{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,23]],"date-time":"2025-10-23T11:17:39Z","timestamp":1761218259696,"version":"build-2065373602"},"reference-count":59,"publisher":"MDPI AG","issue":"14","license":[{"start":{"date-parts":[[2020,7,12]],"date-time":"2020-07-12T00:00:00Z","timestamp":1594512000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100003130","name":"Fonds Wetenschappelijk Onderzoek","doi-asserted-by":"publisher","award":["A.C. & J.L. Postdoctoral research Fellowship"],"award-info":[{"award-number":["A.C. & J.L. Postdoctoral research Fellowship"]}],"id":[{"id":"10.13039\/501100003130","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Magnetic nanoparticles are increasingly employed in biomedical applications such as disease detection and tumor treatment. To ensure a safe and efficient operation of these applications, a noninvasive and accurate characterization of the particles is required. In this work, a magnetic characterization technique is presented in which the particles are excited by specific pulsed time-varying magnetic fields. This way, we can selectively excite nanoparticles of a given size so that the resulting measurement gives direct information on the size distribution without the need for any a priori assumptions or complex postprocessing procedures to decompose the measurement signal. This contrasts state-of-the-art magnetic characterization techniques. The possibility to selectively excite certain particle types opens up perspectives in \u201cmulticolor\u201d particle imaging, where different particle types need to be imaged independently within one sample. Moreover, the presented methodology allows one to simultaneously determine the size-dependent coercivity of the particles. This is not only a valuable structure\u2013property relation from a fundamental point of view, it is also practically relevant to optimize applications like magnetic particle hyperthermia. We numerically demonstrate that the novel characterization technique can accurately reconstruct several particle size distributions and is able to retrieve the coercivity\u2013size relation of the particles. The developed technique advances current magnetic nanoparticle characterization possibilities and opens up exciting pathways for biomedical applications and particle imaging procedures.<\/jats:p>","DOI":"10.3390\/s20143882","type":"journal-article","created":{"date-parts":[[2020,7,14]],"date-time":"2020-07-14T09:30:49Z","timestamp":1594719049000},"page":"3882","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":11,"title":["Simultaneous Coercivity and Size Determination of Magnetic Nanoparticles"],"prefix":"10.3390","volume":"20","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-4280-8991","authenticated-orcid":false,"given":"Annelies","family":"Coene","sequence":"first","affiliation":[{"name":"Department of Electromechanical, Systems and Metal Engineering, Ghent University, 9052 Zwijnaarde, Belgium"},{"name":"Cancer Research Institute Ghent, 9000 Ghent, Belgium"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8778-3092","authenticated-orcid":false,"given":"Jonathan","family":"Leliaert","sequence":"additional","affiliation":[{"name":"Department of Solid State Sciences, Ghent University, 9000 Ghent, Belgium"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2020,7,12]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"R167","DOI":"10.1088\/0022-3727\/36\/13\/201","article-title":"Applications of magnetic nanoparticles in biomedicine","volume":"36","author":"Pankhurst","year":"2003","journal-title":"J. Phys. D Appl. Phys."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"224001","DOI":"10.1088\/0022-3727\/42\/22\/224001","article-title":"Progress in applications of magnetic nanoparticles in biomedicine","volume":"42","author":"Pankhurst","year":"2009","journal-title":"J. Phys. D Appl. Phys."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"023501","DOI":"10.1088\/1468-6996\/16\/2\/023501","article-title":"Recent progress on magnetic iron oxide nanoparticles: Synthesis, surface functional strategies and biomedical applications","volume":"16","author":"Wu","year":"2015","journal-title":"Sci. Technol. Adv. Mater."