Coil optimisation for transcranial magnetic stimulation in realistic head geometry

A Closed Formalism for Anatomy-Independent Projection and Optimization of Magnetic Stimulation Coils on Arbitrarily Shaped Surfaces

INTRODUCTION

Transcranial magnetic stimulation (TMS) is a popular method for the noninvasive stimulation of neurons in the brain. It has become a standard instrument in experimental brain research and has been approved for a range of diagnostic and therapeutic applications. These applications require appropriately shaped coils. Various applications have been established or approved for specific coil designs with their corresponding spatial electric field distributions. However, the specific coil implementation may no longer be appropriate from the perspective of available material and manufacturing opportunities or considering the latest understanding of how to achieve induced electric fields in the head most efficiently. Furthermore, in some cases, field measurements of coils with unknown winding or a user-defined field are available and require an actual implementation. Similar applications exist for magnetic resonance imaging coils.

OBJECTIVE

This work aims at introducing a complete formalism free from heuristics, iterative optimization, and ad-hoc or manual steps to form practical stimulation coils with individual turns to either equivalently match an existing coil or produce a given field. The target coil can reside on practically any sufficiently large or closed surface adjacent to or around the head.

METHODS

The method derives an equivalent field through vector projection exploiting the well-known Huygens' and Love's equivalence principle. In contrast to other coil design or optimization approaches recently presented, the procedure is an explicit forward Hilbert-space vector projection or basis change. For demonstration, we map a commercial figure-of-eight coil as one of the most widely used devices and a more intricate coil recently approved clinically for addiction treatment (H4) onto a bent surface close to the head for highest efficiency and lowest field energy.

RESULTS

The resulting projections are within ≤4% of the target field and reduce the necessary pulse energy by more than 40%.

A review of algorithms and software for real-time electric field modeling techniques for transcranial magnetic stimulation

Transcranial magnetic stimulation (TMS) is a device-based neuromodulation technique increasingly used to treat brain diseases. Electric field (E-field) modeling is an important technique in several TMS clinical applications, including the precision stimulation of brain targets with accurate stimulation density for the treatment of mental disorders and the localization of brain function areas for neurosurgical planning. Classical methods for E-field modeling usually take a long computation time. Fast algorithms are usually developed with significantly lower spatial resolutions that reduce the prediction accuracy and limit their usage in real-time or near real-time TMS applications. This review paper discusses several modern algorithms for real-time or near real-time TMS E-field modeling and their advantages and limitations. The reviewed methods include techniques such as basis representation techniques and deep neural-network-based methods. This paper also provides a review of software tools that can integrate E-field modeling with navigated TMS, including a recent software for real-time navigated E-field mapping based on deep neural-network models.

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.

Optimized monophasic pulses with equivalent electric field for rapid-rate transcranial magnetic stimulation

Objective.Transcranial magnetic stimulation (TMS) with monophasic pulses achieves greater changes in neuronal excitability but requires higher energy and generates more coil heating than TMS with biphasic pulses, and this limits the use of monophasic pulses in rapid-rate protocols. We sought to design a stimulation waveform that retains the characteristics of monophasic TMS but significantly reduces coil heating, thereby enabling higher pulse rates and increased neuromodulation effectiveness.Approach.A two-step optimization method was developed that uses the temporal relationship between the electric field (E-field) and coil current waveforms. The model-free optimization step reduced the ohmic losses of the coil current and constrained the error of the E-field waveform compared to a template monophasic pulse, with pulse duration as a second constraint. The second, amplitude adjustment step scaled the candidate waveforms based on simulated neural activation to account for differences in stimulation thresholds. The optimized waveforms were implemented to validate the changes in coil heating.Main results.Depending on the pulse duration and E-field matching constraints, the optimized waveforms produced 12%-75% less heating than the original monophasic pulse. The reduction in coil heating was robust across a range of neural models. The changes in the measured ohmic losses of the optimized pulses compared to the original pulse agreed with numeric predictions.Significance.The first step of the optimization approach was independent of any potentially inaccurate or incorrect model and exhibited robust performance by avoiding the highly nonlinear behavior of neural responses, whereas neural simulations were only run once for amplitude scaling in the second step. This significantly reduced computational cost compared to iterative methods using large populations of candidate solutions and more importantly reduced the sensitivity to the choice of neural model. The reduced coil heating and power losses of the optimized pulses can enable rapid-rate monophasic TMS protocols.

