Uncertainty quantification in transcranial magnetic stimulation via high-dimensional model representation

Uncertainty Quantification in SAR Induced by Ultra-High-Field MRI RF Coil via High-Dimensional Model Representation

As magnetic field strength in Magnetic Resonance Imaging (MRI) technology increases, maintaining the specific absorption rate (SAR) within safe limits across human head tissues becomes challenging due to the formation of standing waves at a shortened wavelength. Compounding this challenge is the uncertainty in the dielectric properties of head tissues, which notably affects the SAR induced by the radiofrequency (RF) coils in an ultra-high-field (UHF) MRI system. To this end, this study introduces a computational framework to quantify the impacts of uncertainties in head tissues' dielectric properties on the induced SAR. The framework employs a surrogate model-assisted Monte Carlo (MC) technique, efficiently generating surrogate models of MRI observables (electric fields and SAR) and utilizing them to compute SAR statistics. Particularly, the framework leverages a high-dimensional model representation technique, which constructs the surrogate models of the MRI observables via univariate and bivariate component functions, approximated through generalized polynomial chaos expansions. The numerical results demonstrate the efficiency of the proposed technique, requiring significantly fewer deterministic simulations compared with traditional MC methods and other surrogate model-assisted MC techniques utilizing machine learning algorithms, all while maintaining high accuracy in SAR statistics. Specifically, the proposed framework constructs surrogate models of a local SAR with an average relative error of 0.28% using 289 simulations, outperforming the machine learning-based surrogate modeling techniques considered in this study. Furthermore, the SAR statistics obtained by the proposed framework reveal fluctuations of up to 30% in SAR values within specific head regions. These findings highlight the critical importance of considering dielectric property uncertainties to ensure MRI safety, particularly in 7 T MRI systems.

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.

Are we really targeting and stimulating DLPFC by placing transcranial electrical stimulation (tES) electrodes over F3/F4?

In many clinical trials involving transcranial electrical stimulation (tES), target electrodes are typically placed over DLPFC with the assumption that this will primarily stimulate the underlying brain region. However, our study aimed to evaluate the electric fields (EF) that are actually delivered and identify prefrontal regions that may be inadvertently targeted in DLPFC tES. Head models were generated from the Human Connectome Project database's T1 + T2-weighted MRIs of 80 healthy adults. Two common DLPFC montages were simulated; symmetric-F4/F3, and asymmetric-F4/Fp1. Averaged EF was extracted from (1) the center of the target electrode (F4), and (2) the top 1% of voxels showing the strongest EF in individualized EF maps. Interindividual variabilities were quantified with the standard deviation of EF peak location/value. Similar steps were repeated with 66 participants with methamphetamine use disorder (MUDs) as an independent clinical population. In healthy adults, the group-level location of EF peaks was situated in the medial-frontopolar, and the individualized EF peaks were positioned in a cube with a volume of 29 cm3 /46 cm3 (symmetric/asymmetric montages). EFs in the frontopolar area were significantly higher than EF "under" the target electrode in both symmetric (peak: 0.41 ± 0.06, F4:0.22 ± 0.04) and asymmetric (peak: 0.38 ± 0.04, F4:0.2 ± 0.04) montages (Heges'g > 0.7). Similar results with slight between-group differences were found in MUDs. We highlighted that in common DLPFC tES montages, in addition to interindividual/intergroup variability, the frontopolar received the highest EFs rather than DLPFC as the main target. We specifically recommended considering the potential involvement of the frontopolar area as a mechanism underlying the effectiveness of DLPFC tES protocols.

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.

The Relation between Induced Electric Field and TMS-Evoked Potentials: A Deep TMS-EEG Study

