{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,16]],"date-time":"2025-10-16T20:43:46Z","timestamp":1760647426374,"version":"build-2065373602"},"reference-count":45,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2021,4,16]],"date-time":"2021-04-16T00:00:00Z","timestamp":1618531200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001602","name":"Science Foundation Ireland","doi-asserted-by":"publisher","award":["17\/CDA\/4771"],"award-info":[{"award-number":["17\/CDA\/4771"]}],"id":[{"id":"10.13039\/501100001602","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Electromagnetic tracking is a safe, reliable, and cost-effective method to track medical instruments in image-guided surgical navigation. However, patient motion and magnetic field distortions heavily impact the accuracy of tracked position and orientation. The use of redundant magnetic sensors can help to map and mitigate for patient movements and magnetic field distortions within the tracking region. We propose a planar inductive sensor design, printed on PCB and embedded into medical patches. The main advantage is the high repeatability and the cost benefit of using mass PCB manufacturing processes. The article presents new operative formulas for electromagnetic tracking of planar coils on the centimetre scale. The full magnetic analytical model is based on the mutual inductance between coils which can be approximated as being composed by straight conductive filaments. The full model is used to perform accurate system simulations and to assess the accuracy of faster simplified magnetic models, which are necessary to achieve real-time tracking in medical applications.<\/jats:p>","DOI":"10.3390\/s21082822","type":"journal-article","created":{"date-parts":[[2021,4,19]],"date-time":"2021-04-19T06:35:53Z","timestamp":1618814153000},"page":"2822","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["Planar Body-Mounted Sensors for Electromagnetic Tracking"],"prefix":"10.3390","volume":"21","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-1901-0041","authenticated-orcid":false,"given":"Marco","family":"Cavaliere","sequence":"first","affiliation":[{"name":"Tyndall National Institute, Dyke Parade, T12 R5CP Cork, Ireland"},{"name":"School of Engineering, University College Cork, College Road, T12 K8AF Cork, Ireland"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4771-8469","authenticated-orcid":false,"given":"Herman Alexander","family":"Jaeger","sequence":"additional","affiliation":[{"name":"Tyndall National Institute, Dyke Parade, T12 R5CP Cork, Ireland"},{"name":"School of Engineering, University College Cork, College Road, T12 K8AF Cork, Ireland"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7347-1386","authenticated-orcid":false,"given":"Kilian","family":"O\u2019Donoghue","sequence":"additional","affiliation":[{"name":"Tyndall National Institute, Dyke Parade, T12 R5CP Cork, Ireland"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6679-2889","authenticated-orcid":false,"given":"P\u00e1draig","family":"Cantillon-Murphy","sequence":"additional","affiliation":[{"name":"Tyndall National Institute, Dyke Parade, T12 R5CP Cork, Ireland"},{"name":"School of Engineering, University College Cork, College Road, T12 K8AF Cork, Ireland"}]}],"member":"1968","published-online":{"date-parts":[[2021,4,16]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"212","DOI":"10.1109\/RBME.2019.2939091","article-title":"Optical and Electromagnetic Tracking Systems for Biomedical Applications: A Critical Review on Potentialities and Limitations","volume":"13","author":"Sorriento","year":"2020","journal-title":"IEEE Rev. Biomed. Eng."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"3279","DOI":"10.21037\/jtd.2020.03.35","article-title":"Robotic Bronchoscopy for Pulmonary Lesions: A Review of Existing Technologies and Clinical Data","volume":"12","author":"Agrawal","year":"2020","journal-title":"J. Thorac. Dis."