A C-shaped miniaturized coil for transcranial magnetic stimulation in rodents

Objective.Transcranial magnetic stimulation (TMS) is a non-invasive technique widely used for neuromodulation. Animal models are essential for investigating the underlying mechanisms of TMS. However, the lack of miniaturized coils hinders the TMS studies in small animals, since most commercial coils are designed for humans and thus incapable of focal stimulation in small animals. Furthermore, it is difficult to perform electrophysiological recordings at the TMS focal point using conventional coils.Approach.We designed, fabricated, and tested a novel miniaturized TMS coil (4-by-7 mm) that consisted of a C-shaped iron powder core and insulated copper wires (30 turns). The resulting magnetic and electric fields were characterized with experimental measurements and finite element modeling. The efficacy of this coil in neuromodulation was validated with electrophysiological recordings of single-unit activities (SUAs), somatosensory evoked potentials (SSEPs), and motor evoked potentials (MEPs) in rats (n= 32) following repetitive TMS (rTMS; 3 min, 10 Hz).Main results.This coil could generate a maximum magnetic field of 460 mT and an electric field of 7.2 V m-1in the rat brain according to our simulations. With subthreshold rTMS focally delivered over the sensorimotor cortex, mean firing rates of primary somatosensory and motor cortical neurons significantly increased (154±5% and 160±9% from the baseline level, respectively); MEP and SSEP amplitude significantly increased (136±9%) and decreased (74±4%), respectively.Significance.This miniaturized C-shaped coil enabled focal TMS and concurrent electrophysiological recording/stimulation at the TMS focal point. It provided a useful tool to investigate the neural responses and underlying mechanisms of TMS in small animal models. Using this paradigm, we for the first time observed distinct modulatory effects on SUAs, SSEPs, and MEPs with the same rTMS protocol in anesthetized rats. These results suggested that multiple neurobiological mechanisms in the sensorimotor pathways were differentially modulated by rTMS.

Fast computational E-field dosimetry for transcranial magnetic stimulation using adaptive cross approximation and auxiliary dipole method (ACA-ADM)

Transcranial Magnetic Stimulation (TMS) is a non-invasive brain stimulation technique that uses a coil to induce an electric field (E-field) in the brain and modulate its activity. Many applications of TMS call for the repeated execution of E-field solvers to determine the E-field induced in the brain for different coil placements. However, the usage of solvers for these applications remains impractical because each coil placement requires the solution of a large linear system of equations. We develop a fast E-field solver that enables the rapid evaluation of the E-field distribution for a brain region of interest (ROI) for a large number of coil placements, which is achieved in two stages. First, during the pre-processing stage, the mapping between coil placement and brain ROI E-field distribution is approximated from E-field results for a few coil placements. Specifically, we discretize the mapping into a matrix with each column having the ROI E-field samples for a fixed coil placement. This matrix is approximated from a few of its rows and columns using adaptive cross approximation (ACA). The accuracy, efficiency, and applicability of the new ACA approach are determined by comparing its E-field predictions with analytical and standard solvers in spherical and MRI-derived head models. During the second stage, the E-field distribution in the brain ROI from a specific coil placement is determined by the obtained rows and columns in milliseconds. For many applications, only the E-field distribution for a comparatively small ROI is required. For example, the solver can complete the pre-processing stage in approximately 4 hours and determine the ROI E-field in approximately 40 ms for a 100 mm diameter ROI with less than 2% error enabling its use for neuro-navigation and other applications. Highlight: We developed a fast solver for TMS computational E-field dosimetry, which can determine the ROI E-field in approximately 40 ms for a 100 mm diameter ROI with less than 2% error.

