Investigation of shape , position , and permeability of shielding material in quadruple butterfly coil for focused transcranial magnetic stimulation

Transcranial magnetic stimulation has been gaining popularity in the therapy for several neurological disorders. A time-varying magnetic field is used to generate electric field in the brain. As the development of TMS methods takes place, emphasis on the coil design increases in order to improve focal stimulation. Ideally reduction of stimulation of neighboring regions of the target area is desired. This study, focused on the improvement of the focality of the Quadruple Butterfly Coil (QBC) with supplemental use of different passive shields. Parameters such as shape, position and permeability of the shields have been explored to improve the focus of stimulation. Results have been obtained with the help of computer modelling of a MRI derived heterogeneous head model over the vertex position and the dorsolateral prefrontal cortex position using a finite element tool. Variables such as maximum electric field induced on the grey matter and scalp, volume and area of stimulation above half of the maximum value of electric field on the grey matter, and ratio of the maximum electric field in the brain versus the scalp have been investigated.


Investigation of shape, position, and permeability of shielding material in quadruple butterfly coil for focused transcranial magnetic stimulation I. INTRODUCTION
Transcranial Magnetic Stimulation (TMS) is a FDA approved non-invasive intervention for Treatment Resistant Depression (TRD) and migraine. 1,2][5][6] TMS works on the principal of Faraday's law of induction in which neural circuits are excited due to a time varying magnetic field.Furthermore, researchers and scholars are interested in fabricating TMS coils which have higher focus, yet still provide a strong enough electric field to depolarize neurons and initiate neuronal firing.The use of magnetic fields for stimulation allows excitation of neural circuits while avoiding painful stimulation in peripheral nerves on the scalp.A challenge with noninvasive stimulation, is that direct stimulation effects can spread a few centimeters beyond the desired target.Therefore, as TMS research progresses, it is important for new coils to be developed that can reduce the spread of the electric field to non-targeted brain regions.Beyond the spread of stimulation, other practical, secondary characteristics of coil design are also important.The main considerations discussed here include the stimulation output of the coil for a given current intensity, and the ratio of stimulation received in the brain as compared to the scalp.The authors have proposed a novel coil design with improved stimulation focality, namely the Quadruple Butterfly Coil (QBC) in a prior publication. 7Since then, the focality of the QBC has been improved with the help of a passive magnetic shield 8 using single material.In this paper, the authors have explored a variety of passive ferromagnetic magnet shield shapes, positions, and permeabilities to improve the focality of stimulation with the QBC.A heterogeneous healthy head model derived from MRIs has been used for all the simulations focused on the vertex of the head to investigate the effects of different shields with the QBC.Several shields of different shapes and sizes have been examined in this study.Presented in this paper are the best three shield configurations paired with both the QBC at the vertex and on the area of the scalp over the dorsolateral prefrontal cortex.

II. METHOD
An average head model for the simulations over the vertex position and four more head models for the simulations over the dorsolateral prefrontal cortex position were chosen by a random number generator from a set of 50 head models. 9The computer modelling tool, 10 simulation settings, post processing method, and parameters of interest including (a) E-Max brain, (b) A-Half, (c) V-Half, and (d) E-Max head were discussed in Rastogi et al. 6 These parameters refer to the (a) maximum electric field intensity in the grey matter (GM) and white matter (WM), (b) the surface area of the brain exposed to electric field intensities at least one half of maximum electric field (E-Max), (c) the volume of the brain exposed to electric field intensities at least one half of E-Max, and (d) the maximum electric field intensity in the entire head respectively.

A. Permeability
Permeability of shielding material has been explored for the shield used in Rastogi et al 6 along with the QBC on the vertex position of the head.In this subsection, the authors have changed the permeability of the shield while keeping all other variables constant: position of the shield, distance of the shield and shape of the shield.The permeabilities tested range from 25,000 -85,000, representing a "soft" ferromagnetic material.It can be seen that permeability has not resulted in any significant change in the focality.This can be seen as the volume and area that receive high stimulation intensities remain fairly constant as shown in Table I.

B. Thickness of the shield
In this subsection, the same configuration was used (permeability = 50,000); only the thickness of the shield is varied while keeping the other parameters constant.The thickness of the shield has been increased in such a way that the distance between the shield and the scalp has remained constant.Increasing the thickness of the shield decreases the E-Max and V-Half proportionally.This does little to help improve the focality of stimulation as shown in Table II.

