Article https://doi.org/10.1038/s41467-025-66468-3 Nuclear magnetic resonance for wireless magnetic tracking M. Efe Tiryaki 1,2,6, Pouria Esmaeili-dokht 1,3,6, Jelena Lazovic 1, Klaas P. Pruessmann1,4 & Metin Sitti 1,5 Wireless trackers have emerged as a crucial technology in minimally invasive medical procedures with their remote localization capabilities. Existing trackers suffer from miniaturization issues and complex designs, which limit their integration intomedical devices.Wepresent nuclearmagnetic resonance (NMR) magnetic sensing, a quantum sensing approach with nT sensitivity for wireless magnetic tracking. NMR magnetic sensing enables millimeter-scale tracking accuracy and versatile miniaturized tracker designs for minimally invasive medical devices in magnetic resonance imaging scanners. As exam- ples, we demonstrate miniature magnetic trackers with submillimeter-scale diameters for guidewires and optic fibers, flexible magnetic trackers for soft devices, and ferrofluidic trackers for shape-morphing devices. With the demonstrated miniaturization and wide range of tracker design possibilities, wireless magnetic tracking with NMR is promising for future minimally inva- sive medical operations. Recent developments in minimally invasive procedures and medical robotics have created a growing demand for medical device tracking methods in the humanbody,where a direct line of sight is not possible. Currently, medical device tracking is performed bymedical imaging1–6 and complementary remote sensing, such as electromagnetic (EM)7–10 and magnetic sensing11–14. However, each approach has specific draw- backs in terms of spatial and temporal resolution, workspace, and miniaturization of tracking devices. The most widely used medical imaging methods, such as X-ray fluoroscopy and magnetic resonance imaging (MRI), suffer temporal resolution issues because of ionizing radiation exposure from X-ray or the inherent spatiotemporal resolu- tion trade-off of MR imaging, respectively. Complementary remote sensing methods compensate for the temporal resolution issues of medical image-based tracking methods by introducing field generators10,11 or onboard field sensors12–14 as tracking devices. Among remote sensing approaches, commercial EM sensors7 and onboard magnetic sensors12–15 are the most common approaches. However, the tethered nature and relatively large size of these trackers limit their usage. Wireless EM tracking, including electrical or mechanical resonators, addresses tether issues with a relatively small size, espe- cially with recently proposed mechanical resonators8–10. Despite their small size, these wireless EM trackers limit overall medical device miniaturization due to the structural restrictions of resonator design. As an alternative, wireless magnetic tracking could enable further miniaturization and versatile tracker design by eliminating structural restrictions. However, the µT-level sensitivity of hall-effect magnetic sensors used in existingmagnetic tracking systems is not sufficient for tracker miniaturization below the centimeter scale11. The required sensitivity could be achieved with quantum sensing approaches exploiting quantum properties of matter for magnetic field measurement16, such as superconducting quantum devices17, optically pumped magnetic sensors18, electron spin magnetic resonance19, and nuclear magnetic resonance (NMR) magnetic sensors20. While some of these quantum sensors have found their way into biomedical applications in magneto-encephalography and cardi- ography, they require high hardware and installation costs, preventing their mainstream adoption in clinical environments. Among these quantum sensors, NMR magnetic sensors offer a unique opportunity Received: 26 January 2025 Accepted: 6 November 2025 Check for updates 1Physical Intelligence Department, Max Planck Institute for Intelligent Systems, Stuttgart, Germany. 2Mechanical Engineering Department, Middle East Technical University, Ankara, Turkey. 3Stuttgart Center for Simulation Science, University of Stuttgart, Stuttgart, Germany. 4Institute for Biomedical Engi- neering, ETH Zurich and University of Zurich, Zurich, Switzerland. 5School of Medicine and College of Engineering, Koç University, Istanbul, Turkey. 6These authors contributed equally: M. Efe Tiryaki, Pouria Esmaeili-dokht. e-mail: msitti@ku.edu.tr Nature Communications | (2025) 16:10840 1 12 34 56 78 9 0 () :,; 12 34 56 78 9 0 () :,; http://orcid.org/0000-0002-2646-1775 http://orcid.org/0000-0002-2646-1775 http://orcid.org/0000-0002-2646-1775 http://orcid.org/0000-0002-2646-1775 http://orcid.org/0000-0002-2646-1775 http://orcid.org/0000-0002-0388-6957 http://orcid.org/0000-0002-0388-6957 http://orcid.org/0000-0002-0388-6957 http://orcid.org/0000-0002-0388-6957 http://orcid.org/0000-0002-0388-6957 http://orcid.org/0000-0001-7646-6104 http://orcid.org/0000-0001-7646-6104 http://orcid.org/0000-0001-7646-6104 http://orcid.org/0000-0001-7646-6104 http://orcid.org/0000-0001-7646-6104 http://orcid.org/0000-0001-8249-3854 http://orcid.org/0000-0001-8249-3854 http://orcid.org/0000-0001-8249-3854 http://orcid.org/0000-0001-8249-3854 http://orcid.org/0000-0001-8249-3854 http://crossmark.crossref.org/dialog/?doi=10.1038/s41467-025-66468-3&domain=pdf http://crossmark.crossref.org/dialog/?doi=10.1038/s41467-025-66468-3&domain=pdf http://crossmark.crossref.org/dialog/?doi=10.1038/s41467-025-66468-3&domain=pdf http://crossmark.crossref.org/dialog/?doi=10.1038/s41467-025-66468-3&domain=pdf mailto:msitti@ku.edu.tr www.nature.com/naturecommunications