The effect of head and coil modeling for the calculation of induced electric field during transcranial magnetic stimulation

In the present work we studied some of the features related to transcranial magnetic stimulation (TMS) computational modeling. Particularly we investigated the impact of head model resolution on the estimated distribution of the induced electric field, as well as the role of the stimulating magnetic coil model in TMS. Using the impedance method we calculated the induced electric field inside a realistic numerical phantom of the human head from a commercially available eight-shaped coil, which was modeled in two ways. The results showed that finer resolution of the model has better performance at tissue interfaces eliminating numerical artifacts of local peaks. Furthermore, the geometrical details of a TMS coil must be taken into account since the predicted amount of volume of brain tissue involved can have great variation. Finally, the secondary magnetic field that is generated by the induced eddy currents in the tissues can be neglected.     

经颅磁刺激电场分析研究进展

经颅磁刺激是一种利用通电线圈在脑部的诱发电场来调节皮质兴奋性的技术,广泛应用于神经病学、康复学等领域。经颅磁刺激诱发电场分析与安全性、刺激效果密切相关,在优化刺激方案、线圈设计方面具有重要意义,成为相关领域的研究重点。首先介绍经颅磁刺激3种常见的临床副作用,然后阐述经颅磁刺激现有研究中的常规电场分析方法,包括解析法和数值分析法及其应用场景,并讨论与电场分析密切相关的生物模型建模方法。此外,由于磁刺激线圈与组织中电场分布的密切相关性,介绍常规的刺激线圈结构类型,并结合磁刺激线圈的7种典型设计,分析基于有限元分析的球模型下的电场分布特征。最后,展望经颅磁刺激电场分析研究未来的发展趋势。     

经颅磁刺激线圈的磁聚焦优化设计

经颅磁刺激是利用变化磁场产生的感应电场作用于可兴奋人体脑组织的过程,磁聚焦性能是经颅磁刺激线圈设计的一项重要指标。根据磁刺激线圈感应电场理论,我们设计了半圆螺线管用于经颅磁刺激,计算了其载流线圈随刺激深度的感应电场分布,并与传统的经颅磁刺激8字形线圈作比较。结果表明,半圆螺旋管线圈既继承了8字形线圈感应电场的主瓣聚焦性强的优良特性,又摒弃了其相对较大的旁瓣对浅表非靶组织的兴奋刺激的不良影响,完全达到了磁聚焦优化设计的目的,也更利于磁刺激兴奋点的定位。     

经颅磁刺激和脑电联合作用时电磁场分布的仿真研究

目的：研究分析经颅磁刺激和脑电（TMS-EEG）联合作用时磁感应强度和感应电场强度的分布情况。方法：利用有限元多物理场仿真软件COMSOL，搭建3层同心球人头模型、TMS线圈模型和EEG电极模型，在TMS线圈的作用下，对比分析了有无脑电极时，人头模型当中磁感应强度和感应电场强度的不同。结果：取头部组织几个特殊位置点，放置脑电极后，各点处磁感应强度和感应电场强度均发生变化，磁感应强度最大变化达19.19%，感应电场强度最大变化达75.33%。添加脑电极后，人体头部组织YZ纵切面的最大磁感应强度降低7 mT，最大感应电场强度值降低0.6 V/m。大脑处的三维磁感应强度和感应电场强度均随着深度的增加而逐渐减小，放置脑电极后，脑组织中的最大磁感应强度值减少1.4 mT，最大感应电场强度值减少0.13 V/m。结论：经TMS-EEG联合作用时，在人头皮处放置脑电极会对电磁场的分布产生影响，间接影响TMS的治疗作用。     

Transcranial magnetic stimulation and brain atrophy: a computer-based human brain model study

This paper is aimed at exploring the effect of cortical brain atrophy on the currents induced by transcranial magnetic stimulation (TMS). We compared the currents induced by various TMS conditions on several different MRI derived finite element head models of brain atrophy, incorporating both decreasing cortical volume and widened sulci. The current densities induced in the cortex were dependent upon the degree and type of cortical atrophy and were altered in magnitude, location, and orientation when compared to healthy head models. Predictive models of the degree of current density attenuation as a function of the scalp-to-cortex distance were analyzed, concluding that those which ignore the electromagnetic field–tissue interactions lead to inaccurate conclusions. Ultimately, the precise site and population of neural elements stimulated by TMS in an atrophic brain cannot be predicted based on healthy head models which ignore the effects of the altered cortex on the stimulating currents. Clinical applications of TMS should be carefully considered in light of these findings.     

