{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:25:21Z","timestamp":1760145921509,"version":"build-2065373602"},"reference-count":42,"publisher":"MDPI AG","issue":"17","license":[{"start":{"date-parts":[[2024,9,2]],"date-time":"2024-09-02T00:00:00Z","timestamp":1725235200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Radiofrequency (RF) transmitter and receiver coils are employed in in magnetic resonance (MR) applications to, respectively, excite the nuclei in the object to be imaged and to pick up the signals emitted by the nuclei with a high signal-to-noise ratio (SNR). The ability to obtain high-quality images and spectra in MR strongly depends on the RF coil\u2019s efficiency. Local coil efficiency can be estimated with magnetic field mapping methods evaluated at a fixed point in space. Different methods have been described in the literature, divided into electromagnetic bench tests and MR techniques. In this paper, we review our experience in designing and testing RF coils for MR in our electromagnetic laboratory with the use of the perturbing sphere method, which permits coil efficiency and magnetic field mapping to be estimated with great accuracy and in a short space of time, which is useful for periodic coil quality control checks. The method\u2019s accuracy has been verified with simulations and workbench tests performed on RF coils with different surfaces and of different volumes. Furthermore, all the precautions taken to improve the measurement sensitivity are also included in this review, in addition to the various applications of the method that have been described over the last twenty years of research in our electromagnetic laboratory.<\/jats:p>","DOI":"10.3390\/s24175705","type":"journal-article","created":{"date-parts":[[2024,9,2]],"date-time":"2024-09-02T12:54:42Z","timestamp":1725281682000},"page":"5705","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Use of the Perturbing Sphere Method for the Estimation of Radiofrequency Coils\u2019 Efficiency in Magnetic Resonance Applications: Experience from an Electromagnetic Laboratory"],"prefix":"10.3390","volume":"24","author":[{"given":"Giulio","family":"Giovannetti","sequence":"first","affiliation":[{"name":"Institute of Clinical Physiology, National Council of Research, 56124 Pisa, Italy"}]},{"given":"Francesca","family":"Frijia","sequence":"additional","affiliation":[{"name":"Bioengineering Unit, Fondazione Toscana G. Monasterio, 56124 Pisa, Italy"}]}],"member":"1968","published-online":{"date-parts":[[2024,9,2]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"233","DOI":"10.1016\/j.jmir.2017.06.004","article-title":"Magnetic Resonance Spectroscopy and its Clinical Applications: A Review","volume":"48","author":"Faghihi","year":"2017","journal-title":"J. Med. Imaging Radiat. Sci."},{"key":"ref_2","unstructured":"Jin, J. (1999). Electromagnetic Analysis and Design in Magnetic Resonance Imaging, CRC."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"361","DOI":"10.1002\/1099-0534(2000)12:6<361::AID-CMR1>3.0.CO;2-L","article-title":"NMR probeheads for in vivo applications","volume":"12","author":"Haase","year":"2000","journal-title":"Conc. Magn. Reson."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"192","DOI":"10.1002\/mrm.1910160203","article-title":"The NMR phased array","volume":"16","author":"Roemer","year":"1990","journal-title":"Magn. Reson. Med."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"1841","DOI":"10.1063\/1.1144020","article-title":"Quick measurement of NMR-coil sensitivity with a dual-loop probe","volume":"64","author":"Darrasse","year":"1993","journal-title":"Rev. Sci. Instrum."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"173","DOI":"10.1002\/1099-0534(2000)12:4<173::AID-CMR1>3.0.CO;2-Q","article-title":"The principle of reciprocity in signal strength calculations\u2014A mathematical guide","volume":"12","author":"Hoult","year":"2000","journal-title":"Concepts Magn. Reson."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"425","DOI":"10.1016\/0022-2364(79)90019-2","article-title":"The sensitivity of the zeugmatographic experiment involving human samples","volume":"34","author":"Hoult","year":"1979","journal-title":"J. Magn. Reson. (1969)"},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Hornak, J.P. (2002). Encyclopedia of Imaging Science and Technology, Wiley.","DOI":"10.1002\/0471443395"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"68","DOI":"10.1063\/1.1701980","article-title":"Field Strength Measurements in Resonant Cavities","volume":"23","author":"Maier","year":"1952","journal-title":"J. Appl. Phys."