Transcranial Magnetic Stimulation-coil design with improved focality

Transcranial Magnetic Stimulation (TMS) is a technique for neuromodulation that can be used as a noninvasive therapy for various neurological disorders. In TMS, a time varying magnetic field generated from an electromagnetic coilplaced on the scalp is used to induce an electric field inside the brain. TMS coilgeometry plays an important role in determining the focality and depth of penetration of the induced electric field responsible for stimulation. Clinicians and basic scientists are interested in stimulating a localized area of the brain,while minimizing the stimulation of surrounding neural networks. In this paper, a novel coil has been proposed, namely Quadruple Butterfly Coil (QBC) with an improved focality over the commercial Figure-8 coil. Finite element simulations were conducted with both the QBC and the conventional Figure-8 coil. The two coil’s stimulation profiles were assessed with 50 anatomically realistic MRIderived head models. The coils were positioned on the vertex and the scalp over the dorsolateral prefrontal cortex to stimulate the brain. Computer modeling of the coils has been done to determine the parameters of interest-volume of stimulation, maximum electric field, location of maximum electric field and area of stimulation across all 50 head models for both coils.


I. INTRODUCTION
2][3][4][5] The time varying magnetic field generated from a TMS coil will induce an electric field and cause depolarization of neurons.TMS can be administered as a single pulse or a train of pluses, which is called repetitive TMS (rTMS).Different repetition rates, also called stimulation frequencies, can be used to either up regulate or down regulate neuronal activity.The ability to modulate the activity of neural networks noninvasively and relatively painlessly allows researchers to explore brain stimulation as a tool to treat disease with much more ease than previous neuromodulation techniques such as deep brain stimulation (DBS) and electroconvulsive therapy (ECT) have allowed.
The shape and size of the magnetic coils plays an important role in determining focality and depth of stimulation in the brain.There have been many coils designed in the last twenty years utilizing different geometrical layouts, but no coils have shown significant improvement in focality over the  [8][9][10] But it is not clear that the focal nature of Figure-8 coils is what makes them effective at treating depression, because the H-Coil, which allows for deeper and less focal stimulation of the brain, has also proven to be effective at treating depression. 11In neurotherapeutics, the ideal stimulation site for TMS is unknown and will likely prove to be dependent on the nature of the disease to be treated and also potentially the subject.TMS is still a relatively new technique and there is much that needs to be tested before researchers develop an understanding of what the ideal stimulation parameters are.Any development of TMS coils that allow for stimulation beyond the resolution of Figure-8 coils will give researchers more opportunities to stimulate specific neural circuits that are identified to be important in neurological disorders.Further, more precise stimulation methods also limit the modulation of neighboring brain regions whose relationship with a given disease may be unknown or dissimilar to that of the target stimulation site.Beyond therapeutics, as researchers continue to use TMS to explore different physiological measures or concurrent TMS & fMRI (functional magnetic resonance imaging) or TMS & EEG (electroencephalogram), more focal stimulation will be desired as it allows for more direct understanding of TMS outcomes.
In this paper, a new coil design namely, Quadruple Butterfly Coil (QBC) has been developed with the main purpose of allowing researchers a finer resolution for stimulation.This new coil aims to decrease the stimulation volume over the cortex and not to achieve deeper brain stimulation as highlighted in previous work. 12The focality term used in this paper refers to the decrease in volume of stimulation due to the QBC when compared with the Figure-8 coil.Also, QBC has been compared with Figure-8 coil using 50 anatomically realistic heterogeneous MRI derived head models that we have developed.These coils were positioned on the vertex of the head and also on the area of the scalp over the dorsolateral prefrontal cortex.

II. METHOD
][15] These models consist of seven different segmented anatomies including skin, skull, cerebrospinal fluid, grey matter (GM), white matter (WM), cerebellum and ventricles.Also, these models were created from healthy young adults in the age range from 22-35 years, with an equal number of female and male head models.
Calculation of the electric field (E-field) and modeling of TMS coils was performed using SEMCAD X. 16 The current supplied to the TMS coils was 5000A peak to peak at a frequency of 2.5 kHz.The corresponding relative permittivity and electrical conductivity values were taken from Hasgall et al. 17 A quasi-static, low frequency solver was used for the calculation of the induced electric field in the brain and magnetic fields generated from the coils.Results from SEMCAD X were exported to MATLAB for data processing and construction of plots.A Magstim 70mm Figure-8 coil was used as a comparison coil for the results with QBC. 18Results from the Figure-8 coil were included in this paper for the purposes of comparison, since this coil has been widely used in TMS literature and is able to provide a reference for the results from the new QBC. 19,20he QBC is designed with two sets of coils, two larger coils which are the same size as the Figure-8 coil, and two smaller coils, which are 40% of the size of the larger coils with an inclination of 45 degrees as shown in Fig. 1.QBC geometry, without the additional set of smaller coils, is based on Eaton et al. and highlighted in Deng et al. as a 50mm V-coil. 21,22There are equal number of windings in both the bigger and smaller coils as in the Figure-8 coil, and left and right coils have current flowing in the same direction at the point where the windings are closest, allowing for summation of field intensities.The reason for adding the smaller coils on top of larger coils in the QBC is to increase the magnetic vector potential over the target stimulation site, which is decreased when the coils are angled upwards.This in turn increases the induced electric field in the QBC to be more comparable to that of a Figure-8 Coil, while maintaining the increased focality from the angle adjustment.The reason for limiting the size of the second set of coils was to allow the QBC to constrain the increased field intensities to be more center to the desired target of stimulation.Although increasing the size of the coils may increase depth of penetration, it would also decrease stimulation specificity along the axis defined by the green arrow in Figs.1(a)-1(b).There is a limitation for further reduction in the coil dimension because small coils overheat quickly, and it is more difficult to maintain the temperature than in the case of larger coils.
To compare the simulation results of the two coils at the two test locations, several metrics were employed.These metrics include E-Max (the maximum E-Field intensity in the brain, or other anatomy if specified), V-Half (the volume of the brain exposed to E-Field intensities at least one half E-Max), distance of E-Max from origin (distance from expected location of E-Max, which is directly below the coil), and A-Half (surface area of the brain exposed to E-Field intensities at least one half E-Max).