Modeling transcranial magnetic stimulation coil with magnetic cores

Objective.Accurate modeling of transcranial magnetic stimulation (TMS) coils with the magnetic core is largely an open problem since commercial (quasi) magnetostatic solvers do not output specific field characteristics (e.g. induced electric field) and have difficulties when incorporating realistic head models. Many open-source TMS softwares do not include magnetic cores into consideration. This present study reports an algorithm for modeling TMS coils with a (nonlinear) magnetic core and validates the algorithm through comparison with finite-element method simulations and experiments.Approach.The algorithm uses the boundary element fast multipole method applied to all facets of a tetrahedral core mesh for a single-state solution and the successive substitution method for nonlinear convergence of the subsequent core states. The algorithm also outputs coil inductances, with or without magnetic cores. The coil-core combination is solved only once i.e. before incorporating the head model. The resulting primary TMS electric field is proportional to the total vector potential in the quasistatic approximation; it therefore also employs the precomputed core magnetization.Main results.The solver demonstrates excellent convergence for typical TMS field strengths and for analyticalB-Happroximations of experimental magnetization curves such as Froelich's equation or an arctangent equation. Typical execution times are 1-3 min on a common multicore workstation. For a simple test case of a cylindrical core within a one-turn coil, our solver computed the small-signal inductance nearly identical to that from ANSYS Maxwell. For a multiturn rodent TMS coil with a core, the modeled inductance matched the experimental measured value to within 5%.Significance.Incorporating magnetic core in TMS coil design has advantages of field shaping and energy efficiency. Our software package can facilitate model-informed design of more efficiency TMS systems and guide selection of core material. These models can also inform dosing with existing clinical TMS systems that use magnetic cores.

Magnetic temporal interference for noninvasive and focal brain stimulation

Objective. Noninvasive focal stimulation of deep brain regions has been a major goal for neuroscience and neuromodulation in the past three decades. Transcranial magnetic stimulation (TMS), for instance, cannot target deep regions in the brain without activating the overlying tissues and has poor spatial resolution. In this manuscript, we propose a new concept that relies on the temporal interference (TI) of two high-frequency magnetic fields generated by two electromagnetic solenoids.Approach. To illustrate the concept, custom solenoids were fabricated and optimized to generate temporal interfering electric fields for rodent brain stimulation. C-Fos expression was used to track neuronal activation.Main result. C-Fos expression was not present in regions impacted by only one high-frequency magnetic field indicating ineffective recruitment of neural activity in non-target regions. In contrast, regions impacted by two fields that interfere to create a low-frequency envelope display a strong increase in c-Fos expression.Significance. Therefore, this magnetic temporal interference solenoid-based system provides a framework to perform further stimulation studies that would investigate the advantages it could bring over conventional TMS systems.

Computation of transcranial magnetic stimulation electric fields using self-supervised deep learning

Electric fields (E-fields) induced by transcranial magnetic stimulation (TMS) can be modeled using partial differential equations (PDEs). Using state-of-the-art finite-element methods (FEM), it often takes tens of seconds to solve the PDEs for computing a high-resolution E-field, hampering the wide application of the E-field modeling in practice and research. To improve the E-field modeling's computational efficiency, we developed a self-supervised deep learning (DL) method to compute precise TMS E-fields. Given a head model and the primary E-field generated by TMS coils, a DL model was built to generate a E-field by minimizing a loss function that measures how well the generated E-field fits the governing PDE. The DL model was trained in a self-supervised manner, which does not require any external supervision. We evaluated the DL model using both a simulated sphere head model and realistic head models of 125 individuals and compared the accuracy and computational speed of the DL model with a state-of-the-art FEM. In realistic head models, the DL model obtained accurate E-fields that were significantly correlated with the FEM solutions. The DL model could obtain precise E-fields within seconds for whole head models at a high spatial resolution, faster than the FEM. The DL model built for the simulated sphere head model also obtained an accurate E-field whose average difference from the analytical E-fields was 0.0054, comparable to the FEM solution. These results demonstrated that the self-supervised DL method could obtain precise E-fields comparable to the FEM solutions with improved computational speed.

Modular pulse synthesizer for transcranial magnetic stimulation with fully adjustable pulse shape and sequence

The temporal shape of a pulse in transcranial magnetic stimulation (TMS) influences which neuron populations are activated preferentially as well as the strength and even direction of neuromodulation effects. Furthermore, various pulse shapes differ in their efficiency, coil heating, sensory perception, and clicking sound. However, the available TMS pulse shape repertoire is still very limited to a few biphasic, monophasic, and polyphasic pulses with sinusoidal or near-rectangular shapes. Monophasic pulses, though found to be more selective and stronger in neuromodulation, are generated inefficiently and therefore only available in simple low-frequency repetitive protocols. Despite a strong interest to exploit the temporal effects of TMS pulse shapes and pulse sequences, waveform control is relatively inflexible and only possible parametrically within certain limits. Previously proposed approaches for flexible pulse shape control, such as through power electronic inverters, have significant limitations: The semiconductor switches can fail under the immense electrical stress associated with free pulse shaping, and most conventional power inverter topologies are incapable of generating smooth electric fields or existing pulse shapes. Leveraging intensive preliminary work on modular power electronics, we present a modular pulse synthesizer (MPS) technology that can, for the first time, flexibly generate high-power TMS pulses (one-side peak ∼4000 V, ∼8000 A) with user-defined electric field shape as well as rapid sequences of pulses with high output quality. The circuit topology breaks the problem of simultaneous high power and switching speed into smaller, manageable portions, distributed across several identical modules. In consequence, the MPS TMS techology can use semiconductor devices with voltage and current ratings lower than the overall pulse voltage and distribute the overall switching of several hundred kilohertz among multiple transistors. MPS TMS can synthesize practically any pulse shape, including conventional ones, with fine quantization of the induced electric field (⩽17% granularity without modulation and ∼300 kHz bandwidth). Moreover, the technology allows optional symmetric differential coil driving so that the average electric potential of the coil, in contrast to conventional TMS devices, stays constant to prevent capacitive artifacts in sensitive recording amplifiers, such as electroencephalography. MPS TMS can enable the optimization of stimulation paradigms for more sophisticated probing of brain function as well as stronger and more selective neuromodulation, further expanding the parameter space available to users.