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"302","DOI":"10.1016\/j.addr.2019.01.005","article-title":"Iron oxide nanoparticles: Diagnostic, therapeutic and theranostic applications","volume":"138","author":"Dadfar","year":"2019","journal-title":"Adv. Drug Deliv. Rev."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"86","DOI":"10.1016\/j.mattod.2019.06.003","article-title":"Magnetic iron oxide nanoparticles for disease detection and therapy","volume":"31","author":"Tong","year":"2019","journal-title":"Mater. Today"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"5818","DOI":"10.1021\/cr300068p","article-title":"Magnetic nanoparticles: Design and characterization, toxicity and biocompatibility, pharmaceutical and biomedical applications","volume":"112","author":"Reddy","year":"2012","journal-title":"Chem. Rev."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"5652","DOI":"10.1021\/acs.nanolett.6b02261","article-title":"Magnetic Drug Targeting: Preclinical in Vivo Studies, Mathematical Modeling, and Extrapolation to Humans","volume":"16","author":"Bai","year":"2016","journal-title":"Nano Lett."},{"key":"ref_8","first-page":"445","article-title":"Magnetic relaxometry as applied to sensitive cancer detection and localization","volume":"60","author":"Karaulanov","year":"2015","journal-title":"Biomed. Eng. Tech."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"715","DOI":"10.3109\/02656736.2013.836758","article-title":"Physics of heat generation using magnetic nanoparticles for hyperthermia","volume":"29","author":"Dennis","year":"2013","journal-title":"Int. J. Hyperth."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"041302","DOI":"10.1063\/1.4935688","article-title":"Fundamentals and advances in magnetic hyperthermia","volume":"2","author":"Hemery","year":"2015","journal-title":"Appl. Phys. Rev."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"20308","DOI":"10.3390\/ijms160920308","article-title":"Classification of Magnetic Nanoparticle Systems\u2014Synthesis, Standardization and Analysis Methods in the NanoMag Project","volume":"16","author":"Bogren","year":"2015","journal-title":"Int. J. Mol. Sci."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"206","DOI":"10.1016\/j.jmmm.2016.11.079","article-title":"The effect of the magnetic nanoparticle\u2019s size dependence of the relaxation time constant on the specific loss power of magnetic nanoparticle hyperthermia","volume":"426","author":"Harabech","year":"2017","journal-title":"J. Magn. Magn. Mater."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"1077","DOI":"10.1109\/TMI.2014.2375065","article-title":"Magnetic Particle Imaging With Tailored Iron Oxide Nanoparticle Tracers","volume":"34","author":"Ferguson","year":"2015","journal-title":"IEEE Trans. Med. Imaging"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"110","DOI":"10.1016\/j.jmmm.2013.10.025","article-title":"Non-regularized inversion method from light scattering applied to ferrofluid magnetization curves for magnetic size distribution analysis","volume":"353","author":"Kuipers","year":"2014","journal-title":"J. Magn. Magn. Mater."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"106102","DOI":"10.1063\/1.2069776","article-title":"Magnetorelaxometry of magnetic nanoparticles in magnetically unshielded environment utilizing a differential fluxgate arrangement","volume":"76","author":"Ludwig","year":"2005","journal-title":"Rev. Sci. Instrum."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"381","DOI":"10.1016\/S0304-8853(02)00657-1","article-title":"Magnetorelaxometry\u2014A new binding specific detection method based on magnetic nanoparticles","volume":"252","author":"Lange","year":"2002","journal-title":"J. Magn. Magn. Mater."},{"key":"ref_17","first-page":"1","article-title":"Analysis of ac susceptibility spectra for the characterization of magnetic nanoparticles","volume":"53","author":"Ludwig","year":"2017","journal-title":"IEEE Trans. Magn."