Novel multi-magnetic material transcranial magnetic stimulation coils for small animals application Open Access

Transcranial magnetic stimulation (TMS) is a safe, effective and non-invasive treatment for several mental and psychiatric disorders.^1,2 TMS is an FDA approved treatment and is commonly applied to patients who do not respond to medications for the treatment of clinical depression, smoking cessation and obsessive-compulsive.^3–7 Recently, there has been an increase in the development of electromagnetic neuromodulation techniques targeted at enhancing the effectiveness of TMS devices for the treatment of mental diseases.^8,9 In TMS stimulation, focality is an important factor which determines the specificity of the pulses induced in different brain tissues.⁸ The electromagnetic pulses must be confined to specific regions of the brain and avoid stimulation of the surrounding areas.¹⁰ 

Studies of TMS in small animals are critical to enhancing the efficacy of TMS therapy and its applicability to neurological disorders which necessitates precise focal stimulation. To activate specific brain regions in small animals, TMS stimulation coils must be highly advanced to accommodate their small head sizes. Current investigations are limited in that most researchers are utilizing commercially available coils designed for human use. These coils result in unwanted stimulation well beyond the intended target with unavoidable side effects. There is a scarcity of reports that systematically compare innovative coil designs and suitable soft magnetic materials for the development of TMS coils for small animal applications.

TMS coil design requires careful consideration when it comes to core material selection and coil shape.¹¹ Magnetic material characteristics that are important are frequency dependent relative permeability, saturation magnetization, and coercivity. relative permeability, saturation magnetization, and coercivity. Due to its superior magnetic characteristics, we chose to investigate iron-cobalt-vanadium (Permendur) alloy as the coil core in our coil design.¹² The shape of TMS coils plays a critical role in the distribution of the magnetic field and induced e-field in the small animal’s grey matter.^13–15 For example, in the case of a single solenoid wound around a ferromagnetic core, the max magnetic field is at the center of the coil,¹¹ whereas the e-field is maximized at the periphery of the coil. To achieve maximum values for both the magnetic and e-fields at the center, innovative coil designs involving different types of magnetic materials must be developed.

In this study, we compared the simulation results of different novel TMS coil designs on a customized anatomically accurate rat head model which is developed by acquiring magnetic resonance images (MRIs) and computed tomography (CT) images.¹⁶ The model accounts for the different electrical conductivity, permittivity, and density for the rat’s skin, skull, cerebrospinal fluid (CSF) grey matter and white matter. To ensure focal stimulation of the targeted areas, we based our comparison on the induced e-field, as well as the focality of the coils. ANSYS Maxwell, a finite element analysis software, was used to compute induced e-field and magnetic field in the brain models of the rat considering the non-linear, hysteretic behavior of the ferromagnetic cores. The e-field variation on the rat head model using four different proposed coil designs. This work, presents small animals coil designs incorporating multi-magnetic materials where a diamagnetic plate was introduced to the parabolic ferromagnetic core which performed better than the other coils. Our coil design with the diamagnetic plate succeeded to confine the magnetic field lines exclusively to the intended regions, thereby preventing excessive stimulation of adjacent areas. The simulation results were validated here by comparing measured magnetic field data for the v-tip core with the simulated results at different distances from the coil tip.

The focality and stimulation intensity of novel TMS coils for small animal application were analyzed in this work (using ANSYS Maxwell software). Iron-Cobalt-Vanadium alloy was used for all core design, except for the coil used for our simulation validation. In this case, validation was conducted by measuring the magnetic field at different depths with the v-tip coil featuring an AISI-1010 core, which was interfaced with a TMS stimulator as outlined in the work of Selvaraj et al.¹⁷ 

In this study, we considered four different types of coil configurations to analyze: figure of eight, Double C- shape, v-tip and the parabolic ferromagnetic core (PFC) with chamfered edges. Following a thorough evaluation of the e-field distribution of these coils, we enhanced the top performing coil, the parabolic ferromagnetic core (PFC) coil, by introducing a shape-conforming, flexible, pyrolytic graphite diamagnetic plate with a susceptibility of -4.5×10^-4.¹⁸ To avoid moving the coil farther away from the rat head model due to the thickness of the diamagnetic plate, the diamagnetic plate of the dimensions (45mm × 45mm × 5mm) was designed with a concave mold that precisely matches the contour of the rat's head. The diamagnetic plate has a varying thickness ranging from zero near the targeted region to 5 mm at its periphery. The PFC coil has 75 turns on each leg of the parabola with 1 mm coil wire diameter, featuring a core diameter of 20 mm and a 4 mm separation between core tips. The PFC coil configuration with the diamagnetic plate is shown in Fig. 1.

