Ferrite-based junction circulators [1,2] are microwave devices made of at least three ports that have been widely used in emission/reception applications ensuring an
isolation between the incoming and outgoing signals. They are especially useful in single antenna applications where signals are being transmitted and received simultaneously.
Conventional circulators are based on a ferrite disk, magnetized to saturation, placed under the central conductor ensuring electromagnetic waves to propagate in a non-reciprocal manner.
The external magnetic field allowing this saturation is provided by a permanent magnet positioned right above of the central conductor.
Due to the size, weight, cost of these systems and the fact that high frequency applications are recently the main concern, the miniaturization of the circulator is inevitable. This can be
achieved using self-biased hexagonal ferrite materials [3,4] which eliminates the use of a permanent magnet. These self-polarized materials, suitable for high frequency applications, are
pellets made out of hexaferrite powder pressed and sintered. During pressing, the orientation of the particles should be achieved in the remanence state using an external magnetic field. In
order to avoid the application of a magnetic field during pressing, and thus to minimize the cost of manufacturing circulators, we propose to design and manufacture circulators based on
hexaferrite particles in the form of platelets. It has been shown that this platelet shape, as shown in Fig. 1, induces a self-alignment of the crystals with the particles orienting themselves
spontaneously, therefore dropping the application of an external magnetic field in any way. This material will be then characterized using a coaxial cell capable of determining its dielectric
and magnetic properties such as the permittivity and the permeability [5]. The values obtained will then be used in the simulation of a coplanar circulator [6,7], that operates in the 5G band
especially around 28 GHz, using HFSS simulator. 

**References ** 
1. H. Bosma, IEEE Transactions on Microwave Theory and Techniques, Vol 12(1), p. 61-72 (1964). 
2. Y. S. Wu and F. J. Rosenbaum. IEEE Transactions on Microwave Theory and Techniques Vol 22(10), p. 849-856 (1974). 
3. N. Zeina, H. How, C. Vittoria, In 1992 IEEE International Magnetics Conference (INTERMAG), pp. 458-458 (1992). 
4. N. Noutehou, C. Patris, D. Névo, Circulateur planaire ultra-compact en bande Q." In JNM (2019). 
5. F. Costa, M. Borgese, M. Degiorgi, In Electronics, Vol 6(4), p. 95 (2017). 
6. O. Zahwe,H. Harb and H. Nasrallah, Int. Arab J. Inf. Technol., Vol 16(3A), p.600-608 (2019). 
7. R. El Bouslemti,F. Salah-Belkhodja and Y. H. A. Fekhar, Revue Méditerranéenne des Télécommunications, Vol 4(1) (2014). 

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Development of an Auto Oriented Circulator Based on Hexaferrite Materials in the 5G Frequency Band

One of the most important parts of a fluxgate sensor is the magnetic core. This work is dedicated to the study of fluxgate sensors based on the nanocrystalline wire as a core
and comparing them to the performance of amorphous wire with chemical composition (Co94Fe6)75Si15B10 [1]. Both wires were manufactured by the Institute of Technical Physics, Iasi,
Romania. Compared to the previous studies on nanocrystalline materials, we demonstrate that proper processing of nanocrystalline alloys can bring sensors with properties comparable to
the traditionally used amorphous alloys, but with better stability at elevated temperatures.
The amorphous Fe73,5Si13,5B9Cu1Nb3 master alloy wires 0.5m in length, and 0.12 mm in diameter were annealed by DC pulse to achieve the nanocrystalline structure. Contrary to other
researchers we found problems with surface oxidation in air, so our annealing was performed in Argon. During the annealing and cooling, we applied mechanical stress to achieve
transverse anisotropy. The character of changing Hc varies depending on tension as shown in Fig.1. Higher tension increases anisotropy and reduces the longitudinal permeability (Fig. 2).
Best results were shown by wires annealed under tension 9 g and 13 g with the current in the range 485 mA up to 510 mA. In these cases, coercivity was in the range of 7 A/m up to 17
A/m at 1 kHz. Annealed wires were used as a core for fluxgate sensors of the Förster and Vacquier types and with ring core.
As an example, Förster type sensor with amorphous (Hc = 20 A/m) wire as a core had max. sensitivity of 0.88 V/mT and min. the noise of 164pT/√Hz at 1 Hz.
By using nanocrystalline wire with Hc = 17A/m we achieved lower sensitivity (0.7 V/mT) but lower noise (111 pT/√Hz). The nanocrystalline core with lower Hc (9 A/m) had higher
sensitivity (1.1 V/mT) but higher noise (204 pT/√Hz) compared to the amorphous core. And the core with Hc = 13A/m had almost the same results as the amorphous wire.
This study was supported by the Grant Agency of the Czech Republic within the Nanofluxgate project (GACR GA20-27150S). 

