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。     

磁刺激中深度感应电场分布的计算

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组织的过程.根据磁刺激感应电场理论,计算8字形和四叶形线圈刺激深度感应电场的分布.结果表明通过线圈的电流方向直接影响感应电场的聚焦性.8字形线圈电流方向相反时用于刺激大脑皮层神经效果较好,而四叶形线圈电流方向左右相反,上下相同时,刺激外周神经纤维效果较好.     

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.     

磁刺激人体可兴奋组织的模及其感应电场的三维分析

磁刺激是利用时变电流流入线圈,产生时变磁场,从而在组织内感应出电流使某些可兴奋性组织产生兴奋的一种无创的诊断和治疗技术。本文建立了磁刺激可兴奋性组织的一般模型。确定了一些无量纲参数,对感应电场的分布函数进行无量纲化,并给出强度三维分布的计算机仿真。文中分析和讨论了决定刺激聚焦和刺激深度的因素,确定了设计合理的磁刺激线圈和可以使刺激效果和磁刺激装置都得到优化的依据。     

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。     

脑磁刺激空间感应电场分布的数学模型与计算机仿真

本研究建立了脑神经磁刺激研究中较常用的八字线圈感应电场分布的半无界空间数学模型 ,应用数值积分和图形旋转与消隐技术建立了计算机仿真方法 ,据此分析了八字线圈感应电场空间分布的特性 ,为设计具有更好空间定位性和矢量选择性的脑神经磁刺激线圈提供了有效的仿真手段和研究方法。     

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。     

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.     

Electric fields induced in a spherical volume conductor by temporally varying magnetic field gradients

A homogeneous spherical volume conductor is used as a model system for the purpose of calculating electric fields induced in the human head by externally applied time-varying magnetic fields. We present results for the case where magnetic field gradient coils, used in magnetic resonance imaging (MRI), form the magnetic field, and we use these data to put limits on the rates of gradient change with time needed to produce nerve stimulation. The electric field is calculated analytically for the case of ideal longitudinal and transverse linear field gradients. We also show results from computer calculations yielding the electric field maps in a sphere when the field gradients are generated by a real MRI gradient coil set. In addition, the effect of shifting the sphere within each gradient coil volume is investigated. Numerical analysis shows similar results when applied to a model human head.     

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。     

A theoretical comparison of electric and magnetic stimulation of the brain

We present a theoretical comparison of the electric field produced in the brain by three modalities of transcranial stimulation of the cortex: magnetic stimulation, bifocal electric stimulation, and unifocal electric stimulation. The primary focus of this comparison is the focality and direction of the electric fields produced. A three-sphere model is used to represent the scalp, skull, and brain. All electric fields are calculated numerically. For magnetic stimulation we consider only a figure-of-eight coil. We find that magnetic stimulation produces the most focal field, while unifocal electric produces the least. Fields produced during magnetic stimulation are parallel to the head surface, while fields produced during electric stimulation have components both parallel and perpendicular to the head surface. The electric field produced by magnetic stimulation is shown to be insensitive to the skull conductivity, while that produced by electric stimulation is very sensitive to it.     

磁刺激8字形线圈的结构对感应电场分布影响

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组织的过程.8字形线圈由于结构简单,常用于磁刺激中.故根据磁刺激感应电场理论,对8字形线圈改进了两种空间结构,计算其刺激深度感应电场分布,并与改进前作比较,结果表明扇形空间结构聚焦性好,更利于磁刺激兴奋点定位.     

一种抑制反向感应电场的磁刺激线圈设计方法探讨

在无创性脑神经磁刺激技术中,多采用8字形磁刺激线圈,在线圈周围一定距离的空间中,对应8字线圈中心出现感应电场最大值,对应两个边缘处出现反向感应电场峰值,后者容易在刺激目标处产生副刺激,分析了8字形磁刺激线圈感应电场的分布,针对其反应方向感应电场幅值较大,容易引起副刺激的问题提出了新的磁刺激线圈设计方法,以抑制感应电场副峰,并进行了计算机模拟和验证。     

磁刺激中线圈感应电场的聚焦性研究

根据磁刺激线圈感应电场理论,对圆形线圈、8字形线圈、四圆形线圈和四叶形线圈感应电场的分布进行研究,结果表明四叶形聚焦性好,更利于磁刺激兴奋点的定位.     

