3D modeling of the total electric field induced by transcranial magnetic stimulation using the boundary element method

Quasistatic approximation in neuromodulation

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

Bias correction for phase-based cr-MREPT using low resolution B1+ magnitude

ObjectiveFull-form Magnetic Resonance Electrical Properties Tomography (MREPT) requires bothB1+magnitude and phase information. SinceB1+phase can be obtained faster and with higher SNR compared toB1+magnitude, several phase-based methods have been developed for conductivity imaging. However, phase-based methods suffer from a concave bias due to the assumption that∇|B1+|is negligible in the ROI.ApproachIn this paper, we re-derive the central equation of phase-based cr-MREPT without assuming that∇|B1+|is negligible and thus propose a correction method directly integrated into the equation system.Main resultsProposed method successfully corrects the concave bias on both simulated and experimental data and significantly increases image quality.SignificanceThe proposed correction method depends on a very low-resolution|B1+|map, and therefore the imaging time does not increase significantly for obtainingB1+magnitude. Moreover, correction can be achieved using simulatedB1+magnitude, hence completely removing the additional imaging requirement.

Software Package for Transcranial Magnetic Stimulation Coil and Coil Array Analysis and Design

Objective

This study aims to describe a MATLAB software package for transcranial magnetic stimulation (TMS) coil analysis and design.

Approach

Electric and magnetic fields of the coils as well as their self- and mutual (for coil arrays) inductances are computed, with or without a magnetic core. Solid and stranded (Litz wire) conductors are also taken into consideration. The starting point is the centerline of a coil conductor(s), which is a 3D curve defined by the user. Then, a wire mesh and a computer aided design (CAD) mesh for the volume conductor of a given cross-section (circular, elliptical, or rectangular) are automatically generated. Self- and mutual inductances of the coil(s) are computed. Given the conductor current and its time derivative, electric and magnetic fields of the coil(s) are determined anywhere in space.Computations are performed with the fast multipole method (FMM), which is the most efficient way to evaluate the fields of many elementary current elements (current dipoles) comprising the current carrying conductor at a large number of observation points. This is the major underlying mathematical operation behind both inductance and field calculations.

Main Results

The wire-based approach enables precise replication of even the most complex physical conductor geometries, while the FMM acceleration quickly evaluates large quantities of elementary current filaments. Agreement to within 0.74% was obtained between the inductances computed by the FMM method and ANSYS Maxwell 3D for the same coil model. Although not provided in this study, it is possible to evaluate non-linear magnetic cores in addition to the linear core exemplified. An experimental comparison was carried out against a physical MagVenture C-B60 coil; the measured and simulated inductances differed by only 1.25%, and nearly perfect correlation was found between the measured and computed E-field values at each observation point.

Significance

The developed software package is applicable to any quasistatic inductor design, not necessarily to the TMS coils only.

[The influence of tissue conductivity on the calculation of electric field in the transcranial magnetic stimulation head model]

In transcranial magnetic stimulation (TMS), the conductivity of brain tissue is obtained by using diffusion tensor imaging (DTI) data processing. However, the specific impact of different processing methods on the induced electric field in the tissue has not been thoroughly studied. In this paper, we first used magnetic resonance image (MRI) data to create a three-dimensional head model, and then estimated the conductivity of gray matter (GM) and white matter (WM) using four conductivity models, namely scalar (SC), direct mapping (DM), volume normalization (VN) and average conductivity (MC), respectively. Isotropic empirical conductivity values were used for the conductivity of other tissues such as the scalp, skull, and cerebrospinal fluid (CSF), and then the TMS simulations were performed when the coil was parallel and perpendicular to the gyrus of the target. When the coil was perpendicular to the gyrus where the target was located, it was easy to get the maximum electric field in the head model. The maximum electric field in the DM model was 45.66% higher than that in the SC model. The results showed that the conductivity component along the electric field direction of which conductivity model was smaller in TMS, the induced electric field in the corresponding domain corresponding to the conductivity model was larger. This study has guiding significance for TMS precise stimulation.

Low-frequency rTMS targeting individual self-initiated finger-tapping task activation modulates the amplitude of local neural activity in the putamen

Repetitive transcranial magnetic stimulation (rTMS) has been used in the clinical treatment of Parkinson's disease (PD). Most of rTMS studies on PD used high-frequency stimulation; however, excessive nonvoluntary movement may represent abnormally cortical excitability, which is likely to be suppressed by low-frequency rTMS. Decreased neural activity in the basal ganglia on functional magnetic resonance imaging (fMRI) is a characteristic of PD. In the present study, we found that low-frequency (1 Hz) rTMS targeting individual finger-tapping activation elevated the amplitude of local neural activity (percentage amplitude fluctuation, PerAF) in the putamen as well as the functional connectivity (FC) of the stimulation target and basal ganglia in healthy participants. These results provide evidence for our hypothesis that low-frequency rTMS over the individual task activation site can modulate deep brain functions, and that FC might serve as a bridge transmitting the impact of rTMS to the deep brain regions. It suggested that a precisely localized individual task activation site can act as a target for low-frequency rTMS when it is used as a therapeutic tool for PD.

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.

Angle-tuned coils: attractive building blocks for TMS with improved depth-spread performance

Objective.A novel angle-tuned ring coil is proposed for improving the depth-spread performance of transcranial magnetic stimulation (TMS) coils and serve as the building blocks for high-performance composite coils and multisite TMS systems.Approach.Improving depth-spread performance by reducing field divergence through creating a more elliptical emitted field distribution from the coil. To accomplish that, instead of enriching the Fourier components along the planarized (x-y) directions, which requires different arrays to occupy large brain surface areas, we worked along the radial (z) direction by using tilted coil angles and stacking coil numbers to reduce the divergence of the emitted near field without occupying large head surface areas. The emitted electric field distributions were theoretically simulated in spherical and real human head models to analyze the depth-spread performance of proposed coils and compare with existing figure-8 coils. The results were then experimentally validated with field probes andin-vivoanimal tests.Main results.The proposed 'angle-tuning' concept improves the depth-spread performance of individual coils with a significantly smaller footprint than existing and proposed coils. For composite structures, using the proposed coils as basic building blocks simplifies the design and manufacturing process and helps accomplish a leading depth-spread performance. In addition, the footprint of the proposed system is intrinsically small, making them suitable for multisite stimulations of inter and intra-hemispheric brain regions with an improved spread and less electric field divergence.Significance.Few brain functions are operated by isolated single brain regions but rather by coordinated networks involving multiple brain regions. Simultaneous or sequential multisite stimulations may provide tools for mechanistic studies of brain functions and the treatment of neuropsychiatric disorders. The proposed AT coil goes beyond the traditional depth-spread tradeoff rule of TMS coils, which provides the possibility of building new composite structures and new multisite TMS tools.