Transcranial magnetic stimulation set-up for small animals

Transcranial magnetic stimulation (TMS) is widely applied on humans for research and clinical purposes. TMS studies on small animals, e.g., rodents, can provide valuable knowledge of the underlying neurophysiological mechanisms. Administering TMS on small animals is, however, prone to technical difficulties, mainly due to their small head size. In this study, we aimed to develop an energy-efficient coil and a compatible experimental set-up for administering TMS on rodents. We applied a convex optimization process to develop a minimum-energy coil for TMS on rats. As the coil windings of the optimized coil extend to a wide region, we designed and manufactured a holder on which the rat lies upside down, with its head supported by the coil. We used the set-up to record TMS-electromyography, with electromyography recorded from limb muscles with intramuscular electrodes. The upside-down placement of the rat allowed the operator to easily navigate the TMS without the coil blocking their field of view. With this paradigm, we obtained consistent motor evoked potentials from all tested animals.

Design of Optimal Coils for Deep Transcranial Magnetic Stimulation

In this work, a stream function inverse boundary element method (IBEM) has been used for designing different deep transcranial magnetic stimulation (dTMS)coils to activate the prefrontal cortex and the temporal lobe have been set as the target regions. In addition, the performances of these coils have been described and the electric field induced by them has been obtained by using a computational forward technique. These results show that the stream function IBEM is an ideal approach to design optimal dTMS coils capable of producing deep stimulation in the target brain regions. Clinical relevance - The design problem proposed here can be used to produce efficient dTMS stimulators for neurological disorders, which can overcome some of the currently existing limitations of the most common devices employed in TMS.

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.

TMS with fast and accurate electronic control: Measuring the orientation sensitivity of corticomotor pathways

BACKGROUND

Transcranial magnetic stimulation (TMS) coils allow only a slow, mechanical adjustment of the stimulating electric field (E-field) orientation in the cerebral tissue. Fast E-field control is needed to synchronize the stimulation with the ongoing brain activity. Also, empirical models that fully describe the relationship between evoked responses and the stimulus orientation and intensity are still missing.

OBJECTIVE

We aimed to (1) develop a TMS transducer for manipulating the E-field orientation electronically with high accuracy at the neuronally meaningful millisecond-level time scale and (2) devise and validate a physiologically based model describing the orientation selectivity of neuronal excitability.

METHODS

We designed and manufactured a two-coil TMS transducer. The coil windings were computed with a minimum-energy optimization procedure, and the transducer was controlled with our custom-made electronics. The electronic E-field control was verified with a TMS characterizer. The motor evoked potential amplitude and latency of a hand muscle were mapped in 3° steps of the stimulus orientation in 16 healthy subjects for three stimulation intensities. We fitted a logistic model to the motor response amplitude.

RESULTS

The two-coil TMS transducer allows one to manipulate the pulse orientation accurately without manual coil movement. The motor response amplitude followed a logistic function of the stimulus orientation; this dependency was strongly affected by the stimulus intensity.

CONCLUSION

The developed electronic control of the E-field orientation allows exploring new stimulation paradigms and probing neuronal mechanisms. The presented model helps to disentangle the neuronal mechanisms of brain function and guide future non-invasive stimulation protocols.

Multi-locus transcranial magnetic stimulation system for electronically targeted brain stimulation

BACKGROUND

Transcranial magnetic stimulation (TMS) allows non-invasive stimulation of the cortex. In multi-locus TMS (mTMS), the stimulating electric field (E-field) is controlled electronically without coil movement by adjusting currents in the coils of a transducer.