Transcranial magnetic stimulation (TMS) in humans induces electric fields (E-fields, EF) that perturb and modulate the brain’s endogenous neuronal activity and result in the generation of TMS-evoked potentials (TEPs). The exact relation of the characteristics of the induced E-field and the intensity of the brains’ response, as measured by electroencephalography (EEG), is presently unclear. In this pilot study, conducted on three healthy subjects and two patients with generalized epilepsy (total: 3 males, 2 females, mean age of 26 years; healthy: 2 males, 1 female, mean age of 25.7 years; patients: 1 male, 1 female, mean age of 26.5 years), we investigated the temporal and spatial relations of the E-field, induced by single-pulse stimuli, and the brain’s response to TMS. Brain stimulation was performed with a deep TMS device (BrainsWay Ltd., Jerusalem, Israel) and an H7 coil placed over the central area. The induced EF was computed on personalized anatomical models of the subjects through magneto quasi-static simulations. We identified specific time instances and brain regions that exhibit high positive or negative associations of the E-field with brain activity. In addition, we identified significant correlations of the brain’s response intensity with the strength of the induced E-field and finally prove that TEPs are better correlated with E-field characteristics than with the stimulator’s output. These observations provide further insight in the relation between E-field and the ensuing cortical activation, validate in a clinically relevant manner the results of E-field modeling and reinforce the view that personalized approaches should be adopted in the field of non-invasive brain stimulation.

Genetic Algorithm for TMS Coil Position Optimization in Stroke Treatment

Transcranial magnetic stimulation (TMS), a non-invasive technique to stimulate human brain, has been widely used in stroke treatment for its capability of regulating synaptic plasticity and promoting cortical functional reconstruction. As shown in previous studies, the high electric field (E-field) intensity around the lesion helps in the recovery of brain function, thus the spatial location and angle of coil truly matter for the significant correlation with therapeutic effect of TMS. But, the error caused by coil placement in current clinical setting is still non-negligible and a more precise coil positioning method needs to be proposed. In this study, two kinds of real brain stroke models of ischemic stroke and hemorrhagic stroke were established by inserting relative lesions into three human head models. A coil position optimization algorithm, based on the genetic algorithm (GA), was developed to search the spatial location and rotation angle of the coil in four 4 × 4 cm search domains around the lesion. It maximized the average intensity of the E-field in the voxel of interest (VOI). In this way, maximum 17.48% higher E-field intensity than that of clinical TMS stimulation was obtained. Besides, our method also shows the potential to avoid unnecessary exposure to the non-target regions. The proposed algorithm was verified to provide an optimal position after nine iterations and displayed good robustness for coil location optimization between different stroke models. To conclude, the optimized spatial location and rotation angle of the coil for TMS stroke treatment could be obtained through our algorithm, reducing the intensity and duration of human electromagnetic exposure and presenting a significant therapeutic potential of TMS for stroke.

Stochastic modeling of geometrical uncertainties on complex domains, with application to additive manufacturing and brain interface geometries

We present a stochastic modeling framework to represent and simulate spatially-dependent geometrical uncertainties on complex geometries. While the consideration of random geometrical perturbations has long been a subject of interest in computational engineering, most studies proposed so far have addressed the case of regular geometries such as cylinders and plates. Here, standard random field representations, such as Kahrunen-Loève expansions, can readily be used owing, in particular, to the relative simplicity to construct covariance operators on regular shapes. On the contrary, applying such techniques on arbitrary, non-convex domains remains difficult in general. In this work, we formulate a new representation for spatially-correlated geometrical uncertainties that allows complex domains to be efficiently handled. Building on previous contributions by the authors, the approach relies on the combination of a stochastic partial differential equation approach, introduced to capture salient features of the underlying geometry such as local curvature and singularities on the fly, and an information-theoretic model, aimed to enforce non-Gaussianity. More specifically, we propose a methodology where the interface of interest is immersed into a fictitious domain, and define algorithmic procedures to directly sample random perturbations on the manifold. A simple strategy based on statistical conditioning is also presented to update realizations and prevent self-intersections in the perturbed finite element mesh. We finally provide challenging examples to demonstrate the robustness of the framework, including the case of a gyroid structure produced by additive manufacturing and brain interfaces in patient-specific geometries. In both applications, we discuss suitable parameterization for the filtering operator and quantify the impact of the uncertainties through forward propagation.

Effect of skin conductivity on the electric field induced by transcranial stimulation techniques in different head models

This study aims at quantifying the effect that using different skin conductivity values has on the estimation of the electric (E)-field distribution induced by transcranial magnetic stimulation (TMS) and transcranial direct current stimulation (tDCS) in the brain of two anatomical models. The induced E-field was calculated with numerical simulations inside MIDA and Duke models, assigning to the skin a conductivity value estimated from a multi-layered skin model and three values taken from literature. The effect of skin conductivity variations on the local E-field induced by tDCS in the brain was up to 70%. In TMS, minor local differences, in the order of 20%, were obtained in regions of interest for the onset of possible side effects. Results suggested that an accurate model of the skin is necessary in all numerical studies that aim at precisely estimating the E-field induced during TMS and tDCS applications. This also highlights the importance of further experimental studies on human skin characterization, especially at low frequencies.