to be integrated into the hardware of clinically available MRI scanners and provide inherent potential for intraoperative imaging. Moreover, operating at highmagnetic fields, theNMRmagnetic sensor enables the use of soft magnetic materials for trackers, which is not possible with other quantum sensors. This enables further miniatur- ization and design versatility due to higher saturation magnetization and simpler manufacturing processes compared to permanent mag- netic trackers. Considering the miniaturization and integration limitations of existing wireless trackingmethods and the potential of NMRmagnetic sensing, we developed a wireless magnetic tracking system using an NMR magnetic sensor array (Fig. 1). We localized miniaturized mag- netic trackers, such as soft magnetic rigid, hollow trackers, flexible magnetic trackers, and ferrofluidic trackers, by remotely measuring the magnetic field inhomogeneity in an MRI scanner. The NMR mag- netic sensor is composed of a small radiofrequency (RF) coil encircling a glass tube of water and a matching circuit (Fig. 2a). It measures the magnetic field difference, δB= γ�1 Δϕ Δt ð1Þ relative to the background magnetic field (B0 =B0ẑ) of the MRI scan- ner in ẑ direction of the MRI scanner through the rate of phase accu- mulation of nuclear spin precession in the free-induction decay (FID) signal of 1H nuclei in water placed in the sensor20, where γ is the gyromagnetic ratio of 1H nuclei (Supplementary Note 1 and Fig. 1). This nuclear spin frequency-modulated magnetic measurement provided nTmagneticfieldmeasurement sensitivity—three orders ofmagnitude lower than hall-effect sensors—and a broad magnetic measurement range of ±700 µT for 30 kHz excitation BW. The NMR sensors are integrated into a sensor array through an RF switch that connects to the RF hardware of theMRI scanner (Supplementary Fig. 2). This setup enables sequential excitation and acquisition of FID signals with a high temporal resolution of 25Hz due to the short phase accumulation duration of 2.5ms. Results Magnetic modelling at high fields for NMR magnetic tracking Traditionally, magnetic tracking is performed using hard magnetic trackers, such as Neodymium magnets, due to their high remanence magnetization11. However, soft magnetic trackers, such as iron and spring steel, have higher saturation magnetization values at a high magnetic field (see Supplementary Note 2 and Supplementary Fig. 3); thus, they allow further miniaturization. Moreover, unlike hard mag- netic trackers at low fields, the magnetization of soft magnets aligns substantiallywith the highB0field 6, whichdecouples tracking from the tracker orientation (Supplementary Fig. 4). Consequently, we could model the measured high-field dipole magnetic field as (Supplemen- tary Note 3): BdðrÞ= μ0 M 4π 3jjẑ � rjj2 � jjrjj2 jjrjj5 ð2Þ where M is the saturation magnetization of the soft magnet, r is the relative position of themagnet to the sensor, ẑ is the unit vector in the B0 direction, and ||�|| is the Euclidean norm. We verified the model by measuring themagnetic field of a 1mm-diameter steel bead, 0.56 emu, along predetermined channels inside a 7-Tesla (7 T) preclinical small- animal MRI scanner (Supplementary Fig. 5). The magnetic field values varied between −7 and 14 µT at a 2 cm distance (Fig. 2b) and −70 to 110 nT at a 10 cm distance (Fig. 2c), with model matching between the 2–8 cm range. The observed deviation from the model at close distances, especially between 45° and 60°, is due to the curvature of the dipole field (Supplementary Note 4 and Supplementary Fig. 6). The deviation from themodel at greater distances is due to the interaction of the magnetic tracker with the MRI’s superconducting main field coils (Supplementary Note 5; Supplementary Figs. 7–8, and Supple- mentary Movie 1). Characterization of magnetic tracking workspace Next, we built a hexagonally placed array of seven NMR magnetic sensors for magnetic tracking (Fig. 2d). Each sensor is placed in an RF Tracker Position Magnetic Fields Guidewire MRI Scanner NMR Wireless Magnetic Tracking Rigid Tracker Flexible Tracker Ferrofluid Tracker B0 Sensor Array z Magnetic Dipole y x Magnetic Sensor Bd(r) 3D Visualization NMR Sequence Fig. 1 | Nuclear magnetic resonance (NMR) for wireless magnetic tracking concept. The tracking concept, where the magnetic field of a magnetic tracker (e.g., a magnetic dipole placed at the tip of a guidewire) is measured by an array of seven NMR magnetic sensors. The 3D tracker position is shown in the user interface. Different magnetic tracker examples are depicted: rigid magnetic tracker, hollowmagnetic tracker,flexiblemagnetic tracker, and ferrofluidmagnetic tracker. Article https://doi.org/10.1038/s41467-025-66468-3 Nature Communications | (2025) 16:10840 2 www.nature.com/naturecommunications shielding composed of aluminum foil (Supplementary Fig. 15a), which eliminates interference between sensors and also the nearby tissue (see Supplementary Note 13). We also introduced a reference NMR magnetic sensor placed far from the other sensors to monitor the variation of the background field, which could change substantially over a long duration of operation (Supplementary Fig. 9). Then, we performed a gradient-based sensor position calibrationwith respect to the center of the MRI scanner using the gradient hardware of the 0° 45° 60° 90° 30° 20 Distance (mm) 30 40 50 60 B /m ( μT ) d m θ 20 -10 0 10 5 mm RF CoilCM2 CM1 CT d a b c Distance (mm) B /m ( μT ) 10060 70 80 90 0° 45° 60° 90° 30° 0.0 0.2 -0.2 0.6 0.4 e B0 B0 B0 