Transcranial magnetic stimulation (TMS) is a non-invasive neuromodulation technique used to regulate the synaptic activity of neurons in the brain, improving the functionality of connecting regions and bringing effective treatment to different neurological and psychiatric disorders. The TMS induced E-field needs to be focal enough to avoid unwanted side effects caused by stimulation of the regions adjacent to the target. Attempts at TMS in small animals like rodents are highly constrained, since most of these studies use commercial equipment intended for humans, with power and coil geometries not designed for small animals. Using finite element modeling in ANSYS Maxwell, the present work shows the design and evaluation of customized arrays of two and five dual-winding solenoids, including a ferromagnetic core, to restrict the stimulation to areas as small as 1 mm2. Each solenoid is made with 50 turns of a wire with thickness = 1 mm, height = 25.4 mm and elliptical top-view cross section. Ferromagnetic cores with V-shape tip sharpening were included, using AISI 1010 carbon steel of 2 T of saturation flux density (Bsat) at 4×104 A/m, and an initial relative permeability µr=667.75. Electric fields and magnetic flux densities were calculated around 4.00 mm below the coil (vertical distance from the top of the scalp to the cortical layer 5/6 in adult rats) with peak currents of 10kA, in a single non-repetitive pulse at 2.5kHz. The achieved 100V/m in a small area of 1 mm2 suggests the suitability of the coil for in vivo experimentation in rodents. Future works will seek to improve the duration of the pulses for repetitive TMS with pulse shaping techniques and validate the novel coil with in vivo experiments in rat models.
I. INTRODUCTION
The understanding of complex neuronal networks in the human brain requires the study of connections in different pathways, as well as the projections that the synaptic activity of one region may have in another one. This is the case for the motor pathway, a complex association of neurons in a network responsible for the motion of the musculoskeletal system.
Investigations of motor pathways are helping researchers understand alterations in the normal functioning of the motor system, responsible for such disorders as Parkinson’s disease, dystonia or Huntington disease.
The transcranial magnetic stimulation (TMS) investigations in animals contribute to identify connections between different areas of the motor pathways, exploiting anatomical similarities existing between human and experimental animal brains. As utilized in humans, TMS allows to discreetly alter the synaptic activity of selected regions in small animal brains, applying an external time-varying magnetic field that produces an associated electric field, according to the Maxwell-Faraday’s Induction Law.
One of the current limitations of TMS for studies in small animal however is the need for appreciably more focal coils to selectively stimulate small sub-regions in the cortex, such as the primary motor cortex (M1) and secondary motor cortex (M2).
Non-focal coils produce unwanted overstimulation of adjacent areas to the target, which not only generates undesired side effect in the study, but also prevent researchers from accurately identifying the connections of single specific regions, and investigating their projections in deeper regions.
Although several TMS coils for small animals -both commercial and experimental-are described in the literature,1–4 their reported stimulated areas by the induced e-field of about 1cm25 are too large to be useful in rodents to stimulate, for example, the M1 and M2 regions, whose dimensions are in the order of a few mm2.
This works presents the results of the design and evaluation of a configuration of coils in double and quintuple arrays of elliptical dual-winding solenoids with ferromagnetic cores of AISI 1010 low-carbon steel, which permits -for the first time to our knowledge-restriction of TMS to an area of 1mm2.
II. METHODOLOGY
To evaluate different configurations of TMS coils designed to achieve highly focused stimulation, we performed recurrent simulations using finite element modeling on ANSYS Electronics Desktop (Maxwell 3D). Each modeled coil is a dual-winding solenoid of elliptical top-view cross section with a ferromagnetic core of the same shape (Fig. 1). In early stages of this work we predicted required magnetic flux densities of above 2 T per solenoid, in order to induce E-fields of around 100V/m with reasonable dB/dt (defined by the typical range of TMS frequencies, up to 3.5kHz). Then, we conducted preliminary research looking for cost-effective ferromagnetic materials with saturation magnetization (SM) over 2 T, significantly high relative permeability -in order to reduce power requirements- and with relative ease for machining or future additive manufacturing processes. This way we found the AISI 1010 low-carbon steel to be an appropriate material for our ferromagnetic cores, having a SM ≅ 2 T with a magnetic flux intensity (H) of 4×104 A/m, an initial relative permeability of µr=667.75 and standardized for relatively low complexity machining, given the low carbon composition. All the reference parameters for this material were extracted from the SysLibrary of ANSYS.