**References:** 

[1] P. Ripka, D. Hrakova, “Multiwire Parallel Fluxgate Sensors”, IEEE Transactions on Magnetics. 2022, 58(2), 1-5. ISSN 0018-9464. DOI 10.1109/TMAG.2021.3093017 
[2] Y.-F. Li, M. Vazquez, D.-X. Chen, “Circular magnetization process of nanocrystalline wires as deduced from impedance measurements”, Journal of Applied Physics 97, 124311 (2005) 

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Creep induced Magnetic Anisotropy of Nanocrystalline Wire as a Core of Fluxgate Sensor

Susceptibility measurement of magnetic nanoparticles (MNPs) in radio frequency (RF) has been widely studied. However, most of the studies only examined frequencies
up to 20 GHz [1]. In addtion, applying two axial DC fields to increase resonance in specific frequency range and magnetic susceptibility has hardly been done before, since applying a
single static DC field is more common [2-3]. The MNPs can be used for magnetic hyperthermia and biological substances detection [4-6]. In this study, we proposed a novel method for
measuring magnetic susceptibility by a broadband microstrip line type probe up to 67 GHz [7]. Fig. 1 shows the basic principle of the experimental setup. The microtube with MNPs
(SVM-025-5H, 200 nmf, about 300 ml) was put on the microstrip line type probe, which is connected with a network analyzer (N5227A) to generate a magnetic field in a range of 10 MHz
to 67 GHz. The MNPs were put between two electromagnets connected with power supplies to generate a changeable DC field up to 1000 Oe and another orthogonal about 35 Oe DC field.
When the two orthogonal DC fields are around equal, the magnetic susceptibility of MNPs should maximize because of the magnetic switching theory [8], which results in enhancing the
signal to noise ratio. By applying the bias magnetic field, we measured the transmission coefficient, S21, of the microstrip line type probe and obtained magnetic susceptibility [7]. Fig. 2
shows the magnetic susceptibility when the DC field ranges from 0 Oe to 1000 Oe. In the DC field around 0 Oe, the magnetic susceptibility was very low because the MNPs were relaxed.
However, in the DC field of 25 Oe-75 Oe, we observed clear magnetic resonances in 20 - 40 GHz. The resonance frequency increased as the DC field increased. In this case, both fixed and
changeable DC fields are around 35 Oe, which means the magnetic susceptibility is biggest at this condition and the orthogonal DC field enhance the signal to noise ratio to detect magnetic
nanoparticle. The clear magnetic resonance of MNPs has hardly been observed in this broad bandwidth up to 67 GHz before. 


**References:** 

[1] B. K. Kuanr, V. Veerakumar and K. Lingam, Journal of Applied Physics, Vol. 105 (2009). 
[2] M. Jadav, S. P. Bhatnagar, IEEE Transactions on Magnetics, Vol. 56, p. 1-8 (2020). 
[3] P. C. Fannin, I. Malaescu and C. N. Marin, The European Physical Journal E, Vol. 27, p. 145-148 (2008). 
[4] A. Shikano, L. Tonthat, Transaction of the Magnetics Society of Japan Special Issues, Vol. 6, p. 100-104 (2022). 
[5] S. Yabukami, T. Murayama and S. Takahashi, IEEE Transactions on Magnetics, Vol. 58, 6100305 (2022, in press). 
[6] T. Yoneyama, A. Kuwahata and T. Murayama, IEEE Transactions on Magnetics, Vol. 58 (2022, in press). 
[7] S. Yabukami, C. Iwasaki and K. Nozawa, IEEE Transactions on Magnetics, Vol. 58, No. 2, p. 1-5 (2022) 

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Method for Measuring Magnetic Susceptibility of Magnetic Nanoparticles up to Millimeter Wave Frequency Range