Electric field simulations for transcranial brain stimulation using FEM: an efficient implementation and error analysis

OBJECTIVE

Transcranial magnetic stimulation (TMS) and transcranial electric stimulation (TES) modulate brain activity non-invasively by generating electric fields either by electromagnetic induction or by injecting currents via skin electrodes. Numerical simulations based on anatomically detailed head models of the TMS and TES electric fields can help us to understand and optimize the spatial stimulation pattern in the brain. However, most realistic simulations are still slow, and the role of anatomical fidelity on simulation accuracy has not been evaluated in detail so far.

APPROACH

We present and validate a new implementation of the finite element method (FEM) for TMS and TES that is based on modern algorithms and libraries. We also evaluate the convergence of the simulations and estimate errors stemming from numerical and modelling aspects.

MAIN RESULTS

Comparisons with analytical solutions for spherical phantoms validate our new FEM implementation, which is three to six times faster than previous implementations. The convergence results suggest that accurately capturing the tissue geometry in addition to choosing a sufficiently accurate numerical method is of fundamental importance for accurate simulations.

SIGNIFICANCE

The new implementation allows for a substantial increase in computational efficiency of FEM TMS and TES simulations. This is especially relevant for applications such as the systematic assessment of model uncertainty and the optimization of multi-electrode TES montages. The results of our systematic error analysis allow the user to select the best tradeoff between model resolution and simulation speed for a specific application. The new FEM code is openly available as a part of our open-source software SimNIBS 3.0.

Conditions for numerically accurate TMS electric field simulation

BACKGROUND

Computational simulations of the E-field induced by transcranial magnetic stimulation (TMS) are increasingly used to understand its mechanisms and to inform its administration. However, characterization of the accuracy of the simulation methods and the factors that affect it is lacking.

OBJECTIVE

To ensure the accuracy of TMS E-field simulations, we systematically quantify their numerical error and provide guidelines for their setup.

METHOD

We benchmark the accuracy of computational approaches that are commonly used for TMS E-field simulations, including the finite element method (FEM) with and without superconvergent patch recovery (SPR), boundary element method (BEM), finite difference method (FDM), and coil modeling methods.

RESULTS

To achieve cortical E-field error levels below 2%, the commonly used FDM and 1st order FEM require meshes with an average edge length below 0.4 mm, 1st order SPR-FEM requires edge lengths below 0.8 mm, and BEM and 2nd (or higher) order FEM require edge lengths below 2.9 mm. Coil models employing magnetic and current dipoles require at least 200 and 3000 dipoles, respectively. For thick solid-conductor coils and frequencies above 3 kHz, winding eddy currents may have to be modeled.

CONCLUSION

BEM, FDM, and FEM all converge to the same solution. Compared to the common FDM and 1st order FEM approaches, BEM and 2nd (or higher) order FEM require significantly lower mesh densities to achieve the same error level. In some cases, coil winding eddy-currents must be modeled. Both electric current dipole and magnetic dipole models of the coil current can be accurate with sufficiently fine discretization.

Noninvasive Estimation of Electrical Properties From Magnetic Resonance Measurements via Global Maxwell Tomography and Match Regularization

OBJECTIVE

In this paper, we introduce global Maxwell tomography (GMT), a novel volumetric technique that estimates electric conductivity and permittivity by solving an inverse scattering problem based on magnetic resonance measurements.

METHODS

GMT relies on a fast volume integral equation solver, MARIE, for the forward path, and a novel regularization method, match regularization, designed specifically for electrical property estimation from noisy measurements. We performed simulations with three different tissue-mimicking numerical phantoms of different complexity, using synthetic transmit sensitivity maps with realistic noise levels as the measurements. We performed an experiment at 7 T using an eight-channel coil and a uniform phantom.

RESULTS

We showed that GMT could estimate relative permittivity and conductivity from noisy magnetic resonance measurements with an average error as low as 0.3% and 0.2%, respectively, over the entire volume of the numerical phantom. Voxel resolution did not affect GMT performance and is currently limited only by the memory of the graphics processing unit. In the experiment, GMT could estimate electrical properties within 5% of the values measured with a dielectric probe.