Task-dependent changes in cortical excitability and effective connectivity: a combined TMS-EEG study

The brain's electrical response to transcranial magnetic stimulation (TMS) is known to be influenced by exogenous factors such as the frequency and intensity of stimulation and the orientation and positioning of the stimulating coil. Less understood, however, is the influence of endogenous neural factors, such as global brain state, on the TMS-evoked response (TMS-ER). In the present study, we explored how changes in behavioral state affect the TMS-ER by perturbing the superior parietal lobule (SPL) with single pulses of TMS and measuring consequent differences in the frequency, strength, and spatial spread of TMS-evoked currents during the delay period of a spatial short-term memory task and during a period of passive fixation. Results revealed that task performance increased the overall strength of electrical currents induced by TMS, increased the spatial spread of TMS-evoked activity to distal brain regions, and increased the ability of TMS to reset the phase of ongoing broadband cortical oscillations. By contrast, task performance had little effect on the dominant frequency of the TMS-ER, both locally and at distal brain areas. These findings contribute to a growing body of work using combined TMS and neuroimaging methods to explore task-dependent changes in the functional organization of cortical networks implicated in task performance.     

经颅磁刺激放电回路参数对线圈脉冲电流特性的影响

目的 本文分析了经颅磁刺激放电回路参数,包括放电回路中总电容（C）、放电电压（U）以及放电线圈的电感值（L）和电阻值（R）对线圈放电电流特性的影响,为经颅磁刺激放电回路参数的优化提供理论指导.方法 首先理论上对经颅磁刺激系统基本电路进行分析,得出放电电流与放电回路参数的关系式,然后通过仿真和实验相结合的方法,研究放电回路参数对线圈脉冲电流的影响.同时,利用傅里叶变换分析线圈脉冲放电电流的频域特性.结果 单独增大储能电容值,增大了线圈放电电流幅值,延长了脉冲电流上升沿时间和脉宽持续时间,减小了电流信号的主频.单独减小回路总电阻值,增大了脉冲电流的幅值,提高了电流信号的主频,但更容易使脉冲电流出现多次振荡.单独增大回路电感值,减小了脉冲电流幅值,延长了脉冲电流的上升沿时间和脉宽持续时间,电流信号主频先增大后减小.结论 在经颅磁刺激系统工程设计中,放电回路参数值要匹配,不同的回路参数取值直接影响线圈脉冲电流的特性.本研究对设计特定指标要求的经颅磁刺激系统具有理论参考价值.     

Technical approaches to hemisphere-selective transcranial magnetic brain stimulation

Clinical application of transcranial magnetic brain stimulation is mainly used to determine central motor conduction times. With the stimulation coil (Magstim 200, Novametrix) centered conventionally over the midline of the skull convexity and using high stimulus intensities, which are often required in pathological states, the motor cortices of both hemispheres are usually activated simultaneously. Under this condition it is not possible to determine from which hemisphere the descending excitatory volleys to a particular motoneurone pool originate and how the input to the lower motoneurons is organized (uni-/bilateral, ipsi-/contralateral). This limitation can be overcome by two different techniques for selective stimulation of the motor cortex of one hemisphere without coactivation of the other even when using maximal stimulus intensities: 1. A large 12 cm (outer diameter) stimulation coil could be used for selective stimulation when a) the magnetic field radiated over the non-stimulated hemisphere is modified by using a prototype coil shield covering the half of the coil over the nonstimulated hemisphere in combination with b) placing the coil away from the midline towards the preferentially excited hemisphere. The coil shield consists of a sheet of a nickel iron alloy which alters the time course of the induced currents by reducing the initial rate of current intensity change (dI/dt). 2. The use of a smaller 6.5 cm (outer diameter) coil also provided a useful tool for selective stimulation of one hemisphere but was restricted to subjects with low excitation thresholds. In subjects with high excitation thresholds the described use of the large stimulation coil is advisable.     