ANSYS-Maxwell (eddy current solver) was used to solve for the induced e-fields (E) and magnetic fields (H) on the rat’s grey matter. The stimulation intensity of all the coils in this study was set to 1000 A at 2.5 kHz to match the work of Selvaraj et al.¹⁷ A B-H curve was used to describe the material property of our TMS cores. This is accepted to be a precise approach when compared to assigning constant initial relative permeability for the material. The B-H curve for iron-cobalt-vanadium alloy as shown in Fig. 2, was derived from data obtained from Carpenter Electrification Company data sheets.¹⁹ The material properties for the individualized rats’ brain segments were assigned according to Sim4life IT’IS LF database (IT’IS Foundation, v4.0).²⁰ 

Incorporating a ferromagnetic core in TMS coils markedly improved the focality of the e-field distribution for our coil designs. The simulated e-field distributions for the four coil configurations are shown in Fig. 3. The e-field distributions induced in the rat’s grey matter were also directly compared among the four coil configurations (Fig. 4).

Further analysis of these coils has been conducted, as illustrated in Fig. 4. The e-field distribution at the top of the rat’s grey matter have been compared among all coil configurations. The actual e-field values is shown in Fig. 4(a). The e-field values were normalized in Fig. 4(b) to the maximum value of each coil to compare their focality. After determining that the PFC coil exhibited the most favorable e-field distribution, additional efforts were made to further enhance the focality of the PFC coil. A diamagnetic plate was introduced to the PFC coil configuration which yielded a significant improvement on the e-field distribution, particularly at the surface of the grey matter, by minimizing stimulation of adjacent cortical regions. However, with the diamagnetic plate the maximum e-field intensity for the PFC coil dropped by 40%. Nonetheless, we were able to maintain a substantial e-field intensity of 84 V/m at the intended target region. Fig. 5 displays the e-field of the updated PFC coil configuration with the diamagnetic plate, showing the reduction of the e-field intensity to 84 V/m, but targeted to a very small region on the top of the grey matter. The full width half maximum of the normalized e-field values for the figure of eight, double C-shape, PFC, and the PFC coil with a diamagnetic plate were 8.9, 7.2, 5.3, 4.4 mm. The v-tip coil has an inverted e-field distribution due to the fact that the e-field is at a minimum right below the center of the coil for a single core geometry making the hotspots at the periphery of the coil.

To validate our present simulation results, we compared the results produced with ANSYS Maxwell simulations against experimental measurements for the v-tip coil using our current manufactured carbon steel AISI-1010 core design.^11,17 The coil has 40 turns with an inductance of 65 μH with the v-tip carbon steel core. A uniaxial hall probe (Lake Shore 400 Series Hall Probe),²¹ and a gaussmeter (Model 475 DSP),²² were used to measure the magnetic field generated in the TMS focused coil at different distances from the coil tip.¹¹ The magnetic field measurement setup incorporating a v-tip core using a hall probe is shown in Fig. 6. Using the same coil parameters and locations, magnetic fields simulation results at progressive distances (0, 1, 2, 3 and 4 mm) from the v-tip coil were inspected, as shown in Fig. 7 (a, b). As demonstrated in Fig. 7(c), the simulation magnetic field results closely approximate that measured experimentally.

Using ANSYS Maxwell to simulate TMS coil designs enabled us to use the B-H curves of the material incorporated in our design instead of using an initial maximum relative permeability of the materials. This represents a substantial enhancement in accurately characterizing the material properties of the designed coils, as they vary according to the generated magnetic field in the coils. This permitted a more realistic characterization of the materials used in the simulations.