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"043903","DOI":"10.1063\/1.4940724","article-title":"Magnetic-field dependence of Brownian and N\u00e9el relaxation times","volume":"119","author":"Dieckhoff","year":"2016","journal-title":"J. Appl. Phys."},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Wawrzik, T., Schilling, M., and Ludwig, F. (2012). Perspectives of magnetic particle spectroscopy for magnetic nanoparticle characterization. Magnetic Particle Imaging, Springer.","DOI":"10.1007\/978-3-642-24133-8_7"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"6787","DOI":"10.1021\/acs.jpcc.8b10763","article-title":"Multiparametric magnetic particle spectroscopy of CoFe2O4 nanoparticles in viscous media","volume":"123","author":"Draack","year":"2019","journal-title":"J. Phys. Chem. C"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"222401","DOI":"10.1063\/1.4936890","article-title":"Thermal magnetic noise spectra of nanoparticle ensembles","volume":"107","author":"Leliaert","year":"2015","journal-title":"Appl. Phys. Lett."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"085004","DOI":"10.1088\/1361-6463\/aa5944","article-title":"The complementarity and similarity of magnetorelaxometry and thermal magnetic noise spectroscopy for magnetic nanoparticle characterization","volume":"50","author":"Leliaert","year":"2017","journal-title":"J. Phys. D Appl. Phys."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"1233","DOI":"10.1063\/1.1149581","article-title":"Exponential analysis in physical phenomena","volume":"70","author":"Istratov","year":"1999","journal-title":"Rev. Sci. Instrum."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"073012","DOI":"10.1088\/1367-2630\/aa73b4","article-title":"Distribution functions of magnetic nanoparticles determined by a numerical inversion method","volume":"19","author":"Bender","year":"2017","journal-title":"New J. Phys."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"3068","DOI":"10.1021\/acs.jpcc.7b11255","article-title":"Relating magnetic properties and high hyperthermia performance of iron oxide nanoflowers","volume":"122","author":"Bender","year":"2018","journal-title":"J. Phys. Chem. C"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"S2829","DOI":"10.1088\/0953-8984\/18\/38\/S20","article-title":"Aggregation behaviour of magnetic nanoparticle suspensions investigated by magnetorelaxometry","volume":"18","author":"Eberbeck","year":"2006","journal-title":"J. Phys. Condens. Matter"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"1800287","DOI":"10.1002\/adhm.201800287","article-title":"Coercivity Determines Magnetic Particle Heating","volume":"7","author":"Starsich","year":"2018","journal-title":"Adv. Healthc. Mater."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"358","DOI":"10.1016\/j.jmmm.2004.03.034","article-title":"Enhancement of AC-losses of magnetic nanoparticles for heating applications","volume":"280","author":"Hergt","year":"2004","journal-title":"J. Magn. Magn. Mater."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"385214","DOI":"10.1088\/0953-8984\/20\/38\/385214","article-title":"Effects of size distribution on hysteresis losses of magnetic nanoparticles for hyperthermia","volume":"20","author":"Hergt","year":"2008","journal-title":"J. Phys. Condens. Matter."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"1287","DOI":"10.1126\/science.236.4806.1287","article-title":"Magnetic Properties of Hydrothermally Recrystallized Magnetite Crystals","volume":"236","author":"Heider","year":"1987","journal-title":"Science"},{"key":"ref_31","first-page":"153","article-title":"Theory of the dispersion of magnetic permeability in ferromagnetic bodies","volume":"8","author":"Landau","year":"1935","journal-title":"Phys. Z. Sowietunion"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"1677","DOI":"10.1103\/PhysRev.130.1677","article-title":"Thermal Fluctuations of a Single-Domain Particle","volume":"130","author":"Brown","year":"1963","journal-title":"Phys. Rev."