Controlled E-field gradient coils for MRI

Peripheral neural stimulation is a major problem in current gradient coil designs. Induced current problems in patients relate directly to gradient strength and modulation frequency. Present designs of gradient coil tend to limit ultra-high-speed imaging methods such as echo-planar imaging (EPI) and echo-volumar imaging (EVI) because of the effect of induced currents in the patient which produce neural stimulation resulting in tingling sensations and involuntary muscle twitch. Neural stimulation could also trigger epileptic fits and/or cardiac fibrillation. For reduction of induced currents, an important aspect is the coil geometry. It is desirable to design the gradient coil in such a way as to prevent closed loop circulating currents within the body. Preliminary results using a four-sector gradient coil with a rectangular geometry, operating in a low mutual coupling mode and using passive E-field control, indicate significant reduction of the E-field within the subject volume of the coil, leading to a reduction of induced currents in a patient. Such a reduction allows safer operation using higher magnetic gradient strengths together with faster scans. Currently very fast scans are prohibited by virtue of the neural stimulation effects produced in present standard coil geometries.     

Single pulse stimulation of the human subthalamic nucleus facilitates the motor cortex at short intervals

Deep brain stimulation (DBS) of the subthalamic nucleus (STN) is an effective treatment for Parkinson's disease (PD). The mechanism is poorly understood. High-frequency STN DBS has been reported to affect motor cortex excitability in a complex way, but the timing between STN stimuli and changes in motor cortical (M1) excitability has not been investigated. We examined the time course of changes in motor cortical excitability following single pulse STN DBS. We studied 14 PD patients with implanted DBS electrodes in the STN, 2 patients with electrodes in internal globus pallidus (GPi), and 1 patient with an electrode in the sensory thalamus. Transcranial magnetic stimulation (TMS) was delivered to the M1 ipsilateral to the DBS with induced currents either in the anterior-posterior direction in the brain to evoke indirect (I) waves or in the lateral-medial direction to activate corticospinal axons directly. Single pulse stimulation through the DBS contacts preceded the TMS by 0-10 ms. Surface EMG was recorded from the contralateral first dorsal interosseous muscle. Three milliseconds after STN stimulation, the motor evoked potential (MEP) amplitudes produced by anterior-posterior current were significantly larger than control responses, while the responses to lateral-medial currents were unchanged. Similar facilitation also occurred after GPi stimulation, but not with thalamic stimulation. Single pulse STN stimulation facilitates the M1 at short latencies. The possible mechanisms include antidromic excitation of the cortico-STN fibers or transmission through the basal ganglia-thalamocortical pathway.     

Magnetic stimulation of the nervous system: Induced electric field in unbounded,semi-infinite,spherical, and cylindrical media

Knowledge of the electric field that is induced in the brain or the limbs is of importance in magnetic stimulation of the nervous system. Here, an analytical model based on the reciprocity theorem is used to compare the induced electric field in unbounded, semi-infinite, spherical, and cylinder-like volume conductors. Typical stimulation coil arrangements are considered, including the double coil and various orientations of the single coil. The results can be used to determine when the influence of the boundaries is negligible enough to allow the use of more simplified geometries.     

Effect of transcranial magnetic stimulation on single-unit activity in the cat primary visual cortex

Transcranial magnetic stimulation (TMS) has become a well established procedure for testing and modulating the neuronal excitability of human brain areas, but relatively little is known about the cellular processes induced by this rather coarse stimulus. In a first attempt, we performed extracellular single-unit recordings in the primary visual cortex (area 17) of the anaesthetised and paralysed cat, with the stimulating magnetic field centred at the recording site (2 × 70 mm figure-of-eight coil). The effect of single biphasic TMS pulses, which induce a lateral-to-medial electric current within the occipital pole of the right hemisphere, was tested for spontaneous as well as visually evoked activity. For cat visual cortex we found that a single TMS pulse elicited distinct episodes of enhanced and suppressed activity: in general, a facilitation of activity was found during the first 500 ms, followed thereafter by a suppression of activity lasting up to a few seconds. Strong stimuli exceeding 50 % of maximal stimulator output could also lead to an early suppression of activity during the first 100–200 ms, followed by stronger (rebound) facilitation. Early suppression and facilitation of activity may be related to a more or less direct stimulation of inhibitory and excitatory interneurons, probably with different thresholds. The late, long-lasting suppression is more likely to be related to metabotropic or metabolic processes, or even vascular responses. The time course of facilitation/inhibition may provide clues regarding the action of repetitive TMS application.     