OBJECTIVE

To develop an mTMS system that allows adjusting the location and orientation of the E-field maximum within a cortical region.

METHODS

We designed and manufactured a planar 5-coil mTMS transducer to allow controlling the maximum of the induced E-field within a cortical region approximately 30 mm in diameter. We developed electronics with a design consisting of independently controlled H-bridge circuits to drive up to six TMS coils. To control the hardware, we programmed software that runs on a field-programmable gate array and a computer. To induce the desired E-field in the cortex, we developed an optimization method to calculate the currents needed in the coils. We characterized the mTMS system and conducted a proof-of-concept motor-mapping experiment on a healthy volunteer. In the motor mapping, we kept the transducer placement fixed while electronically shifting the E-field maximum on the precentral gyrus and measuring electromyography from the contralateral hand.

RESULTS

The transducer consists of an oval coil, two figure-of-eight coils, and two four-leaf-clover coils stacked on top of each other. The technical characterization indicated that the mTMS system performs as designed. The measured motor evoked potential amplitudes varied consistently as a function of the location of the E-field maximum.

CONCLUSION

The developed mTMS system enables electronically targeted brain stimulation within a cortical region.

Trade-off between stimulation focality and the number of coils in multi-locus transcranial magnetic stimulation

Objective. Coils designed for transcranial magnetic stimulation (TMS) must incorporate trade-offs between the required electrical power or energy, focality and depth penetration of the induced electric field (E-field), coil size, and mechanical properties of the coil, as all of them cannot be optimally met at the same time. In multi-locus TMS (mTMS), a transducer consisting of several coils allows electronically targeted stimulation of the cortex without physically moving a coil. In this study, we aimed to investigate the relationship between the number of coils in an mTMS transducer, the focality of the induced E-field, and the extent of the cortical region within which the location and orientation of the maximum of the induced E-field can be controlled.Approach.We applied convex optimization to design planar and spherically curved mTMS transducers of different E-field focalities and analyzed their properties. We characterized the trade-off between the focality of the induced E-field and the extent of the cortical region that can be stimulated with an mTMS transducer with a given number of coils.Main results.At the expense of the E-field focality, one can, with the same number of coils, design an mTMS transducer that can control the location and orientation of the peak of the induced E-field within a wider cortical region.Significance. With E-fields of moderate focality, the problem of electronically targeted TMS becomes considerably easier compared with highly focal E-fields; this may speed up the development of mTMS and the emergence of new clinical and research applications.

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.

Precise Modulation Strategies for Transcranial Magnetic Stimulation: Advances and Future Directions

Transcranial magnetic stimulation (TMS) is a popular modulatory technique for the noninvasive diagnosis and therapy of neurological and psychiatric diseases. Unfortunately, current modulation strategies are only modestly effective. The literature provides strong evidence that the modulatory effects of TMS vary depending on device components and stimulation protocols. These differential effects are important when designing precise modulatory strategies for clinical or research applications. Developments in TMS have been accompanied by advances in combining TMS with neuroimaging techniques, including electroencephalography, functional near-infrared spectroscopy, functional magnetic resonance imaging, and positron emission tomography. Such studies appear particularly promising as they may not only allow us to probe affected brain areas during TMS but also seem to predict underlying research directions that may enable us to precisely target and remodel impaired cortices or circuits. However, few precise modulation strategies are available, and the long-term safety and efficacy of these strategies need to be confirmed. Here, we review the literature on possible technologies for precise modulation to highlight progress along with limitations with the goal of suggesting future directions for this field.

Mapping of multiple muscles with transcranial magnetic stimulation: absolute and relative test-retest reliability