Top view Ref. 40 mm 100 nT 200 nT 1000 nT 5000 nT 4 2 1 0.5 Axial view Fig. 2 | NMRmagnetic sensorarray. aTheNMRmagnetic sensor and the resonator circuit. b, c The magnetic field measurement of 0.65 emu magnetic dipole. The solid lines are the analytic model at different orientations. Points show the mean value and error bars represent the standard deviation (s.d.) of measured magnetic field. d The 3D configuration of the hexagonal sensor array and reference sensor in axial and top views. e The tracking workspace for 1 emu soft magnet. The dashed lines are the averagemagneticfieldmeasured by seven sensors. The blue colormap is the expected tracking precision. Article https://doi.org/10.1038/s41467-025-66468-3 Nature Communications | (2025) 16:10840 3 www.nature.com/naturecommunications scanner (see “Methods”, “sensor array calibration”). We investigated the theoretical limits for workspace for magnetic tracking with NMR using the soft magnetic dipole model Eq. (2). We model the lower bound for tracking precision for hexagonal planar sensor arrays using measurement covariance, I =HTR−1H, where H and R are the local observation matrix and sensor noise covariance matrix. Then, we could express the static tracking precision as Σ / σB r 5 MV ð3Þ whereσB, r, andV are the sensor noise, thedistance to the sensor plane, and the magnetic tracker volume, respectively. We calculated the modeled tracking precision for a 1 emu tracker in a 2D plane together with the mean magnetic field measured by tracking sensors (Fig. 2e), which showed a 1mm lower bound of tracking precision in 100mm proximity of the array. Next, we performed tracking experiments on mechanically con- strained linear channels for ground truth while tracking the guidewire with a particle filter-based tracking algorithm using magnetic field measurements (Supplementary Fig. 10). Then, we evaluated the pre- cision and accuracy of the tracker position. Our tracking results showed less than 1mm precision, matching our model, and below 2mm accuracy in a 60 × 80mm2 workspace. We observed that the deviation from the dipole model prohibits tracking at a larger work- space in our small animal MRI scanner. However, the workspace could be further expanded in clinical MRI scanners. Increasing tracker size will increaseworkspace, according to Eq. (3), but itwill reduce trackers’ versatility and integration capabilities. Thus, we discuss methods to expand the workspace bymodifying the sensors’ position and number in the Supplementary Note 6 (Supplementary Fig. 11 and Supplemen- tary Movie 2). Integration of miniaturized wireless magnetic trackers To demonstrate tracker miniaturization, we developed guidewires with spring steel trackers at the distal end. The high saturation mag- netization of steel, reaching 1.7 × 106 A/m2, enables amagneticmoment of 1 emu within 0.56mm3, the smallest wireless tracker (Supplemen- tary Table 1 and Supplementary Fig. 13). The small size allowed us to integrate the tracker in 0.8mm-diameter guidewires (Fig. 3a). Trackers for smaller guidewires would also be possible with different aspect ratios (Supplementary Fig. 14). Later, we illustratedwireless tracking in an ex vivo porcine brain, simulating a needle insertion operation into the brain (Fig. 3b).We inserted a straight catheter in the brain and took pre-operational MR images of the brain using an imaging surface coil shown in Fig. 3c, d. Next, we manually switched the RF connection from the surface coil to the NMR sensor array. Then, we calibrated the background field with the diamagnetic brain tissue, which caused 1–2 µT variation on different sensors (Supplementary Fig. 15), and tracked the guidewire in the catheter in real time with NMR magnetic tracking (Supplementary Movies 3 and 4). We observed that the magnetic tracking matched with the catheter’s image artifact with 0.78 ± 0.30mm accuracy, where ±SD is a 95% confidence interval. Themain benefit ofminiaturizationwith NMRmagnetic sensing is the higher versatility in designing functional devices. While previous wireless trackingmethods obstructmedical devices10, we could design hollow structures to provide a working channel. To demonstrate the potential, we created a magnetically tracked laser fiber using a micro- machined hollow iron tracker, smaller than 0.8mm in diameter, at the distal end (Fig. 4a and Supplementary Movie 5). We showed that magnetic tracking could be performed in 3D space while the laser was continuouslyoperated (Fig. 4b, c).Wemeasured a tracking accuracyof 2.10 ±0.80mm with respect to the closest point in the center of the spiral channel, which is close to the 3mm diameter of the channel (Supplementary Fig. 16). Next, we integrated the miniaturized tracker with 1.3 emu magnetic moment into a custom-made endoscope cam- era system, and performed tracking in ex vivo on a porcine esophagus to demonstrate wireless tracking while performing endoscope video capturing (see Supplementary Movie 6 and Supplementary Fig. 17). Deformable magnetic soft trackers To further highlight the versatility of the tracker design, we developed flexible magnetic trackers made of magnetic soft composite materials (Fig. 5a). Softmagneticmicroparticle-embedded elastomericmaterials Surface Coil Insertion Angle 20 40 60 0 0 5 Z(mm) X(mm) -5 0 10 -10 Y( m m ) B0 0 Sensor Plane10 mm b c 20 mm 1 mm a d Fig. 3 | Miniature rigidmagnetic tracker. a Themagnetic guidewire has a 0.6mm diameter and a spring steel tracker that is 2mm (0.565mm3). b The wireless magnetic tracking with NMR inside a porcine brain ex vivo. c The