CONCLUSION

This work demonstrated the feasibility of GMT with match regularization, suggesting that it could be effective for accurate in vivo electrical property estimation. GMT does not rely on any symmetry assumption for the electromagnetic field, and can be generalized to estimate also the spin magnetization, at the expense of increased computational complexity.

SIGNIFICANCE

GMT could provide insight into the distribution of electromagnetic fields inside the body, which represents one of the key ongoing challenges for various diagnostic and therapeutic applications.

A principled approach to conductivity uncertainty analysis in electric field calculations

Uncertainty surrounding ohmic tissue conductivity impedes accurate calculation of the electric fields generated by non-invasive brain stimulation. We present an efficient and generic technique for uncertainty and sensitivity analyses, which quantifies the reliability of field estimates and identifies the most influential parameters. For this purpose, we employ a non-intrusive generalized polynomial chaos expansion to compactly approximate the multidimensional dependency of the field on the conductivities. We demonstrate that the proposed pipeline yields detailed insight into the uncertainty of field estimates for transcranial magnetic stimulation (TMS) and transcranial direct current stimulation (tDCS), identifies the most relevant tissue conductivities, and highlights characteristic differences between stimulation methods. Specifically, we test the influence of conductivity variations on (i) the magnitude of the electric field generated at each gray matter location, (ii) its normal component relative to the cortical sheet, (iii) its overall magnitude (indexed by the 98th percentile), and (iv) its overall spatial distribution. We show that TMS fields are generally less affected by conductivity variations than tDCS fields. For both TMS and tDCS, conductivity uncertainty causes much higher uncertainty in the magnitude as compared to the direction and overall spatial distribution of the electric field. Whereas the TMS fields were predominantly influenced by gray and white matter conductivity, the tDCS fields were additionally dependent on skull and scalp conductivities. Comprehensive uncertainty analyses of complex systems achieved by the proposed technique are not possible with classical methods, such as Monte Carlo sampling, without extreme computational effort. In addition, our method has the advantages of directly yielding interpretable and intuitive output metrics and of being easily adaptable to new problems.

Design of transcranial magnetic stimulation coils with optimal trade-off between depth, focality, and energy

OBJECTIVE

Transcranial magnetic stimulation (TMS) is a noninvasive brain stimulation technique used for research and clinical applications. Existent TMS coils are limited in their precision of spatial targeting (focality), especially for deeper targets. This paper presents a methodology for designing TMS coils to achieve optimal trade-off between the depth and focality of the induced electric field (E-field), as well as the energy required by the coil.

APPROACH

A multi-objective optimization technique is used for computationally designing TMS coils that achieve optimal trade-offs between E-field focality, depth, and energy (fdTMS coils). The fdTMS coil winding(s) maximize focality (minimize the volume of the brain region with E-field above a given threshold) while reaching a target at a specified depth and not exceeding predefined peak E-field strength and required coil energy. Spherical and MRI-derived head models are used to compute the fundamental depth-focality trade-off as well as focality-energy trade-offs for specific target depths.

MAIN RESULTS

Across stimulation target depths of 1.0-3.4 cm from the brain surface, the suprathreshold volume can be theoretically decreased by 42%-55% compared to existing TMS coil designs. The suprathreshold volume of a figure-8 coil can be decreased by 36%, 44%, or 46%, for matched, doubled, or quadrupled energy. For matched focality and energy, the depth of a figure-8 coil can be increased by 22%.

SIGNIFICANCE

Computational design of TMS coils could enable more selective targeting of the induced E-field. The presented results appear to be the first significant advancement in the depth-focality trade-off of TMS coils since the introduction of the figure-8 coil three decades ago, and likely represent the fundamental physical limit.

An FMM-FFT Accelerated SIE Simulator for Analyzing EM Wave Propagation in Mine Environments Loaded With Conductors

A fast and memory efficient three-dimensional full-wave simulator for analyzing electromagnetic (EM) wave propagation in electrically large and realistic mine tunnels/galleries loaded with conductors is proposed. The simulator relies on Muller and combined field surface integral equations (SIEs) to account for scattering from mine walls and conductors, respectively. During the iterative solution of the system of SIEs, the simulator uses a fast multipole method-fast Fourier transform (FMM-FFT) scheme to reduce CPU and memory requirements. The memory requirement is further reduced by compressing large data structures via singular value and Tucker decompositions. The efficiency, accuracy, and real-world applicability of the simulator are demonstrated through characterization of EM wave propagation in electrically large mine tunnels/galleries loaded with conducting cables and mine carts.