C. Distance of the shield from the scalp
Distance of the shield from the scalp has been varied while the other parameters were kept constant.This includes the position of the coil itself.Since the QBC is conical in shape, the shield can be shifted vertically without having to move the QBC.Seeing as the shield is moving progressively closer to the coil as it moves away from the scalp the interaction between the QBC and the shield increases.This is apparent, as the E-Max has increased 4 % as the distance from the scalp increases (Table III).This may prove to be useful when the desired field is not met even after the power level is at its maximum output, the shield can then be shifted to increase the induced E-Max.

D. Different shapes of the shield
We have also investigated shield geometry and position of the shield with respect to the coil while holding the permeability constant.There are three different shapes of the shield which have been explored:  placed on both the vertex and dorsolateral prefrontal cortex position of the head model.The exact placement of the shield with respect to the coil and scalp can be seen in Table IV.The chosen arc angle of the V shape and semicircles of the shields are the results of several simulation iterations which resulted in the improved focality.

E. Dorsolateral prefrontal cortex
The shields discussed in section III D were used in additional simulations over the dorsolateral prefrontal cortex.This includes four more head models that have been chosen by a random number generator from the 50 head model set used in Rastogi et al. 6 It has been previously shown by the authors that the QBC with a shield has improved the focus by 25% when compared with the conventional Magstim Figure-8 coil.In this paper, the authors have compared the simulation results using a QBC with and without the aforementioned coils.As presented in Table V, E-Max in GM &WM has increased due to the presence of three shields whilst E-Max (Entire Head) has decreased when the simulation was run without shields, at the vertex position.In addition, the stimulation with the QBC alone results in more volume and area than when stimulation using magnetic shielding.The electric field ratio on scalp to brain at the vertex for this head model is 2.12 for QBC alone, 1.80 for V-shape, 1.79 for Brick and 1.75 for Two Semicircles along with QBC.
1,12 When the coils were positioned at the vertex of the head the results showed trends similar to the trends observed in Table V.The electric field ratio between the scalp and brain at the dorsolateral prefrontal cortex for five head models is 1.98 for the QBC alone, 1.34 for V-shape, 1.37 for Brick and 1.42 for Two-Semicircles along with QBC which is very close to the Figure-8 (1.47).From these findings, it is clear that the focality has indeed been improved by the addition of magnetic shielding.

IV. DISCUSSION AND CONCLUSION
In addition to the results derived from these three shield shapes, many other shapes have been tested.In the interest of brevity, the authors have planned to publish the rest of the results in future paper.
It is clear to the authors that by changing the parameters such as thickness, distance, and permeability of the shielding material, it seemed to show miniscule variation, but this could be due to the range of the values tested.This should be investigated further.Additionally, the researchers used a single model because the variation due to different shields was explored as opposed to the variation across many models.If the number of head models is increased, the variability among the models will make it difficult to isolate the effects of the shields alone.However, the results with one head model showed the same trend when tested with more models.
When the shields are within close proximity (approximately within 50 mm) to the coils, shifting the shield in any direction by 1cm, did not vary the results significantly.This result can be used to the researchers' advantage during clinical trials as head geometry varies with each person. 9Also, the shields used in this article or those used in the Rastogi et al. 6 were of small dimensions relative to the head and the coils.The reason smaller shields were selected is because they absorb less magnetic flux lines.Using bigger shields such as enclosed shields tends to absorb more magnetic flux lines and ultimately reduce the E-Max to values below 100 V/m.Furthermore, the use of magnetic shielding has displayed strong potential for improving the electric field ratio from scalp to brain and also to improve the E-Max and reduced the V-Half, thus improving the focality.
FIG. 1. Shows the shields position (a,d) V-shaped, (b,e) Two Semicircles (c,f) Brick, on the head model along with the QBC on the vertex and the dorsolateral prefrontal cortex position.

TABLE I .
Varying the value of the permeability of the shield.

TABLE II .
Varying the thickness of the shield.

TABLE III .
Varying the distance of the shield from the scalp.

TABLE IV .
Shield dimensions and position.

TABLE V .
Simulations results with three different shields.