France



Magnetic nanostructures attract considerable scientific and technological efforts in diverse applications, such as magnetic recording, magnetic sensors, biomedicine, etc.&lt;sup&gt;[1,2]&lt;/sup&gt; Whereas patterned nanomagnets are mostly 2D planar structures, recently research has been expanded into 3D aspect. In 3D nanomagnets, more delicate and complicated magnetic configurations, with novel properties, become possible.&lt;sup&gt; [3,4]&lt;/sup&gt; Imaging and understanding the magnetic configurations in 3D nanomagnets is an increasingly important issue for a wide range of modern applications.&lt;br/&gt;&lt;br/&gt;Here, aligned, isolated iron nanocuboids [Fig. 1 (a)] have been fabricated by taking advantage of epitaxial, three-dimensional-island growth on GaAs(001) during electrodeposition at low deposition rates.&lt;sup&gt;[5]&lt;/sup&gt; The nanoparticles exhibit lateral size between 10 and 250 nm and heights below 80 nm. Surface {100} facets predominate with a thin crystalline oxide shell that protects the nanoparticles during prolonged storage in air [Fig. 1 (b)]. The magnetic configurations inside the cuboids are systematically investigated by combining quantitative magnetic force microscopy (qMFM) with micromagnetic simulations [Fig. 1 (c, d)]. Experimental results and micromagnetic simulations give evidence for a transition from single-domain state to vortex state, and even to Landau pattern with increasing the size of the cuboids, demonstrating the key importance of nanometric size control of magnetic nanoparticles. The simulated and experimental magnetic charge profiles are compared and show good agreement [Fig. 1 (e-h)]. Such measurements open the door to fine tuning the magnetic configuration of nano-objects that will find applications in fields of sensor, magnetic recording, and biomedicine.

**References:**

1. C. Gatel, F. J. Bonilla, A. Meffre, et al. Nano Lett. 2015, 15, 6952−6957.&lt;br/&gt;2. M. Bode, A. Wachowiak, J. Wiebe, et al. Appl. Phys. Lett. 2004, 84, 948−950.&lt;br/&gt;3. L. A. Fomin, I. V. Malikov, S. V. Pyatkin, et al. J. Magn. Magn. Mater. 2010, &lt;i&gt;322&lt;/i&gt;, 851−857.&lt;br/&gt;4. F. J. Bonilla, L.-M. Lacroix, T. Blon, J. Magn. Magn. Mater. 2017, &lt;i&gt;428,&lt;/i&gt; 394−400.&lt;br/&gt;5. K. Leistner, M. Yang, C. Damm, et al. Nanoscale, 2017, 9, 5315–5322.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/5a71d36f584e8493e8281fc8b8ff7eca.jpg)
Fig.1 (a) SEM image showing isolated iron cuboids with different size distribution. (b) EELS mapping of Ga, Fe and O elements in iron cuboid. (c) qMFM scan of one cuboid with a lateral size of 54 nm, and the related micromagnetic simulation showing vortex state (d). Experimental MFM phase of one cuboid with a lateral size of 170 nm (e) and the calculated MFM phase (f). (g) Extracted profiles from (e) and (f), (h) Simulation of (e) showing Landau pattern.



INTERMAG 2021

 Size-specific magnetic configurations in epitaxial iron nano-cuboids

Magnetic nanostructures attract considerable scientific and technological efforts in diverse applications, such as magnetic recording, magnetic sensors, biomedicine, etc.[1,2] Whereas patterned nanomagnets are mostly 2D planar structures, recently research has been expanded into 3D aspect. In 3D nanomagnets, more delicate and complicated magnetic configurations, with novel properties, become possible. [3,4] Imaging and understanding the magnetic configurations in 3D nanomagnets is an increasingly important issue for a wide range of modern applications. Here, aligned, isolated iron nanocuboids [Fig. 1 (a)] have been fabricated by taking advantage of epitaxial, three-dimensional-island growth on GaAs(001) during electrodeposition at low deposition rates.[5] The nanoparticles exhibit lateral size between 10 and 250 nm and heights below 80 nm. Surface {100} facets predominate with a thin crystalline oxide shell that protects the nanoparticles during prolonged storage in air [Fig. 1 (b)]. The magnetic configurations inside the cuboids are systematically investigated by combining quantitative magnetic force microscopy (qMFM) with micromagnetic simulations [Fig. 1 (c, d)]. Experimental results and micromagnetic simulations give evidence for a transition from single-domain state to vortex state, and even to Landau pattern with increasing the size of the cuboids, demonstrating the key importance of nanometric size control of magnetic nanoparticles. The simulated and experimental magnetic charge profiles are compared and show good agreement [Fig. 1 (e-h)]. Such measurements open the door to fine tuning the magnetic configuration of nano-objects that will find applications in fields of sensor, magnetic recording, and biomedicine.

**References:**

1. C. Gatel, F. J. Bonilla, A. Meffre, et al. Nano Lett. 2015, 15, 6952−6957. 2. M. Bode, A. Wachowiak, J. Wiebe, et al. Appl. Phys. Lett. 2004, 84, 948−950. 3. L. A. Fomin, I. V. Malikov, S. V. Pyatkin, et al. J. Magn. Magn. Mater. 2010, 322, 851−857. 4. F. J. Bonilla, L.-M. Lacroix, T. Blon, J. Magn. Magn. Mater. 2017, 428, 394−400. 5. K. Leistner, M. Yang, C. Damm, et al. Nanoscale, 2017, 9, 5315–5322.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/5a71d36f584e8493e8281fc8b8ff7eca.jpg)
Fig.1 (a) SEM image showing isolated iron cuboids with different size distribution. (b) EELS mapping of Ga, Fe and O elements in iron cuboid. (c) qMFM scan of one cuboid with a lateral size of 54 nm, and the related micromagnetic simulation showing vortex state (d). Experimental MFM phase of one cuboid with a lateral size of 170 nm (e) and the calculated MFM phase (f). (g) Extracted profiles from (e) and (f), (h) Simulation of (e) showing Landau pattern.