Optimal Design of Transcranial Magnetic Stimulation Coil with Iron Core

OBJECTIVE

Iron core coils offer a passive way to increase the induced electric field intensity during transcranial magnetic stimulation (TMS), but the influences of core position and dimensions on coil performance have not been elaborately discussed before.

APPROACH

In this study, with the basic figure-of-eight (Fo8) and slinky coil structures, iron core coil optimization is performed with the finite element method considering core position and dimensions. A performance factor combining performance parameters, including the maximum induced electric field, stimulation depth, focus, and heat loss, is utilized to evaluate the comprehensive coil performance.

MAIN RESULTS

According to the performance factor, both iron core coils obtain the best overall performance with a fill factor 0.4 and the two legs of the iron core close to the inner sides of the coil. Finally, three prototypes are constructed-the basic, optimized, and full-size slinky iron core coil-and magnetic field detection demonstrates a good agreement with the simulation results.

SIGNIFICANCE

The proposed systematic optimization approach for iron core coil based on Fo8 and slinky basic structure can be applied to improve TMS coil performance, reduce power requirements, and guide the design of other iron core TMS coils.

Fast Individualized High-resolution Electric Field Modeling for Computational TMS Neuronavigation

Transcranial Magnetic Stimulation (TMS) is a non-invasive method for safe and painless activation of cortical neurons. On-line visualization of the induced Electric field (E-field) has the potential to improve quantitative targeting and dosing of stimulation, however present commercially available systems are limited by simplified approximations of the anatomy. Here, we developed a near real-time method to accurately approximate the induced E-field of a freely moving TMS coil with an individualized high-resolution head model. We use a set of magnetic dipoles around the head to approximate the total E-field of a moving TMS coil. First, we match the incident field of the dipole basis set with the incident E-field of the moving coil. Then, based on the principle of superposition and uniqueness of the solutions, we apply same basis coefficients to the total E-field of the basis set. The computed E-fields results show high similarity with an established TMS solver both in terms of the amplitude and the spatial distribution patterns. The proposed method enables rapid visualization of the E-field with ~100 ms of computation time enabling interactive planning, targeting, dosing and coil positioning tasks for TMS neuronavigation.

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.

Magnetically Induced Temporal Interference for Focal and Deep-Brain Stimulation

Transcranial magnetic stimulation (TMS) is a non-invasive brain stimulation technique that has been clinically applied for neural modulation. Conventional TMS systems are restricted by the trade-off between depth penetration and the focality of the induced electric field. In this study, we integrated the concept of temporal interference (TI) stimulation, which has been demonstrated as a non-invasive deep-brain stimulation method, with magnetic stimulation in a four-coil configuration. The attenuation depth and spread of the electric field were obtained by performing numerical simulation. Consequently, the proposed temporally interfered magnetic stimulation scheme was demonstrated to be capable of stimulating deeper regions of the brain model while maintaining a relatively narrow spread of the electric field, in comparison to conventional TMS systems. These results demonstrate that TI magnetic stimulation could be a potential candidate to recruit brain regions underneath the cortex. Additionally, by controlling the geometry of the coil array, an analogous relationship between the field depth and focality was observed, in the case of the newly proposed method. The major limitations of the methods, however, would be the considerable intensity and frequency of the input current, followed by the frustration in the thermal management of the hardware.

Rapid whole-brain electric field mapping in transcranial magnetic stimulation using deep learning

Transcranial magnetic stimulation (TMS) is a non-invasive neurostimulation technique that is increasingly used in the treatment of neuropsychiatric disorders and neuroscience research. Due to the complex structure of the brain and the electrical conductivity variation across subjects, identification of subject-specific brain regions for TMS is important to improve the treatment efficacy and understand the mechanism of treatment response. Numerical computations have been used to estimate the stimulated electric field (E-field) by TMS in brain tissue. But the relative long computation time limits the application of this approach. In this paper, we propose a deep-neural-network based approach to expedite the estimation of whole-brain E-field by using a neural network architecture, named 3D-MSResUnet and multimodal imaging data. The 3D-MSResUnet network integrates the 3D U-net architecture, residual modules and a mechanism to combine multi-scale feature maps. It is trained using a large dataset with finite element method (FEM) based E-field and diffusion magnetic resonance imaging (MRI) based anisotropic volume conductivity or anatomical images. The performance of 3D-MSResUnet is evaluated using several evaluation metrics and different combinations of imaging modalities and coils. The experimental results show that the output E-field of 3D-MSResUnet provides reliable estimation of the E-field estimated by the state-of-the-art FEM method with significant reduction in prediction time to about 0.24 second. Thus, this study demonstrates that neural networks are potentially useful tools to accelerate the prediction of E-field for TMS targeting.

Electric field calculation and peripheral nerve stimulation prediction for head and body gradient coils

PURPOSE

To demonstrate and validate electric field (E-field) calculation and peripheral nerve stimulation (PNS) prediction methods that are accurate, computationally efficient, and that could be used to inform regulatory standards.

METHODS

We describe a simplified method for calculating the spatial distribution of induced E-field over the volume of a body model given a gradient coil vector potential field. The method is easily programmed without finite element or finite difference software, allowing for straightforward and computationally efficient E-field evaluation. Using these E-field calculations and a range of body models, population-weighted PNS thresholds are determined using established methods and compared against published experimental PNS data for two head gradient coils and one body gradient coil.

RESULTS

A head-gradient-appropriate chronaxie value of 669 µs was determined by meta-analysis. Prediction errors between our calculated PNS parameters and the corresponding experimentally measured values were ~5% for the body gradient and ~20% for the symmetric head gradient. Our calculated PNS parameters matched experimental measurements to within experimental uncertainty for 73% of ∆G_min estimates and 80% of SR_min estimates. Computation time is seconds for initial E-field maps and milliseconds for E-field updates for different gradient designs, allowing for highly efficient iterative optimization of gradient designs and enabling new dimensions in PNS-optimal gradient design.