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"223106","DOI":"10.1063\/1.4936930","article-title":"Combined N\u00e9el and Brown rotational Langevin dynamics in magnetic particle imaging, sensing, and therapy","volume":"107","author":"Reeves","year":"2015","journal-title":"Appl. Phys. Lett."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"309","DOI":"10.1007\/s11517-014-1239-6","article-title":"Vinamax: A macrospin simulation tool for magnetic nanoparticles","volume":"53","author":"Leliaert","year":"2015","journal-title":"Med. Biol. Eng. Comput."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"125010","DOI":"10.1063\/1.5003957","article-title":"Adaptively time stepping the stochastic Landau-Lifshitz-Gilbert equation at nonzero temperature: Implementation and validation in MuMax3","volume":"7","author":"Leliaert","year":"2017","journal-title":"AIP Adv."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"234303","DOI":"10.1063\/1.4937919","article-title":"Dynamics of magnetic single domain particles embedded in a viscous liquid","volume":"118","author":"Usadel","year":"2015","journal-title":"J. Appl. Phys."},{"key":"ref_37","first-page":"427","article-title":"Magnetorelaxometry procedures for quantitative imaging and characterization of magnetic nanoparticles in biomedical applications","volume":"60","author":"Liebl","year":"2015","journal-title":"Biomed. Eng. Tech."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"1189","DOI":"10.1007\/s11095-011-0630-3","article-title":"Magnetorelaxometry assisting biomedical applications of magnetic nanoparticles","volume":"29","author":"Wiekhorst","year":"2012","journal-title":"Pharm. Res."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"104431","DOI":"10.1103\/PhysRevB.77.104431","article-title":"Ferromagnetic nanoparticles with strong surface anisotropy: Spin structures and magnetization processes","volume":"77","author":"Berger","year":"2008","journal-title":"Phys. Rev. B"},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"268","DOI":"10.1088\/0957-4484\/14\/2\/332","article-title":"Multidomain to single-domain transition for uniform Co80Ni20nanoparticles","volume":"14","author":"Luna","year":"2003","journal-title":"Nanotechnology"},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"656","DOI":"10.1063\/1.1729324","article-title":"Particle Size Dependence of Coercivity and Remanence of Single-Domain Particles","volume":"34","author":"Kneller","year":"1963","journal-title":"J. Appl. Phys."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"463","DOI":"10.1111\/j.1749-6632.1969.tb41269.x","article-title":"The fundamental theorem of the theory of fine ferromagnetic particles","volume":"147","author":"Brown","year":"1969","journal-title":"Ann. New York Acad. Sci."},{"key":"ref_43","first-page":"1","article-title":"Magnetic multi-granule nanoclusters: A model system that exhibits universal size effect of magnetic coercivity","volume":"5","author":"Lee","year":"2015","journal-title":"Sci. Rep."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"3139","DOI":"10.1088\/1361-6560\/aa5e90","article-title":"Multi-color magnetic nanoparticle imaging using magnetorelaxometry","volume":"62","author":"Coene","year":"2017","journal-title":"Phys. Med. Biol."},{"key":"ref_45","doi-asserted-by":"crossref","unstructured":"Jaufenthaler, A., Schier, P., Middelmann, T., Liebl, M., Wiekhorst, F., and Baumgarten, D. (2020). Quantitative 2D magnetorelaxometry imaging of magnetic nanoparticles using optically pumped magnetometers. Sensors, 20.","DOI":"10.3390\/s20030753"},{"key":"ref_46","unstructured":"Einstein, A. (1956). Investigations on the Theory of the Brownian Movement, Dover Publications."},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"49","DOI":"10.1051\/jphysrad:0195000110204900","article-title":"Th\u00e9orie du tra\u00eenage magn\u00e9tique des substances massives dans le domaine de Rayleigh","volume":"11","author":"Louis","year":"1950","journal-title":"J. Phys. Radium"},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"163914","DOI":"10.1063\/1.4900916","article-title":"Regarding the N\u00e9el relaxation time constant in magnetorelaxometry","volume":"116","author":"Leliaert","year":"2014","journal-title":"J. Appl. Phys."