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Magnetic hyperthermia is a promising cancer therapy gaining great interest in recent years using heat generation ascribed to magnetic particles subjected to a high-frequency magnetic field. To make this therapy feasible in clinical settings, in addition to magnetic particles, important elements include techniques for detecting their position and temperature in a tumor region in determining the effectiveness of therapeutic heating. In previous studies, we developed thermosensitive magnetic micro/nanoparticles with high heating efficiency and considerable permeability change around the therapeutic temperature range of 42-45°C [1]. We also proposed a wireless temperature measurement method for monitoring the tumor temperature using pickup coils to detect the temperature-dependent stray magnetic field caused by the magnetic particles [2]. A challenge remains when the particles injected into the tumor region deviate from the longitudinal axis of drive coil (heating coil). As a result, the heating generation of the particles and the accuracy of the proposed thermometry are decreased. To solve this problem, by taking the advantage of the fact that the induced voltage in pickup coil depends on the position of the particles, we developed a localization system using three pickup coils symmetrically installed inside drive coil. The position of particles could be automatically localized by using a robot arm to operate the unit composed of drive coil and pickup coils in two modes of coarse adjustment (rotary scanning) and fine adjustment (linear scanning) [3]. In this study, we propose a simpler, faster and more cost-effective localization method by using only figure-8 coil instead of three pickup coils (loop type coils) and operating the unit of drive coil and figure-8 coil (hereafter the unit) only in linear scanning mode. Fig. 1 shows the conceptual diagram of the proposed localization method using figure-8 coil. Figure-8 coil consists of two reverse-winding loop coils and is adjusted so that its initial bias (the voltage without sample) close to 0 V and fixed to the center of drive coil. As a result, the induced voltage changes depending on the relative position of the implant (i.e., magnetic particles) as seen from the unit when the implant moves along the longitudinal axis of figure-8 coil (x-axis) on xz-plane. Here, xyz and x’y’z’ are the coordinate systems of the unit (known) and the implant (unknown), respectively. That is, in actual localization, by monitoring the voltage during moving the unit linearly over the existence possibility area of the implant, it is possible to specify the symmetry plane of the implant (e.g., y’z’-plane which is perpendicular to the moving x-axis when the voltage is at the inflection point). Similarly, as shown in Fig. 1(b), by simply rotating the unit 90° counter-clockwise on xy-plane, and then moving the unit along the longitudinal axis of figure-8 coil, it is possible to specify the symmetry plane x’z’. Finally, for specifying the symmetry plane x’y’, rotating the unit 90° around y-axis counter-clockwise, and the resulting three symmetry plane intersect at the position of the implant. Next, we verified the validity of the proposed method using the constructed experimental setup as shown in Fig. 2(a). The strength and frequency of magnetic field applied at the center of drive coil (pancake coil, 40 turns, internal diameter 28.1 mm, external diameter 113.5 mm) were 2.88 mT and 2 kHz, respectively. The induced voltage in figure-8 coil (each loop 1 turn, diameter 10 mm) without the sample was subtracted from the induced voltage with the sample. The sample (1 g of magnetic particles dispersed in 1mL of deionized water) used in the following experiments was our previously-developed micromagnetic particles with a Curie point of 45°C [1]. As shown in Fig. 2(b), when the sample moved manually along the x-axis (z = 10 mm; y= 0 mm or -10mm), the average voltage (all experiments were repeated three times) changed depending on the position of sample, and the voltage was at the inflection point when the sample was directly above the intersection of two loops of figure-8 coil. In Fig. 2(c), when the sample moved along the y-axis (z = 10 mm; x= 0 mm), the voltage (almost 0 V) was extremely small compared to the one when the sample moved along the x-axis around the intersection of two loops of figure-8 coil (z = 10 mm; y= 0 mm). This means that the symmetric plane of the implant can be specified with high accuracy by using figure-8 coil. As shown in Fig. 2(d), with our currently constructed experimental setup, it is possible to detect the sample up to 5 cm from the unit. Future studies are needed to investigate the optimal design of drive coil and figure-8 coil to extend the detectable distance for deeper tumor.

**References:**

[1] L. Tonthat, Y. Yamamoto, F. Aki et al, IEEE Trans. Magn., Vol. 54(7), p. 5400506 (2018) [2] F. Aki, L. Tonthat, H. Saito et al, Electron. Comm. Jpn., Vol. 101 (6), p. 58–66 (2018) [3] L. Tonthat, K. Mitobe, S. Yabukami, IEEE Trans. Magn., Vol. 57(2), doi: 10.1109/TMAG.2020.3008490 (early access).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/eb9288a7a69c6bd175f360d34d4b58ed.jpg)
Fig. 1 The conceptual diagram of the proposed localization method for magnetic particles using a figure-8 coil. (a) The voltage changes depending on the relative position of the implant as seen from the unit when the implant moves along x-axis on xz-plane. (b) By simply rotating the unit 90° counter-clockwise on xy-plane, it is possible to specify the symmetry plane x’z’ and rotating the unit 90° around y-axis counter-clockwise for specifying the symmetry plane x’y’.

![](https://assets.underline.io/uploads/markdown_image/1/image/42c1dd14e9741c112ca8fe9f33ccc20e.png)
Fig. 2 (a) The constructed experimental setup and (b), (c), (d) the relationship between the average voltage (n=3) and the position of the sample when the sample moved manually above the fixed unit.

 A Simple Localization Method of Magnetic Particles for Hyperthermia Therapy using Figure-8 Coil

Introduction: Delivery of biological fluids and agents requires precision and can benefit from separation between substance and user for accurate results and safety, for example, in studies involving contagious organisms or viruses or when experimenting on sensitive cellular behaviors. Using a robot that contacts only the substance to be loaded and the unloading site provides that degree of separation needed for safety and study integrity. In this work, we demonstrate the use of optically powered diamagnetically levitated pyrolytic graphite robots with end effector micropipettes for a contact-free fluid delivery solution for use in biological studies. Specifically, we demonstrate loading, transporting, and releasing dyed water into agarose gel with autonomous control. Optical control of diamagnetically levitated PyG has been demonstrated in our previous work [1]. Using projector-based optical sources or independent control of laser beams, multiple samples may be controlled in parallel in an unsegmented workspace [2, 3]. An unsegmented workspace allows multiple robots to collaborate in a factory set-up with no extra circuitry or boundaries specific to each robot. All that is needed is a light source for each sample, which can be provided with a projector setup or a laser-splitting device. The alternative system design is the actuation of Neodymium-Iron Boron (NdFeB) magnets levitated on top of graphite [4, 5]. Control is achieved using active current traces in printed circuit boards under the graphite. This arrangement has segmented work surfaces, limited motion in close proximity, and requires extensive changes to expand the workspace. It also requires continuous power to ensure levitation and movement. In our work, the experimental setup includes PyG samples passively levitating on top of a checkerboard permanent magnet array. Instead of complicated circuitry, the displacement of the PyG robot is controlled using single laser sources for individual control. Given the low levitation height of the PyG, the load mass is constrained, which limits the end effectors and manipulands employed. With the contactless design, static end effectors, such as the micropipettes used in this study, are preferable. These micropipettes work on pressure differences, which keeps the system as autonomous as possible. The advantages that arise from a passively levitated, optically actuated platform are accompanied by loading and handling challenges and limitations. System Design: PyG, an artificial graphite, has the strongest known diamagnetism at room temperature, allowing it to levitate over an array of checkerboard permanent magnets at room temperature. Its large out-of-plane temperature-dependent diamagnetic susceptibility allows it to be actuated by localized temperature changes. Optical irradiation, such as that from a laser or projector, increases the local temperature, which decreases its local diamagnetic susceptibility, resulting in an in-plane force due to asymmetric out-of-plane forces and an induced tilting in the sample. In this study, a vision-based autonomously controlled laser source on a motorized stage irradiates the PyG sample, moving it towards the laser spot. The end effector micropipette is placed on the PyG sample, which is levitated on top of a magnet array, as shown in Fig. 1. The micropipette loads fluids from droplets placed on a glass slide via capillary action. A coefficient of penetration is used to determine the loadable fluids, while also considering adhesion between the glass slide and fluid to facilitate the retreat of the micropipette. To ensure liquid forces on the micropipette do not draw the PyG onto the droplet, a plastic barrier with holes that allow passage of the micropipette but not the PyG is placed at the edge of the magnet array. During the unloading process, the fluid diffuses when the micropipette penetrates an agarose gel. Experiment: Photographs taken during operation are shown in Fig. 2. In response to joystick user input, a motorized stage translates and moves the laser and levitated robot carrying a glass micropipette end effector (25-100µm dia.) fixed to the PyG with vacuum grease. The robot’s pipette approaches the fluid and loads within &lt;10 seconds for the liquid solutions tested (5% xylene cyanol, 1% bromophenol blue, 0.1M NaCl). To retreat, the stage for the fluid droplet is lowered mechanically, releasing the pipette. Laser power is insufficient to retreat the PyG from the fluid droplet after loading due to high surface tension forces. Once free of the droplet, the PyG is moved by the laser to the agarose at the unloading site. After penetration, diffusion of the fluid into the agarose is visible within 30s and takes several minutes to completely unload the pipette. The main focus for future work is process automation. Currently, the process is executed by a user with a joystick, but the future goal is to develop a single input program that will complete the whole process, including finding the robot and executing the loading and unloading procedure.

