A Novel Brain Stimulation Technology Provides Compatibility with MRI

Clinical electrical stimulation systems — such as pacemakers and deep brain stimulators (DBS) — are an increasingly common therapeutic option to treat a large range of medical conditions. Despite their remarkable success, one of the significant limitations of these medical devices is the limited compatibility with magnetic resonance imaging (MRI), a standard diagnostic tool in medicine. During an MRI exam, the leads used with these devices, implanted in the body of the patient, act as an electric antenna potentially causing a large amount of energy to be absorbed in the tissue, which can lead to serious heat-related injury. This study presents a novel lead design that reduces the antenna effect and allows for decreased tissue heating during MRI. The optimal parameters of the wire design were determined by a combination of computational modeling and experimental measurements. The results of these simulations were used to build a prototype, which was tested in a gel phantom during an MRI scan. Measurement results showed a three-fold decrease in heating when compared to a commercially available DBS lead. Accordingly, the proposed design may allow a significantly increased number of patients with medical implants to have safe access to the diagnostic benefits of MRI.

Equation (S2) has been introduced only to give an insight into the theory of RTS design. The following section presents a more detailed description of the fields inside the RTS leads.
The peak inductance of the lead can be estimated as follows: where ‖ , , ‖ is the complex magnitude of the Fourier transform or harmonic component of the magnetic field at the Larmor frequency f 0 = 128 MHz, is the permeability of the material (see Supplementary Table S1), is the domain composed of RTS wire and insulation,  1,2 is the section, is the unitary vector between layers 1 and 2 of the RTS, and , , is the current density inside the lead. One can only estimate or the peak inductance of an ideal inductor which is an ideal magnetic field generator that stores the magnetic field energy generated by the supplied current, whereas in a real inductor the inductance L is always lower than because of magnetic flux losses.
The main or static magnetic field B 0 present in an MRI will produce a spin or precession of nuclei of the hydrogen atoms (protons) in the water molecules in the tissue. The precessional path of these protons around the magnetic field is circular like and sometimes described in terms of a spinning top. The Larmor or precessional frequency in MRI refers to the rate of precession of the magnetic moment of the proton around the external magnetic field and is related to the strength of the magnetic field B 0 . The frequency of all fields considered here is the Larmor frequency (i.e., 128 MHz at 3T). The behavior of a RTS wire inside an electromagnetic field can be studied as a linear antenna under the thin wire assumption (i.e., the diameter d of the geometry is  100 ⁄ , i.e. d=100 µm). For an ideal linear thin antenna the current density , , , which determines the fundamental fields x, y, z and x, y, z is 6 : where and are the unit vector and current intensity along the implant along the z-axis, as shown in Fig. 1c. The current density field can be found by solving the following Pocklington's integral equation 7 : (S9) Equation (S9) is the typical shape of the ideal current distribution in an RTS wire as sketched in Fig. 1c. A more precise current distribution estimated using EM numerical simulations is shown in Fig. 2d. The RTS design reduces the overall inductance of the lead (Fig. 2c). Additionally, the current density has a minimum value along the lead in proximity to the electrode (Fig. 2d) at the electrode, where the highest electric field was observed 12-14 . The parameter used to evaluate numerically the energy deposition in the phantom was the specific absorption rate (SAR) averaged in a volume with a 10g mass (10g-avg. SAR) 15 . SAR (W/kg) is a measure of the energy rate absorbed by the human body when exposed to a RF field and is the dosimetric parameter used in RF safety guidelines. For each lead design simulation, the 10g-avg. SAR was computed in a location at 0.1 mm from the anterior face of the lead contact in the direction of the positive Z-axis. In order to obtain a high increase of 10g-avg. SAR, the lead was placed in a volume with high tangential electric field magnitude 16 (see Fig.1e).
The flat-design RTS lead ( Fig. 3a) contained two discrete sections of variable conductivity and length, connected in series. Three requirements were used to minimize the optimal design search including: a) total length fixed to 40 cm to match common lead lengths for implantable devices 17 , b) conductivity of the proximal section higher than the distal section; and c) total lowfrequency resistance of the lead equal to 400 Ω, i.e., less than the typical impedance in patients 18 .
Additional numerical simulations were also performed in order to determine the best design parameters and estimate the performance of the wire-based RTS design since it utilizes different materials and geometry. A detailed view of this model can be seen in Fig. 4d. The model contains four identical RTS fibers each divided into six fixed-length sections of variable thickness which allow the model to simulate the effects of varying length (by making two or more adjacent sections equal in thickness) and number of sections (by choosing the number of changes in adjacent section thickness). Total lead resistance was still R = 400 Ω and the ratio of layer thicknesses t 1/ t 2 = 20. The simulation showed that the optimal design was obtained by dividing the lead into two sections of equal lengths L 1 = 0.2 m and L 2 = 0.2 m and yielded a 33% reduction in peak 10g-avg. SAR within 1cm of the lead (see also Fig. S1 for electric field and magnetic field maps). A summary of optimal designs by number of sections can be seen in Fig.   4e.
Additional analysis on effect of lead design -Additional simulations were performed to evaluate the effect on 10g-avg. SAR of different design variables, including: shape (i.e., wire vs. thin), lead conductivity, and proximal end boundary conditions (i.e., insulated vs. uninsulated).
The results of the simulations are shown in the Supplementary Fig. S2. Notably, the simulations, manufacturing, and bench testing were performed with the electrode exposed only on a single side, although additional simulations included the case of two exposed ends. Higher SAR was predicted for models with wires compared to thin RTS geometries, in line with the skin depth calculations discussed in equation (S10). Furthermore, based on the selected design the RTS leads showed lower SAR than leads with homogeneous conductivity (see also Fig. 2a, case Temperature simulations -The temperature simulations were performed by implementing the following heat equation in solids, which corresponds to the differential form of Fourier's law:  Table S1 for values) and ∅ is the volume of 10 g