The usage of antibody selective biding for the detection of biomolecules provides a fast and low-cost testing platform. The most common type of antibody selective biding
bio-detection tags the bio-molecule of interest with a visual marker. An example of this type of bio-detection is the lateral flow immunoassays like the pregnancy or rapid COVID tests [1].
These visual nanotags are a valid solution for binary detection in high concentrated samples. To have a quantifiable and high sensitivity bio-sensing we use magnetic nanoparticles. The
measurements of this type of magnetic nanotags require expensive laboratory equipment. A novel method using the self-resonant frequency (SRF) of inductors allows high sensitivity with
low-cost and portable systems.
Using the equivalent impedance calculation [2] and the Lichtenecker’s mixing formulas [3] we extracted an analytic simplification to describe the relation between masses of nanomaterial
in the sensing area to variations of the SRF of the inductor. The model correlates variations of the refraction index of the nanotag making the technique able to quantify not only magnetic
nanotags but other types of nanomaterials like gold or latex.
The mathematical model and its simplifications are tested against electromagnetic simulations and experimental measurements. These verifications demonstrate the validity of the model,
the value of magnetic nanoparticles as nanotags for precise quantification, and the advantages of the SRF measuring method for low-cost, high-sensitivity systems. 

**References:** 

1] Moyano, A. et al., 2020. Magnetic Lateral Flow Immunoassays. Diagnostics. 
[2] Qin Yu. et al., 2002. RF Equivalent Circuit Modeling of Ferrite-Core Inductors and Characterization of Core Materials. 
[3] A.V. Goncharenko. et al., 1999. Lichtenecker’s equation: applicability and limitations. 

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Self resonant frequency of inductors for quantification of magnetic nanoparticles

Permanents magnets, or hard ferromagnets, provide a “free” source of magnetic field, with no need of external power. Considering the integration with microsystems,
permanent micromagnets are critical components for the fabrication of microscale motors, generators, switches, pumps, acoustic speakers and energy harvester. Even though the
understanding of magnetism and magnetic materials has led to advancements in their magnetic properties [1], the application of permanent magnets in microsystems is still limited. The
reasons for that are: i) the methods for magnet fabrication at the macroscale (casting and powder processing) are fundamentally different to thin-film microfabrication approaches (physical
vapor deposition, chemical vapor deposition, electrochemical deposition); ii) even if microfabrication approaches are exploited, difficulties remain in depositing thick magnetic films (> 1
μm) and issues due to process compatibility [2].
In this work, we present a process to integrate MEMS (MicroElectroMechanical Systems) and thick permanent magnets. We have designed test structures (Fig. 1) and optimized a process
to fabricate the devices. The optimizations concern: i) deposition of a micron-thick layer of a magnetic material; ii) thermal treatment to enhance the magnetic characteristics of the
material; iii) patterning technique employed to obtain micromagnets; iv) introduction of a passivation layer to protect the material from the subsequent process steps. An image of the final
fabricated device is shown in Fig.2. Examples of application of said process to devices for energy harvesting and magnetic sensing will be discussed. 

**References:** 

M. Sagawa, S. Fujimura, N. Togawa, Journal of Applied Physics, Vol. 55, p. 2083 (1984) 
D. P. Arnold, N. Wang, Journal of microelectromechanical systems, Vol. 18, p.1255 (2009) 

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Integration of hard magnetic layer in MEMS process

The use of time-varying magnetic field sources is indispensable in numerous applications, such as magnetic resonance imaging, sensors, motors, actuators, magnetometers or magnetic
refrigerators. Halbach cylinders have been used as an alternative to electromagnets, since they have no losses by the Joule effect. However, rod mangle systems are cheap and promising
alternatives to the currently used Halbach cylinders [1-3]. The use of rotation patterns has potential for application in several innovative áreas [4].
In this work, we modeled rod mangle structures with different number of rods, aiming to control the magnitude, direction and homogeneity of the magnetic field. Figure 1 (a) shows the
modeled system for 3 rods. After determining the configuration with the maximum magnetic flux density at the center of each system, it was possible to generate a homogeneous magnetic
field. The homogeneity increases with the number of rods and for a large number of rods, the rod mangle structure begins to resemble an ideal Halbach. We also analyzed two different
rotation patterns to generate a decreasing magnetic field over time. For the first pattern only the direction of the magnetic field of the odd configurations remained constant. For the second
rotation pattern, after the magnetic field is reduced to zero, it starts to increase in the opposite direction and then decreases to zero again. If we rotate all rods counterclockwise, the
magnetic field will rotate clockwise, keeping the magnitude fairly constant. Finally, we validated the results experimentally with structures of 3 and 4 rods (Fig 1 (b)). 