**References:**

 [1] M. Ewall-Wice, et al., IEEE Transactions on Magnetics 55.7 (2019): 1-6. [2] J. Young, et al. AIP Advances 9.12 (2019): 125038. [3] J. Young, et al. Proc. SPIE 112930S (2020). [4] E. E. Hunter, et al., IEEE Robotics and Automation Letters 4.2 (2019): 997-1004. [5] A. Hsu, et al., IEEE Robotics and Automation Letters 5.2 (2020): 2913-2920.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/b95426e192053b147205ba6b02cdb4cc.jpg)
Figure 1. Photograph of a micropipette (50µm inner diameter tip, overall length 10mm) placed on top of a levitated 15mmØ PyG sample.

![](https://assets.underline.io/uploads/markdown_image/1/image/6f2ee93f3564459652b63544d99b4958.jpg)
Figure 2. Photographs of the operation. The PyG sample is counterbalanced with a tip of toothpick. a) PyG approaches the fluid behind the wall. b) Micropipette loads the fluid, which is placed on a glass slide and a tilting stage. c) PyG retreats after the tilting stage is lowered. d) PyG moves towards agarose. e) Micropipette penetrates agarose. f) Fluid diffuses into agarose.

 Optically Powered Diamagnetically Levitated Robots for Biomedical Applications

A major fraction of airborne particulate matter is magnetic. The origin of these magnetic particles is anthropogenic (industry, traffic), and often accompanied by traces of very toxic heavy metal pollutants. The magnetic fraction of airborne particulate matter is therefore a good indicator for the amount of air pollution, and can serve as a first indicator for toxicity. We collected airborne magnetic particulate matter directly onto silicon substrates by means of a stack of permanent NdFeB magnets (Figure 1). Collection was performed in open air along a campus road for a period of 2-4 weeks. For comparison, a control substrate was mounted in a similar fashion, nearby but not on a magnet. The silicon substrates can be readily used in a variety of surface analysis techniques. The morphology of the captured particles was analyzed by optical and electron microscopy, as well as by AFM. The substrate that was on the magnet stack showed an increased amount of particles. The particle size varied from 50 micrometer down to diameters below 100 nm. Many of the particles are perfectly round spheres with a diameter of a few up to tens of micrometers. SEM-EDX analysis showed that particles that are captured magnetically mainly consist of iron-oxide. VSM analysis showed that the substrate that was on the magnet has a magnetic moment that is six times higher than the substrate that was not in the magnetic field gradient (Figure 2). The average collection of magnetic particulate matter on the 5mm×5mm area is approximately 4 nAm2/day, which translates to 46 ng/day if the particles are made entirely of iron-oxide. These experiments show that one can collect magnetic particulate matter directly from the air, without using filters and complex post-treatment procedures that change the particle composition and cause clustering. Magnetic particulate matter sampling is therefore a promising complementary technique that can be applied in for instance air quality monitoring stations.

**References:**



**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/11c6c4c908f151e15109ac69ec88de7b.jpg)
Fig 1. A stack of NdFeB magnets ranging in diameter from 70 down to 4 mm is used to attract magnetic particulate matter onto a 5 mm x 5 mm silicon substrates. The substrate is shielded from rain by a tube, and the magnets are protected by a PVC enclosure.

![](https://assets.underline.io/uploads/markdown_image/1/image/7752478b701390e1c101a1464837f6ef.jpg)
Fig. 2. The magnetic moment of the substrate that was outside on the magnet stack for a month (red curve) is at least six times higher than that of a substrate that was outside for the same period, but not on a magnet (blue curve). The reference (black curve) is the signal of a substrate that was kept in a box.

 Capture of magnetic particulate matter directly from air on silicon substrates

Transcranial Magnetic Stimulation (TMS) has proven in recent years to be an effective method for neuromodulation without surgical interventions. Such non-invasive stimulation treatment has been approved by the U.S. Federal Drug Administration (FDA) for treating major depressive disorder (MDD), obsessive compulsive disorder (OCD) and certain types of migraine headaches [1]. Current research is investigating the use of TMS for treating Parkinson’s Disease (PD) and Post-Traumatic Stress Disorder (PTSD) [2][3]. Despite the promise that TMS offers for non-invasive neuromodulation, most commercial TMS coils deliver a uniform H field to the brain. In the process of delivering a sufficiently strong H field to the targeted region, surrounding areas of the brain can be stimulated unnecessarily. Stimulating non-target areas can result in side effects ranging from tingling sensations in the scalp to seizures [4]. Due to this, the ability for conventional TMS coils to treat a wider variety of systemic neurological disorders is limited. We have developed a novel hybrid coil design that incorporates a traditional single circular coil with a group of 8 solenoids. This design, shown in Fig. 1, allows for a shapeable H field HHH in order to target a specific area for stimulation through selective activation of the solenoid architecture. By activating the solenoids with either a clockwise or counter-clockwise current of varying intensity, the H field of the overall coil can be shaped in a non-uniform manner. This shapeable architecture allows localized stimulation of various neural structures with less risk of stimulating non-target regions. This coil design also presents the possibility for patient-specific customized focality of the H field.