CONCLUSIONS

We have developed accurate and computationally efficient methods for prospectively determining PNS limits, with specific application to head gradient coils.

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.

Fast computational optimization of TMS coil placement for individualized electric field targeting

Background:

During transcranial magnetic stimulation (TMS) a coil placed on the scalp is used to non-invasively modulate activity of targeted brain networks via a magnetically induced electric field (E-field). Ideally, the E-field induced during TMS is concentrated on a targeted cortical region of interest (ROI). Determination of the coil position and orientation that best achieve this objective presently requires a large computational effort.

Objective:

To improve the accuracy of TMS we have developed a fast computational auxiliary dipole method (ADM) for determining the optimum coil position and orientation. The optimum coil placement maximizes the E-field along a predetermined direction or, alternatively, the overall E-field magnitude in the targeted ROI. Furthermore, ADM can assess E-field uncertainty resulting from precision limitations of TMS coil placement protocols.

Method:

ADM leverages the electromagnetic reciprocity principle to compute rapidly the TMS induced E-field in the ROI by using the E-field generated by a virtual constant current source residing in the ROI. The framework starts by solving for the conduction currents resulting from this ROI current source. Then, it rapidly determines the average E-field induced in the ROI for each coil position by using the conduction currents and a fast-multipole method. To further speed-up the computations, the coil is approximated using auxiliary dipoles enabling it to represent all coil orientations for a given coil position with less than 600 dipoles.

Results:

Using ADM, the E-fields generated in an MRI-derived head model when the coil is placed at 5900 different scalp positions and 360 coil orientations per position (over 2.1 million unique configurations) can be determined in under 15 min on a standard laptop computer. This enables rapid extraction of the optimum coil position and orientation as well as the E-field variation resulting from coil positioning uncertainty. ADM is implemented in SimNIBS 3.2.

Conclusion:

ADM enables the rapid determination of coil placement that maximizes E-field delivery to a specific brain target. This method can find the optimum coil placement in under 15 min enabling its routine use for TMS. Furthermore, it enables the fast quantification of uncertainty in the induced E-field due to limited precision of TMS coil placement protocols, enabling minimization and statistical analysis of the E-field dose variability.

Focality of the Induced E-Field Is a Contributing Factor in the Choice of TMS Parameters: Evidence from a 3D Computational Model of the Human Brain

Transcranial magnetic stimulation (TMS) is a promising, non-invasive approach in the diagnosis and treatment of several neurological conditions. However, the specific results in the cortex of the magnitude and spatial distribution of the secondary electrical field (E-field) resulting from TMS at different stimulation sites/orientations and varied TMS parameters are not clearly understood. The objective of this study is to identify the impact of TMS stimulation site and coil orientation on the induced E-field, including spatial distribution and the volume of activation in the cortex across brain areas, and hence demonstrate the need for customized optimization, using a three-dimensional finite element model (FEM). A considerable difference was noted in E-field values and distribution at different brain areas. We observed that the volume of activated cortex varied from 3000 to 7000 mm3 between the selected nine clinically relevant coil locations. Coil orientation also changed the induced E-field by a maximum of 10%, and we noted the least optimal values at the standard coil orientation pointing to the nose. The volume of gray matter activated varied by 10% on average between stimulation sites in homologous brain areas in the two hemispheres of the brain. This FEM simulation model clearly demonstrates the importance of TMS parameters for optimal results in clinically relevant brain areas. The results show that TMS parameters cannot be interchangeably used between individuals, hemispheres, and brain areas. The focality of the TMS induced E-field along with its optimal magnitude should be considered as critical TMS parameters that should be individually optimized.

A generalized workflow for conducting electric field-optimized, fMRI-guided, transcranial magnetic stimulation

Transcranial magnetic stimulation (TMS) is a noninvasive method to stimulate the cerebral cortex that has applications in psychiatry, such as in the treatment of depression and anxiety. Although many TMS targeting methods that use figure-8 coils exist, many do not account for individual differences in anatomy or are not generalizable across target sites. This protocol combines functional magnetic resonance imaging (fMRI) and iterative electric-field (E-field) modeling in a generalized approach to subject-specific TMS targeting that is capable of optimizing the stimulation site and TMS coil orientation. To apply this protocol, the user should (i) operationally define a region of interest (ROI), (ii) generate the head model from the structural MRI data, (iii) preprocess the functional MRI data, (iv) identify the single-subject stimulation site within the ROI, and (iv) conduct E-field modeling to identify the optimal coil orientation. In comparison with standard targeting methods, this approach demonstrates (i) reduced variability in the stimulation site across subjects, (ii) reduced scalp-to-cortical-target distance, and (iii) reduced variability in optimal coil orientation. Execution of this protocol requires intermediate-level skills in structural and functional MRI processing. This protocol takes ~24 h to complete and demonstrates how constrained fMRI targeting combined with iterative E-field modeling can be used as a general method to optimize both the TMS coil site and its orientation.

Obtaining accurate and calibrated coil models for transcranial magnetic stimulation using magnetic field measurements

Currently, simulations of the induced currents in the brain produced by transcranial magnetic stimulation (TMS) are used to elucidate the regions reached by stimuli. However, models commonly found in the literature are too general and neglect imperfections in the windings. Aiming to predict the stimulation sites in patients requires precise modeling of the electric field (E-field), and a proper calibration to adequate to the empirical data of the particular coil employed. Furthermore, most fabricators do not provide precise information about the coil geometries, and even using X-ray images may lead to subjective interpretations. We measured the three components of the vector magnetic field induced by a TMS figure-8 coil with spatial resolutions of up to 1 mm. Starting from a computerized tomography-based coil model, we applied a multivariate optimization algorithm to automatically modify the original model and obtain one that optimally fits the measurements. Differences between models were assessed in a human brain mesh using the finite-elements method showing up to 6% variations in the E-field magnitude. Our calibrated model could increase the precision of the estimated E-field induced in the brain during TMS, enhance the accuracy of delivered stimulation during functional brain mapping, and improve dosimetry for repetitive TMS. Graphical Abstract Geometrical model of TMS coil based on TAC images is optimally deformed to match magnetic field measurements. The calibrated model's induced electric field in the brain differs from the original.