},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"182502","DOI":"10.1063\/1.3586776","article-title":"How the size distribution of magnetic nanoparticles determines their magnetic particle imaging performance","volume":"98","author":"Eberbeck","year":"2011","journal-title":"Appl. Phys. Lett."},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"33","DOI":"10.1016\/j.jmmm.2016.09.108","article-title":"Finding the magnetic size distribution of magnetic nanoparticles from magnetization measurements via the iterative Kaczmarz algorithm","volume":"431","author":"Schmidt","year":"2016","journal-title":"J. Magn. Magn. Mater."},{"key":"ref_51","doi-asserted-by":"crossref","first-page":"195002","DOI":"10.1088\/1361-6463\/aa695d","article-title":"Interpreting the magnetorelaxometry signal of suspended magnetic nanoparticles with Kaczmarz\u2019 algorithm","volume":"50","author":"Leliaert","year":"2017","journal-title":"J. Phys. D Appl. Phys."},{"key":"ref_52","doi-asserted-by":"crossref","first-page":"1940001","DOI":"10.1142\/S2010324719400010","article-title":"Iron Oxide Nanoparticles for Magnetic Hyperthermia","volume":"9","author":"Usov","year":"2019","journal-title":"SPIN"},{"key":"ref_53","doi-asserted-by":"crossref","first-page":"1368","DOI":"10.1016\/j.physb.2011.10.010","article-title":"A generalization of the fundamental theorem of Brown for fine ferromagnetic particles","volume":"407","author":"Fratta","year":"2012","journal-title":"Phys. B Condens. Matter"},{"key":"ref_54","doi-asserted-by":"crossref","first-page":"941","DOI":"10.1038\/s41565-018-0221-0","article-title":"Lifetime-engineered NIR-II nanoparticles unlock multiplexed in vivo imaging","volume":"13","author":"Fan","year":"2018","journal-title":"Nat. Nanotechnol."},{"key":"ref_55","doi-asserted-by":"crossref","first-page":"73","DOI":"10.2217\/nnm-2016-0316","article-title":"Magnetic nanoparticles for precision oncology: Theranostic magnetic iron oxide nanoparticles for image-guided and targeted cancer therapy","volume":"12","author":"Zhu","year":"2017","journal-title":"Nanomedicine"},{"key":"ref_56","doi-asserted-by":"crossref","first-page":"1775","DOI":"10.1088\/0031-9155\/60\/5\/1775","article-title":"First experimental evidence of the feasibility of multi-color magnetic particle imaging","volume":"60","author":"Rahmer","year":"2015","journal-title":"Phys. Med. Biol."},{"key":"ref_57","doi-asserted-by":"crossref","first-page":"2842","DOI":"10.1109\/TMAG.2012.2201706","article-title":"Adaptive control of excitation coil arrays for targeted magnetic nanoparticle reconstruction using magnetorelaxometry","volume":"48","author":"Coene","year":"2012","journal-title":"IEEE Trans. Magn."},{"key":"ref_58","doi-asserted-by":"crossref","first-page":"6853","DOI":"10.1118\/1.4935147","article-title":"Quantitative model selection for enhanced magnetic nanoparticle imaging in magnetorelaxometry","volume":"42","author":"Coene","year":"2015","journal-title":"Med. Phys."},{"key":"ref_59","doi-asserted-by":"crossref","first-page":"238","DOI":"10.1007\/s10851-019-00934-8","article-title":"Optimizing excitation coil currents for advanced magnetorelaxometry imaging","volume":"62","author":"Schier","year":"2020","journal-title":"J. Math. Imaging Vis."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/20\/14\/3882\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T09:50:33Z","timestamp":1760176233000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/20\/14\/3882"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,7,12]]},"references-count":59,"journal-issue":{"issue":"14","published-online":{"date-parts":[[2020,7]]}},"alternative-id":["s20143882"],"URL":"https:\/\/doi.org\/10.3390\/s20143882","relation":{},"ISSN":["1424-8220"],"issn-type":[{"type":"electronic","value":"1424-8220"}],"subject":[],"published":{"date-parts":[[2020,7,12]]}}}