Localization of diaphragm motor cortical representation and determination of corticodiaphragmatic latencies by using magnetic stimulation in normal adult human subjects

The aims of this study were to identify the motor cortical representation of the diaphragm and to assess the corticodiaphragmatic pathway from both hemispheres. Specially designed bipolar surface electrodes were used to record the ipsilateral and contralateral compound motor evoked potentials (CMEPs) of the diaphragm after transcranial magnetic stimulation (TMS) of the motor cortex. In addition, the response to cervical magnetic stimulation of the phrenic nerve roots, effected using a figure-of-eight magnetic coil, was also recorded. The study involved 30 normal adult male volunteers. The average point of optimal excitability (POE) was determined to be 3.7 cm lateral to the mid-sagittal plane and 0.89 cm anterior to the preauricular plane. The largest response was obtained at a stimulus coil orientation of 0–90°. The TMS of either hemisphere produced CMEPs in the contralateral and ipsilateral diaphragm muscles. TMS of either hemisphere elicited CMEPs that had significantly greater amplitudes and shorter latencies from the contralateral muscles compared with the ipsilateral response (P<0.0001). The central motor conduction time of the crossed tract (8.8 ms) was significantly shorter than that of the uncrossed tract (12.2 ms). No significant interhemispheric differences were recorded. The recorded CMEPs recorded in response to TMS were facilitated during volitional inspiration. Phrenic nerve latency was 5.7 ms and 5.6 ms for the right and left phrenic nerves, respectively, with no significant difference between these values. Both bilateral crossed and uncrossed corticospinal connections to the diaphragm were usually present, with the crossed tract predominating. The technique used in this study may be useful for investigations into the function and integrity of central and peripheral pathway of the diaphragm muscles in various neurological disorders. Electronic Publication     

MR‐based measurements and simulations of the magnetic field created by a realistic transcranial magnetic stimulation (TMS) coil and stimulator

Transcranial magnetic stimulation (TMS) is an emerging technique that allows non‐invasive neurostimulation. However, the correct validation of electromagnetic models of typical TMS coils and the correct assessment of the incident TMS field (B_TMS) produced by standard TMS stimulators are still lacking. Such a validation can be performed by mapping B_TMS produced by a realistic TMS setup. In this study, we show that MRI can provide precise quantification of the magnetic field produced by a realistic TMS coil and a clinically used TMS stimulator in the region in which neurostimulation occurs. Measurements of the phase accumulation created by TMS pulses applied during a tailored MR sequence were performed in a phantom. Dedicated hardware was developed to synchronize a typical, clinically used, TMS setup with a 3‐T MR scanner. For comparison purposes, electromagnetic simulations of B_TMS were performed. MR‐based measurements allow the mapping and quantification of B_TMS starting 2.5 cm from the TMS coil. For closer regions, the intra‐voxel dephasing induced by B_TMS prohibits TMS field measurements. For 1% TMS output, the maximum measured value was ~0.1 mT. Simulations reflect quantitatively the experimental data. These measurements can be used to validate electromagnetic models of TMS coils, to guide TMS coil positioning, and for dosimetry and quality assessment of concurrent TMS‐MRI studies without the need for crude methods, such as motor threshold, for stimulation dose determination.     

Accuracy of Stereotaxic Positioning of Transcranial Magnetic Stimulation

Summary: In cognitive neuroscience, optically tracked frameless stereotaxic navigation has been successfully used to precisely guide transcranial magnetic stimulation (TMS) to desired cortical areas for brain-mapping purposes. Thereby, potential sources of imprecision are the fixation of a reference frame to the head of the subject and the referencing procedure according to certain landmarks (LM). The aim of our study was to evaluate the accuracy of frameless stereotaxic coil positioning in a standard experimental setting. A parameter for accuracy is the reproducibility of LM coordinates. In order to test the stability of the referencing for stereotaxic positioning within a single TMS session (within-session stability), the coordinates of six predefined facial LM in nine subjects were recorded first after the initial registration and second after a 20 minutes TMS session. The two sets of coordinates were then compared. The reliability of the positioning coordinates between different TMS sessions (inter-session repeatability) was addressed by registering the subjects LM coordinates in two independent TMS sessions. The variance of the recorded coordinates was analyzed. Altogether, LM were registered 1728 times (192 measures per subject). Within-session stability: The mean Euclidean distance (MED) between the LM position coordinates before and after a TMS session was 1.6 mm, when pooling over all LM. Inter-session repeatability: The MED between the LM positions recorded after the reference procedures of two different sessions showed an average deviation of 2.5 mm. In conclusion, optically tracked frameless stereotaxic coil positioning is from the technical viewpoint of high stability and repeatability. It is therefore a precise method for TMS brain mapping studies or for repeated TMS treatments, with the need of topographically exact stimulation.     

