TMS activation site estimation using multiscale realistic head models

A boundary element method of bidomain modeling for predicting cellular responses to electromagnetic fields

Objective.Commonly used cable equation approaches for simulating the effects of electromagnetic fields on excitable cells make several simplifying assumptions that could limit their predictive power. Bidomain or 'whole' finite element methods have been developed to fully couple cells and electric fields for more realistic neuron modeling. Here, we introduce a novel bidomain integral equation designed for determining the full electromagnetic coupling between stimulation devices and the intracellular, membrane, and extracellular regions of neurons.Approach.Our proposed boundary element formulation offers a solution to an integral equation that connects the device, tissue inhomogeneity, and cell membrane-induced E-fields. We solve this integral equation using first-order nodal elements and an unconditionally stable Crank-Nicholson time-stepping scheme. To validate and demonstrate our approach, we simulated cylindrical Hodgkin-Huxley axons and spherical cells in multiple brain stimulation scenarios.Main Results.Comparison studies show that a boundary element approach produces accurate results for both electric and magnetic stimulation. Unlike bidomain finite element methods, the bidomain boundary element method does not require volume meshes containing features at multiple scales. As a result, modeling cells, or tightly packed populations of cells, with microscale features embedded in a macroscale head model, is simplified, and the relative placement of devices and cells can be varied without the need to generate a new mesh.Significance.Device-induced electromagnetic fields are commonly used to modulate brain activity for research and therapeutic applications. Bidomain solvers allow for the full incorporation of realistic cell geometries, device E-fields, and neuron populations. Thus, multi-cell studies of advanced neuronal mechanisms would greatly benefit from the development of fast-bidomain solvers to ensure scalability and the practical execution of neural network simulations with realistic neuron morphologies.

A Boundary Element Method of Bidomain Modeling for Predicting Cellular Responses to Electromagnetic Fields

Objective

Commonly used cable equation-based approaches for determining the effects of electromagnetic fields on excitable cells make several simplifying assumptions that could limit their predictive power. Bidomain or "whole" finite element methods have been developed to fully couple cells and electric fields for more realistic neuron modeling. Here, we introduce a novel bidomain integral equation designed for determining the full electromagnetic coupling between stimulation devices and the intracellular, membrane, and extracellular regions of neurons.

Methods

Our proposed boundary element formulation offers a solution to an integral equation that connects the device, tissue inhomogeneity, and cell membrane-induced E-fields. We solve this integral equation using first-order nodal elements and an unconditionally stable Crank-Nicholson time-stepping scheme. To validate and demonstrate our approach, we simulated cylindrical Hodgkin-Huxley axons and spherical cells in multiple brain stimulation scenarios.

Main Results

Comparison studies show that a boundary element approach produces accurate results for both electric and magnetic stimulation. Unlike bidomain finite element methods, the bidomain boundary element method does not require volume meshes containing features at multiple scales. As a result, modeling cells, or tightly packed populations of cells, with microscale features embedded in a macroscale head model, is made computationally tractable, and the relative placement of devices and cells can be varied without the need to generate a new mesh.

Significance

Device-induced electromagnetic fields are commonly used to modulate brain activity for research and therapeutic applications. Bidomain solvers allow for the full incorporation of realistic cell geometries, device E-fields, and neuron populations. Thus, multi-cell studies of advanced neuronal mechanisms would greatly benefit from the development of fast-bidomain solvers to ensure scalability and the practical execution of neural network simulations with realistic neuron morphologies.

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.

Mapping Brain Motor Functions Using Transcranial Magnetic Stimulation with a Volume Conductor Model and Electrophysiological Experiments

Transcranial magnetic stimulation (TMS) activates brain cells in a noninvasive manner and can be used for mapping brain motor functions. However, the complexity of the brain anatomy prevents the determination of the exact location of the stimulated sites, resulting in the limitation of the spatial resolution of multiple targets. The aim of this study is to map two neighboring muscles in cortical motor areas accurately and quickly. Multiple stimuli were applied to the subject using a TMS stimulator to measure the motor-evoked potentials (MEPs) in the corresponding muscles. For each stimulation condition (coil location and angle), the induced electric field (EF) in the brain was computed using a volume conductor model for an individualized head model of the subject constructed from magnetic resonance images. A post-processing method was implemented to determine a TMS hotspot using EF corresponding to multiple stimuli, considering the amplitude of the measured MEPs. The dependence of the computationally estimated hotspot distribution on two target muscles was evaluated (n = 11). The center of gravity of the first dorsal interosseous cortical representation was lateral to the abductor digiti minimi by a minimum of 2 mm. The localizations were consistent with the putative sites obtained from previous EF-based studies and fMRI studies. The simultaneous cortical mapping of two finger muscles was achieved with only several stimuli, which is one or two orders of magnitude smaller than that in previous studies. Our proposal would be useful in the preoperative mapping of motor or speech areas to plan brain surgery interventions.

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.

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.