tracking data in the oblique planeMR image. The tracker positions are overlaidwith red dots.d The 3D image trackingdata overlayedon theMR image in the sagittal planewith respect to the sensor plane. Article https://doi.org/10.1038/s41467-025-66468-3 Nature Communications | (2025) 16:10840 4 www.nature.com/naturecommunications have recently emerged in miniaturized continuum robots2; however, the low magnetic moments of these soft magnets prevent their use in magnetic tracking with previous approaches. We created a curved guidewire with flexible magnetic trackers with 1.35 emus using a 3 µL 75% iron microparticle-silicone elastomer mixture at the distal end (Supplementary Fig. 18). To demonstrate functionality, we performed repeated manual navigation experiments inside 3D-printed channels (Fig. 5b and Supplementary Movie 7). We observed high-accuracy tracking of less than 0.72 ± 0.67mmwhen the flexible tracker was in a straight configuration.However, the tracking error increased as high as 4.3mm as the guidewire approached the sensor array (Fig. 5c). We discussed the shape effects of flexible magnetic trackers in the Sup- plementary Note 7 (Supplementary Fig. 19). Finally, we illustrated the potential for ferrofluidic magnetic trackers using a balloon catheter filled with an iron-oxide (Fe2O3) nanoparticle solution (Fig. 6). Ferrofluids provide the potential for reconfigurable and shape-changing magnetic systems21. However, the low magnetization of ferrofluids has prohibited them from being tracked magnetically using previous magnetic tracking methods (Supplementary Fig. 20). First, we showed that the NMR magnetic sensing could be used to monitor the inflation of the balloon (Sup- plementary Fig. 21 and Supplementary Movie 8). Next, we demon- strated magnetic tracking of the ferrofluid-injected balloon with 1.75mL volume and 0.25 emu magnetic moment (Supplementary Movie 9 andFig. 6b).Although trackingprecision is reduceddue to low magnetic moment (Supplementary Fig. 22), the maximum tracking B0 10 mm Sensorsb c 5 mm a Fig. 5 | Flexible magnetic tracker-integrated guidewire tracking. a The custom- made angled-tip guidewirewith aflexiblemagnetic tip.bThe tracking data overlaid on the channels. The data is composed of four separate experiments targeting different channels each time. c The snapshots of the guidewire tracking during different shapes and positions of the flexible tip. ba c 30mm 1mm 10 mm B0 S en so rs Fig. 4 | Hollow magnetic tracker-integrated optic fiber tracking. a The optic fiber with a laser connector. The hollow magnetic tracker with 0.8mm outer and 0.3mm diameter is placed at the tip of the optic fiber and fixed with glue and heat shrink tube.bThe long exposure image of the optic fiber overlayedwith the tracker position. c Snapshots of the experiment. The scale bars are 10mm. Article https://doi.org/10.1038/s41467-025-66468-3 Nature Communications | (2025) 16:10840 5 www.nature.com/naturecommunications error reaches 5.5mm when the balloon approaches the sensors, remaining within the large volume of the balloon (Supplemen- tary Note 8). Discussions The magnetic tracking with NMR enables the miniaturization of mag- netic trackers by ~3 orders of magnitude compared with previous magnetic tracking methods for the same workspace11. It provides a versatile tracker design for integration into functionalmedical devices. The distributed magnetic moment allows magnetic trackers to have diameters smaller than state-of-the-art wireless EM trackers10—ranging between 0.4–0.8mm—which could be easily integrated into com- mercial guidewires with above 0.025”(~0.64mm) diameter. The ability to track hollow magnetic trackers brings unparalleled versatility in tracker integration compared to other remote tracking methods. For instance, magnetic trackers could be placed around commercial catheters, biopsy needles, and neurostimulation electrodes without obstructing working channels. They could also be used together with sensing systems, such as micro-endoscope cameras (Supplementary Movie 3) and fiber Bragg grating sensors, for improved in situ bio- sensing and tissue interaction. Moreover, previous remote tracking methods have been limited to rigid trackers, whereas most medical devices today are shifting to flexible and soft designs. For instance, an optimal tip stiffness profile is crucial for the effective and safe navigation of guidewires in vascular structures. The rigid remote trackers placed at the distal tip of guidewires prevent stiffness tuning and limit the steerability of the guidewire. The NMR magnetic sensing addresses this issue by allowingflexiblemagnetic trackers to bemadeusing a soft magnetic powder and elastomer mixture, which enables magnetically trackable guidewires with flexible tips. These flexible magnetic track- ers could also enable integration into emerging soft robotic designs3. At the other end of the rigidity spectrum, we can also track magnetic liquids composed of iron-oxide nanoparticles, which provide on- demand, injectable magnetic trackers. This could be used in marking certain tissues with magnetic liquid and tracking their motion when higher sensitivity NMR magnetic sensors are used in magnetic tracking20. Besides, NMR magnetic sensing provides a larger workspace compared to previous magnetic tracking methods11 and a comparable workspace to wireless EM trackers of the same size10, with similar tracking accuracy (Supplementary Table 1 and Supplementary Fig. 13), without the RF-induced heating risks. Although our demonstrations have been limited by