**References:** 

[1] J. M. D. Coey, Permanent magnet applications, Journal of Magnetism and Magnetic Materials 248 (3) (2002) 441–456. 
[2] O. Cugat, P. Hansson, J. M. D.Coey, Permanent magnet variable flux sources, IEEE Transactions on Magnetics 30 (6) (1994) 4602–4604. 
[3] F. Hiptmair, Z. Major, R. Haßlacher, S. Hild, Design and application of permanent magnet flux sources for mechanical testing of magnetoactive elastomers at variable field directions,
Review of Scientific Instruments 86 (8) (2015) 085107. 
[4] H. Sakuma, T. Nakagawara, Optimization of rotation patterns of a mangle-type magnetic field source using covariance matrix adaptation evolution strategy, Journal of Magnetism and
Magnetic Materials 527 (2021) 167752. 

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Rod mangle rotation patterns for magnetic field generation

Magnetorheological fluids (MRFs) can change their viscosity in response to applied magnetic field. Magnetorheological energy absorbers (MREAs) are being investigated for adaptive shock isolation because MREAs can adjust their stroking load to severity of impact when magnetic field is used to control MRF viscosity. Employing MRFs in MREAs requires a highly stable suspension to maintain a uniform concentration, because MREAs would be used only in the event of an impact or crash event, that is, rarely. Suspension stability of MRFs can be studied using an automated vertical axis inductance monitoring system (AVAIMS), where an inductance sensor is translated vertically along a column of MRF to measure particle concentration as a function of column height and time [1,2]. The AVAIMS allows for tracking discontinuities in density or shocks including: the mud-line (boundary between the topmost supernatant (clear fluid) zone and the original concentration zone), the gel-line (boundary between the original concentration zone below mud-line and variable concentration zone), and the cake-line (boundary between the variable concentration zone and the sediment zone at the bottom of the column). MRF sedimentation can be evaluated comprehensively analyzing these boundaries. The AVAIMS developed here (Fig. 1) seeks to improve sedimentation zone boundary localization using an optimized inductance sensor to measure concentration gradient as a function of time. The inductance sensor design, material selection, and geometry were optimized and permalloy and plastic were used advantageously to improve sensor sensitivity. The calibration curve of the sensor was obtained by measuring samples with different particle volume fractions. The sensor design was validated by examining a uniformly mixed MRF column for seven consecutive days after preparation of an MRF with an Fe solids loading of 20 vol%. These tests show that the AVAIMS developed here was able to better localize sedimentation zone boundaries using concentration gradient profile method (Fig. 2).

Sedimentation of Magnetorheological Fluids Measured Using a Automated Vertical Axis Inductance Monitoring System

Magnetorheological fluids (MRFs) consist of micron-sized magnetic particles dispersed in a carrier fluid for which rheological properties can be tuned reversibly with
magnetic field.1 If an MRF is contained in a cellular elastomeric encapsulant (CEE), its mechanical properties, such as stiffness and damping, can be controlled via magnetic field. Such
tunability can be exploited for adaptive vibration control or energy absorption systems. A magnetorheological damper often uses an accumulator to modulate pressure injected by external
forces applied to the damper.2 An accumulator is implemented into the cellular encapsulant to enable essentially incompressible fluid to enter the accumulator and to allow compression of
the cellular material to take place, and also enables a mechanical bulge stiffness to the design.
Here, MRF was prepared with silicon oil (40% vol. fraction). Thermoplastic polyurethane (TPU) was 3-D printed as the CEE system. (Fig. 1 a). The MRF was injected into the TPU-CEE,
followed by the printing of a sealing layer. The wall adjacent to the sealing layer had a circular opening and a TPU membrane was bonded to its perimeter so that the pressurized MRF
could flow through the opening and be accumulated in the resulting pocket.
An external magnetic field (0 and 7 kG) was applied along the sample longitudinal axis at the time of uniaxial dynamic testing with 5% pre-strain. The TPU-CEE samples were
characterized via force-displacement tests at 1 Hz under strain amplitudes. The MR effect on the dynamic stiffness is defined as the ratio of the dynamic stiffness under the maximum
magnetic field to the dynamic stiffness in the absence of a magnetic field. Dynamic stiffness in the presence as opposed to the absence of magnetic field was 264%. (Fig.2a) The area of the
force-displacement curve of the system with an accumulator is about 41% greater than one without an accumulator. The accumulator enhanced the increase in damping (Fig. 2b). The
increase in damping capacity generally increased as strain amplitude increased. 

