A novel electric design for electromagnetic stimulation--the Slinky coil

High-frequency rTMS over the left DLPFC improves the response inhibition control of young healthy participants: an ERP combined 1H-MRS study

Introduction

Unlike the effect of repetitive transcranial magnetic stimulation (rTMS) in treating neuropsychiatric diseases, little is known about how personal factors might account for the disparity of results from studies of cognition and rTMS. In this study, we investigated the effects of high-frequency rTMS on response inhibition control and explored the time course changes in cognitive processing and brain metabolic mechanisms after rTMS using event-related potentials (ERPs) and magnetic resonance spectroscopy (¹H-MRS).

Methods

Participants were all right-handed and were naive to rTMS and the Go/NoGo task. Twenty-five healthy young participants underwent one 10 Hz rTMS session per day in which stimulation was applied over the left dorsolateral prefrontal cortex (DLPFC), and a homogeneous participant group of 25 individuals received a sham rTMS treatment for 1  week. A Go/NoGo task was performed, an electroencephalogram (EEG) was recorded, and ¹H-MRS was performed.

Results

The results revealed that there was a strong trend of decreasing commission errors of NoGo stimuli by high frequency rTMS over the left DLPFC, whereas there was no significant difference between before and after rTMS treatment with respect to these parameters in the sham rTMS group. High-frequency rTMS significantly increased the amplitude of NoGo-N2 but not Go-N2, Go-P3, or NoGo-P3. The myo-inositol /creatine complex (MI/Cr) ratio, indexing cerebral metabolism, in the left DLPFC was decreased in the rTMS treated group.

Discussion

This observation supports the view that high-frequency rTMS over the left DLPFC has the strong tendency of reducing commission errors behaviorally, increase the amplitude of NoGo-N2 and improve the response inhibition control of healthy young participants. The results are consistent with the excitatory properties of high frequency rTMS. We suggest that the increase in the NoGo-N2 amplitude may be related to the increased excitability of the DLPFC-anterior cingulate cortex (ACC) neural loop. Metabolic changes in the DLPFC may be a possible mechanism for the improvement of the response inhibition control of rTMS.

Optimal Design of Array Coils for Multi-Target Adjustable Electromagnetic Brain Stimulation System

Temporal interference magnetic stimulation is a novel noninvasive deep brain neuromodulation technology that can solve the problem of balance between focus area and stimulation depth. However, at present, the stimulation target of this technology is relatively single, and it is difficult to realize the coordinated stimulation of multiple brain regions, which limits its application in the modulation of multiple nodes in the brain network. This paper first proposes a multi-target temporal interference magnetic stimulation system with array coils. The array coils are composed of seven coil units with an outer radius of 25 mm, and the spacing between coil units is 2 mm. Secondly, models of human tissue fluid and the human brain sphere are established. Finally, the relationship between the movement of the focus area and the amplitude ratio of the difference frequency excitation sources under time interference is discussed. The results show that in the case of a ratio of 1:5, the peak position of the amplitude modulation intensity of the induced electric field has moved 45 mm; that is, the movement of the focus area is related to the amplitude ratio of the difference frequency excitation sources. The conclusion is that multi-target temporal interference magnetic stimulation with array coils can simultaneously stimulate multiple network nodes in the brain region; rough positioning can be performed by controlling the conduction of different coils, fine-tuning the position by changing the current ratio of the conduction coils, and realizing accurate stimulation of multiple targets in the brain area.

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.

Simulation-Based Optimization of Figure-of-Eight Coil Designs and Orientations for Magnetic Stimulation of Peripheral Nerve

Although magnetic neural stimulation has many advantages over electrical neural stimulation, its main disadvantages are higher energy requirement and poor stimulation selectivity. The orientation and location of the coil with respect to the stimulation site play a critical role in determining the stimulation threshold and stimulation selectivity. Utilizing numerical simulations in this work, we optimized the design parameters, orientation, and positioning of magnetic coils with respect to the peripheral nerve for improved stimulation efficacy. Specifically, we investigated different orientations and positions of the figure-of-eight coils for neural stimulation of the rat sciatic nerve. We also examined the effect of coil design parameters (number of layers and turns) and different coil electrical configurations (opposite vs. same direction of coil currents and series vs. parallel coil connections) on the stimulation threshold. We leveraged the multi-resolution impedance method and a heterogeneous multi-fascicular anatomical model of rat sciatic nerve to explore the possibility of selective stimulation as well. Neural excitation of a nerve fiber was implemented by an equivalent cable model and Frankenhaeuser-Huxley equations using NEURON software. Results suggest that inter-fascicular selectivity could be achieved by properly orienting and positioning the coil with respect to the nerve. Further, by orienting the figure-of-eight coil at an angle of 90° and 6 mm offset, we could switch between primarily activating one fascicle (and barely activating the other) and reversing those roles by merely switching the current direction in the two coils of the figure-of-eight coil.