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"2762","DOI":"10.1063\/1.1712295","article-title":"Theory of Saturation and Double Resonance Effects in ESR Spectra. III. rf Coherence and Line Shapes","volume":"47","author":"Freed","year":"1967","journal-title":"J. Chem. Phys."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"501","DOI":"10.1016\/0022-2364(86)90387-2","article-title":"Spectral rotation in pulsed ESR spectroscopy","volume":"67","author":"Hornak","year":"1986","journal-title":"J. Magn. Reson. (1969)"},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Alecci, M., Seimenis, I., McCallum, S.J., Lurie, D.J., and Foster, M.A. (1998). Nitroxide free radical clearance in the live rat monitored by radio-frequency CW-EPR and PEDRI. Phys. Med. Biol., 43.","DOI":"10.1088\/0031-9155\/43\/7\/011"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"1057","DOI":"10.1002\/mrm.10302","article-title":"Mapping of the B1 field distribution of a surface coil resonator using EPR imaging","volume":"48","author":"He","year":"2002","journal-title":"Magn. Reson. Med."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"124","DOI":"10.1016\/j.jmr.2007.10.012","article-title":"A loop resonator for slice-selective in vivo EPR imaging in rats","volume":"190","author":"Hirata","year":"2008","journal-title":"J. Magn. Reson."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"127","DOI":"10.1093\/rpd\/ncw167","article-title":"Surface Dielectric Resonators for X-band EPR Spectroscopy","volume":"172","author":"Petryakov","year":"2016","journal-title":"Radiat. Prot. Dosim."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"1301","DOI":"10.1007\/s00723-017-0955-0","article-title":"Uniform Field Re-entrant Cylindrical TE[Formula: See text] Cavity for Pulse Electron Paramagnetic Resonance Spectroscopy at Q-band","volume":"48","author":"Sidabras","year":"2017","journal-title":"Appl. Magn. Reson."},{"key":"ref_17","first-page":"1124","article-title":"A 750-MHz Electronically Tunable Resonator Using Microstrip Line Couplers for Electron Paramagnetic Resonance Imaging of a Mouse Tumor-Bearing Leg","volume":"65","author":"Amida","year":"2018","journal-title":"IEEE Trans. Biomed. Eng."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"107519","DOI":"10.1016\/j.jmr.2023.107519","article-title":"Towards high performance dielectric microwave resonators for X-band EPR spectroscopy","volume":"354","author":"Wiedemann","year":"2023","journal-title":"J. Magn. Reson."},{"key":"ref_19","first-page":"324","article-title":"A further 2 improvement in sensitivity","volume":"54","author":"Chen","year":"1983","journal-title":"J. Magn. Reson."},{"key":"ref_20","unstructured":"Mispelter, J., Lupu, M., and Briguet, A. (2015). NMR Probeheads for Biophysical and Biomedical Experiments: Theoretical Principles & Practical Guidelines, Imperial College Press. [2nd ed.]."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"394","DOI":"10.1002\/(SICI)1099-1492(199712)10:8<394::AID-NBM494>3.0.CO;2-0","article-title":"Theory and application of array coils in MR spectroscopy","volume":"10","author":"Wright","year":"1997","journal-title":"NMR Biomed."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"1","DOI":"10.2528\/PIERB13100101","article-title":"Field Measurements within a Large Resonant Cavity Based on the Perturbation Theory","volume":"57","author":"Nasserdine","year":"2014","journal-title":"Progress. Electromagn. Res. B"},{"key":"ref_23","first-page":"221","article-title":"Lateral skin effect in a flat conductor","volume":"32","author":"Belevitch","year":"1971","journal-title":"Philips. Tech. Rev."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"144","DOI":"10.1006\/jmre.1998.1703","article-title":"Practical aspects of birdcage coils","volume":"138","author":"Doty","year":"1999","journal-title":"J. Magn. Reson."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"163","DOI":"10.1007\/BF01771702","article-title":"An efficient birdcage resonator at 2.5 MHz using a novel multilayer self-capacitance construction technique","volume":"3","author":"Yeung","year":"1995","journal-title":"Magn. Reson. Mater. Phys. Bioiogy Med."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"9","DOI":"10.1002\/cmr.b.20005","article-title":"Conductor geometry and capacitor quality for performance optimization of low-frequency birdcage coils","volume":"20","author":"Giovannetti","year":"2004","journal-title":"Concepts Magn. Reson. Part B Magn. Reson. Eng."},{"key":"ref_27","unstructured":"Chen, C.N., and Hoult, D.I. (1989). Biomedical Magnetic Resonance Technology, Adam Hilger."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"511","DOI":"10.1007\/s00723-012-0323-z","article-title":"Coil Sensitivity Estimation with Perturbing Sphere Method: Application to 13C Birdcages","volume":"42","author":"Giovannetti","year":"2012","journal-title":"Appl. Magn. Reson."