**References:**

[1] “FDA permits marketing of transcranial magnetic stimulation for treatment of obsessive compulsive disorder | FDA.” [Online]. Available: https://www.fda.gov/news-events/press-announcements/fda-permits-marketing-transcranial-magnetic-stimulation-treatment-obsessive-compulsive-disorder. [Accessed: 010-Jun-2020]. [2] C. Fricke et al., “Dual-Site Transcranial Magnetic Stimulation for the Treatment of Parkinson’s Disease,” Front. Neurol., vol. 10, no. March, pp. 1–9, 2019, doi: 10.3389/fneur.2019.00174. [3] R. J. Koek et al., “Neuromodulatory treatments for post-traumatic stress disorder (PTSD),” Prog. Neuro-Psychopharmacology Biol. Psychiatry, vol. 92, no. December 2018, pp. 148–160, 2019, doi: 10.1016/j.pnpbp.2019.01.004. [4] S. Rossi et al., “Safety, ethical considerations, and application guidelines for the use of transcranial magnetic stimulation in clinical practice and research,” Clin. Neurophysiol., vol. 120, no. 12, pp. 2008–2039, 2009.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/de93a530b8971e509db30b6d60d8325b.jpg)
Fig. 1. Hybrid circular-solenoid coil and simulation head model in Sim4Life software.

 Hybrid Coil Design for Shapeable Magnetic Field for Transcranial Magnetic Stimulation

In order to improve the spatial distribution characteristics of induced electromagnetic field, the eccentric trapezoidal magnetic coil (ETM coil) is designed based on the inspiration of special shaped magnets. And to overcome the overheat problem during repetitive stimulation, the inner cooling cycle is designed for the ETM coil as well. The proposed ETM coil consists of two identical coil units and each unit is in the shape of eccentric trapezoid when projected onto the plane parallel to stimulating target plane. The two coil units are placed adjacent or overlapped which is referred to as Type I-ETM coil and Type II-ETM coil in this paper, respectively. To limit the induced electromagnetic field within a smaller domain, the ETM coil is bent along the symmetrical axis at specific angles. Results show that the ETM coil can produce the same stimulation intensity as the traditional FOE coil with less driving current, and it can also significantly improve the intracranial stimulation focalization while reducing the risk of side effects. Because of the internal cooling design, the temperature of the ETM coil could be maintained at room temperature after 3000 effective pulses were applied, while the temperature rise of the FOE coil is over 40K. To verified our method, an anatomically realistic human head model with different electrical properties assigned to each tissue of the brain is employed in this paper. Index Terms- induced electromagnetic field, Magnetic Coil, stimulation intensity. Introduction Transcranial magnetic stimulation (TMS) has been proved to be an effective tool in medical researches[1], [2]. The stimulated volume or stimulated area within human brain need to be limited into a smaller domain to avoid unnecessary side effects [3]-[7]. Also, The geometry of the magnetic coil not only influences to the spatial distributions of induced field but also relates to the heating problem [8]. In order to provide reliable and efficient experimental conditions for scientific exploration, the eccentric trapezoidal magnetic coil (ETM coil) is introduced and optimized in this paper. Results prove that the ETM coil is superior to the traditional FOE coil in terms of stimulation performance and continuous working performance. Method A. The Geometry of ETM coil The ETM coil can be obtained by bending two eccentric trapezoidal coils along an axis of symmetry. When the two coil units are placed adjacent, the coil is referred as Type I-ETM coil and when the two coil units are placed overlapped, the coil is referred as Type II-ETM coil. In this paper, all ETM coil is described as a (mm), b (mm), θ° and φ°. a (mm) represents the length of upper side of the trapezoid. b represents the length of bottom side of the trapezoid. θ° represents the bottom corner of the trapezoid. φ° stands for the bending angle of the eccentric trapezoidal coil pair. The geometry the of Type I-ETM coil when projected to XY plane is shown in Fig. 1. The transparent red circle in Fig.1 represents the targeted plane below the ETM coil.The relative position between Type I-ETM coil and human head is shown in Fig.2. B. Real Human Head Model The real human head model used in this study is model numbered 101309 in the Population Head Model (PHM) Repository (https://itis.swiss/virtual-population/regional human-models/phm-repository/). The PHM repository was developed by Lee et al. using the SimNIBS pipeline, which was utilized to segment anatomical regions from Human Connectome Project MRI images. C．Optimization Steps Firstly, multiple Type I-ETM coil and Type II-ETM coils are construct under the power loss constraint. Both the Type I-ETM coil experimental group and Type II-ETM coil experimental group are divided into three sets including the a/b set, the θ° set and the φ° set. Secondly, the influence of coil geometry parameters on the spatial distribution of intracranial induced electromagnetic field was analyzed qualitatively. A mathematical model reflecting the mapping relationship between the geometric parameters of the coil and the spatial distribution characteristics of the intracranial induced electromagnetic field is established. Thirdly, the particle swarm optimization method (PSO) is adopted to obtain the optimized values of the ETM coil geometric parameters. Results prove that the overall performance of the optimum ETM coil is improved by about 40% comparing to the traditional FOE coil. Fourthly, the copper wire used in the optimum ETM coil is replaced with hollow copper wire and the central hollow part is used to circulate low-temperature deionized water. The pressure and temperature distribution on the cooling water channel is simulated based on non-isothermal water pipe model. Finally, the induced neurologic damage which may be caused during a typical treatment are calculated. Results In this paper, we have proposed and verified the ETM coil design for magnetic stimulation. Type I-ETM coil is advantageous in generating stronger induced field while the Type II-ETM coil is beneficial to improving the stimulation focalization. The bending structure of the ETM coil helps to reduce the risk of side effects. The overall performance of the optimum ETM coil is improved by about 40% comparing to the traditional FOE coil. And the inner cooling cycle of the optimum ETM coil makes it possible to work continuously without overheat. In conclusion, the proposed ETM coil is superior to the traditional FOE coil in terms of stimulation performance and continuous working performance which may bring more possibilities for the applications of TMS.