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.

The effects of high-frequency rTMS over the left DLPFC on cognitive control in young healthy participants

A large body of evidence suggests that repetitive transcranial magnetic stimulation (rTMS) is clinically effective in treating neuropsychiatric disorders and multiple sessions are commonly used. However, it is unknown whether multiple sessions of rTMS improve cognitive control, which is a function of the neural circuitry of the left dorsolateral prefrontal cortex (DLPFC)-cingulate cortex in healthy individuals. In addition, it is still unclear which stages of neural processing are altered by rTMS. In this study, we investigated the effects of high-frequency rTMS on cognitive control and explored the time course changes of cognitive processing after rTMS using event-related potentials (ERPs). For seven consecutive days, 25 young healthy participants underwent one 10-Hz rTMS session per day in which stimulation was applied over the left DLPFC, and a homogeneous participant group of 25 individuals received a sham rTMS treatment. A Stroop task was performed, and an electroencephalogram (EEG) was recorded. The results revealed that multiple sessions of rTMS can decrease reaction time (RTs) under both congruent and incongruent conditions and also increased the amplitudes of both N2 and N450 compared with sham rTMS. The negative correlations between the mean amplitudes of both N2 and N450 and the RTs were found, however, the latter correlation were restricted to incongruent trials and the correlation was enhanced significantly by rTMS. This observation supports the view that high-frequency rTMS over the left DLPFC can not only recruit more neural resources from the prefrontal cortex by inducing an electrophysiologically excitatory effect but also enhance efficiency of resources to deploy for conflict resolution during multiple stages of cognitive control processing in healthy young people.

Computational Study Toward Deep Transcranial Magnetic Stimulation Using Coaxial Circular Coils

OBJECTIVE

To investigate the possibility for stimulating deeper brain regions while decreasing the electrical field in superficial cortical regions by employing coaxial circular coils.

METHODS

The Halo coil, Halo-circular assembly coil (HCA coil) and Halo coil working with two circular coils (HTC coil) were applied over a 36-tissue anatomically based head model. Three-dimensional distributions of magnetic flux density, induced electric field in head tissues were obtained by 3-D impedance method.

RESULTS

For the case of HCA coil with current flowing in the same direction in each of two coils, the field penetration depth by the conventional circular coil can be effectively increased at the expense of reduced focality. For the case of the HTC coil with currents flowing in opposite direction in the neighboring coils, overthreshold electric fields can be produced in deep brain regions, while the subthreshold fields were produced in superficial cortical areas.

CONCLUSION

The HTC coil with varied coil parameters and different injected currents provides a flexible way for deep brain stimulation with better ratio of deep region field relative to field at the shallow areas.

SIGNIFICANCE

The HTC coil is promising for deep transcranial magnetic stimulation, which may offer a new tool with potential for both research and clinical applications for psychiatric and neurological disorders associated with dysfunctions of deep brain regions.

Simulation Study to Improve Focalization of a Figure Eight Coil by Using a Conductive Shield Plate and a Ferromagnetic Block

A new method to improve the focalization and efficiency of the Figure of Eight (FOE) coil in rTMS is discussed in this paper. In order to decrease the half width of the distribution curve (HWDC), as well to increase the ratio of positive peak value to negative peak value (RPN) of the induced electric field, a shield plate with a window and a ferromagnetic block are assumed to enhance the positive peak value of the induced electrical field. The shield is made of highly conductive copper, and the block is made of highly permeable soft magnetic ferrite. A computer simulation is conducted on ANSYS® software to conduct the finite element analysis (FEA). Two comparing coefficients were set up to optimize the sizes of the shield window and the block. Simulation results show that a shield with a 60 mm × 30 mm sized window, together with a block 40 mm thick, can decrease the focal area of a FOE coil by 46.7%, while increasing the RPN by 135.9%. The block enhances the peak value of the electrical field induced by a shield-FOE by 8.4%. A real human head model was occupied in this paper to further verify our method.