III. RESULTS AND DISCUSSION
The results in this paper show the effect of coil geometry and anatomical variation in brain structure.Most published research either compares different coil geometries or the effects of anatomical variation, but previous studies have not been able to utilize a broad range of subjects to confirm the potential differences in the stimulation site of different coils. 13,21,23This paper introduces a new coil design, compares its results with the Figure-8 coil and also discusses the effect of anatomical variation by using 50 head models.
In Fig. 2, the induced electric field on the surface of grey matter (GM) and scalp due to both Figure-8 coil and QBC on the vertex and dorsolateral prefrontal cortex is shown.Results in both sets of simulations show increased focality of the QBC towards the direction of the outer coil windings.Further, the images of the E-Field profile on the scalp illustrate that the QBC stimulates a much ) and for QBC is (79.78,111.17, 135.94, 153.12, and 233.88).Results show that the QBC stimulates at weaker intensities than the Figure-8 coil for a given current intensity, but both coils have a comparable ratio of electric field on scalp to brain (2.17 for QBC and 1.69 for Figure-8 at vertex), which is important for not over-stimulating nerves near the site of stimulation.The induced electric field intensity from both coils are sufficient to meet standards which are required for neuronal depolarization. 24The second box plot illustrates the location of E-Max relative to the expected E-Field maximum (directly below coil).This metric is relevant to understanding the precision of stimulation for different coils.Results show there is a modest improvement of 8 % in the QBC over the Further seen in Table I is an interesting finding that was not intended to be a main point of this work, but is still necessary to mention.Simulations showed that for a Figure-8 coil, the intensity of stimulation is nearly 20% greater over the dorsolateral prefrontal cortex than over the vertex.As most places of interest to TMS researchers are outside of cortical areas that give easily observable physiological responses to indicate what potentially ideal stimulation intensities are, scaling stimulation intensities from motor (aka motor threshold) to non-motor regions can be a challenge.Future work will need to follow this up in detail for researchers to have a better understanding of how different cortical stimulation sites may require higher/lower stimulation intensities.

IV. CONCLUSION
In this paper a novel coil design QBC is proposed, which has modest improvements in focality over the Magstim 70mm Figure-8 coil.The QBC has been positioned at two different locations on the head and the TMS induced stimulation profile was calculated for 50 head models.This work outlines the first major version of the QBC.Future work may use magnetic shielding and refinements to coil to increase size/angle to further increase the focality of the QBC.
Figure-8 coils while maintaining the field intensity required to stimulate at the depth of the surface of the brain.The Figure-8 coil configuration was first proposed by Uneo et al. in 1988 and functional mapping of the motor cortex was successfully obtained in a 5mm resolution in 1990 by the same group. 6,7Different varieties of the Figure-8 coil are FDA approved for the treatment of depression.

FIG. 1 .
FIG. 1. Figure-8 coil and Quadruple Butterfly Coil positioned (a-b) on the vertex (c-d) on the dorsolateral prefrontal cortex region of the head model.

FIG. 2 .
FIG. 2. Induced electric field on the grey matter and scalp due to (a) Figure-8 coil on the vertex (b) Quadruple Butterfly Coil on vertex (c) Figure-8 coil on dorsolateral prefrontal cortex (d) Quadruple Butterfly Coil on dorsolateral prefrontal cortex.
FIG. 3. Three sets of boxplots showing the five number summary (minimum, first quartile, median, third quartile and maximum, outliers) for E-Max, the distance of E-max from expected location, and V-Half for Figure-8 coil and Quadruple Butterfly Coil using 50 set of head models.

TABLE I .
Measures of interest for both QBC and Figure-8 coil on two positions.