The parameters of the coil are: wire diameter = 1mm; turns = 50 (2x25); height = 25.4mm; core cross section: semi-mayor axis = 10.6mm, semi-minor axis = 2.8mm.
Fig. 2 shows the B-H curve of the core material, whereas the electric and magnetic properties of the simulated materials for the coils are in Table I.
. | Electrical . | Relative Electric . | Relative Magnetic . |
---|---|---|---|
Material . | Conductivity (σ) [S/m] . | Permittivity (εr) . | Permeability (µr) . |
Copper | 5.8E7 | 1 | 0.999991 |
1010 Steel | 2.0E6 | 1 | 667.75 (peak) |
Air | 0 | 1.0006 | 1.0000004 |
. | Electrical . | Relative Electric . | Relative Magnetic . |
---|---|---|---|
Material . | Conductivity (σ) [S/m] . | Permittivity (εr) . | Permeability (µr) . |
Copper | 5.8E7 | 1 | 0.999991 |
1010 Steel | 2.0E6 | 1 | 667.75 (peak) |
Air | 0 | 1.0006 | 1.0000004 |
The initial configuration is made of two elliptical dual-winding solenoids placed in pairs, vertically standing on orthogonal axes over the plane z = 0mm (using the lowest point of the coils as reference). This setup was repeated with and without a magnetic core (replaced by air), and then with a V-profile tip, sharpened toward the centroid of the array. The results of this part would be used to create the final configuration of five solenoids (Fig. 3b), explained later in this text.
To accurately predict the induced E-field that it would be obtained in practical implementations, we identified the location of the pyramidal neurons of the layers V and VI (Fig. 4a) in the M1 region of the motor cortex, using the rat brain atlas6,7 in stereotaxic coordinates.
In order to accurately determine the depth of stimulation, the thickness of scalp, skull and connective tissue layers (Fig. 4b) were considered for the rat head.8
The relative coordinates of the targeted cortical region9 with respect to the bregma (reference point for stereotaxis on the rat skull)10,11 were: ML=3mm, AP=2mm and DV=2mm.
Fig. 5a-d illustrates the targeted point in the corresponding coronal, sagittal and horizontal planes. The desired stimulated region needs to be restricted to a radius of ∼0.56 mm around the target point (red dot in Fig. 5). Given the reduced scale, this highlights how small the dimensions of the target and its surroundings are, as well as the difficulty to obtain a focal stimulation.
Using a 3D surface model of the rat brain, we extracted a simpler spherical approximation of the rat head with diameter of 30.00 mm (blue sphere in Fig. 5a), extended from the target to the closest point in the head surface.
Subsequently, we built a spherical head model (Fig. 6a-b) with the same curvature of the section, adding layers of tissue with thickness and electromagnetic properties similar to those present in an adult rat head (Fig. 4b and Table II).