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"610","DOI":"10.1016\/j.eururo.2017.03.011","article-title":"Ureteroscopy-Assisted Percutaneous Kidney Access Made Easy: First Clinical Experience with a Novel Navigation System Using Electromagnetic Guidance (IDEAL Stage 1)","volume":"72","author":"Lima","year":"2017","journal-title":"Eur. Urol."},{"key":"ref_4","unstructured":"Martins, B., Dagnino, G., and Dogramadzi, S. (2018, January 10\u201311). Real-Time Electromagnetic Tracking of Orthopaedic Pins for Robot-Assisted Fracture Surgery. Proceedings of the Computer and Robot Assisted Surgery (CRAS), London, UK."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"97","DOI":"10.4070\/kcj.2018.0319","article-title":"Non-Fluoroscopic Catheter Tracking System for Atrial Fibrillation Ablation","volume":"49","author":"Kim","year":"2018","journal-title":"Korean Circ. J."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"84","DOI":"10.4070\/kcj.2018.0195","article-title":"The Accuracy and Clinical Applicability of a Sensor Based Electromagnetic Non-Fluoroscopic Catheter Tracking System","volume":"49","author":"Yamada","year":"2019","journal-title":"Korean Circ. J."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"7","DOI":"10.1109\/TANE3.1962.4201833","article-title":"A New Guiding and Tracking System","volume":"ANE-9","author":"Kalmus","year":"1962","journal-title":"IRE Trans. Aerosp. Navig. Electron."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1109\/TASC.2013.2294406","article-title":"The Simulations and Experiments of the Electromagnetic Tracking System Based on Magnetic Dipole Model","volume":"24","author":"Xie","year":"2014","journal-title":"IEEE Trans. Appl. Supercond."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"248","DOI":"10.1016\/j.sna.2004.01.004","article-title":"Cylindrical Induction Coil to Accurately Imitate the Ideal Magnetic Dipole","volume":"112","author":"Paperno","year":"2004","journal-title":"Sens. Actuators A Phys."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"224504","DOI":"10.1063\/1.4922667","article-title":"An Accurate Magnetic Field Solution for Medical Electromagnetic Tracking Coils at Close Range","volume":"117","author":"Schroeder","year":"2015","journal-title":"J. Appl. Phys."},{"key":"ref_11","unstructured":"Anderson, P.T. (2001). A Source of Accurately Calculable Quasi-Static Magnetic Fields. [Ph.D. Thesis, The University of Vermont]."},{"key":"ref_12","first-page":"1","article-title":"Catheter Position Tracking System Using Planar Magnetics and Closed Loop Current Control","volume":"50","author":"Mansfield","year":"2014","journal-title":"IEEE Trans. Magn."},{"key":"ref_13","first-page":"27","article-title":"Magnetic Calibration by Tetrahedral Interpolation","volume":"5","author":"Briggs","year":"1999","journal-title":"Proc. NIST-ASME Ind. Virtual Real. Symp."},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Bryson, S.T. (1992). Measurement and Calibration of Static Distortion of Position Data from 3D Trackers. Stereoscopic Displays and Applications III, International Society for Optics and Photonics.","DOI":"10.1117\/12.60417"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"42","DOI":"10.1080\/24699322.2018.1529199","article-title":"A Novel Electromagnetic Tracking System for Surgery Navigation","volume":"23","author":"Attivissimo","year":"2018","journal-title":"Comput. Assist. Surg."},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Mulder, J., and van Liere, R. (2000). Evaluation of Rotation Correction Techniques for Electromagnetic Position Tracking Systems. Virtual Environments 2000, Springer.","DOI":"10.1007\/978-3-7091-6785-4"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"70","DOI":"10.1007\/s10055-005-0005-3","article-title":"Neural Network-Based Calibration of Electromagnetic Tracking Systems","volume":"9","author":"Kindratenko","year":"2005","journal-title":"Virtual Real."