Numerical analysis and design of single-source multicoil TMS for deep and focused brain stimulation

Transcranial magnetic stimulation (TMS) is a tool for noninvasive stimulation of neuronal tissue used for research in cognitive neuroscience and to treat neurological disorders. Many TMS applications call for large electric fields to be sharply focused on regions that often lie deep inside the brain. Unfortunately, the fields generated by present-day TMS coils diffuse and decay rapidly as they penetrate into the head. As a result, they tend to stimulate relatively large regions of tissue near the brain surface. Earlier studies suggested that a focused TMS excitation can be attained using multiple nonuniformly fed coils in a multichannel array. We propose a systematic, genetic algorithm-based technique for synthesizing multichannel arrays that minimize the volume of the excited region required to achieve a prescribed penetration depth and maintain realistic values for the input driving currents. Because multichannel arrays are costly to build, we also propose a method to convert the multichannel arrays into single-channel ones while minimally materially deteriorating performance. Numerical results show that the new multi- and single-channel arrays stimulate tissue 2.4 cm into the head while exciting 3.0 and 2.6 times less volume than conventional Figure-8 coils, respectively.

Physiological and modeling evidence for focal transcranial electrical brain stimulation in humans: a basis for high-definition tDCS

Transcranial Direct Current Stimulation (tDCS) is a non-invasive, low-cost, well-tolerated technique producing lasting modulation of cortical excitability. Behavioral and therapeutic outcomes of tDCS are linked to the targeted brain regions, but there is little evidence that current reaches the brain as intended. We aimed to: (1) validate a computational model for estimating cortical electric fields in human transcranial stimulation, and (2) assess the magnitude and spread of cortical electric field with a novel High-Definition tDCS (HD-tDCS) scalp montage using a 4 × 1-Ring electrode configuration. In three healthy adults, Transcranial Electrical Stimulation (TES) over primary motor cortex (M1) was delivered using the 4 × 1 montage (4 × cathode, surrounding a single central anode; montage radius ~3 cm) with sufficient intensity to elicit a discrete muscle twitch in the hand. The estimated current distribution in M1 was calculated using the individualized MRI-based model, and compared with the observed motor response across subjects. The response magnitude was quantified with stimulation over motor cortex as well as anterior and posterior to motor cortex. In each case the model data were consistent with the motor response across subjects. The estimated cortical electric fields with the 4 × 1 montage were compared (area, magnitude, direction) for TES and tDCS in each subject. We provide direct evidence in humans that TES with a 4 × 1-Ring configuration can activate motor cortex and that current does not substantially spread outside the stimulation area. Computational models predict that both TES and tDCS waveforms using the 4 × 1-Ring configuration generate electric fields in cortex with comparable gross current distribution, and preferentially directed normal (inward) currents. The agreement of modeling and experimental data for both current delivery and focality support the use of the HD-tDCS 4 × 1-Ring montage for cortically targeted neuromodulation.

Electric field depth-focality tradeoff in transcranial magnetic stimulation: simulation comparison of 50 coil designs

BACKGROUND

Various transcranial magnetic stimulation (TMS) coil designs are available or have been proposed. However, key coil characteristics such as electric field focality and attenuation in depth have not been adequately compared. Knowledge of the coil focality and depth characteristics can help TMS researchers and clinicians with coil selection and interpretation of TMS studies.

OBJECTIVE

To quantify the electric field focality and depth of penetration of various TMS coils.

METHODS

The electric field distributions induced by 50 TMS coils were simulated in a spherical human head model using the finite element method. For each coil design, we quantified the electric field penetration by the half-value depth, d(1/2), and focality by the tangential spread, S(1/2), defined as the half-value volume (V(1/2)) divided by the half-value depth, S(1/2) = V(1/2)/d(1/2).

RESULTS

The 50 TMS coils exhibit a wide range of electric field focality and depth, but all followed a depth-focality tradeoff: coils with larger half-value depth cannot be as focal as more superficial coils. The ranges of achievable d(1/2) are similar between coils producing circular and figure-8 electric field patterns, ranging 1.0-3.5 cm and 0.9-3.4 cm, respectively. However, figure-8 field coils are more focal, having S(1/2) as low as 5 cm(2) compared to 34 cm(2) for circular field coils.