Actual Layer in the . | Layer in the Simplified . | . | Electrical Conductivity . | Relative Electric . | Relative Magnetic . |
---|---|---|---|---|---|
Rat Head . | Head Model . | Thickness (µm) . | (σ) [S/m] . | Permittivity (εr) . | Permeability (µr) . |
Scalp | Scalp | 500 | 0.17 | 12000 | ≈ 1 |
Periosteum | 100 | Approximated to the same as the scalp | |||
Skull | Skull | 1000 | 0.01 | 800 | ≈ 1 |
Dura mater | 300 | Approximated to the same as the skull | |||
Arachnoid | Cerebrospinal Fluid (CSF) | 75 | 1.654 | 6000 | ≈ 1 |
Sub-arachn. S. | 750 | Approximated to the same as the CSF | |||
Pia Matter | Brain cortex | 25 | Approximated to the same as the GM | ||
Gray Matter (GM) | ... | 0.276 | 12000 | ≈ 1 |
Actual Layer in the . | Layer in the Simplified . | . | Electrical Conductivity . | Relative Electric . | Relative Magnetic . |
---|---|---|---|---|---|
Rat Head . | Head Model . | Thickness (µm) . | (σ) [S/m] . | Permittivity (εr) . | Permeability (µr) . |
Scalp | Scalp | 500 | 0.17 | 12000 | ≈ 1 |
Periosteum | 100 | Approximated to the same as the scalp | |||
Skull | Skull | 1000 | 0.01 | 800 | ≈ 1 |
Dura mater | 300 | Approximated to the same as the skull | |||
Arachnoid | Cerebrospinal Fluid (CSF) | 75 | 1.654 | 6000 | ≈ 1 |
Sub-arachn. S. | 750 | Approximated to the same as the CSF | |||
Pia Matter | Brain cortex | 25 | Approximated to the same as the GM | ||
Gray Matter (GM) | ... | 0.276 | 12000 | ≈ 1 |
In order to simplify the complex calculations of the E-field in relatively thin layers, our head model merged these layers with the thicker contiguous layers of highest proximity in electromagnetic properties. The result is the simplified four-layers rat head model in Fig. 6 and Table II.
For the evaluation of the ability of the coil to focally stimulate the M1 -and analogously the M2-, we have created three secant planes (Fig. 6) at depths of 3.75, 4.00 and 4.25 mm -same depths of the targeted pyramidal neurons-in which we have obtained the distributions for the magnitudes of the E-fields and B-field.
The simulations have been configured in transient state, using a single bipolar pulse of current of cosine waveform, with a peak amplitude of 5kA. The frequency of the pulse is 2500Hz (within the typical TMS range12–14) and the duration is one period (400µs).
In the meshing process, we have chosen a non-adaptative initial grid, provided by ANSYS Maxwell 3D for transient solution, applied to all geometries. After generating tetrahedral elements of varying sizes, we carefully refined the mesh in all the layer of our head-brain model to ensure a high resolution around a target of about 1 mm of diameter. Then, we have restricted the average element size (RMS edge length) in these layers to 1mm, obtaining minimum element sizes of 0.3842mm. This means a resolution of about 15.64 elements/mm2 in the target (most sensitive region), which is high enough to observe variation patterns and gradients in the fields. For the rest of the elements, we have assured average element sizes no bigger than 1.05mm for the coils, 2.07mm for the cores and 1.32mm for the air enclosure. For more details, please see supplementary material.
The previous setup was repeated for recurrent simulations with air core, as well as with planar-faced and V-shaped AISI 1010 carbon steel cores. Then, different configurations were obtained by varying the relative position of the 2 and 5 coils with respect to the center. The next section reports the more significant configurations and results.
III. RESULTS
The first group of simulations with two elliptical solenoids (Fig. 3a) shows the effect of the relative position of the coils on the distribution of the magnetic flux density (B) and the electric field (E) over the plane z=0.
As it is observed in Fig. 7i, when placed close to each other (Fig. 6), the coils generate two hotspots of the E-field, as a consequence of the same distribution for J, indicating a high concentration of induced charges toward the center.
This is a highly focal behavior of the E-field induced at the surface of the coil. We have termed this referential current density distribution at z=0 “nucleation of charges” (Fig.7i).
On the other hand, the analysis in consecutive secant planes below z=0 reveals how the initial distributions of B, E and J change as a function of the depth. This is due to both the dispersion of the magnetic flux lines (shown as a decrease of B, in Fig. 7a-h), and the dispersion of the induced charges (and E) from the nucleation point, which tend to repel each other and spread out (Fig. 7i-p).