A robust electrical conductivity imaging method with total variation and wavelet regularization

PURPOSE

This study aims to develop and evaluate a robust conductivity imaging method that combines total variation and wavelet regularization to enhance the accuracy of conductivity maps.

THEORY AND METHODS

The proposed approach is based on a gradient-based method. The central equation is derived from Maxwell's equation and describes the relationship between conductivity and the transceive phase. A linear system equation is obtained via a finite-difference method and solved using a least-squares method. Total variation and wavelet transform regularization terms are added to the minimization problem and solved using the Split Bregman method to improve reconstruction stability. The proposed approach is compared with conventional and gradient-based methods. Numerical simulations are performed to validate the accuracy of the developed method, and the effects of noise are determined. Phantom and in vivo experiments are conducted at 3 T to verify the clinical applicability of the proposed method.

RESULTS

Numerical simulations show that the proposed method is more robust than other methods and can suppress the effects of noise. The quantitative conductivity value of the phantom experiment agrees with the measured value. The in vivo experiment results present a clear structure, and the conductivity value of the tumor region is significantly higher than that around healthy tissues.

CONCLUSION

The proposed electrical conductivity imaging method can improve the quality of conductivity reconstruction, and thus, has future clinical applications.

Patient Semi-specific Computational Modeling of Electromagnetic Stimulation Applied to Neuroprotective Treatments in Acute Ischemic Stroke

Neuroprotective effects of pulsed electromagnetic fields (PEMFs) have been demonstrated both in vivo and in vitro. Moreover, preliminary clinical studies have been conducted and suggested PEMFs as a possible alternative therapy to treat acute ischemic stroke. In this work, we show that it's possible to build-up a patient semi-specific head model, where the 3D reconstruction of the ischemic lesion of the patient under treatment is inserted in the head of the human body model "Duke" (v.1.0, Zurich MedTech AG). The semi-specific model will be used in the randomized, placebo-controlled, double-blind study currently ongoing. Three patients were modelled and simulated, and results showed that each ischemic lesion experiences a magnetic flux density field comparable to the one for which biological effects have been attested. Such a kind of dosimetric analysis reveals a reliable tool to assess the correlation between levels of exposure and the beneficial effect. Thus, once the on-going double blind study is complete it will prove if PEMFs treatment triggers a clinical effect, and we will then be able to characterize a dose-response curve with the methodology arranged in this study.

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.

Influence of Anatomical Model and Skin Conductivity on the Electric Field Induced in the Head by Transcranial Magnetic Stimulation

Numerical evaluation of the electromagnetic (EM) quantities induced inside the brain during transcranial magnetic stimulation (TMS) applications is a fundamental step to obtain the optimization of the treatment in terms of coil position and current intensity. In this sense, the human head model considered and the electromagnetic properties used to characterize the tissues have an influence on the EM solution. Thus, the aim of this study is to evaluate how different skin conductivities and different computational head models, i.e. the ViP Duke and the MIDA, influence the electric field induced inside the brain by a typical TMS coil.

Variation in Reported Human Head Tissue Electrical Conductivity Values

Electromagnetic source characterisation requires accurate volume conductor models representing head geometry and the electrical conductivity field. Head tissue conductivity is often assumed from previous literature, however, despite extensive research, measurements are inconsistent. A meta-analysis of reported human head electrical conductivity values was therefore conducted to determine significant variation and subsequent influential factors. Of 3121 identified publications spanning three databases, 56 papers were included in data extraction. Conductivity values were categorised according to tissue type, and recorded alongside methodology, measurement condition, current frequency, tissue temperature, participant pathology and age. We found variation in electrical conductivity of the whole-skull, the spongiform layer of the skull, isotropic, perpendicularly- and parallelly-oriented white matter (WM) and the brain-to-skull-conductivity ratio (BSCR) could be significantly attributed to a combination of differences in methodology and demographics. This large variation should be acknowledged, and care should be taken when creating volume conductor models, ideally constructing them on an individual basis, rather than assuming them from the literature. When personalised models are unavailable, it is suggested weighted average means from the current meta-analysis are used. Assigning conductivity as: 0.41 S/m for the scalp, 0.02 S/m for the whole skull, or when better modelled as a three-layer skull 0.048 S/m for the spongiform layer, 0.007 S/m for the inner compact and 0.005 S/m for the outer compact, as well as 1.71 S/m for the CSF, 0.47 S/m for the grey matter, 0.22 S/m for WM and 50.4 for the BSCR.

Use of dielectric padding to eliminate low convective field artifact in cr-MREPT conductivity images

PURPOSE

Convection-reaction equation-based magnetic resonance electrical properties tomography (cr-MREPT) provides conductivity images that are boundary artifact-free and robust against noise. However, these images suffer from the low convective field (LCF) artifact. We propose to use dielectric pads to alter the transmit magnetic field (B₁ ⁺ ), shift the LCF region, and eliminate the LCF artifact.

METHODS

Computer simulations were conducted to analyze the effects of pad electrical properties, pad thickness, pad height, arc angle, and thickness of the pad-object gap. In 3T MR experiments, water pads and BaTiO₃ pads were used with agar-saline phantoms. Two data sets (e.g., with the pad located on the left or on the right of the object [phantom]) were acquired, and the corresponding linear systems were simultaneously solved to get LCF artifact-free conductivity images.

RESULTS

A pad needed to have 180° arc angle and the same height with the phantom for maximum benefit. Increasing the pad thickness and/or the relative permittivity of the pad increased the LCF shift, whereas excessive amounts of these parameters caused errors in conductivity reconstructions because the effect of neglected B_z terms became noticeable. Conductivity of the pad, on the other hand, had minimal effect on elimination of the LCF artifact. Combining 2 data sets (i.e., with 2 different dielectric pad positions) resulted in more accurate conductivity maps (low L² -errors) as opposed to no pad or single pad cases in experiments and simulations.

CONCLUSIONS

Using the proposed technique, LCF artifact is significantly removed, and the reconstructed conductivity values are improved.