The spatial accuracy of transcranial magnetic stimulation (TMS) may be as small as a few millimeters. Despite such great potential, navigated TMS (nTMS) mapping is still underused for the assessment of motor plasticity, particularly in clinical settings. Here, we investigate the within-limb somatotopy gradient as well as absolute and relative reliability of three hand muscle cortical representations (MCRs) using a comprehensive grid-based sulcus-informed nTMS motor mapping. We enrolled 22 young healthy male volunteers. Two nTMS mapping sessions were separated by 5-10 days. Motor evoked potentials were obtained from abductor pollicis brevis (APB), abductor digiti minimi, and extensor digitorum communis. In addition to individual MRI-based analysis, we studied normalized MNI MCRs. For the reliability assessment, we calculated intraclass correlation and the smallest detectable change. Our results revealed a somatotopy gradient reflected by APB MCR having the most lateral location. Reliability analysis showed that the commonly used metrics of MCRs, such as areas, volumes, centers of gravity (COGs), and hotspots had a high relative and low absolute reliability for all three muscles. For within-limb TMS somatotopy, the most common metrics such as the shifts between MCR COGs and hotspots had poor relative reliability. However, overlaps between different muscle MCRs were highly reliable. We, thus, provide novel evidence that inter-muscle MCR interaction can be reliably traced using MCR overlaps while shifts between the COGs and hotspots of different MCRs are not suitable for this purpose. Our results have implications for the interpretation of nTMS motor mapping results in healthy subjects and patients with neurological conditions.

Double-Containment Coil With Enhanced Winding Mounting for Transcranial Magnetic Stimulation With Reduced Acoustic Noise

OBJECTIVE

This work aims to reduce the acoustic noise level of transcranial magnetic stimulation (TMS) coils. TMS requires high currents (several thousand amperes) to be pulsed through the coil, which generates a loud acoustic impulse whose peak sound pressure level (SPL) can exceed 130 dB(Z). This sound poses a risk to hearing and elicits unwanted neural activation of auditory brain circuits.

METHODS

We propose a new double-containment coil with enhanced winding mounting (DCC), which utilizes acoustic impedance mismatch to contain and dissipate the impulsive sound within an air-tight outer casing. The coil winding is potted into a rigid block, which is mounted to the outer casing through the block´s acoustic nodes that are subject to minimum vibration during the pulse. The rest of the winding block is isolated from the casing by an air gap, and the sound is absorbed by polyester fiber panels within the casing. The casing thickness under the winding center is minimized to maximize the electric field output.

RESULTS

Compared to commercial figure-of-eight TMS coils, the DCC prototype has 18-41 dB(Z) lower peak SPL at matched stimulation strength, whilst providing 28% higher maximum stimulation strength than equally focal coils.

CONCLUSION

The DCC design greatly reduces the acoustic noise of TMS while increasing the achievable stimulation strength.

SIGNIFICANCE

The acoustic noise reduction from our coil design is comparable to that provided by typical hearing protection devices. This coil design approach can enhance hearing safety and reduce auditory co-activations in the brain and other detrimental effects of TMS sound.

Individual head models for estimating the TMS-induced electric field in rat brain

In transcranial magnetic stimulation (TMS), the initial cortical activation due to stimulation is determined by the state of the brain and the magnitude, waveform, and direction of the induced electric field (E-field) in the cortex. The E-field distribution depends on the conductivity geometry of the head. The effects of deviations from a spherically symmetric conductivity profile have been studied in detail in humans. In small mammals, such as rats, these effects are more pronounced due to their less spherical head, proportionally much thicker neck region, and overall much smaller size compared to the TMS coils. In this study, we describe a simple method for building individual realistically shaped head models for rats from high-resolution X-ray tomography images. We computed the TMS-induced E-field with the boundary element method and assessed the effect of head-model simplifications on the estimated E-field. The deviations from spherical symmetry have large, non-trivial effects on the E-field distribution: for some coil orientations, the strongest stimulation is in the brainstem even when the coil is over the motor cortex. With modelling prior to an experiment, such problematic coil orientations can be avoided for more accurate targeting.

Neuromodulation Management of Chronic Neuropathic Pain in The Central Nervous system

Neuromodulation is becoming one of the clinical tools for treating chronic neuropathic pain by transmitting controlled physical energy to the pre-identified neural targets in the central nervous system. Its nature of drug-free, non-addictive and improved targeting have attracted increasing attention among neuroscience research and clinical practices. This article provides a brief overview of the neuropathic pain and pharmacological routines for treatment, summarizes both the invasive and non-invasive neuromodulation modalities for pain management, and highlights an emerging brain stimulation technology, transcranial focused ultrasound (tFUS) with a focus on ultrasound transducer devices and the achieved neuromodulation effects and applications on pain management. Practical considerations of spatial guidance for tFUS are discussed for clinical applications. The safety of transcranial ultrasound neuromodulation and its future prospectives on pain management are also discussed.