The PFC coil design represents a notable advancement over the figure-of-8, v-tip, and double C coils. It provides a substantially improved e-field distribution while preserving nearly identical stimulation intensity. This development holds considerable significance in the context of TMS focal stimulation applied to small animals. To further enhance the coil’s focal precision and mitigate undesired stimulation of a large region within the rat’s grey matter, a simulated diamagnetic pyrolytic graphite plate was employed as a shielding component. This plate effectively redirects the magnetic flux toward the plate opening, resulting in superior focal e-field distribution in the targeted area.

It was challenging to achieve the necessary stimulation intensity at the top layer of the rat’s grey matter due to a trade-off between the focality versus intensity of e-field. Using an innovative PFC coil’s integration with the diamagnetic plate an effective e-field was achieved while reducing unintended stimulation of the surrounding tissue, which successfully adjusted these tradeoff parameters. The thickness of the pyrolytic graphite plate has to be carefully considered during the novel coil design. A simple 5 mm thick plate would force the coil to be placed farther from the rat head model, compromising the coil’s intensity. However, by utilizing a plate with a concave mold, we were able to effectively shield adjacent areas while still achieving an acceptable e-field intensity within the target region of the rat's grey matter by keeping an opening right above the target.

To validate our simulations derived in ANSYS Maxwell, the simulated magnetic field values were compared to experimental magnetic field measurements using a hall probe. The resultant very similar results indeed provided essential validation of our simulation results. Although the simulated magnetic fields values were somewhat larger than those generated in vitro, they reproduced well the curve of the simulated results. Further, we suggest that much of these discrepancies are likely to be attributable to inaccuracies in the in vitro measurements.

This present study findings significantly advance our understanding of TMS coil designs and their optimization, particularly for small animal applications. TMS shows great promise as a non-invasive therapy for a range of mental and neurological problems. It is crucial to be able to precisely target particular brain regions in order to achieve effectiveness. We investigated innovative TMS coil designs for small animal application using finite element analysis in ANSYS Maxwell software. The shape of TMS coils was investigated, revealing its critical role in the e-field distribution within the targeted cortical grey matter. The simulated results here were validated by comparing simulated magnetic field values with in vitro magnetic field measurements using our current carbon steel AISI-1010 TMS coil.

Distinct coil configurations were explored, with the PFC coil emerging as the most favorable coil with a superior e-field distribution. Our subsequent addition of the shape-conforming, flexible, pyrolytic graphite plate to the bare PFC coil resulted in further appreciable focality of the e-field distribution. Furthermore, the choice of iron-cobalt-vanadium alloy as the coil core material, known for its exceptional magnetic properties, contributed significantly to the overall success of the design. In TMS applications, there is a well-recognized trade-off between focality and penetration depth. Our findings here nevertheless support the capability of our novel TMS coil design to be capable of stimulating the cortical grey matter of small animals, while effectively focusing the e-field.

Current commercial human systems are not suitable for usage in animals, and especially in smaller animals. This present study results significantly advance the field of TMS coil design for studies particularly involving small animals. By integrating novel materials and cutting-edge design approaches and testing in animals, it will be possible to enhance TMS outcomes in humans and to expand their applicability to a wider spectrum of neurological and psychiatric illnesses.

Authors would like to acknowledge 2023 VCU Presidential Research Quest Fund.

The authors have no conflicts to disclose.

Mohannad Tashli: Conceptualization (equal); Data curation (equal); Formal analysis (equal); Investigation (equal); Methodology (equal); Project administration (equal); Software (equal); Supervision (equal); Validation (equal); Visualization (equal); Writing – original draft (equal); Writing – review & editing (equal). Aryan Mhaskar: Data curation (equal); Formal analysis (equal); Investigation (equal); Methodology (equal); Software (equal). George Weistroffer: Data curation (supporting); Methodology (supporting); Resources (supporting); Validation (supporting). Mark S. Baron: Data curation (equal); Funding acquisition (equal); Project administration (equal); Visualization (equal); Writing – review & editing (equal). Ravi L. Hadimani: Conceptualization (lead); Data curation (supporting); Formal analysis (supporting); Funding acquisition (lead); Investigation (supporting); Methodology (supporting); Project administration (lead); Resources (supporting); Software (supporting); Supervision (lead); Validation (equal); Visualization (lead); Writing – original draft (equal); Writing – review & editing (lead).

The data that support the findings of this study are available from the corresponding authors upon reasonable request.