The Resistivity of Human Brain Tumours In Vivo

The histological structure of tumour tissues differs from healthy brain tissues. It can therefore be assumed that there are differences also in the electrical characteristics of these tissues. The electrical characteristics of the tissues define how electric current is distributed within volume conductors, such as the human body or head. Incorrect values affect, for example, the accuracy of impedance tomography or EEG source localisation. However, no controlled experimental data for human in vivo brain tumour resistivity values have been reported thus far. We have developed a controlled method for detecting the electrical resistivities of living brain tissue and investigated different types of brain tumours. The measurements were taken during brain surgeries conducted to remove the tumours. For analysis purposes, the tumours were divided into the following categories: meningiomas, low-grade gliomas, high-grade gliomas (glioblastomas) and other tumours or lesions. The averages of the measured resistivity values were 530 Ω-cm for meningiomas, 160 Ω-cm for low-grade gliomas, and 498 Ω-cm for high-grade gliomas. The differences in high- and low-grade glioma values and meningioma and low-grade glioma values were statistically highly significant. The tumour values were also compared to surrounding healthy brain tissues, and the difference ranged from 40 to 330%. The results suggest that certain tumour types have different electronic properties and that the resistivity values could be used to distinguish tumour tissue from surrounding healthy tissue and to identify and classify certain brain tumour types.

Electrically Small Dipole Antenna Probe for Quasistatic Electric Field Measurements in Transcranial Magnetic Stimulation

The present paper designs, constructs, and tests an electrically small dipole antenna probe for the measurement of electric field distributions with the ultimate purpose to directly measure electric fields induced by a transcranial magnetic stimulation (TMS) coil. Its unique features include applicability to measurements in both air and conducting medium, high spatial resolution, large frequency band from 100 Hz to 300 KHz, efficient feedline isolation via a printed Dyson balun, and accurate mitigation of noise. Prior work in this area is thoroughly reviewed. The proposed probe design is realized in hardware; implementation details and design tradeoffs are described. Test data are presented for the measurement of a constant wave capacitor electric field, demonstrating the probe's ability to properly measure electric fields caused by a charge distribution. Test data are also presented for the measurement of a constant wave solenoidal electric field, demonstrating the probe's ability to measure electric fields caused by Faraday's law of induction. Those are the primary fields for the transcranial magnetic stimulation. Further steps necessary for the application of this probe as an instrument for TMS coil design are discussed.

Simulation of electromyographic recordings following transcranial magnetic stimulation

Transcranial magnetic stimulation (TMS) is a technique that enables noninvasive manipulation of neural activity and holds promise in both clinical and basic research settings. The effect of TMS on the motor cortex is often measured by electromyography (EMG) recordings from a small hand muscle. However, the details of how TMS generates responses measured with EMG are not completely understood. We aim to develop a biophysically detailed computational model to study the potential mechanisms underlying the generation of EMG signals following TMS. Our model comprises a feed-forward network of cortical layer 2/3 cells, which drive morphologically detailed layer 5 corticomotoneuronal cells, which in turn project to a pool of motoneurons. EMG signals are modeled as the sum of motor unit action potentials. EMG recordings from the first dorsal interosseous muscle were performed in four subjects and compared with simulated EMG signals. Our model successfully reproduces several characteristics of the experimental data. The simulated EMG signals match experimental EMG recordings in shape and size, and change with stimulus intensity and contraction level as in experimental recordings. They exhibit cortical silent periods that are close to the biological values and reveal an interesting dependence on inhibitory synaptic transmission properties. Our model predicts several characteristics of the firing patterns of neurons along the entire pathway from cortical layer 2/3 cells down to spinal motoneurons and should be considered as a viable tool for explaining and analyzing EMG signals following TMS. NEW & NOTEWORTHY A biophysically detailed model of EMG signal generation following transcranial magnetic stimulation (TMS) is proposed. Simulated EMG signals match experimental EMG recordings in shape and amplitude. Motor-evoked potential and cortical silent period properties match experimental data. The model is a viable tool to analyze, explain, and predict EMG signals following TMS.

A Quasi-Static Boundary Element Approach With Fast Multipole Acceleration for High-Resolution Bioelectromagnetic Models

OBJECTIVE

We develop a new accurate version of the boundary element fast multipole method for transcranial magnetic stimulation (TMS) related problems. This method is based on the surface-charge formulation and is using the highly efficient fast multipole accelerator along with analytical computations of neighbor surface integrals.

RESULTS

The method accuracy is demonstrated by comparison with the proven commercial finite-element method (FEM) software ANSYS Maxwell 18.2 2017 operating on unstructured grids and with adaptive mesh refinement. Five realistic high-definition head models from the Population Head Repository (IT'IS Foundation, Switzerland) have been acquired and augmented with a commercial TMS coil model (MRi-B91, MagVenture, Denmark). For each head model, simulations with our method and simulations with the FEM software ANSYS Maxwell 18.2 2017 have been performed. These simulations have been compared with each other and an excellent agreement was established in every case.

SIGNIFICANCE

At the same time, our new method runs approximately 500 times faster than the ANSYS FEM, finishes in about 200 s on a standard server, and naturally provides a submillimeter field resolution, which is justified using mesh refinement.

CONCLUSIONS

Our method can be applied to modeling of brain stimulation and recording technologies such as TMS and magnetoencephalography, and has the potential to become a real-time high-resolution simulation tool.

A high-resolution computational localization method for transcranial magnetic stimulation mapping

BACKGROUND

Transcranial magnetic stimulation (TMS) is used for the mapping of brain motor functions. The complexity of the brain deters determining the exact localization of the stimulation site using simplified methods (e.g., the region below the center of the TMS coil) or conventional computational approaches.

OBJECTIVE

This study aimed to present a high-precision localization method for a specific motor area by synthesizing computed non-uniform current distributions in the brain for multiple sessions of TMS.

METHODS

Peritumoral mapping by TMS was conducted on patients who had intra-axial brain neoplasms located within or close to the motor speech area. The electric field induced by TMS was computed using realistic head models constructed from magnetic resonance images of patients. A post-processing method was implemented to determine a TMS hotspot by combining the computed electric fields for the coil orientations and positions that delivered high motor-evoked potentials during peritumoral mapping. The method was compared to the stimulation site localized via intraoperative direct brain stimulation and navigated TMS.