CONCLUSIONS

For any coil design, the ability to directly stimulate deeper brain structures is obtained at the expense of inducing wider electrical field spread. Novel coil designs should be benchmarked against comparison coils with consistent metrics such as d(1/2) and S(1/2).

[Transcranial magnetic stimulation (TMS) in basic and clinical neuroscience research]

INTRODUCTION

Non-invasive brain stimulation methods such as transcranial magnetic stimulation (TMS) are starting to be widely used to make causality-based inferences about brain-behavior interactions. Moreover, TMS-based clinical applications are under development to treat specific neurological or psychiatric conditions, such as depression, dystonia, pain, tinnitus and the sequels of stroke, among others.

BACKGROUND

TMS works by inducing non-invasively electric currents in localized cortical regions thus modulating their activity levels according to settings, such as frequency, number of pulses, train and regime duration and intertrain intervals. For instance, it is known for the motor cortex that low frequency or continuous patterns of TMS pulses tend to depress local activity whereas high frequency and discontinuous TMS patterns tend to enhance it. Additionally, local cortical effects of TMS can result in dramatic patterns in distant brain regions. These distant effects are mediated via anatomical connectivity in a magnitude that depends on the efficiency and sign of such connections.

PERSPECTIVES

An efficient use of TMS in both fields requires however, a deep understanding of its operational principles, its risks, its potential and limitations. In this article, we will briefly present the principles through which non-invasive brain stimulation methods, and in particular TMS, operate.

CONCLUSION

Readers will be provided with fundamental information needed to critically discuss TMS studies and design hypothesis-driven TMS applications for cognitive and clinical neuroscience research.

Gyri-precise head model of transcranial direct current stimulation: improved spatial focality using a ring electrode versus conventional rectangular pad

The spatial resolution of conventional transcranial direct current stimulation (tDCS) is considered to be relatively diffuse owing to skull dispersion. However, we show that electric fields may be clustered at distinct gyri/sulci sites because of details in tissue architecture/conductivity, notably cerebrospinal fluid (CSF). We calculated the cortical electric field/current density magnitude induced during tDCS using a high spatial resolution (1 mm3) magnetic resonance imaging (MRI)-derived finite element human head model; cortical gyri/sulci were resolved. The spatial focality of conventional rectangular-pad (7 x 5 cm2) and the ring (4 x 1) electrode configurations were compared. The rectangular-pad configuration resulted in diffuse (unfocal) modulation, with discrete clusters of electric field magnitude maxima. Peak-induced electric field magnitude was not observed directly underneath the pads, but at an intermediate lobe. The 4 x 1 ring resulted in enhanced spatial focality, with peak-induced electric field magnitude at the sulcus and adjacent gyri directly underneath the active electrode. Cortical structures may be focally targeted by using ring configurations. Anatomically accurate high-resolution MRI-based forward-models may guide the "rational" clinical design and optimization of tDCS.

Generalized series solution for the induced E-field distribution of slinky-type magnetic stimulators

Magnetic stimulation is a technique to excite biological tissues by means of a time-varying magnetic field. This induced electric field can depolarize the cell membrane so as to evoke an action potential that propagates along neurons, eventually being transmitted to other neurons or to a muscular cell. Design of a magnetic stimulator requires modeling of the impulse propagation along the nerve cell, as well as numerical simulations for coil design optimization to determine adequate excitation levels as well as the degree of focalization on a given target cell. In this paper we report on a new methodology to calculate the stimulation field for the case of the traditional slinky coil geometry, that greatly reduces computation time, thus facilitating simulation studies of the dynamics of electric impulse propagation along a nerve cell.

Improved field localization in transcranial magnetic stimulation of the brain with the utilization of a conductive shield plate in the stimulator

In this paper, a carefully designed conductive shield plate is presented, which helps to improve localization of the electric field distribution induced by transcranial magnetic stimulation for neuron stimulation. The shield plate is introduced between a figure-of-eight coil and the head. In order to accurately predict the field distribution inside the brain and to examine the effects of the shield plate, a realistic head model is constructed from magnetic resonance image data with the help of image processing tools and the finite-element method in three dimensions is employed. Finally, to show the improvements obtained, the results are compared with two conventional coil designs. It is found that an incorporation of the shield plate into the coil, effectively improves the induced field localization by more than 50%, and prevents other parts of the brain from exposure to high pulsed magnetic fields.