the size of our preclinical MRI scanner, the NMR magnetic sensing technology offers a potentially largerworkspace due to the relatively small size of NMR magnetic sensors compared with planar coils used in EM trackers10. It is possible to create denser NMR magnetic arrays with more sensors or distribute the sensors around a desired volume to increase the workspace without interference from one another. Increasing sensor numbers could also beused to increase tracking accuracy further; however, this will limit the temporal reso- lution of tracking and require parallel hardware instead of the current serial hardware. Importantly, NMR magnetic sensing also addresses the position-calibration challenges that EM tracking systems face during integration with medical imaging. The gradient-based sensor positioning enables spatial calibration without the need for external hardware, allowing themagnetic tracker to be registered directly onto MR images (Fig. 2f) and enabling single-stage, real-time positioning of stereotactic neurosurgery robots4. Finally, NMR trackers do not suffer from the dead-angle issues inherent to EM trackers, since NMR track- ing does not require external excitation9. Additionally, the NMR magnetic sensing technology addresses certain drawbacks of MR image-based tracking. Despite continuous improvements inMRI speed, real-time3D trackingwith passivefiducial markers, such as magnetic22, 19-fluorine23, and RF coils24, and active MRI pickup coils25, remains limited by slice thickness22 and RF-induced tissue heating. In contrast, NMR sensors provide continuous 3D tracking without requiring the deposition of RF energy (see Supple- mentary Note 14), enabling continuous navigation with no risk of heating. Furthermore, NMR magnetic sensing eliminates acoustic noise, which in fast MRI-based tracking can exceed safe exposure limits3,5 and hinder communication between clinicians during inter- ventionalMRI operations. Because NMRdoes not rely onMRgradients (Supplementary Note 10; Supplementary Fig. 23 and Supplementary Movie 10), it is inherently silent, creating a safer acoustic environment for both patients and clinicians. Moreover, NMR tracking also func- tions in air-filled cavities, where most MRI-based tracking methods, except 19F tracking23, fail due to the absence of 1H of the surrounding water or tissue, allowing for the uninterrupted tracking of tools suchas needles during insertion from outside the skin. We envision that the NMRmagnetic sensing could also be used in conjunction with 2D MRI and recently emerging MRI-powered mag- netic actuation methods, by using an alternating MR sequence5. We can perform high-speed magnetic tracking with NMR simultaneously during slower MR image acquisition, which is safe in terms of RF heating and acoustic noise, and we can also integrate magnetic actuationat the same time. Furthermore,while clinical use of high-field MRI scanners is becoming popular26, the integration of NMRmagnetic sensor arrays into lower field MRI scanners, such as 1.5 T and 3 T, and emerging ultra-low-field MRI scanners could increase the affordability of magnetically guided minimally invasive operations in the future27; However, we must note that the magnetic sensing precision will bb 10 mmB010 mm a Fig. 6 | Ferrofluidicmagnetic tracker-basedballoon catheter tracking. aThe empty commercial balloon catheter tip.bThe snapshots of a balloon catheter inflatedwith the ferrofluidic tracker during the tracking experiment with the overlaid positions. The images are the initial point of corresponding overlaid tracking data. Article https://doi.org/10.1038/s41467-025-66468-3 Nature Communications | (2025) 16:10840 6 www.nature.com/naturecommunications decreasewith the static field strength since signal-to-noise ratio inMRI scanners scale with ∝B0 7/428. Moreover, NMR magnetic sensors con- structed in a single-sided MR configuration could allow the use of magnetic tracking outside of the MRI scanners29. There are also certain limitations of magnetic tracking with NMR. First, it cannot be used on patients with ferromagnetic implants, a general limitation inherent toMRI technology. The second limitation is the difficulty in tracking magnetic trackers from near-moving tissues. While themagnetization calibrationenables trackingnear static tissues by subtracting the diamagnetic background, tracking near moving tissues, such as the chest during breathing motion, is challenging due to changing background signals20. This issue could be addressed in the future by incorporating the actuation dynamics into the particle filter rather than using a static model and modifying the proposed back- ground field estimation using basis functions that approximate the dynamic component of the background30, while utilizing more NMR magnetic sensors for increased measurement redundancy. Another limitation is the number of trackers that can be tracked accurately. While two magnetic trackers could be tracked with the current sensor number, seven, the tracking accuracy decreases due to increased measurement covariance (Supplementary Note 11; Supplementary Figs. 24 and 25). The sensor number should be increased, and sensors should be distributed over the tracking space to use a higher number of trackers. In conclusion, NMR for wireless magnetic tracking enables ver- satile miniature wireless magnetic trackers inside MRI scanners. Demonstrating a high-sensitivity quantum sensing approach for mag- netic tracking, the presented wireless magnetic tracking approach paves the way for precise, real-time