},{"key":"ref_18","unstructured":"Whitmire, E., Salemi Parizi, F., and Patel, S. (2019, January 17\u201321). Aura: Inside-out Electromagnetic Controller Tracking. Proceedings of the 17th Annual International Conference on Mobile Systems, Applications, and Services-MobiSys \u201919, Seoul, Korea."},{"key":"ref_19","unstructured":"Czernuszenko, M., Sandin, D., and DeFanti, T. (1988, January 11\u201312). Line of Sight Method for Tracker Calibration in Projection-Based VR Systems. Proceedings of the 2nd International Immersive Projection Technology Workshop, Ames, IA, USA."},{"key":"ref_20","unstructured":"Ghazisaedy, M., Adamczyk, D., Sandin, D., Kenyon, R., and DeFanti, T. (1995, January 11\u201315). Ultrasonic Calibration of a Magnetic Tracker in a Virtual Reality Space. Proceedings of the Virtual Reality Annual International Symposium \u201995, Research Triangle Park, NC, USA."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"532","DOI":"10.1162\/pres.1997.6.5.532","article-title":"Magnetic Tracker Calibration for Improved Augmented Reality Registration","volume":"6","author":"Livingston","year":"1997","journal-title":"Presence Teleoperators Virtual Environ."},{"key":"ref_22","unstructured":"Cantillon-Murphy, P., and Jaeger, H.A. (2021, April 14). Anser EMT, OSF Repository. Available online: https:\/\/osf.io\/47q8q\/."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"157","DOI":"10.1111\/pace.12231","article-title":"Impact of Fluoroscopy Unit on the Accuracy of a Magnet-Based Electroanatomic Mapping and Navigation System: An In Vitro and In Vivo Validation Study","volume":"37","author":"Ahmad","year":"2014","journal-title":"Pacing Clin. Electrophysiol."},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Jaeger, H.A., and Cantillon-Murphy, P. (2018). Distorter Characterisation Using Mutual Inductance in Electromagnetic Tracking. Sensors, 18.","DOI":"10.3390\/s18093059"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"4845","DOI":"10.1109\/TIM.2019.2900884","article-title":"Electromagnetic Tracking Using Modular, Tiled Field Generators","volume":"68","author":"Jaeger","year":"2019","journal-title":"IEEE Trans. Instrum. Meas."},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Jaeger, H.A., Franz, A.M., O\u2019Donoghue, K., Seitel, A., Trauzettel, F., Maier-Hein, L., and Cantillon-Murphy, P. (2017). Anser EMT: The First Open-Source Electromagnetic Tracking Platform for Image-Guided Interventions. Int. J. Comput. Assist. Radiol. Surg.","DOI":"10.1007\/s11548-017-1568-7"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"8623","DOI":"10.1109\/JSEN.2020.2984323","article-title":"Inductive Sensor Design for Electromagnetic Tracking in Image Guided Interventions","volume":"20","author":"Cavaliere","year":"2020","journal-title":"IEEE Sens. J."},{"key":"ref_28","unstructured":"(2021, April 14). Aurora Sensors-NDI. Available online: https:\/\/www.ndigital.com\/products\/aurora\/aurora-sensors\/."},{"key":"ref_29","unstructured":"Johnk, C.T.A. (1975). Engineering Electromagnetic Fields and Waves, John Wiley and Sons, Inc."},{"key":"ref_30","unstructured":"Paul, C.R., and Nasar, S.A. (1987). Introduction to Electromagnetic Fields, McGraw-Hill."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"31","DOI":"10.1002\/andp.18461430103","article-title":"Allgemeine Gesetze der inducirten elektrischen Str\u00f6me","volume":"143","author":"Neumann","year":"1846","journal-title":"Ann. Der Phys. Und Chem."},{"key":"ref_32","doi-asserted-by":"crossref","unstructured":"Chan, H.L., Cheng, K.W.E., and Sutanto, D. (2000, January 18\u201319). A Simplified Neumann\u2019s Formula for Calculation of Inductance of Spiral Coil. Proceedings of the 8th International Conference on Power Electronics and Variable Speed Drives, London, UK.","DOI":"10.1049\/cp:20000222"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"101","DOI":"10.1109\/TPHP.1974.1134841","article-title":"Design of Planar Rectangular Microelectronic Inductors","volume":"10","author":"Greenhouse","year":"1974","journal-title":"IEEE Trans. Parts Hybrids Packag."