Multichannel Magnetic Stimulation System Design Considering Mutual Couplings Among the Stimulation Coils

We introduce some simulation and experiment results of the multichannel magnetic stimulator development that has been carried out as an initial attempt to realize a multichannel functional magnetic stimulator. For efficient functional magnetic stimulations, precise spatial localization of stimulation sites without any movements of the stimulation coils is very important. We have found that the mutual coupling effect among the adjacent stimulation coils in the coil array has to be considered in the determination of the charge voltages in some coil array configurations. Experimental results obtained with a 4-channel magnetic stimulator are presented.

Analysis of efficiency of magnetic stimulation

Magnetic stimulation can activate excitable tissues noninvasively. However, this method requires high energy to operate and can produce equipment heat that leads to inefficient stimulation. In this study, a comprehensive optimization of efficiency for magnetic stimulation has been conducted. A total of 16 781 coil designs were tested in order to determine the optimal coil geometry and inductance for neural excitation. Induced electric fields were calculated to find the optimal stimulation site (OSS) of a given coil. The threshold energy of a magnetic pulse for neural excitation was then calculated based on the transmembrane responses of a nerve model. Simulation results show that there exists an optimal inductance, as a consequence of an optimal pulse duration, corresponding to a minimum threshold energy. A longer pulse width is required to obtain the maximum efficiency for axons with slower membrane dynamics, a longer coil-to-fiber distance, and greater values of resistance (R) and capacitance (C) of the resistance-inductance-capacitance circuit. The optimal geometry features a minimum coil height, suggesting a flat coil design for optimal efficiency. The dimension of the optimal coil design increases with the coil-to-fiber distance. Moreover, the cloverleaf design achieves the highest efficiency for infinitely long fibers whereas the butterfly design is optimal for terminating or bending fibers.

Magnetic stimulation for non-homogeneous biological structures

BACKGROUND

Magnetic stimulation has gained relatively wide application in studying nervous system structures. This technology has the advantage of reduced excitation of sensory nerve endings, and hence results in quasi-painless action. It has become clinically accepted modality for brain stimulation. However, theoretical and practical solutions for assessment of induced current distribution need more detailed and accurate consideration. Some possible analyses are proposed for distribution of the current induced from excitation current contours of different shape and disposition. Relatively non-difficult solutions are shown, applicable for two- and three-dimensional analysis.

METHODS

The boundary conditions for field analysis by the internal Dirichlet problem are introduced, based on the vector potential field excited by external current coils. The feedback from the induced eddy currents is neglected. Finite element modeling is applied for obtaining the electromagnetic fields distribution in a non-homogeneous domain.

RESULTS

The distributions were obtained in a non-homogeneous structure comprised of homogeneous layers. A tendency was found of the induced currents to follow paths in lower resistivity layers, deviating from the expected theoretical course for a homogeneous domain. Current density concentrations occur at the boundary between layers, suggesting the possibility for focusing on, or predicting of, a zone of stimulation.

CONCLUSION

The theoretical basis and simplified approach for generation of 3D FEM networks for magnetic stimulation analysis are presented, applicable in non-homogeneous and non-linear media. The inconveniences of introducing external excitation currents are avoided. Thus, the possibilities are improved for analysis of distributions induced by time-varying currents from contours of various geometry and position with respect to the medium.

Iron-core coils for transcranial magnetic stimulation

Transcranial magnetic stimulation requires a great deal of power, which mandates bulky power supplies and produces rapid coil heating. The authors describe the construction, modeling, and testing of an iron-core TMS coil that reduces power requirements and heat generation substantially, while improving the penetration of the magnetic field. Experimental measurements and numeric boundary element analysis show that the iron-core stimulation coil induces much stronger electrical fields, allows greater charge recovery, and generates less heat than air-core counterparts when excited on a constant-energy basis. These advantages are magnified in constant-effect comparisons. Examples are given in which the iron-core coil allows more effective operation in research and clinical applications.

