Toroidal coil models for transcutaneous magnetic stimulation of nerves

Coil efficiency for inductive peripheral nerve stimulation

Magnetic stimulation of peripheral nerves is evoked by electric field gradients caused by high-intensity, pulsed magnetic fields created from a coil. Currents required for stimulation are very high, therefore devices are large, expensive, and often too complex for many applications like rehabilitation therapy. For repetitive stimulation, coil heating due to power loss poses a further limitation. The geometry of the magnetic coil determines field depth and focality, making it the most important factor that determines the current required for neuronal excitation. However, the comparison between different coil geometries is difficult and depends on the specific application. Especially the distance between nerve and coil plays a crucial role. In this investigation, the electric field distribution of 14 different coil geometries was calculated for a typical peripheral nerve stimulation with a 27mm distance between axon and coil. Coil parameters like field strength and focality were determined with electromagnetic field simulations. In a second analysis, the activating function along the axon was calculated, which quantifies the efficiency of neuronal stimulation. Moreover, coil designs were evaluated concerning power efficacy based on ohmic losses. Our results indicate that power efficacy of magnetic neurostimulation can be improved significantly by up to 40% with optimized coil designs.

Optimization of multiple coils immersed in a conducting liquid for half-hemisphere or whole-brain deep transcranial magnetic stimulation: a simulation study

Transcranial magnetic stimulation (TMS) was proposed in 1985. Nevertheless, its wider use in the treatment of several neurologic diseases has been hindered by its inability to stimulate deep-brain regions. This is mainly due to the physical limiting effect arising from the presence of surface discontinuities, particularly between the scalp and air. Here, we present the optimization of a system of large multiple coils for whole-brain and half-hemisphere deep TMS, termed orthogonal configuration. COMSOL(®)-based simulations show that the system is capable of reaching the very center of a spherical brain phantom with 58% induction relative to surface maximum. Such penetration capability surpasses to the best of our knowledge that of existing state of the art TMS systems. This induction capability strongly relies on the immersion of the stimulating coils and part of the head of the patient in a conducting liquid (e.g. simple saline solution). We show the impact of the presence of this surrounding conducting liquid by comparing the performance of our system with and without such liquid. In addition, we also compare the performance of the proposed coil with that of a circular coil, a figure-eight coil, and the H-coil. Finally, in addition to its whole-brain stimulation capability (e.g. potentially useful for prophylaxis of epileptic patients) the system is also able to stimulate mainly one brain hemisphere, which may be useful in stroke rehabilitation, among other applications.

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).

A finite element analysis of the effect of electrode area and inter-electrode distance on the spatial distribution of the current density in tDCS

We investigated the effect of electrode area and inter-electrode distance on the spatial distribution of the current density in transcranial direct current stimulation (tDCS). For this purpose, we used the finite element method to compute the distribution of the current density in a four-layered spherical head model using various electrode montages, corresponding to a range of electrode sizes and inter-electrode distances. We found that smaller electrodes required slightly less current to achieve a constant value of the current density at a reference point on the brain surface located directly under the electrode center. Under these conditions, smaller electrodes also produced a more focal current density distribution in the brain, i.e. the magnitude of the current density fell more rapidly with distance from the reference point. The combination of two electrodes with different areas produced an asymmetric current distribution that could lead to more effective and localized neural modulation under the smaller electrode than under the larger one. Focality improved rapidly with decreasing electrode size when the larger electrode sizes were considered but the improvement was less marked for the smaller electrode sizes. Also, focality was not affected significantly by inter-electrode distance unless two large electrodes were placed close together. Increasing the inter-electrode distance resulted in decreased shunting of the current through the scalp and the cerebrospinal fluid, and decreasing electrode area resulted in increased current density on the scalp under the edges of the electrode. Our calculations suggest that when working with conventional electrodes (25-35 cm(2)), one of the electrodes should be placed just 'behind' the target relative to the other electrode, for maximum current density on the target. Also electrodes with areas in the range 3.5-12 cm(2) may provide a better compromise between focality and current density in the scalp than the traditional electrodes. Finally, the use of multiple small return electrodes may be more efficient than the use of a single large return electrode.

Charge and energy minimization in electrical/magnetic stimulation of nervous tissue

In this work we address the problem of stimulating nervous tissue with the minimal necessary energy at reduced/minimal charge. Charge minimization is related to a valid safety concern (avoidance and reduction of stimulation-induced tissue and electrode damage). Energy minimization plays a role in battery-driven electrical or magnetic stimulation systems (increased lifetime, repetition rates, reduction of power requirements, thermal management). Extensive new theoretical results are derived by employing an optimal control theory framework. These results include derivation of the optimal electrical stimulation waveform for a mixed energy/charge minimization problem, derivation of the charge-balanced energy-minimal electrical stimulation waveform, solutions of a pure charge minimization problem with and without a constraint on the stimulation amplitude, and derivation of the energy-minimal magnetic stimulation waveform. Depending on the set stimulus pulse duration, energy and charge reductions of up to 80% are deemed possible. Results are verified in simulations with an active, mammalian-like nerve fiber model.

Comparing different electrode configurations using the 10-10 international system in tDCS: a finite element model analysis

For the past few years, the potential of transcranial direct current stimulation (tDCS) for the treatment of several pathologies has been investigated. Knowledge of the current density distribution is an important factor in optimizing such applications of tDCS. We use the finite element method to compare three different models in tDCS, where the stimulation electrodes (EEG electrodes) are placed in the 10-10 international system coordinates. We studied the focality and the distribution of the current density in depth and at the surface of the brain for three different electrode configurations. We show that the use of EEG electrodes increases the focality of tDCS, especially when one cathode and several anodes are used. Additionally, these electrodes need less injected current, can be placed at scalp positions whose relationship with the underlying cerebral cortex are known and allow the use of tDCS and EEG recording concomitantly.