localization for minimally invasive medical operations and medical robotic instruments. Methods Magnetic sensor The NMR sensor comprises a 5-turn inductive coil of 400μmdiameter copperwireswrapped around a cylindrical glass capillarywith anouter diameter of 4mmand a height of 5mm (Fig. 2a). After thewinding, the capillaries are filled with deionized water and sealed permanently with epoxy (Loctite 401) to prevent evaporation. We use two constant matching capacitors, ranging from 0.5 to 1 pF, and one 0.5 to 12 pF range tuning capacitor (Knowles Voltronics) to tune the frequency of the resonator circuit to 300MHz and match it to a 50Ω impedance. The sensor is placed inside an aluminum-shielded box to prevent crosstalk between neighboring sensors and reduce the effects of high- frequency noises. A capacitive balanced network is used to tune and match the coils through an iterative process of tuning and adjusting the matching capacitors while connected to a Network Analyzer (Keysight E5061B). The matching capacitors are manually selected for each RF coil. Sensor switch The switching setup features a non-reflective RF switch (HMC253ALC4, Hittite Microwave Corporation, USA) and a microprocessor (Arduino Uno) (Supplementary Fig. 2). The Arduino is connected to the trigger- out channel of the 7 T preclinical MRI scanner (Biospec 30/70, Bruker, Germany) and three input channels of the RF switch using optocou- plers (FOD8001, Onsemi) to prevent any noise originating in external systems. A Li-ion battery, combined with an ultra-high PSRR (power supply rejection ratio) voltage regulator (LT3097, AnalogDevices Inc.), powers up the RF switch. Except for the RF switching board, all the other components of the system were placed outside of the MRI scanner. The connections with the RF switch are made through non- magnetic BNC cables (mmcx connectors, Clinch Connectivity Solu- tions Johnson). The Arduino code sweeps eight channels in sequence by changing channels in response to a trigger signal from an MRI scanner. NMR sequence The NMR sequence for magnetic field measurement is composed of basic free induction decay (FID)measurements and a trigger-out signal for synchronizationwith the sensor switch (Supplementary Fig. 2). The trigger-out allows Arduino to switch among the different sensors while the NMR sequence operates, without explicitly knowing which sensor is being measured. To synchronize the Arduino and the sequence, we reset the sensor counter in the Arduino code if an NMR signal is not received formore than2 s. In theNMRsequence,we used an excitation pulse with a sinc shape, 0.2ms RF duration (TRF), 31.05 kHz transmis- sion bandwidth (BW), 32 µW RF power, and a readout with 2.5ms acquisition time, 250 sampling, 100 kHz receiver BW. The repetition time for a single sensor is 5ms, and for an eight-sensor array, it is 40ms. The parameters are used in all magnetic sensing experiments. Magnetic field calculation The phase of the FID signal is calculated using the real and imaginary parts provided by the scanner, and phase unwrapping is applied (Supplementary Fig. 1a, b). The first 50 phase data points (0.5ms) of the phase signal are discarded due to the settling time of the receiver and electronics in the readout system. Additionally, the inhomoge- neous B1 field, accompanied by the attenuating nature of the FID sig- nal, introduces nonlinear phase accumulation over time until the total noise dominates the signal amplitude (Supplementary Fig. 1b). To quantify this effect, we calculated SNR by comparing the maximum of the filtered FFT with the amplitude of deviation from the curve as a function of acquisition time (Supplementary Fig. 1c); thus, only the following 200 data points are used for further processing. The phase slope is calculated using linear fitting, and the magnetic field is cal- culated using Eq. (1). We used Eigen and FFTW libraries in C++ for real- time signal processing. Sensor array calibration The calibration routine is composed of background field and sensor position calibrations. The background field ΔB varies with shimming configuration, the patient’s tissue, and themain field coil temperature. Therefore, we need to perform a ΔB calibration. In stationary condi- tions, we collect 10 s of magnetic field measurements with all sensors to calculate the mean (µΔB) and standard deviation (σ) of the ΔB indi- vidually for each sensor (Supplementary Fig. 15b, c). We subtract µΔB from the sensor readingduringoperation anduseσ in theparticlefilter for sensor noise. Next, we perform sensor position calibration using the gradient hardware of the MRI scanner. We apply known gradient values (G) in positive and negative directions in the x-y-z axes for 5 s in positive and negative directions and record magnetic field measurements from all sensors (Supplementary Fig. 15d, e). Later, the average field in each direction is calculated for each sensor, and then we calculate each sensor’s position using rsi = 1 2 B + si +B� si G ! ð4Þ where rsi is the position of the ith sensor relative to the center of the MRI scanner, B+ si and B� si are the measured average magnetic fields in positive and negative directions. To cancel the sensor geometry imperfection error, we averaged the measured value in opposite directions to calculate the position in each direction. As the positions of sensors are a crucial factor in tracking preci- sion, we designed an experiment to determine calibration accuracy in various conditions (Supplementary Fig. 15d–i). The calibration process was repeated 10 times for the systemwith