A coil design for transcranial magnetic stimulation of deep brain regions

Noninvasive magnetic stimulation of the human central nervous system has been used in research and the clinic for several years. However, the coils used previously stimulated mainly the cortical brain regions but could not stimulate deeper brain regions directly. The purpose of the current study was to develop a coil to stimulate deep brain regions. Stimulation of the nucleus accumbens and the nerve fibers connecting the prefrontal cortex with the nucleus accumbens was one major target of the authors' coil design. Numeric simulations of the electrical field induced by several types of coils were performed and accordingly an optimized coil for deep brain stimulation was designed. The electrical field induced by the new coil design was measured in a phantom brain and compared with the double-cone coil. The numeric simulations show that the electrical fields induced by various types of coils are always greater in cortical regions (closer to the coil placement); however, the decrease in electrical field within the brain (as a function of the distance from the coil) is markedly slower for the new coil design. The phantom brain measurements basically confirmed the numeric simulations. The suggested coil is likely to have the ability of deep brain stimulation without the need to increase the intensity to levels that stimulate cortical regions to a much higher extent and possibly cause undesirable side effects.

Effect of contour shape of nervous system electromagnetic stimulation coils on the induced electrical field distribution

BACKGROUND

Electromagnetic stimulation of the nervous system has the advantage of reduced discomfort in activating nerves. For brain structures stimulation, it has become a clinically accepted modality. Coil designs usually consider factors such as optimization of induced power, focussing, field shape etc. In this study we are attempting to find the effect of the coil contour shape on the electrical field distribution for magnetic stimulation.

METHOD AND RESULTS

We use the maximum of the induced electric field stimulation in the region of interest as the optimization criterion. This choice required the application of the calculus of variation, with the contour perimeter taken as a pre-set condition. Four types of coils are studied and compared: circular, square, triangular and an 'optimally' shaped contour. The latter yields higher values of the induced electrical field in depths up to about 30 mm, but for depths around 100 mm, the circular shape has a slight advantage. The validity of the model results was checked by experimental measurements in a tank with saline solution, where differences of about 12% were found. In view the accuracy limitations of the computational and measurement methods used, such differences are considered acceptable.

CONCLUSION

We applied an optimization approach, using the calculus of variation, which allows to obtain a coil contour shape corresponding to a selected criterion. In this case, the optimal contour showed higher intensities for a longer line along the depth-axis. The method allows modifying the induced field structure and focussing the field to a selected zone or line.

A 3-D differential coil design for localized magnetic stimulation

A novel three-dimensional (3-D) differential coil has been designed for improving the localization of magnetic stimulation. This new coil design consists of a butterfly coil with two additional wing units and an extra bottom unit, both perpendicular to the plane of the butterfly coil. The wing units produce opposite fields to restrict the spread of induced fields while the bottom unit enhances the induced fields at the excitation site. The peak induced field generated by this new design is located at the center of the coil, providing an easy identification of the excitation site. The field localization of the new coil is comparable with that of much smaller coils but with an inductance compatible to current magnetic stimulators. Numerical computations based on the principles of electromagnetic induction and using a human nerve model were performed to analyze the induced fields and the stimulation thresholds of new coil designs. The localization of the coil design was assessed by a half power region (HPR), within which the magnitude of the normalized induced field is greater than 1/square root of 2. The HPR for a 3-D differential coil built is improved (decreased) by a factor of three compared with a standard butterfly coil. Induced fields by this new coil were measured and in agreement with theoretical calculations.

Improved coil design for functional magnetic stimulation of expiratory muscles

Our studies have demonstrated effective stimulation of the expiratory muscles in patients with spinal cord injury (SCI) using functional magnetic stimulation (FMS). The observed contraction of the expiratory muscles and functional improvement of the pulmonary functions make functional magnetic stimulation an appropriate tool for expiratory muscle training. To fully capitalize on the benefits of FMS for expiratory muscle training, this study aimed to optimize the magnetic coils (MCs). The primary goal of this study was to investigate how two parameters of the MC size and winding structure, would affect expiratory muscle training. By varying these parameters, our approach was to conceptualize and evaluate the induced electric field and nerve activation function distributions of six coils, round 9.2, 13.7, and 20 cm, and spiral 9.2-, 13.7-, and 20-cm coils in the computer modeling phase. Round 9.2 cm, spiral 13.7 cm, and spiral 20-cm coils were also evaluated in experimental studies for induced electrical field and in clinical studies of expiratory muscles. Both the computer models and experimental measurements indicated that the spiral 20-cm coil can not only stimulate more expiratory spinal nerves but can also stimulate them more evenly. In addition, coils with larger diameters had better penetration than those with smaller diameters. The clinical results showed that the spiral 20-cm coil produced higher expiratory pressure, flow, and volume in five able-bodied subjects, and it was the coil of choice among the subjects when asked their preferences. In our attempt to optimize MC design for FMS of expiratory muscle training, we followed the designing guidelines set out in our previous study and arrived at a more effective tool.

