{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,3]],"date-time":"2026-07-03T22:16:46Z","timestamp":1783117006224,"version":"3.54.6"},"reference-count":25,"publisher":"Wiley","issue":"4","license":[{"start":{"date-parts":[[2026,4,19]],"date-time":"2026-04-19T00:00:00Z","timestamp":1776556800000},"content-version":"vor","delay-in-days":18,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"},{"start":{"date-parts":[[2026,4,1]],"date-time":"2026-04-01T00:00:00Z","timestamp":1775001600000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/doi.wiley.com\/10.1002\/tdm_license_1.1"}],"content-domain":{"domain":["aapm.onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Medical Physics"],"published-print":{"date-parts":[[2026,4]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:sec>\n                    <jats:title>Background<\/jats:title>\n                    <jats:p>Demagnetizing tensors describe the shape anisotropic contribution of magnetic susceptibility, that is, how an object's shape and orientation affect its internal magnetization. Ellipsoids possess a unique geometric property by exhibiting homogeneous internal magnetization, enabling a purely geometrical characterization. A general description of the demagnetizing tensor under arbitrary rotations would broaden their applicability across various fields, most notably in magnetic resonance safety evaluation.<\/jats:p>\n                  <\/jats:sec>\n                  <jats:sec>\n                    <jats:title>Purpose<\/jats:title>\n                    <jats:p>Demagnetizing tensor is a well\u2010defined concept in the ellipsoids principal frame, though its transformation under three\u2010dimensional reorientation is often overlooked, a justifiable omission for spheroidal solutions of the Poisson equation. However, this does not hold for general ellipsoids under arbitrary reorientation. This work is motivated by the concerns in magnetic resonance imaging safety and its practical evaluation in clinical environments, aiming to extend and simplify the process.<\/jats:p>\n                  <\/jats:sec>\n                  <jats:sec>\n                    <jats:title>Methods<\/jats:title>\n                    <jats:p>This work demonstrates the validity of directly rotating the orthogonal basis solutions, derived from Poisson's equation, and uses the procedure to evaluate a practical approximation, based on orthogonal area\u2010projections. The approach is also applied to generalize force and torque calculations for ellipsoids under three\u2010dimensional reorientation.<\/jats:p>\n                  <\/jats:sec>\n                  <jats:sec>\n                    <jats:title>Results<\/jats:title>\n                    <jats:p>The method shows an exact match with the numerical solution and agrees with the standard scalar expressions for translation force and torque. Additionally, a unique connection to the MRI magic angle is found as the point of convergence for prolate spheroid aspect ratios under rotation. The area\u2010projection approximation was demonstrated to perform fairly across prolate and oblate spheroids. Similar approximations might extend to irregular shapes, but numerical approaches remain preferable due to the complexity of internal field distributions.<\/jats:p>\n                  <\/jats:sec>\n                  <jats:sec>\n                    <jats:title>Conclusion<\/jats:title>\n                    <jats:p>The presented approach offers an alternative method for force and torque calculations, such as those provided by ASTM, also generalizing the conventional approach. The area\u2010projection approximation via SVD offers a straightforward extension to the original method. Finally, the connection between demagnetizing tensor rotation and the magic angle provides a new perspective on the phenomenon.<\/jats:p>\n                  <\/jats:sec>","DOI":"10.1002\/mp.70444","type":"journal-article","created":{"date-parts":[[2026,4,20]],"date-time":"2026-04-20T06:30:24Z","timestamp":1776666624000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["On the role of demagnetizing tensors in arbitrary orientations of general ellipsoids and implications for MRI safety assessment"],"prefix":"10.1002","volume":"53","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4992-2693","authenticated-orcid":false,"given":"Tomppa","family":"Pakarinen","sequence":"first","affiliation":[{"name":"Faculty of Medicine and Health Technology Tampere University  Tampere Finland"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"311","published-online":{"date-parts":[[2026,4,19]]},"reference":[{"key":"e_1_2_8_2_1","volume-title":"Introduction to Electrodynamics","author":"Griffiths D","year":"1999"},{"key":"e_1_2_8_3_1","doi-asserted-by":"publisher","DOI":"10.1063\/1.343481"},{"issue":"4","key":"e_1_2_8_4_1","article-title":"An analytical computation of magnetic field generated from a cylinder ferromagnet","volume":"87","author":"Taniguchi T","year":"2018","journal-title":"J Phys Soc Jpn"},{"key":"e_1_2_8_5_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmmm.2015.10.133"},{"key":"e_1_2_8_6_1","doi-asserted-by":"publisher","DOI":"10.1109\/TMAG.2005.847634"},{"key":"e_1_2_8_7_1","doi-asserted-by":"publisher","DOI":"10.2519\/jospt.2011.3906"},{"key":"e_1_2_8_8_1","unstructured":"i. 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O. f. Standardization.Assessment of the safety of magnetic resonance imaging for patients with an active implantable medical device\u2014Part 1: requirements for information before magnetic resonance imaging. ISO\/TS 10974:2018 ISO;2018."},{"key":"e_1_2_8_20_1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevResearch.6.043046"},{"key":"e_1_2_8_21_1","doi-asserted-by":"publisher","DOI":"10.1109\/TMAG.1966.1065973"},{"key":"e_1_2_8_22_1","doi-asserted-by":"publisher","DOI":"10.1002\/jmri.25761"},{"key":"e_1_2_8_23_1","doi-asserted-by":"publisher","DOI":"10.1002\/1522\u20102586(200007)12:1%3c2::AID\u2010JMRI2%3e3.0.CO;2\u2010V"},{"key":"e_1_2_8_24_1","doi-asserted-by":"publisher","DOI":"10.1520\/JTE20190096"},{"issue":"4","key":"e_1_2_8_25_1","first-page":"23","article-title":"Geometrical interpretation of singular value decomposition (svd) & applications of SVD","volume":"5","author":"Raghavendar J","year":"2017","journal-title":"Int J Sci Innov Math Res"},{"key":"e_1_2_8_26_1","doi-asserted-by":"publisher","DOI":"10.1088\/0022\u20103727\/39\/5\/001"}],"container-title":["Medical Physics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/aapm.onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/mp.70444","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/aapm.onlinelibrary.wiley.com\/doi\/full-xml\/10.1002\/mp.70444","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/aapm.onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/mp.70444","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,7,3]],"date-time":"2026-07-03T21:23:37Z","timestamp":1783113817000},"score":1,"resource":{"primary":{"URL":"https:\/\/aapm.onlinelibrary.wiley.com\/doi\/10.1002\/mp.70444"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,4]]},"references-count":25,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2026,4]]}},"alternative-id":["10.1002\/mp.70444"],"URL":"https:\/\/doi.org\/10.1002\/mp.70444","archive":["Portico"],"relation":{},"ISSN":["0094-2405","2473-4209"],"issn-type":[{"value":"0094-2405","type":"print"},{"value":"2473-4209","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,4]]},"assertion":[{"value":"2025-09-14","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2026-04-03","order":2,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2026-04-19","order":3,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}],"article-number":"e70444"}}