Electric field induced in a spherical volume conductor from arbitrary coils: application to magnetic stimulation and MEG

A mathematical method is presented that allows fast and simple computation of the electric field and current density induced inside a homogeneous spherical volume conductor by current flowing in a coil. The total electric field inside the sphere is computed entirely from a set of line integrals performed along the coil current path. Coils of any closed shape are easily accommodated by the method. The technique can be applied to magnetic brain stimulation and to magnetoencephalography. For magnetic brain stimulation, the total electric field anywhere inside the head can be easily computed for any coil shape and placement. The reciprocity theorem may be applied so that the electric field represents the lead field of a magnetometer. The finite coil area and gradiometer loop spacing can be precisely accounted for without any surface integration by using this method. The theory shows that the steady-state, radially oriented induced electric field is zero everywhere inside the sphere for ramping coil current and highly attenuated for sinusoidal coil current. This allows the model to be extended to concentric spheres which have different electrical properties.     

影响感应电场分布的线圈设计因素分析

本文理论上分析了影响头部磁刺激感应电场分布的各种因素,包括刺激线圈的形状、线圈的直径、直径与刺激深度比的影响以及线圈间距和通过线圈电流方向的影响等。分别计算了这些因素的变化引起的感应电场的变化情况,结果表明当直径为刺激浓度的２－４倍时刺激的定位性能较好。     

Some technical aspects of magnetic stimulation coil design with the ferromagnetic effect

The performance of the stimulation coil in a magnetic nerve stimulator can be improved by attaching a ferromagnetic structure to the coil. This reduces heat generation at the coil and increases magnetic field strength for a given unit of current. Some technical aspects of the design of a stimulation coil with a ferromagnetic structure have been studied. Finite element method analysis results are presented for the effect of size, depth and magnetic saturation of the ferromagnetic structure on the stimulation coil performance. The experimental results show that the stimulation coil performance is improved by up to 40% by the attaching of a ferromagnetic structure on the coil.     

Simple metric for scaling motor threshold based on scalp-cortex distance: application to studies using transcranial magnetic stimulation

Transcranial magnetic stimulation (TMS) is a unique method in neuroscience used to stimulate focal regions of the human brain. As TMS gains popularity in experimental and clinical domains, techniques for controlling the extent of brain stimulation are becoming increasingly important. At present, TMS intensity is typically calibrated to the excitability of the human motor cortex, a measure referred to as motor threshold (MT). Although TMS is commonly applied to nonmotor regions, most applications do not consider the effect of changes in distance between the stimulating device and underlying neural tissue. Here we show that for every millimeter from the stimulating coil, an additional 3% of TMS output is required to induce an equivalent level of brain stimulation at the motor cortex. This abrupt spatial gradient will have crucial consequences when TMS is applied to nonmotor regions because of substantial variance in scalp-cortex distances over different regions of the head. Stimulation protocols that do not account for cortical distance therefore risk substantial under- or overstimulation. We describe a simple method for adjusting MT to account for variations in cortical distance, thus providing a more accurate calibration than unadjusted MT for the safe and effective application of TMS in clinical and experimental neuroscience.     

Focusing and targeting of magnetic brain stimulation using multiple coils

Neurones can be excited by an externally applied time-varying electromagnetic field. Focused magnetic brain stimulation is attained using multiple small coils instead of one large coil, the resultant induced electric field being a superposition of the fields from each coil. In multichannel magnetic brain stimulation, partial cancellation of fields from individual coils provides a significant improvement in the focusing of the stimulating field, and independent coil channels allow targeting of the stimuli on a given spot without moving the coils. The problem of shaping the stimulating field in multichannel stimulation is analysed, and a method is derived that yields the driving currents required to induce a field with a user-defined shape. The formulation makes use of lead fields and minimumnorm estimation from magneto-encephalography. Using these methods, some properties of multichannel coil arrays are examined. Computer-assisted multichannel stimulation of the cortex will enable several new studies, including quick determination of the cortical regions, the stimulation of which disrupts cortical processing required by a task.