},{"key":"ref_29","unstructured":"Hendrick, E.R. (2008). Breast MRI: Fundamentals and Technical Aspects, Springer Science and Business Media."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"57","DOI":"10.1002\/cmr.b.21210","article-title":"Classical and lateral skin effect contributions estimation in strip MR coils","volume":"41","author":"Giovannetti","year":"2012","journal-title":"Concepts Magn. Reson. Part B Magn. Reson. Eng."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"2201","DOI":"10.1016\/j.measurement.2013.03.015","article-title":"Efficiency evaluation of a 13C Magnetic Resonance birdcage coil: Theory and comparison of four methods","volume":"46","author":"Giovannetti","year":"2013","journal-title":"Measurement"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"139","DOI":"10.1002\/cmr.b.21223","article-title":"A novel method for coil efficiency estimation: Validation with a 13C birdcage","volume":"41","author":"Giovannetti","year":"2012","journal-title":"Concepts Magn. Reson. Part B Magn. Reson. Eng."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"165","DOI":"10.1002\/(SICI)1099-0534(1999)11:3<165::AID-CMR4>3.0.CO;2-D","article-title":"90\u00b0 pulse width calibrations: How to read a pulse width array","volume":"11","author":"Keifer","year":"1999","journal-title":"Concept. Magn. Res."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"1083","DOI":"10.1007\/s00723-019-01141-9","article-title":"Design and Simulation of a Helmholtz Coil for Magnetic Resonance Imaging and Spectroscopy Experiments with a 3T MR Clinical Scanner","volume":"50","author":"Giovannetti","year":"2019","journal-title":"Appl. Magn. Reson."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"269","DOI":"10.2478\/pjmpe-2020-0032","article-title":"Design of a dedicated circular coil for Magnetic Resonance Spectroscopy studies in small phantoms and animal acquisition with a 3 Tesla Magnetic Resonance clinical scanner","volume":"26","author":"Giovannetti","year":"2020","journal-title":"Pol. J. Med. Phys. Eng."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"081402","DOI":"10.1063\/5.0050788","article-title":"Design, simulation, and test of surface and volume radio frequency coils for 13C magnetic resonance imaging and spectroscopy","volume":"92","author":"Frijia","year":"2021","journal-title":"Rev. Sci. Instrum."},{"key":"ref_37","doi-asserted-by":"crossref","unstructured":"Giovannetti, G., Flori, A., Martini, N., Cademartiri, F., Aquaro, G.D., Pingitore, A., and Frijia, F. (2024). Hardware and Software Setup for Quantitative 23Na Magnetic Resonance Imaging at 3T: A Phantom Study. Sensors, 24.","DOI":"10.3390\/s24092716"},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"173","DOI":"10.1002\/(SICI)1522-2594(199907)42:1<173::AID-MRM23>3.0.CO;2-O","article-title":"A practical double-tuned 1H\/31P quadrature birdcage headcoil optimized for 31P operation","volume":"42","author":"Matson","year":"1999","journal-title":"Magn. Reson. Med."},{"key":"ref_39","first-page":"41","article-title":"A design for a double-tuned birdcage coil for use in an integrated MRI\/MRS examination","volume":"89","author":"Isaac","year":"1990","journal-title":"J. Magn. Reson."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"46","DOI":"10.1002\/1522-2586(200007)12:1<46::AID-JMRI6>3.0.CO;2-D","article-title":"Sensitivity and power deposition in a high-field imaging experiment","volume":"12","author":"Hoult","year":"2000","journal-title":"J. Magn. Reson. Imag."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"898","DOI":"10.1148\/rg.210110","article-title":"Basic Principles of and Practical Guide to Clinical MRI Radiofrequency Coils","volume":"42","author":"Kwok","year":"2022","journal-title":"RadioGraphics"},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"277","DOI":"10.1186\/s43055-021-00659-y","article-title":"Radio Frequency MRI coils and safety: How infrared thermography can support quality assurance","volume":"52","author":"Testagrossa","year":"2021","journal-title":"Egypt. J. Radiol. Nucl. Med."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/24\/17\/5705\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T15:47:09Z","timestamp":1760111229000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/24\/17\/5705"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,9,2]]},"references-count":42,"journal-issue":{"issue":"17","published-online":{"date-parts":[[2024,9]]}},"alternative-id":["s24175705"],"URL":"https:\/\/doi.org\/10.3390\/s24175705","relation":{},"ISSN":["1424-8220"],"issn-type":[{"type":"electronic","value":"1424-8220"}],"subject":[],"published":{"date-parts":[[2024,9,2]]}}}