High permeability cores to optimize the stimulation of deeply located brain regions using transcranial magnetic stimulation

Efficient stimulation of deeply located brain regions with transcranial magnetic stimulation (TMS) poses many challenges, arising from the fact that the induced field decays rapidly and becomes less focal with depth. We propose a new method to improve the efficiency of TMS of deep brain regions that combines high permeability cores, to increase focality and field intensity, with a coil specifically designed to induce a field that decays slowly with increasing depth. The performance of the proposed design was investigated using the finite element method to determine the total electric field induced by this coil/core arrangement on a realistically shaped homogeneous head model. The calculations show that the inclusion of the cores increases the field's magnitude by as much as 25% while also decreasing the field's decay with depth along specific directions. The focality, as measured by the area where the field's norm is greater than 1/sq.rt.2 of its maximum value, is also improved by as much as 15% with some core arrangements. The coil's inductance is not significantly increased by the cores. These results show that the presence of the cores might make this specially designed coil even more suited for the effective stimulation of deep brain regions.

Transcranial magnetic stimulation of small animals: a modeling study of the influence of coil geometry, size and orientation

Several recent studies have investigated the mechanisms of repetitive transcranial magnetic stimulation (rTMS) using small animals. However, there is still limited knowledge about the distribution of the induced electric field, and its dependence on coil size, geometry and orientation. In this work we calculate the electric field induced in a realistically shaped homogeneous mouse model by commercially available coils in several different orientations. The results show that the secondary field, resulting from charge accumulation at the skin - air interface, drastically changes the magnitude, decay and focality of the primary field induced by the coil. Accurate knowledge about the distribution of the field is invaluable in designing experimental protocols and new coils for small animal stimulation.

Biophysical foundations underlying TMS: setting the stage for an effective use of neurostimulation in the cognitive neurosciences

Transcranial Magnetic Stimulation (TMS) induces electrical currents in the brain to stimulate neural tissue. This article reviews our present understanding of TMS methodology, focusing on its biophysical foundations. We concentrate on how the laws of electromagnetic induction apply to TMS; addressing issues such as the location, area (i.e., focality), depth, and mechanism of TMS. We also present a review of the present limitations and future potential of the technique.

High-permeability core coils for transcranial magnetic stimulation of deep brain regions

Stimulation of deep brain regions with Transcranial Magnetic Stimulation (TMS) may have an important role as a therapy to treat chemical dependency and depression. The coils traditionally used in TMS, however, have a poor performance in stimulating deep neurons. In this work we study the usage of high permeability cores combined with coils specifically designed to induce fields that decay slowly with depth. By using the finite elements method we show that the use of such cores increases the field's magnitude, decreases its decay rate and improves its focality. Such improvements make these high permeability core coils more suited to stimulate deep brain regions.

Noninvasive human brain stimulation

Noninvasive brain stimulation with transcranial magnetic stimulation (TMS) or transcranial direct current stimulation (tDCS) is valuable in research and has potential therapeutic applications in cognitive neuroscience, neurophysiology, psychiatry, and neurology. TMS allows neurostimulation and neuromodulation, while tDCS is a purely neuromodulatory application. TMS and tDCS allow diagnostic and interventional neurophysiology applications, and focal neuropharmacology delivery. However, the physics and basic mechanisms of action remain incompletely explored. Following an overview of the history and current applications of noninvasive brain stimulation, we review stimulation device design principles, the electromagnetic and physical foundations of the techniques, and the current knowledge about the electrophysiologic basis of the effects. Finally, we discuss potential biomedical and electrical engineering developments that could lead to more effective stimulation devices, better suited for the specific applications.

Restoration of respiratory muscle function following spinal cord injury

Respiratory complications are a leading cause of morbidity and mortality in patients with spinal cord injury. Several techniques, currently available or in development, have the capacity to restore respiratory muscle function allowing these patients to live more normal lives and hopefully reduce the incidence of respiratory complications. Bilateral phrenic nerve pacing, a clinically accepted technique to restore inspiratory muscle function, allows patients with ventilator dependent tetraplegia complete freedom from mechanical ventilation. Compared to mechanical ventilation, phrenic nerve pacing provides patients with increased mobility, improved speech, improved comfort level and reduction in health care costs. The results of clinical trials of laparoscopically placed intramuscular diaphragm electrodes suggest that diaphragm pacing can also be achieved without the need for a thoracotomy and associated long hospital stay, and without manipulation of the phrenic nerve which carries a risk of phrenic nerve injury. Other clinical trials are being performed to restore inspiratory intercostal function. In patients with only unilateral phrenic nerve function who are not candidates for phrenic nerve pacing, combined intercostal and unilateral diaphragm pacing appears to provide benefits similar to that of bilateral diaphragm pacing. Clinical trials are also underway to restore expiratory muscle function. Magnetic stimulation, surface stimulation and spinal cord stimulation of the expiratory muscles are promising techniques to restore an effective cough mechanism in this patient population. These techniques hold promise to reduce the incidence of respiratory tract infections, atelectasis and respiratory failure in patients with spinal cord injury and reduce the morbidity and mortality associated with these complications.