seven sensors, bothwith and without the patient’s stage, and with a porcine brain sample on the stage. Under all conditions, we achieved an error of less than 5 µm in the x and z directions and less than 10 µm in the y direction. Due to the Article https://doi.org/10.1038/s41467-025-66468-3 Nature Communications | (2025) 16:10840 7 www.nature.com/naturecommunications sensors’ asymmetric profile in the y direction, we observed more errors. Moreover, we observed an average sensor noise of 8 nT in all experiments, with no notable difference. Dipole measurement A custom stage composed of different channel structures and known sensor positions was 3D printed using PLA material to validate the dipole model (Supplementary Fig. 5). Later, sensor heads were posi- tioned inside the designated locations and connected to a matching circuit. This method, combined with the triangled 3-sensor setup, ensured the precision of the position and angle of the sensor com- pared to the channels and B0 field, respectively. The 1mm-diameter steel bead magnetic tracker was moved manually with 5mm incre- mental steps during the experiment using a thin guidewire with delays of 3 s in each step. Measurement covariance To calculate the theoretical lower bound for the sensing precision of a sensor set, we used the local observation matrix, H(xi,yi,zi), by linear- izing the sensor function, h(r) = [h1,h2,h3,…, h7] ∈ ℝ7, where r is the position of the magnet in the inertial frame, hi(xi,yi,zi) is the sensing function for ith sensor hi xi, yi, zi � � = μ0 4π m 2z2i � x2i � y2i x2 i + y 2 i + z 2 i � �5 2 ð5Þ and xi, yi, and zi are the distances between themagnet and the sensor in Eq. (2). The local observationmatrix in the formof the Jacobianmatrix, H ∈ℝ3 × 3, is calculated by H= ∂h ∂r ð6Þ The linearized static sensor precision, I∈ℝ3 × 3, is calculated as I=HTR�1H ð7Þ where R = diag([σ1, σ2, σ3, …, σ6]) ∈ ℝ7 × 7 is diagonal sensor covariance matrix. The diagonal elements of I give the precision in σx, σy, and σz directions. We calculated the final precision by Σ= ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi σ2 x + σ2 y + σ2 z q ð8Þ Particle filter A particle filter is a recursive Bayesian state estimation technique that uses the Monte Carlo method to approximate the posterior distribu- tion of the estimated state in three steps: propagation, reweighting, and resampling31. It has been used in the localization of dipole-based EM trackers32. The algorithm first approximates the state distribution usingN particles, which are distributed uniformly over the state space. Then, in the propagation step, it predicts the next time evolution of each particle using a prediction model with noise. Next, in the reweighting step, it approximates the posterior distribution of the state by calculating the probability of each particle contributing to the observed sensor measurement using a measurement model with noise. Finally, in the resampling step, the algorithm samples N new particles from the approximated posterior distribution and replaces the previous set of N particles with new particles. Then, the algorithm recursively repeats itself for each time step with new sensor data. This method recursively refines the estimated position using the obtained sensor data, generally converging within 1–2 time steps if N is suffi- ciently large. To ensure convergence in the first step, a large initial particle number, N0, is used. Then, in the next step, the particle number is reduced to N during the resampling step. To estimate themagnetic tracker position,we employed aparticle filter-based state estimation model with the state, x = [rT, ΔB]∈ ℝ4, composed of tracker position and monitored background magnetic field variation. We consider the tracking problem as a static prediction model and a nonlinear measurement model: x kð Þ=x k � 1ð Þ+ νðk � 1Þ ð9Þ z kð Þ=Bd kð Þ+ΔB kð Þ+ωðkÞ ð10Þ where k is the time step of estimation, z is the measurement vector ∈ ℝ8, and ν andω are the prediction andmeasurement noisemodeled as a Gaussian distribution with covariance Σν = diag([σx, σy, σz, σΔB]) ∈ ℝ4 × 4 and Σω = diag([σs0, σs1,…., σs7]) ∈ ℝ8 × 8. We used the prediction noise with σx = σy = σz = 1mm and σΔB = 0.1 nT. Themeasurement noise is calculated during the sensor array calibration.Bd (k) = [Bd(r0), Bd (r1), …, Bd (r7)]T ∈ℝ8 is the vector of the sensor measurement model of the sensors at time step k. Note that the reference sensor is included in the estimation as the 0th sensor to estimate the change in the background field. We started the particle filter with N0 = 20,000 and reduced the particle number to N = 500 after the first iteration of estimation. First, the algorithm propagates the particle position and background pre- dictions using Eq. (8). Next, we calculate the expected sensor mea- surement, �z, for each particle using Eq. (9) with the noise term. Then, we calculate the measurement likelihood for each particle using a normal distribution, Pi �zijz � � =N �zijz, Σω � � ð11Þ where i is the index of the particle in N particles. Later, we scale the particle probabilities, βi = PiPN 0 Pi , between 0 and 1. Finally, we resampled the particles using a random number r from a uniform distribution (0, 1). To avoid prediction errors due to the inhomogeneity effect in proximity to the sensors, if any sensor measurement exceeds 20μT, we remove the measurement of the corresponding sensor, exclude it from the resampling stage of the particle filter, and estimate the position using the remaining sensors. Workspace experiment To validate