**References:**

References:: [1] B. J. Hand, G. M. Opie, S. K. Sidhu, et al. Brain Res., vol.1746, no.147027, July 2020. [2] C. C. Sanchez, M. R. Cabello, A. Q. Olozabal, J. Neural. Eng., vol. 17, no.016056, 2020. [3] Y. Wu, H. Yu, Z. Liu, IEEE Trans. Magn, vol. 54, no. 11, pp. 1–5, 2018. [4] Z. Zhang, W. Ai, B. Deng, IEEE Trans. Magn., vol. 53, no. 11, Nov. 2017, Art. no. 9100605 [5] S. Chang, et al. IEEE Trans. Magn, vol. 54, no. 11, pp. 1–5, 2018. [6] A.V. Peterchev, T.A. Wagner, Brain Stimul., vol. 5, pp.435–453, 2012. [7] G. Yi, J. Wang, X. Wei, Appl. Math. Comput. vol.231, pp.100-110, 2014. [8] V. Novickij, A. Grainys, J. Novickij, and A. Lucinskis, IEEE Trans. Magn., vol. 50, no. 11, Nov. 2014, Art. no. 5101004

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/5abd45ac41bd661b5723936f912f8c42.jpg)

![](https://assets.underline.io/uploads/markdown_image/1/image/a79f51dfa70af3c9b5a3095eab239093.jpg)

 Optimum Design of the Eccentric Trapezoidal Magnetic Stimulation Coil with Trade-off between Stimulation Effect and Heat Dissipation

I. INTRODUCTION Magnetorheological (MR) fluids are suspensions of soft-magnetic particles dispersed in a non-magnetic liquid medium, such as silicone oil and mineral oil [1]. Their rheological behaviors can be tuned depending on either the presence or the absence of the applied magnetic field strength. Without an applied magnetic field, they behave like a Newtonian fluid while in the presence of the magnetic field, they become a solid-like a state [2], due to the fact that the dispersed magnetic particles are magnetically polarized and then form a chain structure [3]. When the external magnetic field is removed, they return to an original liquid-like state immediately. Based on this tunable and reversible characteristics, their potential applications cover the areas of robotics, haptic devices, and mechanical systems [4]. As for the MR material, carbonyl iron (CI) microspheres have been widely used because of their high saturation magnetization. However, their high density intrinsically possesses a sedimentation problem [5]. To improve this problem, several methods have been employed such as an introduction of additive particles and coating the CI with either polymers or inorganics [6]. In this work, as an additive material, zinc ferrite nanoparticles were synthesized by a surfactant-assistant solvothermal method and then added into CI-based MR fluid. By adding these particles with high magnetism to MR fluid consisting of fine CI particles, the MR effect is expected to be improved [7]. II. EXPERIMENT The ZnFe2O4 nanoparticles were synthesized by solvothermal synthesis method. Ferric chloride hexahydrate (5.4g) and zinc chloride (1.36g) were put into 200 ml ethylene glycol with stirring using a magnetic bar. After 45 min, the solution turned to be transparent yellow. Both sodium acetate (14.4g) and polyethylene glycol(4g) were then added, and reacted in an autoclave at 200°C for 12 h. The particles were separated using a magnet and washed several times with ethanol. Finally, the synthesized zinc ferrite nanoparticles were dried in a vacuum oven for a day. Morphology of nanoparticles was observed by scanning electron microscope. The CI particles (CM grade, BASF, average particle size: 4.5 m, density: 7.8 g/cm3) were then used as a main component for the MR fluids. The 0.5wt% of was added into 50wt% of CI based MR fluid, while CI-based MR fluid (50 wt%) dispersed in silicone oil (viscosity of 100cS) was also prepared for the comparison. Their MR characteristics were measured using a rotational rheometer under various magnetic field strengths. III. RESULT AND DISCUSSION Figure 1 presents SEM image of the morphology of particles, with a smooth surface and particle size distribution in 300-500nm range. The density of zinc ferrite particles was measured to be 4.8 g/cm3 by a pycnometer. Rheological response of shear stress as a function of shear rate of both MR fluids is presented in Figure 2 under a magnetic field strength range from 0 to 341 kA/m. Without a magnetic field, the MR fluid behaves like a Newtonian fluid. However when magnetic field strength was applied, the shear stress increased as the shear rate increased. MR properties of the CI/ZnFe2O4 based MR fluid (50/0.5wt %) showed a higher shear stress than that of CI-based MR fluid. Under the magnetic field applied, both MR fluids with and without an additive show similarly a wide plateau region which is attributed to the formed columns due to the strong dipole-dipole interaction among the magnetic particles. Additionally, we also measured the sedimentation ratio to confirm the role of zinc ferrite as an additive material for MR fluids through a Turbiscan optical analyser system. The CI-based MR fluid had a faster sedimentation rate than the CI/ZnFe2O4 based MR fluid, indicating that the dispersion stability of CI/ZnFe2O4 based MR fluids increased as compared to the CI based MR fluids. Improved dispersion stability is thought due to the fact that the nanoparticles fill the free space between the CI particles at the same time partially being coated on the surface of the CI particles, contributing to flow resistance. Therefore, in this work, the positive role of zinc ferrite as a proper additive for the CI based MR fluid is confirmed.

**References:**

[1] S. E. Premalatha, R. Chokkalingam and M. Mahendran, Am. J. Polym. Sci, 2, 50 (2012). [2] J. de Vicente, D. J. Klingenberg and R. H.Alvarez, Soft Matter, 7, 3701 (2011) [3] M. J. Hato, H. J. Choi and H. H. Sim, Colloids Surf. A-Physicochem. Eng. Asp, 377, 103 (2011) [4] C. Y. Gao, M. W. Kim, D. H. Bae, Polymer, 125, 21 (2017) [5] J. E. Kim, H. J. Choi, IEEE Trans. Magn, 47, 3173 (2011) [6] Y. Z. Dong, W. J. Han and H. J. Choi, J. Ind. Eng. Chem. 93, 210 (2021) [7] S. H. Piao, H. S. Chae, and H. J. Choi, IEEE Trans. Magn. 51,4600704 (2015)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/1f91e2fab6913903916978f67ff06c37.jpg)
Fig. 1 SEM images of ZnFe2O4 

![](https://assets.underline.io/uploads/markdown_image/1/image/3b0befb13c37f7fd19f325005c241177.jpg)
Fig. 2 Shear stress curves of both pure CI (closed) and CI/ZnFe2O4 (open) MR fluids at different magnetic field strengths