As seen in Fig. 7i-p, the spatial displacement of the two hotspots occurs from the nucleation points, in opposite directions in every XY plane and towards the negative direction of the z-axis. We have called the resulting directions “paths of highest current density.” Then, we understand that the maximum electric field in the target will be obtained as long as this path intersects the target area (which does not occur at this point yet).
Another relevant result observed is the role of the ferromagnetic core in the nucleation of the induced charges, and therefore, in the path of highest conduction current density (J). Fig. 8 shows how the E-field (as a consequence of the current density distribution) tends to be more evenly distributed with a flat-face AISI 1010 steel core (Fig. 8e), becomes higher towards the center with no core (Fig. 8d), and even higher with a V-shaped AISI 1010 steel core (Fig. 8f) at the plane z=0. This is consistent when we compare the associated distributions of B in the same plane (Fig. 8a-c).
Having understood the mechanisms of nucleation of charges right below the coil, and formation of the path of highest current density, we have changed the configuration to the quintuple array of dual solenoids in Fig. 9a. The new coil is an arrangement of four elliptical dual solenoids, making a parallelogram from the top view, with an extra dual solenoid in the center (Fig. 9b).
For this simulation we have kept the same previously described waveform, duration and frequency of the pulse of current, and set the peak amplitude to 10kA. The resulting inductance -calculated during the simulation-is 1.9 mH for each coil, with power factor angle ΦPF=72 deg. The objective of this configuration has been restricting, as much as possible, the dispersion and migration of the charges induced by the coil in the middle (Fig. 10a) to zones of lower charge densities. This restriction is imposed by the quadruple arrangement of peripheral solenoids (Fig. 10b) which generate four nuclei of induced charges in the surroundings. Being of the same sign, the peripheral charges repel the charges induced by the fifth coil in the center such that this last group is forced to propagate vertically along the z-axis. We have termed this deliberately restricted direction of propagation (Fig. 10c) “oriented central path of highest current density.”
Eventually, after certain depth, the dispersion of the peripheral charges allows the central charges to spread out. However, the restriction will provide the central charges the chance to reach the target in a still relatively compact group, with an associated high current density.
In this way, we have confined the path of the central group of induced charges to point and pass through the target point, increasing the E-field on it. We have named this technique “oriented control of the electric field based on the directional vector of highest current density.”
On the other hand, the propagation of peripheral charges will occur outwards in a dispersive manner, which will form a conical pattern to be called “peripheral path of highest current density.” This path, though unoriented, is still necessary to provide control over the central path.
Fig. 11 presents the results for the planes z=-3.75, -4.00 and -4.25 mm, showing the magnetic flux density distribution (Fig. 11a-c) and the correspondent E-field (Fig. 11d-i). Notice in the E-field plots how the group of peripheral charges (rearranged in ring shaped red dot clouds) still prevents the scattering of the central group of charges at these depths, allowing them to penetrate -still together-up to the target. In consequence, the associated E-field is higher in the middle and lower in the outer area due to the dispersion.
IV. DISCUSSION
The designed quintuple AISI 1010 carbon steel core coil of dual solenoids demonstrated to be able to stimulate the M1 sub-region in the rat brain, without appreciable encroachment on the surrounding regions. The key aspect of the novel design is the obtained oriented control of the E-field, based on the control of the directional vector of the central path of highest current density. This path crosses consecutives secant planes in a straight line, from the nucleation point to the target.
The oriented control consists of the prediction of the trajectories of all the paths of highest current densities, and their placement such that at least one of them points and passes though the target point, with acceptable low dispersion, ensuring clearance in the surroundings.
The novel coil showed effective induced E-field at the targeted point, within the spherical rat head model, above the typical neuron stimulating threshold defined around 100V/m.15–19 These values were observed at least over the planes z=-3.75 and z=-4.00 mm, deep enough to reach the layers V and VI of the M1 and M2 regions in the rat brain. The approximate stimulated area is 1mm2 with cleared surrounding areas at the targeted planes with |E| below the stimulation threshold.