RESULTS

Four main results were obtained: 1) the dependence of the computed hotspot area on the number of peritumoral measurements was evaluated; 2) the estimated localization of the hand motor area in eight non-affected hemispheres was in good agreement with the position of a so-called "hand-knob"; 3) the estimated hotspot areas were not sensitive to variations in tissue conductivity; and 4) the hand motor areas estimated by this proposal and direct electric stimulation (DES) were in good agreement in the ipsilateral hemisphere of four glioma patients.

CONCLUSION(S)

The TMS localization method was validated by well-known positions of the "hand-knob" in brains for the non-affected hemisphere, and by a hotspot localized via DES during awake craniotomy for the tumor-containing hemisphere.

Rehabilitating the addicted brain with transcranial magnetic stimulation

Substance use disorders (SUDs) are one of the leading causes of morbidity and mortality worldwide. In spite of considerable advances in understanding the neural underpinnings of SUDs, therapeutic options remain limited. Recent studies have highlighted the potential of transcranial magnetic stimulation (TMS) as an innovative, safe and cost-effective treatment for some SUDs. Repetitive TMS (rTMS) influences neural activity in the short and long term by mechanisms involving neuroplasticity both locally, under the stimulating coil, and at the network level, throughout the brain. The long-term neurophysiological changes induced by rTMS have the potential to affect behaviours relating to drug craving, intake and relapse. Here, we review TMS mechanisms and evidence that rTMS is opening new avenues in addiction treatments.

How much detail is needed in modeling a transcranial magnetic stimulation figure-8 coil: Measurements and brain simulations

Background

Despite TMS wide adoption, its spatial and temporal patterns of neuronal effects are not well understood. Although progress has been made in predicting induced currents in the brain using realistic finite element models (FEM), there is little consensus on how a magnetic field of a typical TMS coil should be modeled. Empirical validation of such models is limited and subject to several limitations.

Methods

We evaluate and empirically validate models of a figure-of-eight TMS coil that are commonly used in published modeling studies, of increasing complexity: simple circular coil model; coil with in-plane spiral winding turns; and finally one with stacked spiral winding turns. We will assess the electric fields induced by all 3 coil models in the motor cortex using a computer FEM model. Biot-Savart models of discretized wires were used to approximate the 3 coil models of increasing complexity. We use a tailored MR based phase mapping technique to get a full 3D validation of the incident magnetic field induced in a cylindrical phantom by our TMS coil. FEM based simulations on a meshed 3D brain model consisting of five tissues types were performed, using two orthogonal coil orientations.

Results

Substantial differences in the induced currents are observed, both theoretically and empirically, between highly idealized coils and coils with correctly modeled spiral winding turns. Thickness of the coil winding turns affect minimally the induced electric field, and it does not influence the predicted activation.

Conclusion

TMS coil models used in FEM simulations should include in-plane coil geometry in order to make reliable predictions of the incident field. Modeling the in-plane coil geometry is important to correctly simulate the induced electric field and to correctly make reliable predictions of neuronal activation

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.

In-vivo measurements of human brain tissue conductivity using focal electrical current injection through intracerebral multicontact electrodes

In-vivo measurements of human brain tissue conductivity at body temperature were conducted using focal electrical currents injected through intracerebral multicontact electrodes. A total of 1,421 measurements in 15 epileptic patients (age: 28 ± 10) using a radiofrequency generator (50 kHz current injection) were analyzed. Each contact pair was classified as being from healthy (gray matter, n = 696; white matter, n = 530) or pathological (epileptogenic zone, n = 195) tissue using neuroimaging analysis of the local tissue environment and intracerebral EEG recordings. Brain tissue conductivities were obtained using numerical simulations based on conductivity estimates that accounted for the current flow in the local brain volume around the contact pairs (a cube with a side length of 13 mm). Conductivity values were 0.26 S/m for gray matter and 0.17 S/m for white matter. Healthy gray and white matter had statistically different median impedances (P < 0.0001). White matter conductivity was found to be homogeneous as normality tests did not find evidence of multiple subgroups. Gray matter had lower conductivity in healthy tissue than in the epileptogenic zone (0.26 vs. 0.29 S/m; P = 0.012), even when the epileptogenic zone was not visible in the magnetic resonance image (MRI) (P = 0.005). The present in-vivo conductivity values could serve to create more accurate volume conduction models and could help to refine the identification of relevant intracerebral contacts, especially when located within the epileptogenic zone of an MRI-invisible lesion. Hum Brain Mapp 38:974-986, 2017. © 2016 Wiley Periodicals, Inc.

Preliminary Upper Estimate of Peak Currents in Transcranial Magnetic Stimulation at Distant Locations From a TMS Coil

GOALS

Transcranial magnetic stimulation (TMS) is increasingly used as a diagnostic and therapeutic tool for numerous neuropsychiatric disorders. The use of TMS might cause whole-body exposure to undesired induced currents in patients and TMS operators. The aim of this study is to test and justify a simple analytical model known previously, which may be helpful as an upper estimate of eddy current density at a particular distant observation point for any body composition and any coil setup.

METHODS

We compare the analytical solution with comprehensive adaptive mesh refinement-based FEM simulations of a detailed full-body human model, two coil types, five coil positions, about 100 000 observation points, and two distinct pulse rise times; thus, providing a representative number of different datasets for comparison, while also using other numerical data.

RESULTS

Our simulations reveal that, after a certain modification, the analytical model provides an upper estimate for the eddy current density at any location within the body. In particular, it overestimates the peak eddy currents at distant locations from a TMS coil by a factor of 10 on average.

CONCLUSION

The simple analytical model tested in this study may be valuable as a rapid method to safely estimate levels of TMS currents at different locations within a human body.

SIGNIFICANCE

At present, safe limits of general exposure to TMS electric and magnetic fields are an open subject, including fetal exposure for pregnant women.