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

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

Dosimetry Analysis in Non-brain Tissues During TMS Exposure of Broca's and M1 Areas

For human protection, the internal electric field is used as a dosimetric quantity for electromagnetic fields lower than 5–10 MHz. According to international standards, in this frequency range, electrostimulation is the main adverse effect against which protection is needed. One of the topics to be investigated is the quantification of the internal electric field threshold levels of perception and pain. Pain has been reported as a side effect during transcranial magnetic stimulation (TMS), especially during stimulation of the Broca’s (speech) area of the brain. In this study, we designed an experiment to conduct a dosimetry analysis to quantify the internal electric field corresponding to perception and pain thresholds when targeting the Broca’s and M1 areas from magnetic stimulator exposure. Dosimetry analysis was conducted using a multi-scale analysis in an individualized head model to investigate electrostimulation in an axonal model. The main finding is that the stimulation on the primary motor cortex has higher perception and pain thresholds when compared to Broca’s area. Also, TMS-induced electric field applied to Broca’s area exhibited dependence on the coil orientation at lower electric field threshold which was found to be related to the location and thickness of pain fibers. The derived dosimetry quantities provide a scientific rationale for the development of human protection guidelines and the estimation of possible side effects of magnetic stimulation in clinical applications.

Evaluating transcranial magnetic stimulation (TMS) induced electric fields in pediatric stroke

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Numerical TMS simulations were performed over and around perinatal stroke lesions.

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The presence of brain lesions locally affects the electric field distribution.

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Brain lesions do not significantly change the mean electric field strength.

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Model driven approaches can inform TMS dosing in a pediatric stroke population.

Transcranial magnetic stimulation (TMS) is an increasingly popular tool for stroke rehabilitation. Consequently, researchers have started to explore the use of TMS in pediatric stroke. However, the application of TMS in a developing brain with pathologies comes with a unique set of challenges. The effect of TMS-induced electric fields has not been explored in children with stroke lesions. Here, we used finite element method (FEM) modeling to study how the electric field strength is affected by the presence of a lesion. We created individual realistic head models from MRIs (n = 6) of children with unilateral cerebral palsy due to perinatal stroke. We conducted TMS electric field simulations for coil locations over lesioned and non-lesioned hemispheres. We found that the presence of a lesion can strongly affect the electric field distribution. On the group level, the mean electric field strength did not differ between lesioned and non-lesioned hemispheres but exhibited a greater variability in the lesioned hemisphere. Other factors such as coil-to-cortex distance have a strong influence on the TMS electric field even in the presence of lesions. Our study has important implications for the delivery of TMS in children with brain lesions with respect to TMS dosing and coil placement.

Primary hand motor representation areas in healthy children, preadolescents, adolescents, and adults

The development of the organization of the motor representation areas in children and adolescents is not well-known. This cross-sectional study aimed to provide an understanding for the development of the functional motor areas of the upper extremity muscles by studying healthy right-handed children (6-9 years, n = 10), preadolescents (10-12 years, n = 13), adolescents (15-17 years, n = 12), and adults (22-34 years, n = 12). The optimal representation site and resting motor threshold (rMT) for the abductor pollicis brevis (APB) were assessed in both hemispheres using navigated transcranial magnetic stimulation (nTMS). Motor mapping was performed at 110% of the rMT while recording the EMG of six upper limb muscles in the hand and forearm. The association between the motor map and manual dexterity (box and block test, BBT) was examined. The mapping was well-tolerated and feasible in all but the youngest participant whose rMT exceeded the maximum stimulator output. The centers-of-gravity (CoG) for individual muscles were scattered to the greatest extent in the group of preadolescents and centered and became more focused with age. In preadolescents, the CoGs in the left hemisphere were located more laterally, and they shifted medially with age. The proportion of hand compared to arm representation increased with age (p = 0.001); in the right hemisphere, this was associated with greater fine motor ability. Similarly, there was less overlap between hand and forearm muscles representations in children compared to adults (p<0.001). There was a posterior-anterior shift in the APB hotspot coordinate with age, and the APB coordinate in the left hemisphere exhibited a lateral to medial shift with age from adolescence to adulthood (p = 0.006). Our results contribute to the elucidation of the developmental course in the organization of the motor cortex and its associations with fine motor skills. It was shown that nTMS motor mapping in relaxed muscles is feasible in developmental studies in children older than seven years of age.

TMS coil orientation and muscle activation influence lower limb intracortical excitability

INTRODUCTION

Previous research with transcranial magnetic stimulation (TMS) indicates that coil orientation (TMS current direction) and muscle activation state (rest or active) modify corticospinal and intracortical excitability of upper limb muscles. However, the extent to which these factors influence corticospinal and intracortical excitability of lower limb muscles is unknown. This study aimed to examine how variations in coil orientation and muscle activation affect corticospinal and intracortical excitability of tibialis anterior (TA), a lower leg muscle.

METHODS

In 21 young (21.6 ± 3.3 years, 11 female) adults, TMS was administered to the motor cortical representation of TA in posterior-anterior (PA) and mediolateral (ML) orientations at rest and during muscle activation. Single-pulse TMS measures of motor evoked potential amplitude, in addition to resting and active motor thresholds, were used to index corticospinal excitability, whereas paired-pulse TMS measures of short-interval intracortical inhibition (SICI) and facilitation (SICF), and long-interval intracortical inhibition (LICI), were used to assess excitability of intracortical circuits.

RESULTS

For single-pulse TMS, motor thresholds and test TMS intensity were lower for ML stimulation (all P < 0.05). In a resting muscle, ML TMS produced greater SICI (P < 0.001) and less SICF (both P < 0.05) when compared with PA TMS. In contrast, ML TMS in an active muscle resulted in reduced SICI but increased SICF (both P ≤ 0.001) when compared with PA TMS.

CONCLUSION

TMS coil orientation and muscle activation influence measurements of intracortical excitability recorded in the tibialis anterior, and are therefore important considerations in TMS studies of lower limb muscles.