Design of coils for lateralized TMS on mice

OBJECTIVE

Translational studies on animals play a vital role in the advancement of transcranial magnetic stimulation (TMS) as clinical technique. Nonetheless the relevance of these procedures is frequently limited by the lack of TMS systems specifically designed for small animals capable of producing comparable stimulation conditions to those found in human TMS. In this work, we propose to take advantage of the versatility of recently introduced TMS coil design methods to produce optimal rodent-specific TMS stimulators.

APPROACH

A stream function inverse boundary element method (IBEM) has been used for producing three small sized mice-specific TMS coils of different geometries. They have been created for unilateral hemispheric stimulation of the rodent brain, and several constraints have been considered in the design process to satisfy essential performance requirements, such as minimum stored magnetic energy, minimum power dissipation, optimised maximum current density or minimization of the undesired electric field induced in non-target regions. In order to validate the presented strategy, three prototype coils have been built. The performance of each prototype has also been numerically investigated, where the electric field induced in a mouse model has been found by using an existing computational forward technique.

MAIN RESULTS

Stream function IBEM represents an ideally suited approach for designing specific TMS coils for small animals, capable of fulfilling many essential functional and technical requirements. The prototypes produced in this work focally stimulate the right hemisphere of the mouse brain, and so they can be successfully used in lateralized TMS experiments.

SIGNIFICANCE

The design scheme proposed here can be used to produce efficient TMS stimulators for small animals, which can overcome some of the existing limitations found when producing more reliable translational experiments.

Design of TMS coils with reduced Lorentz forces: application to concurrent TMS-fMRI

OBJECTIVE

Interleaving TMS (transcranial magnetic stimulation) with fMRI (functional Magnetic Resonance Imaging) is a promising technique to study functional connectivity in the human brain, but its development is being restricted by technical limitations, such as that due to the interaction of the TMS current pulses with the magnetic fields of an MRI scanner. In this work, a TMS coil design method capable of controlling Lorentz forces experienced by the coil in the presence of static magnetic fields is presented.

APPROACH

The suggested approach is based on an existing inverse boundary element method (IBEM) for TMS coil design, in which new electromagnetic computational models of the Lorentz forces have been included to be controlled in the design process.

MAIN RESULTS

To demonstrate the validity of this technique, it has been used for the design and simulation of TMS coils wound on rectangular flat, spherical and hemispherical surfaces with improved mechanical stability. The obtained results confirm that TMS coils with reduced Lorentz forces inside the static main field of an MRI scanner can be produced, which is achieved to the detriment of other coil performance parameters.

SIGNIFICANCE

The proposed approach provides an efficient tool to design TMS stimulators of a wide range of coil geometries with improved mechanical stability, which can be extremely useful to overcome current limitations for interleaved TMS-fMRI.

Exact Solutions to the Maxmin Problem max‖Ax‖ Subject to ‖Bx‖≤1

In this manuscript we provide an exact solution to the maxmin problem max ∥ A x ∥ subject to ∥ B x ∥ ≤ 1 , where A and B are real matrices. This problem comes from a remodeling of max ∥ A x ∥ subject to min ∥ B x ∥ , because the latter problem has no solution. Our mathematical method comes from the Abstract Operator Theory, whose strong machinery allows us to reduce the first problem to max ∥ C x ∥ subject to ∥ x ∥ ≤ 1 , which can be solved exactly by relying on supporting vectors. Finally, as appendices, we provide two applications of our solution: first, we construct a truly optimal minimum stored-energy Transcranian Magnetic Stimulation (TMS) coil, and second, we find an optimal geolocation involving statistical variables.

Evidence-based guidelines on the therapeutic use of repetitive transcranial magnetic stimulation (rTMS): An update (2014-2018)