Uncertainty analysis
A simulation study to assess the uncertainty of design and simulation parameters was performed ( Table 2). The parameters studied were selected such that they could be considered independent. The methods used were based on the work of Neufeld et al. 13 . To determine the impact of the contribution of an individual parameter to the total uncertainty of the simulations, first two simulations were run for each parameter by assigning two different values ("Val1" and "Val2" in Table S2) to each parameter studied. The first value ("Val1") was the one used for the simulations shown in Fig. 2 whereas the modified value ("Val2") was set to a realistic value that could occur due to either design choice or manufacturing tolerance. Assuming linear dependence of the measurement values on the varying parameter, a sensitivity factor was determined for each parameter by calculating the percent error difference between the two evaluation results and then dividing by the absolute value of the change in parameter value. The individual uncertainty contribution was then calculated by multiplying the sensitivity and the standard deviation of the parameter uncertainty. The standard deviations were small for parameters such as the implant length, which can be accurately determined, and large for parameters such as the conductivity.

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The analysis confirmed a high sensitivity -and relative high uncertainty -to the thickness and dispersion properties of the insulation layer, in line with previous studies 8 . Lower SAR values resulted with a 25.4 µm vs. 50.8 µm dielectric thickness of both insulation and substrate, which is consistent with the notion that insulation characteristics strongly affect the antenna behavior 12 .
Moreover, Fig. 2a shows that the ideal length of layer 2 is 3.3 cm, thus microscopic surface mount resistors (e.g., 0.4 × 0.2 × 0.2 mm 3 ), often connected to each electrode in commercial EEG/fMRI caps, and cannot be used to create an ideal RTS geometry since they are too short.
Additionally, larger resistors would be too bulky and rigid to be attached to a microscopic wire of an implant. Finally, the simulations showed that conductor thickness plays a fundamental role in the RF-induced currents 19 , with a low uncertainty coefficient (see Table S2). Notably, a homogenously conductive thin design decreased the current density at thicknesses less than the skin depth ( Supplementary Fig. S2). The uncertainty analysis performed showed that the permittivity of the binder used in conductive inks can significantly affect 10g-avg SAR.
Binders 20 serve to bind together the nanoparticles of the material, ensure the necessary viscosity for proper transfer of the ink from the press to the substrate, provide adhesion to the substrate, and contribute to the drying speed and resistance properties of the ink 21 . The relative permittivity of binders varies from two to fifteen 22 or higher in composites 23 , and it is essential for the RTS effect presented in this paper, as no RTS effect was found in simulations with binders with the unity relative permittivity of vacuum.

Bench test experiments
Manufacturing of flat-design RTS prototype -A flat-design RTS lead prototype was manufactured using two different commercially available conductive ink materials for initial proof-of-concept testing. The first ink (479SS, Electrodag, Acheson LTD., Kitano, Japan) is a silver (Ag) based PTF ink and was fixed to a specified resistivity of 0.02 /sq./mil 24 . This ink was used in the higher conductivity section L 1 . The second ink (423, Electrodag) is a carbon (C) based PTF ink, which has significantly higher resistivity compared with Ag based PTF inks of 42 /sq./mil 25 . The final layer L 2 was fabricated by chemically mixing the two PTF inks to adjust the conductivity of the second section to the value prescribed by the simulations, which was constrained to be within the conductivity values of the Ag and C-based PTF inks. The length of layer 1 was proportional to the conductivity of the silver ink and was fixed to allow a target ratio  1 / 2 = 77 with the optimal total resistance of 400 . Notably, the resistivity of both the carbon traces and silver electrodes is constant from 100 Hz to 200 MHz 21 . The 400  resistance was well within the range of current commercial IPGs considering that the contact electrode/tissue resistance is usually below 1.5 k 18 . The tolerance for resistivity was 5% and the tolerance for length was 50 μm.

Temperature Measurements in MRI -Evaluation of RF-induced heating during MRI was
assessed by loading the MRI RF body coil with a standard ASTM phantom 9 (Fig. 3b). The phantom shell was made of Plexiglas and filled to a volume of 24.6 L with a gel consisting of