**References:** 

1. Ashtiani M, Hashemabadi SH, Ghaffari A. A review on the magnetorheological fluid preparation and stabilization. Journal of Magnetism and Magnetic Materials. 374, 716.
(2015) 
2. Yu, Jianqiang & Dong, Xiaomin & Wang, Xuhong & Pan, Chengwang & Zhou, Yaqin. Asymmetric Dynamic Model of Temperature-Dependent Magnetorheological Damper and
Application for Semi-active System. Frontiers in Materials. 6. 227. (2019) 

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Development of Magnetorheological Fluids within 3D Printed Elastomeric Cellular Structures with an Accumulator

Most research on remotely driven magnetic micro-robots focuses on their manipulation within fluids [1]. Actuating their motion in soft media and living tissue raises
challenges along with new opportunities for minimally invasive medicine. In contrast to fluids, moving solids in soft media irreversibly rearranges the material, leading to highly non-linear
and history dependent reaction forces. The present work demonstrates that this behavior enables solutions of certain long-standing problems. One problem stems from using magnetic field
gradients to generate forces which limits their range particularly for sub-millimeter size magnetic robots. Locomotion by the transfer of energy via a time varying uniform magnetic field
provides an alternative. In fluids where locomotion effectively occurs through swimming at low Reynolds numbers, this strategy can be costly, requiring more complex shapes (e.g. a screw
[2]) and control over a non-reciprocal motion gait [3]. In tissues, such complex shapes have difficulties in changing their trajectory direction over short distances. The novel finding in this
work is that soft media enables locomotion of simple solids, such as a pair of spheres (see Fig. 1), without requiring them to execute a complex motion gait. Using an external uniform
magnetic field to change the relative orientations of the magnetic moments, the disconnected spherical solids of slightly different diameters can locomote as one in a soft medium via
ratchet-like movements that are completely reciprocal. Such a configuration also allows the pair to change the direction of locomotion quickly. A demonstration is carried out in this work
via development of a theoretical model and its numerical simulation, although some experimental observations support these findings. 

**References:** 

[1] J. J. Abbott et al., "How should microrobots swim?," The international journal of Robotics Research, vol. 28, no. 11-12, pp. 1434-1447, 2009. 
[2] T. W. Fountain, P. V. Kailat, and J. J. Abbott, "Wireless control of magnetic helical microrobots using a rotating-permanent-magnet manipulator," in 2010 IEEE International
Conference on Robotics and Automation, 2010: IEEE, pp. 576-581. 
[3] E. Lauga, "Life around the scallop theorem," Soft Matter, vol. 7, no. 7, pp. 3060-3065, 2011. 

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On Locomotion of Magnetized Spherical Solids in Soft Media

Micro helical robots actuated by an external magnetic field have been investigated for a possible application to treat occlusive vascular disease. It requires a high-speed
rotating magnetic field (RMF) which generates fast drilling motion of the micro helical robot to tunnel the clogged lesions in blood vessels.1-3 The RMF is generated by the magnetic
navigation systems (MNSs) composed of multiple coils or electromagnets. However, as the frequency increases, the impedance from the inductance of the coils decreases the current and
the magnetic field. To overcome this problem, prior researchers utilized a resonance by including additional capacitance to their MNS.2,3 The electromagnets with magnetic cores generate
a large magnetic field.4 Unlike the MNS with coils only, the MNS with electromagnets has significant mutual-inductance due to the magnetic flux linkages between electromagnets, but
any resonance method suppressing the self and mutual inductances of the electromagnets of the MNS has not been reported.
We propose a method to suppress both the self and mutual-inductance effect of the 3-phase MNS with multiple electromagnets. First, we set the imaginary part and the real parts except the
resistance in the voltage equation to be zero to express the resonance. After solving the real part of the voltage equation and the actuation matrix equation which relates applied current with
flux density together, we can determine 3-phase currents and corresponding phases at resonance. The capacitance at resonance can be determined by solving the imaginary part in the
voltage equation. Fig. 1 shows the 3-phase MNS developed for the experiments and Fig. 2 shows the calculated and measured 3-phase currents and RMF with the application of the
proposed method to generate a magnetic flux density of 10 mT. It shows that the calculated current matches well with the measured one within 5 % discrepancy. The proposed method in
this research can contribute to improving the tunneling performance of micro helical robots by generating a high-speed RMF even in the MNS with the electromagnets. 