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"301","DOI":"10.6028\/bulletin.088","article-title":"The Self and Mutual-Inductances of Linear Conductors","volume":"4","author":"Rosa","year":"1908","journal-title":"Bull. Bur. Stand."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"452","DOI":"10.1103\/PhysRev.5.452","article-title":"Mutual Inductances of Circuits Composed of Straight Wires","volume":"5","author":"Campbell","year":"1915","journal-title":"Phys. Rev."},{"key":"ref_36","unstructured":"Grover, F.W. (1946). Inductance Calculations: Working Formulas and Tables, Instrument Society of America."},{"key":"ref_37","doi-asserted-by":"crossref","unstructured":"Sonntag, C.L.W., Lomonova, E.A., and Duarte, J.L. (2008, January 6\u20139). Implementation of the Neumann Formula for Calculating the Mutual Inductance between Planar PCB Inductors. Proceedings of the 2008 18th International Conference on Electrical Machines, Vilamoura, Portugal.","DOI":"10.1109\/ICELMACH.2008.4799978"},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"287","DOI":"10.3233\/JAE-141779","article-title":"Mutual Inductance Calculation between Arbitrarily Positioned Rectangular Filaments","volume":"46","author":"Cheng","year":"2014","journal-title":"Int. J. Appl. Electromagn. Mech."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"560","DOI":"10.1109\/16.824729","article-title":"Physical Modeling of Spiral Inductors on Silicon","volume":"47","author":"Yue","year":"2000","journal-title":"IEEE Trans. Electron Devices"},{"key":"ref_40","unstructured":"Zolfaghari, A., Chan, A., and Razavi, B. (2000, January 24). Stacked Inductors and 1-to-2 Transformers in CMOS Technology. Proceedings of the IEEE 2000 Custom Integrated Circuits Conference (Cat. No.00CH37044), Orlando, FL, USA."},{"key":"ref_41","unstructured":"O\u2019Donoghue, K. (2014). Electromagnetic Tracking and Steering for Catheter Navigation. [Ph.D. Thesis, University College Cork]."},{"key":"ref_42","unstructured":"Sonntag, C.L.W., Spr\u00e9e, M., Lomonova, E.A., Duarte, J.L., and Vandenput, A.J.A. (2007, January 24\u201328). Accurate Magnetic Field Intensity Calculations for Contactless Energy Transfer Coils. Proceedings of the 16th International Conference on the Computation of Electromagnetic Fields, Achen, Germany."},{"key":"ref_43","first-page":"1","article-title":"A New Analytical Calculation of the Mutual Inductance of the Coaxial Spiral Rectangular Coils","volume":"50","author":"Cheng","year":"2014","journal-title":"IEEE Trans. Magn."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"876","DOI":"10.1118\/1.3075829","article-title":"Electromagnetic Tracking in the Clinical Environment: Electromagnetic Tracking in the Clinical Environment","volume":"36","author":"Yaniv","year":"2009","journal-title":"Med. Phys."},{"key":"ref_45","doi-asserted-by":"crossref","unstructured":"De Angelis, G., De Angelis, A., Moschitta, A., and Carbone, P. (2017). Comparison of Measurement Models for 3D Magnetic Localization and Tracking. Sensors, 17.","DOI":"10.3390\/s17112527"}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/21\/8\/2822\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T05:49:04Z","timestamp":1760161744000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/21\/8\/2822"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,4,16]]},"references-count":45,"journal-issue":{"issue":"8","published-online":{"date-parts":[[2021,4]]}},"alternative-id":["s21082822"],"URL":"https:\/\/doi.org\/10.3390\/s21082822","relation":{},"ISSN":["1424-8220"],"issn-type":[{"type":"electronic","value":"1424-8220"}],"subject":[],"published":{"date-parts":[[2021,4,16]]}}}