A new method for spatially selective,non-invasive activation of neurons: concept and computer simulation

Currently available non-invasive neurostimulation devices, using skin electrodes or externally applied magnetic coils, are not capable of producing a local stimulation maximum deep inside a homogeneous conductor, because of a fundamental limitation inherent to the Laplace equation. In this paper, a new neurostimulation method (the DeepFocus method) is presented, which avoids this limitation by using an indirect method of producing electric currents inside tissues: First, cylinder-shaped ferromagnetic rotating disks of non-permanent magnetic material are placed near the skin and magnetized by a non-rotating magnetic coil. Each of the disks rotates at high speed around its own axis of symmetry, thus producing a purely electric Lorentz force field having a non-zero divergence outside the disk, and therefore giving rise to charge accumulations inside the tissues. Subsequently, the magnetic field is switched off suddenly, causing a re-distribution of charge, and hence short-lived electrical currents, which can be used to activate neurons. Two magnet configurations are presented in this paper, and analyzed by computer simulation, showing that the DeepFocus method produces a maximum current density (the ‘focus’) deep inside the conducting body. The field strength thus created in the focus (7.9 V/m) is strong enough to activate thick myelinated fibers, but can be kept below the threshold for C-fibers, which makes the new method a possible tool for pain mitigation by targeted neurostimulation.     

Reducing the staircasing error in computational dosimetry of low-frequency electromagnetic fields

From extremely low frequencies to intermediate frequencies, the magnitude of induced electric field inside the human body is used as the metric for human protection. The induced electric field inside the body can be computed using anatomically realistic voxel models and numerical methods such as the finite-difference or finite-element methods. The computed electric field is affected by numerical errors that occur when curved boundaries with large contrasts in electrical conductivity are approximated using a staircase grid. In order to lessen the effect of the staircase approximation error, the use of the 99th percentile electric field, i.e. ignoring the highest 1% of electric field values, is recommended in the ICNIRP guidelines. However, the 99th percentile approach is not applicable to localized exposure scenarios where the majority of significant induced electric field values may be concentrated in a small volume. In this note, a method for removing the staircasing error is proposed. Unlike the 99th percentile, the proposed method is also applicable to localized exposure scenarios. The performance of the method is first verified by comparison with the analytical solution in a layered sphere. The method is then applied for six different exposure scenarios in two anatomically realistic human head models. The results show that the proposed method can provide conservative estimates for the 99th percentile electric field in both localized and uniform exposure scenarios.     

Electromagnetic fields in the human body due to switched transverse gradient coils in MRI

Magnetic resonance imaging scans impose large gradient magnetic fields on the patient. Modern imaging techniques require this magnetic field to be switched rapidly for good resolution. However, it is believed that this can also lead to the unwanted side effect of peripheral nerve stimulation, which proves to be a limiting factor to the advancement of MRI technology. This paper establishes an analytical model for the fields produced within an MRI scanner by transverse gradient coils of known current density. Expressions are obtained for the magnetic induction vector and the electric field vector, as well as for the surface charge and current densities that are induced on the patient's body. The expressions obtained are general enough to allow the study of any combination of gradient coils whose behaviour can be approximated by Fourier series. For a realistic example coil current density and switching function, it is found that spikes of surface charge density are induced on the patient's body as the gradient field is switched, as well as loops of surface current density that mimic the coil current density. For a 10 mT m(-1) gradient field with a rise time of 100 micros, the magnitude of the radial electric field at the body is found to be 10.3 V m(-1). It is also found that there is a finite limit to radial electric field strength as rise time approaches zero.     

Representation of bioelectric current sources using Whitney elements in the finite element method

Bioelectric current sources of magneto- and electroencephalograms (MEG, EEG) are usually modelled with discrete delta-function type current dipoles, despite the fact that the currents in the brain are naturally continuous throughout the neuronal tissue. In this study, we represent bioelectric current sources in terms of Whitney-type elements in the finite element method (FEM) using a tetrahedral mesh. The aim is to study how well the Whitney elements can reproduce the potential and magnetic field patterns generated by a point current dipole in a homogeneous conducting sphere. The electric potential is solved for a unit sphere model with isotropic conductivity and magnetic fields are calculated for points located on a cap outside the sphere. The computed potential and magnetic field are compared with analytical solutions for a current dipole. Relative difference measures between the FEM and analytical solutions are less than 1%, suggesting that Whitney elements as bioelectric current sources are able to produce the same potential and magnetic field patterns as the point dipole sources.     

脑部磁刺激磁场和感应电场的初步研究

作为脑部磁刺激研究的一项基础工作，本文建立了刺激磁场中的球形头模型，对方形线圈在其内产生的时变磁场和感应电场进行了理论研究。导出了Ｂ，Ｅ，Ｊ的解析表达式，分析了场的特性和刺激强度的分布规律。为进一步探索时变磁场对人脑的最佳刺激方式和作用机理提供了初步的理论基础。