**References:** 

1Q. Wang, X. Du, and L. Zhang, “Real-time ultrasound Doppler tracking and autonomous navigation of a miniature helical robot for accelerating thrombolysis in dynamic
blood flow,” ACS Nano, vol. 16, no. 1 (2022). 
2K. T. Nguyen, B. Kang and J. Park, “High-frequency and High-powered electromagnetic actuation system utilizing Two-stage resonant effects,” IEEE/ASME Transactions on
Mechatronics, vol. 25, no. 5 (2020). 
3J. Nam, W. Lee, and G. Jang, “Magnetic navigation system utilizing resonant effect to enhance magnetic field applied to magnetic robots,” IEEE Transactions on Industrial Electronics,
vol. 64, no. 6 (2017). 
4J. Nam, W. Lee, E. Jung, and G. Jang, “Magnetic navigation system utilizing a closed magnetic circuit to maximize magnetic field and a mapping method to precisely control magnetic
field in real time,” IEEE Transactions on Industrial Electronics, vol. 65, no. 7 (2018). 

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Resonant Control Method to Suppress the Self and Mutual Inductances of a 3 phase Magnetic Navigation System for Fast Drilling Motion of Micro Helical Robots

Magnetic catheter (MC) controlled by a magnetic navigation system (MNS) and a feeding device have been developed to overcome the steerability and the pushability of
conventional catheters.1,2 External magnetic field (EMF) produced from the MNS generates magnetic torque at the magnets in the MC to remotely steer the MC’s distal end while the
feeding device pushes the proximal end of the MC to move the MC forward.3,4 Sometimes, it does not work effectively when buckling of a flexible catheter occurs in complex blood
vessels.
We propose a position control method (PCM) of the Robotically Assisted MAgnetic Navigation (RAMAN) system to improve the pushability of the MC by maximizing magnetic force
(MF). Fig 1(a). shows the developed RAMAN system in which the 7-axis stage robot can move the 8 electromagnets (EMs) and the workspace surrounded by them. Fig 1(b). shows the MF
in the region of interest (ROI) which is 80% of the workspace. The PCM takes advantage of the fact that the MF increases as the magnet moves close to the EM. When the MF generated at
the MC is not sufficient, the PCM compares the MF of each vertex in the ROI and controls the 7-axis stage robot to move the ROI in such a way that the MC is located close to one of the
EMs to generate maximum MF. Fig 2. shows calculated maximum MF at the center of the ROI and at the point selected by the PCM where an axially magnetized ring magnet (OD: 2 mm,
ID: 1 mm, Length: 10 mm) of NdFeB 52 is located along θ and Φ directions. It shows that the PCM generates larger MF in any directions and 5 times larger MF on average than the
maximum MF generated at the center. We performed a navigation experiment of the MC along the aorta to the right coronary artery in a cardiac vascular phantom model. We observed a
buckling of the MC, and the maximum MF of 2.61 mN at the center did not overcome the buckling. We applied the PCM which generated the MF of 20.1 mN to release the buckling of the
MC. The PCM may contribute to controlling of the MC for robotic endovascular intervention. 

**References:** 

1B. J. Nelson, I. K. Kaliakatsos, and J. J. Abbott, Annual Review of Biomedical Engineering., Vol. 12, 55 (2010).
2N. Kim, S. Lee, W. Lee, and G. Jang, AIP Advances, Vol. 8, 056708 (2018).
3J. Nam, W. Lee, E. Jung, and G. Jang, IEEE Transactions on Industrial Electronics, Vol. 65, 5673 (2018)..
4E. Jung, W. Lee, N. Kim, J. Kim, J. Park, and G. Jang, AIP Advances, Vol 9, 125230 (2019). 