 Enhanced Magnetorheological Response of Particle Added Carbonyl Iron Suspension

I. INTRODUCTION Actively tunable smart magnetorheological (MR) fluids consisting of soft-magnetic particles suspended in nonmagnetic liquids like mineral oil or silicone oil [1], [2], have drawn extensive attentions with their many potential applications in mechanical engineering, biomedicine, pigments, and even in aerospace devices due to their controllable capability. They exhibit reverse and tunable rheological properties from Newtonian fluid-like to solid-like through applied magnetic field strengths employed within milliseconds order. Among extensive potential magnetic particles for their MR applications, soft-magnetic carbonyl iron (CI) microspheres possessing a large saturation magnetization value, proper size, and large permeability have brought lots of interests [3], [4]. However, CI particles are known to intrinsically possess the limitation of their usage with their much higher particle density than of the non-magnetic fluids, which may easily cause the sedimentation in the MR fluids. In this study, poly(2-methylaniline)(PMAN)-CI core-shell structured particles were synthesized by a chemical grafting method with dopamine hydrochloride as a grafting agent to enhance repulsive interaction or to decrease distance among CI microspheres. Dopamine was coordinated on the surface of magnetic particles by electro-donating bidentate enediol, combined with magnetic particles through a bidentate ligand reaction [5]. At this point, the amine groups of dopamine-modified CI particles can be further modified as functional groups. The morphology of the fabricated core-shell structured particles was examined by transmission electron microscopy and scanning electron microscopy. In addition, the rheological properties of MR fluids were measured by using a rotational rheometer under various magnetic field strengths. II. EXPERIMENT Before PMAN coating, the surface of CI particles was modified with dopamine hydrochloride to improve the affinity between magnetic CI particles and PMAN coated shell. At first, CI particles were dispersed in DI-water, and dopamine hydrochloride was mixed with ultrasonic stirring reaction solution for 12 h to promote dopamine coating. The unattached dopamine was then flushed with excess deionized water and hexane. The CI particles of the surface coating were dried in vacuum for 24 h. The dopamine-modified CI particles were dispersed in deionized water under ultrasonication for 30 min. PMAN was coated by polymerizing 2-methylaniline via a chemical oxidation process induced by ammonia peroxide in an acidic environment. We then added the mixture to poly(vinyl alcohol) dissolved in di-water, transfered the reaction solution to the reactor, and cooled it down. Aniline and ammonia peroxide were added to the reactor. The reaction was kept for 24 h and stirred at 300 rpm. When the reaction was complete, the resulting product was separated using a magnet and dried in a vacuum for 24 h. III. RESULTS AND DISCUSSION The SEM images of CI/PMAN core-shell particles are shown in Figure 1, in which the CI/PMAN particles exhibit a larger particle size because of the PMAN coated shell, compared to a smooth surface of the pristine CI particles. The MR behaviors of CI/PMAN based MR suspension were carried out using a rotational rheometer in a controlled shear rate mode under a series of applied magnetic field strengths from 0 to 342 kA/m. The shear stress increases with increasing shear rate, which implies that the MR fluid exhibits a Newtonian fluid-like behaviour without an external magnetic field as shown in Fig. 2. When the magnetic field was applied, the shear stress demonstrated a significant improvement because of the change from a liquid-like to solid-like behaviour of the MR fluid, followed by stepwise growth with the increase of magnetic field. For each magnetic field strength, the shear stress of MR suspension displayed a wide plateau region over the entire shear rate range. In addition, the shear stress with the external magnetic field of MR suspensions was also fitted with the Herschel-Bulkley model [6], [7] as follows: τ=τ0+KÝn where τ is the shear stress, τ0 represents the dynamic yield stress, is the shear rate, K and n represent the consistency index and power-law exponent, respectively. The relationship between the dynamic yield stressof PANI/CI and the magnetic field strength was observed by measuring the universal yield stress. Even though the saturation magnetization and density ofthe PMAN/CI particles were reduced by the introduction of a non-magnetic PMAN shell, their dispersion stability was observed to be improved according to the Turbiscan test by synthesizing the PMAN-coated CI particles. These results were attributed to the rough surface and low density of the core-shell structure PMAN/CI particles.

**References:**

[1] M. Mrlik, M. Ilcikova and V. Pavlinek, J. Colloid Interf. Sci., 396, 146 (2013). [2] D. J. Klingenberg and J. C. Ulicny, Int. J. Mod. Phys. B, 25, 911 (2011). [3] I. Bica, E. M. Anitas and L. Chirigiu, J. Ind. Eng. Chem. 56, 407 (2017). [4] F. F. Fang, Y. D. Liu and H. J. Choi, ACS Appl. Mater. Inter. 3, 3487 (2011). [5] C. J. Xu, K. M. Xu and H. W. Gu, J. Am. Chem. Soc. 126, 9938 (2004). [6] K. J. Son, Korea-Austral. Rheol. J. 30, 29 (2018). [7] Y. Seo and H. J. Choi, Korea-Austral. Rheol. J. 30, 317 (2018).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/bec31a3e9edbef50d5575e1aa353a6e2.jpg)
Fig.1 SEM images of CI (inset) and CI/PMAN core-shell particles

![](https://assets.underline.io/uploads/markdown_image/1/image/221c24a25d3c5b897f0ef4474fbb4ef1.jpg)
Fig.2 Flow curve of shear stress for CI-PMAN MR fluid under various magnetic field strengths as a function of shear rate

 Fabrication and Magnetorheological Characteristics of Core-shell Typed Poly(2-methylaniline)/Carbonyl Iron Microspheres

Transcranial magnetic stimulation (TMS) is a neuromodulation therapy that can be used to treat neurological and psychiatric conditions and has been approved by the FDA for certain disorders [1]–[4]. Since TMS trials with humans are not always feasible, brain phantoms have been developed as ways of testing without actually stimulating the patient. Although a brain phantom has been developed for humans, a comparable brain phantom for rats or mice has not been created specifically for TMS or other neuromodulation techniques. An individualized brain phantom for rats is needed to accelerate the study of neuromodulation techniques, especially the measurement of induced electric field and voltages in the brain regions when stimulated by a time-varying magnetic field. The main objective of this paper is to develop an individualized, anatomically-accurate rat brain model for finite element simulation and a physical model for experimental measurement of stimulation strengths. We initially obtained magnetic resonance images (MRIs) from public databases to create the anatomically accurate brain models. The Waxholm Space Atlas of the Sprague Dawley rat brain was chosen as the MRI to be created into the preliminary phantom. Using the Skull Stripping tool from the BrainSuite software package, the brain was separated from the surrounding skull and skin. Both the original and skull-stripped brain NIFTI files were downsampled using AFNI software tools. The skull-stripped brain was then inputted as a reference mask into the Skull Stripper Python program, along with the downsampled original MRI [5]. The output was the final file, containing 3D information of the chosen rat brain. Using the 3D Slicer program, the final brain file was converted into a 3-dimensional STL file. The program Meshmixer was then used to reduce the file size and fix any model errors. The anatomically accurate individualized brain model was combined with a TMS coil designed for small animals in SolidWorks. An enclosure was also made that surrounded the coil and brain (serving as air in the simulation). The Maxwell 3D module in ANSYS finite element simulation software was then used to simulate the magnetic flux density and induced electric fields in the rat brain models. Fig. 1 inset shows the orientation of the brain and coil in the simulation. Fig. 1 and Fig. 2 show preliminary results of what is predicted for the physical phantom, with all the layers (skin, skull, and other tissues) hidden except the brain. We had assigned uniform conductivity of 0.2 S/m for the entire brain, a relative permeability of 1, and a relative permittivity of 12,000. A figure of eight coil was used on the top of the rat’s head with 1000A current supplied to the coil. The peak magnetic field of 1.22 T and 2.5 ×10-6A/m2 occurs on the surface of the brain below the center of the coil. We are currently in the process of developing a physical individualized, anatomically-accurate physical brain phantom using the above computation models. Work to consider white an grey matter separately in the model is currently in progress. We will use similar techniques as used in the development of our existing human brain phantoms [6], [7]. Using the phantom, we will systematically measure the stimulations strengths in different regions of the brain using several coils types. Acknowledgement: Authors would like to thank funding from Dean's Early Researcher Initiative (DERI) program at College of Engineering of Virginia Commonwealth University, Richmond, VA, USA.