The ICVSIE: A General Purpose Integral Equation Method for Bio-Electromagnetic Analysis

OBJECTIVE

An internally combined volume surface integral equation (ICVSIE) for analyzing electromagnetic (EM) interactions with biological tissue and wide ranging diagnostic, therapeutic, and research applications, is proposed.

METHOD

The ICVSIE is a system of integral equations in terms of volume and surface equivalent currents in biological tissue subject to fields produced by externally or internally positioned devices. The system is created by using equivalence principles and solved numerically; the resulting current values are used to evaluate scattered and total electric fields, specific absorption rates, and related quantities.

RESULTS

The validity, applicability, and efficiency of the ICVSIE are demonstrated by EM analysis of transcranial magnetic stimulation, magnetic resonance imaging, and neuromuscular electrical stimulation.

CONCLUSION

Unlike previous integral equations, the ICVSIE is stable regardless of the electric permittivities of the tissue or frequency of operation, providing an application-agnostic computational framework for EM-biomedical analysis.

SIGNIFICANCE

Use of the general purpose and robust ICVSIE permits streamlining the development, deployment, and safety analysis of EM-biomedical technologies.

The influence of corticospinal activity on TMS-evoked activity and connectivity in healthy subjects: A TMS-EEG study

Combined transcranial magnetic stimulation (TMS) and electroencephalography (EEG) can be used to analyze cortical reactivity and connectivity. However, the effects of corticospinal and peripheral muscle activity on TMS-evoked potentials (TEPs) are not well understood. The aim of this paper is to evaluate the relationship between cortico-spinal activity, in the form of peripheral motor-evoked potentials (MEPs), and the TEPs from motor areas, along with the connectivity among activated brain areas. TMS was applied to left and right motor cortex (M1), separately, at motor threshold while multi-channel EEG responses were recorded in 17 healthy human subjects. Cortical excitability and source imaging analysis were performed for all trials at each stimulation location, as well as comparing trials resulting in MEPs to those without. Connectivity analysis was also performed comparing trials resulting in MEPs to those without. Cortical excitability results significantly differed between the MEP and no-MEP conditions for left M1 TMS at 60 ms (CP1, CP3, C1) and for right M1 TMS at 54 ms (CP6, C6). Connectivity analysis revealed higher outflow and inflow between M1 and somatosensory cortex bi-directionally for trials with MEPs than those without for both left M1 TMS (at 60, 100, 164 ms) and right M1 TMS (at 54, 100, and 164 ms). Both TEP amplitudes and connectivity measures related to motor and somatosensory areas ipsilateral to the stimulation were shown to correspond with peripheral MEP amplitudes. This suggests that cortico-spinal activation, along with the resulting somatosensory feedback, affects the cortical activity and dynamics within motor areas reflected in the TEPs. The findings suggest that TMS-EEG, along with adaptive connectivity estimators, can be used to evaluate the cortical dynamics associated with sensorimotor integration and proprioceptive manipulation along with the influence of peripheral muscle feedback.

The development and modelling of devices and paradigms for transcranial magnetic stimulation

Magnetic stimulation is a non-invasive neurostimulation technique that can evoke action potentials and modulate neural circuits through induced electric fields. Biophysical models of magnetic stimulation have become a major driver for technological developments and the understanding of the mechanisms of magnetic neurostimulation and neuromodulation. Major technological developments involve stimulation coils with different spatial characteristics and pulse sources to control the pulse waveform. While early technological developments were the result of manual design and invention processes, there is a trend in both stimulation coil and pulse source design to mathematically optimize parameters with the help of computational models. To date, macroscopically highly realistic spatial models of the brain, as well as peripheral targets, and user-friendly software packages enable researchers and practitioners to simulate the treatment-specific and induced electric field distribution in the brains of individual subjects and patients. Neuron models further introduce the microscopic level of neural activation to understand the influence of activation dynamics in response to different pulse shapes. A number of models that were designed for online calibration to extract otherwise covert information and biomarkers from the neural system recently form a third branch of modelling.