Neuromuscular Plasticity: Disentangling Stable and Variable Motor Maps in the Human Sensorimotor Cortex

Motor maps acquired with transcranial magnetic stimulation (TMS) are evolving as a biomarker for monitoring disease progression or the effects of therapeutic interventions. High test-retest reliability of this technique for long observation periods is therefore required to differentiate daily or weekly fluctuations from stable plastic reorganization of corticospinal connectivity. In this study, a novel projection, interpolation, and coregistration technique, which considers the individual gyral anatomy, was applied in healthy subjects for biweekly acquired TMS motor maps over a period of twelve weeks. The intraclass correlation coefficient revealed long-term reliability of motor maps with relevant interhemispheric differences. The sensorimotor cortex and nonprimary motor areas of the dominant hemisphere showed more extended and more stable corticospinal connectivity. Long-term correlations of the MEP amplitudes at each stimulation site revealed mosaic-like clusters of consistent corticospinal excitability. The resting motor threshold, centre of gravity, and mean MEPs across all TMS sites, as highly reliable cortical map parameters, could be disentangled from more variable parameters such as MEP area and volume. Cortical TMS motor maps provide high test-retest reliability for long-term monitoring when analyzed with refined techniques. They may guide restorative interventions which target dormant corticospinal connectivity for neurorehabilitation.

Technical aspects of neurostimulation: Focus on equipment, electric field modeling, and stimulation protocols

Neuromodulation is a field of science, medicine, and bioengineering that encompasses implantable and non-implantable technologies for the purpose of improving quality of life and functioning of humans. Brain neuromodulation involves different neurostimulation techniques: transcranial magnetic stimulation (TMS), transcranial direct current stimulation (tDCS), vagus nerve stimulation (VNS), and deep brain stimulation (DBS), which are being used both to study their effects on cognitive brain functions and to treat neuropsychiatric disorders. The mechanisms of action of neurostimulation remain incompletely understood. Insight into the technical basis of neurostimulation might be a first step towards a more profound understanding of these mechanisms, which might lead to improved clinical outcome and therapeutic potential. This review provides an overview of the technical basis of neurostimulation focusing on the equipment, the present understanding of induced electric fields, and the stimulation protocols. The review is written from a technical perspective aimed at supporting the use of neurostimulation in clinical practice.

Repetitive Transcranial Magnetic Stimulation Educes Frequency-Specific Causal Relationships in the Motor Network

BACKGROUND

Repetitive transcranial magnetic stimulation (rTMS) has the potential to treat brain disorders by modulating the activity of disease-specific brain networks, yet the rTMS frequencies used are delivered in a binary fashion - excitatory (>1 Hz) and inhibitory (≤1 Hz).

OBJECTIVE

To assess the effective connectivity of the motor network at different rTMS stimulation rates during positron-emission tomography (PET) and confirm that not all excitatory rTMS frequencies act on the motor network in the same manner.

METHODS

We delivered image-guided, supra-threshold rTMS at 3 Hz, 5 Hz, 10 Hz, 15 Hz and rest (in separate randomized sessions) to the primary motor cortex (M1) of the lightly anesthetized baboon during PET imaging. Each rTMS/PET session was analyzed using normalized cerebral blood flow (CBF) measurements. Path analysis - using structural equation modeling (SEM) - was employed to determine the effective connectivity of the motor network at all rTMS frequencies. Once determined, the final model of the motor network was used to assess any differences in effective connectivity at each rTMS frequency.

RESULTS

The exploratory SEM produced a very well fitting final network model (χ(2) = 18.04, df = 21, RMSEA = 0.000, p = 0.647, TLI = 1.12) using seven nodes of the motor network. 5 Hz rTMS produced the strongest path coefficients in four of the seven connections, suggesting that this frequency is the optimal rTMS frequency for stimulation the motor network (as a whole); however, the premotor cerebellum connection was optimally stimulated at 10 Hz rTMS and the supplementary motor area caudate connection was optimally driven at 15 Hz rTMS.

CONCLUSION(S)

We have demonstrated that 1) 5 Hz rTMS revealed the strongest path coefficients (i.e. causal influence) on the nodes of the motor network, 2) stimulation at "excitatory" rTMS frequencies did not produce increased CBF in all nodes of the motor network, 3) specific rTMS frequencies may be used to target specific none-to-node interactions in the stimulated brain network, and 4) more research needs to be performed to determine the optimum frequency for each brain circuit and/or node.

Gradient-based electrical conductivity imaging using MR phase

PURPOSE

To develop a fast, practically applicable, and boundary artifact free electrical conductivity imaging method that does not use transceive phase assumption, and that is more robust against the noise.

THEORY

Starting from the Maxwell's equations, a new electrical conductivity imaging method that is based solely on the MR transceive phase has been proposed. Different from the previous phase based electrical properties tomography (EPT) method, a new formulation was derived by including the gradients of the conductivity into the equations.

METHODS

The governing partial differential equation, which is in the form of a convection-reaction-diffusion equation, was solved using a three-dimensional finite-difference scheme. To evaluate the performance of the proposed method numerical simulations, phantom and in vivo human experiments have been conducted at 3T.

RESULTS

Simulation and experimental results of the proposed method and the conventional phase-based EPT method were illustrated to show the superiority of the proposed method over the conventional method, especially in the transition regions and under noisy data.

CONCLUSION

With the contributions of the proposed method to the phase-based EPT approach, a fast and reliable electrical conductivity imaging appears to be feasible, which is promising for clinical diagnoses and local SAR estimation. Magn Reson Med 77:137-150, 2017. © 2016 Wiley Periodicals, Inc.

Computational modeling of neurostimulation in brain diseases

Neurostimulation as a therapeutic tool has been developed and used for a range of different diseases such as Parkinson's disease, epilepsy, and migraine. However, it is not known why the efficacy of the stimulation varies dramatically across patients or why some patients suffer from severe side effects. This is largely due to the lack of mechanistic understanding of neurostimulation. Hence, theoretical computational approaches to address this issue are in demand. This chapter provides a review of mechanistic computational modeling of brain stimulation. In particular, we will focus on brain diseases, where mechanistic models (e.g., neural population models or detailed neuronal models) have been used to bridge the gap between cellular-level processes of affected neural circuits and the symptomatic expression of disease dynamics. We show how such models have been, and can be, used to investigate the effects of neurostimulation in the diseased brain. We argue that these models are crucial for the mechanistic understanding of the effect of stimulation, allowing for a rational design of stimulation protocols. Based on mechanistic models, we argue that the development of closed-loop stimulation is essential in order to avoid inference with healthy ongoing brain activity. Furthermore, patient-specific data, such as neuroanatomic information and connectivity profiles obtainable from neuroimaging, can be readily incorporated to address the clinical issue of variability in efficacy between subjects. We conclude that mechanistic computational models can and should play a key role in the rational design of effective, fully integrated, patient-specific therapeutic brain stimulation.