**References:**

[1] E. M. Wassermann and S. H. Lisanby, “Therapeutic application of repetitive transcranial magnetic stimulation: a review,” Clin. Neurophysiol., vol. 112, no. 8, pp. 1367–1377, Aug. 2001, doi: 10.1016/S1388-2457(01)00585-5. [2] L. Carmi, U. Alyagon, N. Barnea-Ygael, J. Zohar, R. Dar, and A. Zangen, “Clinical and electrophysiological outcomes of deep TMS over the medial prefrontal and anterior cingulate cortices in OCD patients.,” Brain Stimulat., vol. 11, no. 1, pp. 158–165, Sep. 2017, doi: 10.1016/j.brs.2017.09.004. [3] R. B. Lipton et al., “Single-pulse transcranial magnetic stimulation for acute treatment of migraine with aura: a randomised, double-blind, parallel-group, sham-controlled trial.,” Lancet Neurol., vol. 9, no. 4, pp. 373–80, Apr. 2010, doi: 10.1016/S1474-4422(10)70054-5. [4] M. S. George and R. H. Belmaker, Transcranial Magnetic Stimulation in Clinical Psychiatry. American Psychiatric Pub, 2007. [5] A. Delora et al., “A simple rapid process for semi-automated brain extraction from magnetic resonance images of the whole mouse head,” J. Neurosci. Methods, vol. 257, pp. 185–193, Jan. 2016, doi: 10.1016/j.jneumeth.2015.09.031. [6] H. Magsood and R. L. Hadimani, “Development of anatomically accurate brain phantom for experimental validation of stimulation strengths during TMS,” Mater. Sci. Eng. C, p. 111705, Nov. 2020, doi: 10.1016/j.msec.2020.111705. [7] H. Magsood, F. Syeda, K. Holloway, I. C. Carmona, and R. L. Hadimani, “Safety Study of Combination Treatment: Deep Brain Stimulation and Transcranial Magnetic Stimulation,” Front. Hum. Neurosci., vol. 14, p. 123, Apr. 2020, doi: 10.3389/FNHUM.2020.00123.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/3c260949a0c73b00d1141a7be71b9817.jpg)
Figure 1. Magnetic flux density (B) plot of rat brain surface. Inset: Coil and rat brain orientation (scalp, skull and cerebrospinal fluid layers are hidden)

![](https://assets.underline.io/uploads/markdown_image/1/image/eb56630d580e5595f2d0ddbe23bac3d2.jpg)
Figure 2. Electric current density (J) plot of rat brain surface. Inset: Coil and rat brain orientation (scalp, skull and cerebrospinal fluid layers are hidden)

 Development of individualized brain model and physical phantom of small animals for experimental verification of transcranial magnetic stimulation

In recent years, magnetic nanoparticles based on iron oxides have found increasing interest in practical applications in the field of biotechnology and biomedicine. Surface modified magnetic nanoparticles can be used for selective isolation of certain biomolecules, such as nucleic acids and proteins. The method, commonly known as "magnetic separation", has gained popularity in performing tests for diagnostic purposes. The aim of this work was to develop a nanomagnetic construction based on iron oxide nanoparticles for efficient separation of DNA molecules and subsequent investigation by polymerase chain reaction. The magnetic particles were prepared by coprecipitation from a solution of FeCl3 and FeCl2 salts in a molar ratio of 2:1 at room temperature. With constant stirring, an NH4OH solution (25%) was injected into the solution of iron salts until pH = 10 was reached. At the end of the reaction, the magnetic nanoparticles were collected using a magnet and washed several times in distilled water until pH = 7.0. To use nanoparticles in magnetic separation of DNA, we treated them with a solution containing 1.25 M sodium chloride and 10% PEG 6000 to inhibit free radical oxidation. For biomedical applications of magnetic nanoparticles, an important role is played by the blocking temperature - the temperature separating the hysteresis and hysteresis-free responses of an ensemble of particles. For applications such as bio-separation, blocking temperatures close to ambient (body temperature) are considered optimal. This choice is due to a compromise between the better colloidal stability of an ensemble of superparamagnetic particles (hysteresis-free behavior) and the high magnetic susceptibility of blocked nanoparticles (response with hysteresis). For magnetic characterization of our particles, we performed measurements of magnetization curves at various temperatures (Fig. 1). According to Fig. 1, the magnetic hysteresis disappears at temperatures above 100 K. The distribution of particles by size and by the magnitude of magnetic anisotropy can lead to inhomogeneity of the blocking temperature in the ensemble of particles. To quantify this inhomogeneity (blocking temperature distribution), we calculated the data in Fig. 1 by different methods. The temperature behavior of the coercive force in Fig. 2 does not follow the power-law dependence Hc(T)=Hc(0)*(1-(T/TB)α), (1) usually discussed for single-domain non-interacting nanoparticles at temperatures below the blocking temperature (TB) [1,2]. The power exponent α, in this case, is in the range from 0.67 to 1.00 [3,4]. This deviation may be due to the inhomogeneity of the blocking temperature in the system of the studied nanoparticles. Therefore, to describe the coercive force, we used averaging [5]: Hc(T)=Hc(0)*(∫Hc(T)*f(TB)dTB)/(∫(TB)*dTB) (2) where the parameter Hc(0) is the average coercive force at T = 0 K. Describing the experimental behavior of the coercive force by expression (2), we can determine the parameters of the distribution function f (TB) corresponding to the best description of the experiment. The best agreement is achieved using the lognormal distribution function: f(TB)=1/(TBσ√2π)*exp(-ln2(TB/TB0)/2σ2) with the parameters TB0 = 80 K, σ = 0.77. The study of the nanoparticles ability to isolate nucleic acids was carried out as follows. Leukocyte lysate from a blood sample obtained from a patient with chronic myeloproliferative disease was added to the nanoparticle suspension. Then, the nanoparticles bound to DNA molecules were separated using a magnet. Subsequent washing of DNA from nanoparticles was carried out with 70% ethanol at room temperature, then elution was carried out in 50 μl of TE buffer for 5 minutes at 65 °C. Real-time PCR reaction was performed using the resulting eluate to detect the JAK2 gene. As a comparison, a parallel reaction was carried out with DNA samples isolated by the sorption method using a commercial kit "DNA-Sorb-B" (Amplisens, Russia). The comparative concentration of the isolated DNA was 3.9 ng/μl with standard isolation and 2.4 ng/μl with isolation using magnetic nanoparticles. It follows from the PCR results that the proposed method for isolating DNA from human blood samples is not inferior in efficiency to the standard isolation method and does not affect the efficiency of PCR amplification. This work was supported by Russian Foundation for Basic Research, Government of Krasnoyarsk Territory, Krasnoyarsk Region Science and Technology Support Fund to the research projects No. 20-42-242902 and by the Council of the President of the Russian Federation for State Support of Young Scientists and Leading Scientific Schools (project no. MK-1263.2020.3). We are grateful to the Center of collective use of FRC KSC SB RAS for the provided equipment.