It is important to note that, since the propagation of the induced peripheral currents has a radial characteristic, and given the circular nature of the induced E-fields in TMS -defined by the Maxwell-Faraday’s Law-there might exist more halos of E-field with magnitudes above the threshold. However, it is possible to configure the system to make these halos to be outside the perimeter that defines either an established clearance area or the entire specimen’s brain. This will depend on the specific geometry of the specimen’s head and brain, dimensions of the coil and specific parameters of stimulation. Therefore, the use of this coil should always be subjected to a previous study of the conditions to assure minimization of undesired adjacent stimulation.
For a peak amplitude of 10kA, the energy dissipated in the quintuple AISI 1010 core coil was calculated as 208.9 mJ per pulse of current. This means a very low and safe energy dissipation over the coil for non-repetitive (single pulse) TMS, in this case for pathway identification in neural networks. This would also allow an equivalent maximum power dissipation of 208.9mW/pulse in repetitive TMS, with an interlock window of at least 1 sec. For repetitive TMS (r-TMS), thought, the number of consecutive pulses and duration of the interlock may be adjusted, keeping a compromise between the generated real power and the capacity of the coil to effectively dissipate it. This will prevent a temperature rise that causes damages in the device in r-TMS, which is not a concern for the purpose of this work. Similarly, the calculated energy dissipated within the brain tissue, in a volume of 1mm3 over the targeted planes, is 1.10 nJ. The very small energy dissipated and short duration of the single pulse of 400 µs make the temperature rising negligible and represent an evidence of the safety of the designed device to perform non-repetitive TMS in rodents. This is consistent with reports in the literature showing negligible temperature variation in the brain during TMS.20 Future work in progress is aiming to further reduce the dissipated power and improve the thermal response of the coil in r-TMS, using pulse shaping and neuromodulation techniques.
Although the rat head model has been considered of isotropic and homogeneous electromagnetic properties, this might not be the exact case in a real specimen. The complexities in the microscopic structure of tissues such as the brain cortex and the skull bones create tiny localized unbalances in the current densities and electric fields, at a microscopic scale, that are challenging to predict. From a macroscopic engineering point of view, though, the fluxes and densities implicitly reflect these microscopic inhomogeneities -or anisotropies-in averaged values per unit area, reported in the literature by type of tissue. Then, we understand that, as long as we can provide stimulation to the targeted neurons with average E-field above the threshold for enough time (one period in this case), a big proportion of the neurons located in this area will fire at the same time, after the induced pulse of current, despite the microscopic inhomogeneities or anisotropies.
Until this point we have shown that the designed coil is able to induce manageable localized E-fields above the 100 V/m, over a spherical model with the typical conductivities for the rat brain cortex. This predicts high effectiveness in in vivo implementations -even with inhomogeneous or anisotropic properties-given the adaptative capacity of the coil to provide focal stimulation. This capacity is based on the oriented control of the E-field, with even or differentiated modulation in each independent solenoid. Future work is planned to test the new device over rat head phantoms, using previously developed technology in our lab for human head phantoms.21,22 This way we will accurately evaluate the role that the actual rat brain anatomy plays in the final distribution of the E-field. Similarly, work in progress seeks to increase the suitability of the coil for rTMS and reduce overstimulation using high µr shielding materials.
SUPPLEMENTARY MATERIAL
See supplementary material for meshing statistics are available in.tif and.mstat files of the same name. Details about power and energy calculations are available in.mat and.m files.
ACKNOWLEDGMENTS
This study was partially funded by the Merit Review Award, U.S. Department of Veterans Affairs. Dr. Mark Baron. Grant number 2I01BX001147-05A2.
DATA AVAILABILITY
The data that support the findings of this study are available within the article and its supplementary material and from the corresponding author upon reasonable request.