A group of European experts reappraised the guidelines on the therapeutic efficacy of repetitive transcranial magnetic stimulation (rTMS) previously published in 2014 [Lefaucheur et al., Clin Neurophysiol 2014;125:2150-206]. These updated recommendations take into account all rTMS publications, including data prior to 2014, as well as currently reviewed literature until the end of 2018. Level A evidence (definite efficacy) was reached for: high-frequency (HF) rTMS of the primary motor cortex (M1) contralateral to the painful side for neuropathic pain; HF-rTMS of the left dorsolateral prefrontal cortex (DLPFC) using a figure-of-8 or a H1-coil for depression; low-frequency (LF) rTMS of contralesional M1 for hand motor recovery in the post-acute stage of stroke. Level B evidence (probable efficacy) was reached for: HF-rTMS of the left M1 or DLPFC for improving quality of life or pain, respectively, in fibromyalgia; HF-rTMS of bilateral M1 regions or the left DLPFC for improving motor impairment or depression, respectively, in Parkinson's disease; HF-rTMS of ipsilesional M1 for promoting motor recovery at the post-acute stage of stroke; intermittent theta burst stimulation targeted to the leg motor cortex for lower limb spasticity in multiple sclerosis; HF-rTMS of the right DLPFC in posttraumatic stress disorder; LF-rTMS of the right inferior frontal gyrus in chronic post-stroke non-fluent aphasia; LF-rTMS of the right DLPFC in depression; and bihemispheric stimulation of the DLPFC combining right-sided LF-rTMS (or continuous theta burst stimulation) and left-sided HF-rTMS (or intermittent theta burst stimulation) in depression. Level A/B evidence is not reached concerning efficacy of rTMS in any other condition. The current recommendations are based on the differences reached in therapeutic efficacy of real vs. sham rTMS protocols, replicated in a sufficient number of independent studies. This does not mean that the benefit produced by rTMS inevitably reaches a level of clinical relevance.

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.

Multi-locus transcranial magnetic stimulation-theory and implementation

BACKGROUND

Transcranial magnetic stimulation (TMS) is a non-invasive brain stimulation method: a magnetic field pulse from a TMS coil can excite neurons in a desired location of the cortex. Conventional TMS coils cause focal stimulation underneath the coil centre; to change the location of the stimulated spot, the coil must be moved over the new target. This physical movement is inherently slow, which limits, for example, feedback-controlled stimulation.

OBJECTIVE

To overcome the limitations of physical TMS-coil movement by introducing electronic targeting.

METHODS

We propose electronic stimulation targeting using a set of large overlapping coils and introduce a matrix-factorisation-based method to design such sets of coils. We built one such device and demonstrated the electronic stimulation targeting in vivo.

RESULTS

The demonstrated two-coil transducer allows translating the stimulated spot along a 30-mm-long line segment in the cortex; with five coils, a target can be selected from within a region of the cortex and stimulated in any direction. Thus, far fewer coils are required by our approach than by previously suggested ones, none of which have resulted in practical devices.

CONCLUSION

Already with two coils, we can adjust the location of the induced electric field maximum along one dimension, which is sufficient to study, for example, the primary motor cortex.

Noninvasive extraction of microsecond-scale dynamics from human motor cortex

State-of-the-art noninvasive electromagnetic recording techniques allow observing neuronal dynamics down to the millisecond scale. Direct measurement of faster events has been limited to in vitro or invasive recordings. To overcome this limitation, we introduce a new paradigm for transcranial magnetic stimulation. We adjusted the stimulation waveform on the microsecond scale, by varying the duration between the positive and negative phase of the induced electric field, and studied corresponding changes in the elicited motor responses. The magnitude of the electric field needed for given motor-evoked potential amplitude decreased exponentially as a function of this duration with a time constant of 17 µs. Our indirect noninvasive measurement paradigm allows studying neuronal kinetics on the microsecond scale in vivo.

Redesigning existing transcranial magnetic stimulation coils to reduce energy: application to low field magnetic stimulation

OBJECTIVE

To present a systematic framework and exemplar for the development of a compact and energy-efficient coil that replicates the electric field (E-field) distribution induced by an existing transcranial magnetic stimulation coil.

APPROACH

The E-field generated by a conventional low field magnetic stimulation (LFMS) coil was measured for a spherical head model and simulated in both spherical and realistic head models. Then, using a spherical head model and spatial harmonic decomposition, a spherical-shaped cap coil was synthesized such that its windings conformed to a spherical surface and replicated the E-field on the cortical surface while requiring less energy. A prototype coil was built and electrically characterized. The effect of constraining the windings to the upper half of the head was also explored via an alternative coil design.

MAIN RESULTS

The LFMS E-field distribution resembled that of a large double-cone coil, with a peak field strength around 350 mV m^-1 in the cortex. The E-field distributions of the cap coil designs were validated against the original coil, with mean errors of 1%-3%. The cap coil required as little as 2% of the original coil energy and was significantly smaller in size.

SIGNIFICANCE

The redesigned LFMS coil is substantially smaller and more energy-efficient than the original, improving cost, power consumption, and portability. These improvements could facilitate deployment of LFMS in the clinic and potentially at home. This coil redesign approach can also be applied to other magnetic stimulation paradigms. Finally, the anatomically-accurate E-field simulation of LFMS can be used to interpret clinical LFMS data.