-induced polarization, dendritic Ca²⁺ spike, and somato-dendritic coupling. The findings are crucial to interpret how weak EFs achieve specific modulation of cellular activity.

Multi-Scale Computational Models for Electrical Brain Stimulation

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

Morphology controls how hippocampal CA1 pyramidal neuron responds to uniform electric fields: a biophysical modeling study

Responses of different neurons to electric field (EF) are highly variable, which depends on intrinsic properties of cell type. Here we use multi-compartmental biophysical models to investigate how morphologic features affect EF-induced responses in hippocampal CA1 pyramidal neurons. We find that the basic morphologies of neuronal elements, including diameter, length, bend, branch, and axon terminals, are all correlated with somatic depolarization through altering the current sources or sinks created by applied field. Varying them alters the EF threshold for triggering action potentials (APs), and then determines cell sensitivity to suprathreshold field. Introducing excitatory postsynaptic potential increases cell excitability and reduces morphology-dependent EF firing threshold. It is also shown that applying identical subthreshold EF results in distinct polarizations on cell membrane with different realistic morphologies. These findings shed light on the crucial role of morphologies in determining field-induced neural response from the point of view of biophysical models. The predictions are conducive to better understanding the variability in modulatory effects of EF stimulation at the cellular level, which could also aid the interpretations of how applied fields activate central nervous system neurons and affect relevant circuits.

A multi-scale computational model of the effects of TMS on motor cortex

The detailed biophysical mechanisms through which transcranial magnetic stimulation (TMS) activates cortical circuits are still not fully understood. Here we present a multi-scale computational model to describe and explain the activation of different pyramidal cell types in motor cortex due to TMS. Our model determines precise electric fields based on an individual head model derived from magnetic resonance imaging and calculates how these electric fields activate morphologically detailed models of different neuron types. We predict neural activation patterns for different coil orientations consistent with experimental findings. Beyond this, our model allows us to calculate activation thresholds for individual neurons and precise initiation sites of individual action potentials on the neurons’ complex morphologies. Specifically, our model predicts that cortical layer 3 pyramidal neurons are generally easier to stimulate than layer 5 pyramidal neurons, thereby explaining the lower stimulation thresholds observed for I-waves compared to D-waves. It also shows differences in the regions of activated cortical layer 5 and layer 3 pyramidal cells depending on coil orientation. Finally, it predicts that under standard stimulation conditions, action potentials are mostly generated at the axon initial segment of cortical pyramidal cells, with a much less important activation site being the part of a layer 5 pyramidal cell axon where it crosses the boundary between grey matter and white matter. In conclusion, our computational model offers a detailed account of the mechanisms through which TMS activates different cortical pyramidal cell types, paving the way for more targeted application of TMS based on individual brain morphology in clinical and basic research settings.