the precision and accuracy of the tracking in the simulated workspace, a custom stage with parallel channel structures was 3d printed using PLA material (Supplementary Fig. 10a). The stage was mechanically fixed inside the MRI bore, and the channels were exten- ded to theoutsideof theMRI using PTFE tubes. During the experiment, after calibration, the magnetic tracker, composed of two 1mm-dia- meter steel beads, was placed inside one channel andmovedmanually in 5mm incremental steps using a thin guidewire, with a 3-s delay between each step. Finally, the positions were estimated 10 times for each channel using the particle filter (Supplementary Fig. 10b, c). Guidewire and laser manufacturing During the guidewire preparation, we used an MRI-compatible 0.5mm-diameter glass optic fiber as the elastic core and 0.8mm-dia- meter Teflon tubes with a 0.1mmwall thickness (Adtech, UK). We glued a glass fiber, a Teflon tube, and the 0.6mm-diameter 2mm-height spring steel magnetic tracker. We prepared the laser by removing the coating from the last 2mm of the optical fiber. Then, we glue a micro- machined iron tracker with an outer diameter of 0.8mm, an inner dia- meter of 0.3mm, and a length of 2mm. Later, we assembled the optical fiber with a laser connector and placed a black heat-shrink tube to prevent light leakage. We prepared the soft guidewire with a flexible magnetic tracker using a 0.8mm-diameter Teflon tube and 0.5mm-diameter optic fiber as the core. At the last 20 cm of the distal Article https://doi.org/10.1038/s41467-025-66468-3 Nature Communications | (2025) 16:10840 8 www.nature.com/naturecommunications end, we replaced the optic fiber with a 0.3mm-diameter tungsten wire with an angled tip. We filled the tip with 3 µL of soft magnetic material, comprising a 75% mass ratio of µm-sized iron powder and Ecoflex. The endoscope system comprises a 1mm×−1mm miniature camera (ams NanEye2D) inside a 4mm diameter Teflon tube (Adtech, UK) and two 1mm steel beads as the magnetic tracker. The tracker is put at the back of the camera and both of them are fixed with epoxy inside the tip of the Teflon tube. Finally, the camera is connected through a capture box (ams NANO-FIB-BOX) to save the video feed to computer. Data availability The raw data supporting the findings of this study are available in the Edmond repository at https://doi.org/10.17617/3.XZAQ4Z. 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Particle filtering to improve the dynamic accuracy of electromagnetic tracking. In Proc. SENSORS. 1–4 (IEEE, 2013). Acknowledgements The brain image inside Fig. 1 is from the Brain TumorMRI Dataset, Kaggle underCC0.Materials frombiorender.comwereused for Supplementary Figs. 12a, d, f, g, i, 17a, and 28a. We thank Sinan Ozgun Demir, Gaurav Gardi and Asli Aydin for the theoretical discussions, and Devin Sheehan for helpwith theex vivo experiments. Theauthors thank the International Max Planck Research School for Intelligent Systems (IMPRS-IS) for supporting Pouria Esmaeili-Dokht. Funding: This workwas fundedby the Max Planck Society and European Research Council Advanced Grant SoMMoR project (grant no. 834531). Author contributions Conceptualization:M.E.T., P.E., M.S. and K.P.P., Methodology:M.E.T. and P.E., Software: M.E.T., P.E. and J.L., Formal analysis: M.E.T. and P.E., Investigation: M.E.T. and P.E., Visualization: M.E.T. and P.E., Funding acquisition: M.S., Supervision: K.P.P. and M.S., Writing–original draft: M.E.T., P.E., M.S. and K.P.P. Funding Open Access funding enabled and organized by Projekt DEAL. Competing interests The authors declare no competing interests. Article https://doi.org/10.1038/s41467-025-66468-3 Nature Communications | (2025) 16:10840 9 https://doi.org/10.17617/3.XZAQ4Z https://doi.org/10.17617/3.XZAQ4Z www.nature.com/naturecommunications Additional information Supplementary information The online version contains supplementary material available at https://doi.org/10.1038/s41467-025-66468-3. Correspondence and requests for materials should be addressed to Metin Sitti. Peer review information Nature Communications thanks anonymous reviewer(s) for their contribution to the peer review of this work. [A peer review file is available.] Reprints and permissions information is available at http://www.nature.com/reprints Publisher’s note Springer Nature remains neutral with regard to jur- isdictional claims in published maps and institutional affiliations. Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. 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To view a copy of this licence, visit http://creativecommons.org/ licenses/by/4.0/. © The Author(s) 2025 Article https://doi.org/10.1038/s41467-025-66468-3 Nature Communications | (2025) 16:10840 10 https://doi.org/10.1038/s41467-025-66468-3 http://www.nature.com/reprints http://creativecommons.org/licenses/by/4.0/ http://creativecommons.org/licenses/by/4.0/ www.nature.com/naturecommunications Nuclear magnetic resonance for wireless magnetic tracking Results Magnetic modelling at high fields for NMR magnetic tracking Characterization of magnetic tracking workspace Integration of miniaturized wireless magnetic trackers Deformable magnetic soft trackers Discussions Methods Magnetic sensor Sensor switch NMR sequence Magnetic field calculation Sensor array calibration Dipole measurement Measurement covariance Particle filter Workspace experiment Guidewire and laser manufacturing Data availability Code availability References Acknowledgements Author contributions Funding Competing interests Additional information