Computational and experimental analysis of TMS-induced electric field vectors critical to neuronal activation

OBJECTIVE

Transcranial magnetic stimulation (TMS) represents a powerful technique to noninvasively modulate cortical neurophysiology in the brain. However, the relationship between the magnetic fields created by TMS coils and neuronal activation in the cortex is still not well-understood, making predictable cortical activation by TMS difficult to achieve. Our goal in this study was to investigate the relationship between induced electric fields and cortical activation measured by blood flow response. Particularly, we sought to discover the E-field characteristics that lead to cortical activation.

APPROACH

Subject-specific finite element models (FEMs) of the head and brain were constructed for each of six subjects using magnetic resonance image scans. Positron emission tomography (PET) measured each subject's cortical response to image-guided robotically-positioned TMS to the primary motor cortex. FEM models that employed the given coil position, orientation, and stimulus intensity in experimental applications of TMS were used to calculate the electric field (E-field) vectors within a region of interest for each subject. TMS-induced E-fields were analyzed to better understand what vector components led to regional cerebral blood flow (CBF) responses recorded by PET.

MAIN RESULTS

This study found that decomposing the E-field into orthogonal vector components based on the cortical surface geometry (and hence, cortical neuron directions) led to significant differences between the regions of cortex that were active and nonactive. Specifically, active regions had significantly higher E-field components in the normal inward direction (i.e., parallel to pyramidal neurons in the dendrite-to-axon orientation) and in the tangential direction (i.e., parallel to interneurons) at high gradient. In contrast, nonactive regions had higher E-field vectors in the outward normal direction suggesting inhibitory responses.

SIGNIFICANCE

These results provide critical new understanding of the factors by which TMS induces cortical activation necessary for predictive and repeatable use of this noninvasive stimulation modality.

Projecting Navigated TMS Sites on the Gyral Anatomy Decreases Inter-subject Variability of Cortical Motor Maps

BACKGROUND

Magnetic resonance images are being increasingly deployed in conjunction with navigated transcranial magnetic stimulation (nTMS) to account for inter-individual differences in brain anatomy as well as to reduce the variability of mapping findings.

OBJECTIVE

However, despite the fact that the individual gyral anatomy has a significant impact on the TMS-induced electrical field distributions, these approaches still project the TMS coil positions as a plane grid of target points on the brain surface and fail to account for differences in cortex morphology.

METHODS

In this study, we have introduced a technique for projecting nTMS sites onto the gyral anatomy to decrease the variability of cortical motor maps between subjects in normalized space. This involved interpolating the discrete map points in the normalized volume space and performing additional surface coregistration.

RESULTS

By applying this technique, we increased the spatial overlap between the cortical maps of the extensor digitorum communis muscle between subjects from 80% to 100%. We also managed to significantly reduce the mean Euclidean distance between the average center of gravity and the average hotspots to the respective individual spots from 8 mm to 6.5 mm.

CONCLUSION

Our approach facilitates the study of the functional topography of distinct behavioral properties with high spatial resolution, thereby constituting a valuable tool for precise group analysis of cortical TMS maps.

Modeling TMS-induced I-waves in human motor cortex

Despite many years of research, it is still unknown how exactly transcranial magnetic stimulation activates cortical circuits. A recent computational model by Rusu et al. (2014) has attempted to shed light on potential underlying mechanisms and has successfully explained key experimental findings on I-wave physiology. Here, we critically discuss this model, point out some of its shortcomings, and suggest a number of extensions that may be necessary for it to capture additional existing and emerging data on the physiology of I-waves.

Lasting modulation of in vitro oscillatory activity with weak direct current stimulation

Transcranial direct current stimulation (tDCS) is emerging as a versatile tool to affect brain function. While the acute neurophysiological effects of stimulation are well understood, little is know about the long-term effects. One hypothesis is that stimulation modulates ongoing neural activity, which then translates into lasting effects via physiological plasticity. Here we used carbachol-induced gamma oscillations in hippocampal rat slices to establish whether prolonged constant current stimulation has a lasting effect on endogenous neural activity. During 10 min of stimulation, the power and frequency of gamma oscillations, as well as multiunit activity, were modulated in a polarity specific manner. Remarkably, the effects on power and multiunit activity persisted for more than 10 min after stimulation terminated. Using a computational model we propose that altered synaptic efficacy in excitatory and inhibitory pathways could be the source of these lasting effects. Future experimental studies using this novel in vitro preparation may be able to confirm or refute the proposed hypothesis.

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

A computational framework for uncertainty quantification in transcranial magnetic stimulation (TMS) is presented. The framework leverages high-dimensional model representations (HDMRs), which approximate observables (i.e., quantities of interest such as electric (E) fields induced inside targeted cortical regions) via series of iteratively constructed component functions involving only the most significant random variables (i.e., parameters that characterize the uncertainty in a TMS setup such as the position and orientation of TMS coils, as well as the size, shape, and conductivity of the head tissue). The component functions of HDMR expansions are approximated via a multielement probabilistic collocation (ME-PC) method. While approximating each component function, a quasi-static finite-difference simulator is used to compute observables at integration/collocation points dictated by the ME-PC method. The proposed framework requires far fewer simulations than traditional Monte Carlo methods for providing highly accurate statistical information (e.g., the mean and standard deviation) about the observables. The efficiency and accuracy of the proposed framework are demonstrated via its application to the statistical characterization of E-fields generated by TMS inside cortical regions of an MRI-derived realistic head model. Numerical results show that while uncertainties in tissue conductivities have negligible effects on TMS operation, variations in coil position/orientation and brain size significantly affect the induced E-fields. Our numerical results have several implications for the use of TMS during depression therapy: 1) uncertainty in the coil position and orientation may reduce the response rates of patients; 2) practitioners should favor targets on the crest of a gyrus to obtain maximal stimulation; and 3) an increasing scalp-to-cortex distance reduces the magnitude of E-fields on the surface and inside the cortex.