**References:**

[1] R.S. Iskhakov, S.V. Komogortsev, S.V. Stolyar et al. Met. Metallogr., 88, 261–269 (1999) [2] S. V. Komogortsev, R.S. Iskhakov, A.D. Balaev et al. Phys. Solid State. 49, 734–738 (2007) [3] H. Pfeiffer, Phys. Status Solidi. 118, 295–306 (1990) [4] I.S. Poperechny, Y.L. Raikher, V.I. Stepanov, Phys. B Condens. Matter., 435, 58–61 (2014) [5] S. V. Komogortsev, R.S. Iskhakov, A.D. Balaev et al., Phys. Solid State. 51, 2286–2291 (2009)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/a142de32b117ade09ea1fdcd4dd6355f.jpg)
Fig. 1 Magnetization curves

![](https://assets.underline.io/uploads/markdown_image/1/image/a2a097a3f7750bc29552695db104a0b8.jpg)
Fig. 2. The temperature behavior of the coercive force (red symbols) is not described by equation (1) - dashed lines, but is described by equation (2) - solid line.

 Structure and Magnetic Properties of Maghemite Nanoparticles for DNA Extraction

To separate magnetically coupled particles on lab-on-a-chip devices, microfluidic magnetophoresis plays a pivotal role [1]. It can be useful for biomedical applications like cancer detection, drug delivery, screening, clinical diagnostics [2, 3]. When subjected to a non-uniform magnetic field, small-sized (μm-nm) particles suspended in a fluidic medium will translate toward either the maxima or minima of the gradient of the magnetic field. However, it is very difficult to produce high-gradient magnetic field at micro-scale due to several issues such as non-availability of integratable, high energy product permanent magnets and the detrimental effect of strong demagnetization field of the thin film magnets. Therefore, patterning the magnetic surface is required to produce high flux density with micro-scale resolution over large areas. The efficient design and optimization of such micro-magnetic structures along with their magnetic interaction play an important role in the development of the devices for microfluidic magnetophoresis applications. In our work, comparative FEM analysis is performed to show the advantages of using micro-patterned magnets over bulk rectangular magnet for microfluidic magnetophoresis applications, which is also validated using an analytical framework. The width (x-axis) and height (y-axis) of microfluidic channel were considered 1200 µm and 100 µm respectively with varying gap distance from the permanent magnetic structures (Fig. 1(a)). We have considered bulk rectangular magnetic structure of 1000 µm width and a variation in the height from 100 to 500 µm. Micro patterned rectangular magnets, with 50 µm fixed gap distance between succesive patterns, across the width of microfluidic channel are also analyzed to study the advantage of micro-patterned magnets over bulk rectangular magnet as shown comparatively in Fig. 1(b) and (c). All proposed magnetic structures were concocted using a nano-composite of NdFeB magnetic powder embedded in Polydimethylsiloxane (PDMS) matrix. Geometric optimization of the entire structure including the separation size, height, and width of the separate features are explored using FEM and analytical models to efficiently control the particle trajectories within the microfluidic channel. Effect of different geometries (rectangle, square, triangular etc.) of the micro-patterned magnets are also determined by a factor (H●▽) H, which is proportional to the magnetic force and describe the range of impact of magnets [4]. At the various height (wg=50μm, 80μm, 110μm) from the micro-magnet structure, the magnetic flux densities Hx and Hy were extracted and subsequently used in an customized MATLAB code to determine the force Fx and Fy for describing the motional behavior of magnetic particles in the channel with the help of Newton’s second law. A wide magnet comparable to the microfluidic channel can yield a pseudo magnetic field which can magnetize the micro/nano particles in the channel but does not cause cumulative forces, being exerted on them which can be greatly enhanced by using optimized micro-patterns as shown in Fig. 2. Proof-of-concept prototype of the proposed device is being fabricated using standard micro-fabrication processes. Overall, an effective design methodology for developing highly efficient micro-magnetic flux sources is described which can be useful in many micro-scale applications including biological particle separation and mixing.

**References:**

1. R. Zhou, Q. Yang, F. Bai, J. A. Werner, H. Shi, Y. Ma, C. Wang, Microfluid. Nanofluid., 20, 110 (2016). 2. R. Zhou, A. N. Surendran, M. Mejulu, Y. Lin, Micromachines, 11,129. 25 (2019). 3. F. Alnaimat, S. Karam, B. Mathew, B. Mathew, IEEE Nanotech. Mag., 14(3), 24-41 (2020). 3. E. P. Furlani, J. Appl. Phys., 99, 024912 (2006).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/c7e9be793ad6286fdc706ad5898f152d.jpg)
Fig. 1: (a) Proposed device architecture. FEM simulation results of the y component of magnetic flux density in the microfluidic channel due to rectangular magnet of size (b) 1000×100 µm2 (bulk magnet) and (c) 100×100 µm2 (micro-patterned magnets) with 50 µm pattern gap. A thin film (b) produces magnetic field only at the edges whereas the magnetic flux density vis-à-vis the magnetic flux gradient can be significantly improved through micro-patterning (c) of the magnetic surface.

![](https://assets.underline.io/uploads/markdown_image/1/image/32ee19bb927965e9321dee559a17f72e.jpg)
Fig. 2: The Y component of (a) magnetic field intensity (Hy) and (b) Force (Fy) exerted on the particles inside the microfluidic channel at different height (ht.) due to single bulk and patterned micro-magnets.

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A Simple Localization Method of Magnetic Particles for Hyperthermia Therapy using Figure-8 Coil