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Position Control Method of a Robotically Assisted Magnetic Navigation System to Improve the Pushability of a Magnetic Catheter by Maximizing Magnetic Force

Transcranial magnetic stimulation (TMS) is a non-invasive, effective, and safe neuromodulation technique used to diagnose and treat neurological disorders [1]-[2]. A key
challenge involved with TMS is to determine stimulation strength in critical regions of the brain accurately. The induced electric field is affected by complexity and heterogeneity of the
brain and numerical computation methods like finite element analysis (FEA) can be used to estimate electric field distribution. However, these methods need exceedingly high
computational resources and are time-consuming [3]-[6]. The purpose of this study was to develop and test a machine learning algorithm that can efficiently predict stimulation strength
based on neuroanatomy. Head models were developed from magnetic resonance images of eleven recruited subjects using SimNIBS pipeline [7]-[8]. We used Sim4Life, an FEA software
to compute induced electric fields due to simulated TMS; the induced electric fields served as training data. A deep convolutional neural network (DCNN) inspired encoder-decoder
network (Fig 1) was developed to predict induced electric fields from T1-weighted and T2-weighted magnetic resonance imaging (MRI) based anatomical slices. Three representative cases
of electric fields predicted by the DCNN algorithm, along with the corresponding reference electric fields are shown in Fig 2. For the trained network, the training data and the testing data
peak signal to noise ratios are 32.83dB and 28.01dB respectively. The key contribution of this study is the ability to predict the induced electric fields in real-time as well as accurately and
efficiently predicting TMS strength in the targeted brain regions saving both time and computational resources.
Acknowledgment: This work was supported by VCU CERSE. Further funding was provided by the CCI CVN (Proposal ID #: FP00010500). 

**References:** 

[1] D. J. Stultz, S. Osburn, T. Burns, S. Pawlowska-Wajswol, and R. Walton, Transcranial magnetic stimulation (TMS) safety with respect to seizures: A literature review,
Neuropsychiatric disease and treatment, vol. 16, p. 2989 (2020). 
[2] M. Kobayashi, and A. Pascual-Leone, 2003. Transcranial magnetic stimulation in neurology, The Lancet Neurology, vol. 2, no. 3, p. 145-156 (2003). 
[3] E. G. Lee, W. Duffy, R. L. Hadimani, M. Waris, W. Siddiqui, F. Islam, M. Rajamani, R. Nathan, and D. C. Jiles, Investigational effect of brain-scalp distance on the efficacy of
transcranial magnetic stimulation treatment in depression, IEEE Transactions on Magnetics, vol. 52, no. 7, p. 1–4 (2016). 
[4] L. J. Crowther, R. L. Hadimani, A. G. Kanthasamy, and D. C. Jiles, Transcranial magnetic stimulation of mouse brain using high-resolution anatomical models, Journal of Applied
Physics, vol. 115, no. 17, p. 17B303 (2014). 
[5] F. Syeda, H. Magsood, E. G. Lee, A. A. El-Gendy, D. C. Jiles, R. L. Hadimani, Effect of anatomical variability in brain on transcranial magnetic stimulation treatment, AIP Advances,
vol. 7, no. 5, p. 056711 (2017). 
[6] F. Syeda, K. Holloway, A. A. El-Gendy, and R. L. Hadimani, Computational analysis of transcranial magnetic stimulation in the presence of deep brain stimulation probes, AIP
Advances, vol. 7, no. 5, p. 056709 (2017). 
[7] N. Mittal, C. Lewis, Y. Cho, C. L. Peterson, and R. L. Hadimani, Effect of fiber tracts and depolarized brain volume on resting Motor thresholds during transcranial magnetic
stimulation, IEEE Transactions on Magnetics (2022). 
[8] N. Mittal, B. Thakkar, C. B. Hodges, C. Lewis, Y. Cho, R. L. Hadimani, and C. L. Peterson, Effect of neuroanatomy on corticomotor excitability during and after transcranial magnetic
stimulation and intermittent theta burst stimulation, Human Brain Mapping (2022). 

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Prediction of Stimulation Strength of Transcranial Magnetic Stimulation in the Brain with Deep Convolutional Neural Network based Encoder Decoder Network

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