Toroidal coil models for transcutaneous magnetic stimulation of nerves

A novel design of coils for transcutaneous magnetic stimulation of nerves is presented. These coils consist of a toroidal winding around a high-permeability material (Supermendur) core embedded in a conducting medium. Theoretical numerical calculations are used to analyze the effect of the design parameters of these coils, such as coil width, toroidal radius, conducting layer thickness and core transversal shape on the induced electric fields in terms of the electric field strength and distribution. Results indicate that stimulation of nerves with these coils has some of the advantages of both electrical and magnetic stimulation. These coils can produce localized and efficient stimulation of nerves with induced electric fields parallel and perpendicular to the skin similar to surface electrical stimulation. However, they retain some of the advantages of magnetic stimulation such as no risk of tissue damage due to electrochemical reactions at the electrode interface and less uncomfortable sensations or pain. The driving current is reduced by over three orders of magnitude compared to traditional magnetic stimulation, eliminating the problem of coil heating and allowing for long duration and high-frequency magnetic stimulation with inexpensive stimulators.

Transcranial magnetic stimulation and cognitive neuroscience

Transcranial magnetic stimulation has been used to investigate almost all areas of cognitive neuroscience. This article discusses the most important (and least understood) considerations regarding the use of transcranial magnetic stimulation for cognitive neuroscience and outlines advances in the use of this technique for the replication and extension of findings from neuropsychology. We also take a more speculative look forward to the emerging development of strategies for combining transcranial magnetic stimulation with other brain imaging technologies and methods in the cognitive neurosciences.

Magnetic coil design considerations for functional magnetic stimulation

Our studies have demonstrated effective stimulation of the bladder, bowel, and expiratory muscles in patients with spinal cord injury using functional magnetic stimulation. However, one limitation of the magnetic coils (MC) is related to their inability to specifically stimulate the target tissue without activation of surrounding tissue. The primary goal of this study was to determine the governing parameters in the MC design, such as coil configuration, diameter, and number of turns in one loop of the coil. By varying these parameters, our approach was to design, construct, and evaluate the induced electric field distributions of two sets of novel MC's. Based on the slinky coil design, the first set of coils was constructed to compare their abilities in generating induced electric fields for focal nerve excitation. The second set of coils was built to determine the effect that changes in two parameters, coil diameter and number of turns in one loop, had on field penetration. The results showed that the slinky coil design produced more focalized stimulation when compared to the planar round coils. The primary-to-secondary peak ratios of the induced electric field from slinky 1 to 5 were 1.00, 2.20, 2.85, 2.62, and 3.54. We also determined that coils with larger diameters had better penetration than those with smaller diameters. Coils with less number of turns in one loop had higher initial field strengths; when compared to coils that had more turns per loop, initial field strengths remained higher as distance from the coil increased. In our attempt to customize MC design according to each functional magnetic stimulation application and patients of different sizes, the parameters of MC explored in this study may facilitate designing an optimal MC for a certain clinical application.

Functional magnetic stimulation of the respiratory muscles in dogs

This study assessed the ability of functional magnetic stimulation (FMS) to activate the respiratory muscles in dogs. With the animal supine, FMS of the phrenic nerves using a high-speed magnetic stimulator was performed by placing a round magnetic coil (MC) at the carotid triangle. Following hyperventilation-induced apnea, changes in volume (deltaV) and airway pressure (deltaP) against an occluded airway were determined. FMS of the phrenic nerves produced substantial inspired function (deltaV = 373 +/- 20.5 mL and deltaP = -20 +/- 2.0 cm H2O). After bilateral phrenectomies, maximal inspired deltaV (219 +/- 12.2 mL) and deltaP (-10 +/- 1.0 cm H2O) were produced when the MC was placed near the C6-C7 spinous processes, while maximal expired deltaV (-199 +/- 22.5 mL) and deltaP (11 +/- 2.3 cm H2O) were produced following stimulation near the T9-T10 spinous processes. We conclude: (1) FMS of either the phrenic or upper intercostal nerves results in inspired volume production; (2) FMS of the lower intercostal nerves generates expired volume production; and (3) FMS of the respiratory muscles may be a useful noninvasive tool for artificial ventilation and assisted cough in patients with spinal cord injuries or other neurological disorders.