On the role of demagnetizing tensors in arbitrary orientations of general ellipsoids and implications for MRI safety assessment.
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| Title: | On the role of demagnetizing tensors in arbitrary orientations of general ellipsoids and implications for MRI safety assessment. |
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| Authors: | Pakarinen, Tomppa1 (AUTHOR) tomppa.pakarinen@tuni.fi |
| Source: | Medical Physics. Apr2026, Vol. 53 Issue 4, p1-11. 11p. |
| Subjects: | Demagnetization, Magnetic resonance imaging, Magnetic susceptibility, Approximation error, Torque, Poisson's equation, Ellipsoids |
| Abstract: | Background: 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. Purpose: Demagnetizing tensor is a well‐defined concept in the ellipsoids principal frame, though its transformation under three‐dimensional 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. Methods: 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‐projections. The approach is also applied to generalize force and torque calculations for ellipsoids under three‐dimensional reorientation. Results: 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‐projection 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. Conclusion: 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‐projection 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. [ABSTRACT FROM AUTHOR] |
| Copyright of Medical Physics is the property of Wiley-Blackwell and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
| Database: | Engineering Source |
| FullText | Text: Availability: 0 |
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| Header | DbId: egs DbLabel: Engineering Source An: 193122181 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: On the role of demagnetizing tensors in arbitrary orientations of general ellipsoids and implications for MRI safety assessment. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Pakarinen%2C+Tomppa%22">Pakarinen, Tomppa</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> tomppa.pakarinen@tuni.fi</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Medical+Physics%22">Medical Physics</searchLink>. Apr2026, Vol. 53 Issue 4, p1-11. 11p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Demagnetization%22">Demagnetization</searchLink><br /><searchLink fieldCode="DE" term="%22Magnetic+resonance+imaging%22">Magnetic resonance imaging</searchLink><br /><searchLink fieldCode="DE" term="%22Magnetic+susceptibility%22">Magnetic susceptibility</searchLink><br /><searchLink fieldCode="DE" term="%22Approximation+error%22">Approximation error</searchLink><br /><searchLink fieldCode="DE" term="%22Torque%22">Torque</searchLink><br /><searchLink fieldCode="DE" term="%22Poisson's+equation%22">Poisson's equation</searchLink><br /><searchLink fieldCode="DE" term="%22Ellipsoids%22">Ellipsoids</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: Background: 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. Purpose: Demagnetizing tensor is a well‐defined concept in the ellipsoids principal frame, though its transformation under three‐dimensional 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. Methods: 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‐projections. The approach is also applied to generalize force and torque calculations for ellipsoids under three‐dimensional reorientation. Results: 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‐projection 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. Conclusion: 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‐projection 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. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Medical Physics is the property of Wiley-Blackwell and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.) |
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| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1002/mp.70444 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 11 StartPage: 1 Subjects: – SubjectFull: Demagnetization Type: general – SubjectFull: Magnetic resonance imaging Type: general – SubjectFull: Magnetic susceptibility Type: general – SubjectFull: Approximation error Type: general – SubjectFull: Torque Type: general – SubjectFull: Poisson's equation Type: general – SubjectFull: Ellipsoids Type: general Titles: – TitleFull: On the role of demagnetizing tensors in arbitrary orientations of general ellipsoids and implications for MRI safety assessment. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Pakarinen, Tomppa IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 04 Text: Apr2026 Type: published Y: 2026 Identifiers: – Type: issn-print Value: 00942405 Numbering: – Type: volume Value: 53 – Type: issue Value: 4 Titles: – TitleFull: Medical Physics Type: main |
| ResultId | 1 |
