{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,27]],"date-time":"2026-05-27T18:34:08Z","timestamp":1779906848051,"version":"3.53.1"},"reference-count":44,"publisher":"MDPI AG","issue":"17","license":[{"start":{"date-parts":[[2021,8,31]],"date-time":"2021-08-31T00:00:00Z","timestamp":1630368000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100008530","name":"European Regional Development Fund","doi-asserted-by":"publisher","award":["EFRE-0801299"],"award-info":[{"award-number":["EFRE-0801299"]}],"id":[{"id":"10.13039\/501100008530","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Magnetic immunoassays employing Frequency Mixing Magnetic Detection (FMMD) have recently become increasingly popular for quantitative detection of various analytes. Simultaneous analysis of a sample for two or more targets is desirable in order to reduce the sample amount, save consumables, and save time. We show that different types of magnetic beads can be distinguished according to their frequency mixing response to a two-frequency magnetic excitation at different static magnetic offset fields. We recorded the offset field dependent FMMD response of two different particle types at frequencies f1 + n\u22c5f2, n = 1, 2, 3, 4 with f1 = 30.8 kHz and f2 = 63 Hz. Their signals were clearly distinguishable by the locations of the extremes and zeros of their responses. Binary mixtures of the two particle types were prepared with different mixing ratios. The mixture samples were analyzed by determining the best linear combination of the two pure constituents that best resembled the measured signals of the mixtures. Using a quadratic programming algorithm, the mixing ratios could be determined with an accuracy of greater than 14%. If each particle type is functionalized with a different antibody, multiplex detection of two different analytes becomes feasible.<\/jats:p>","DOI":"10.3390\/s21175859","type":"journal-article","created":{"date-parts":[[2021,8,31]],"date-time":"2021-08-31T22:58:15Z","timestamp":1630450695000},"page":"5859","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":16,"title":["Multiplex Detection of Magnetic Beads Using Offset Field Dependent Frequency Mixing Magnetic Detection"],"prefix":"10.3390","volume":"21","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-6904-1447","authenticated-orcid":false,"given":"Ali Mohammad","family":"Pourshahidi","sequence":"first","affiliation":[{"name":"Institute of Biological Information Processing-Biolelectronics (IBI-3), Forschungszentrum J\u00fclich, 52425 J\u00fclich, Germany"},{"name":"Faculty of Mathematics, Computer Science and Natural Sciences, RWTH Aachen University, 52062 Aachen, Germany"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0666-912X","authenticated-orcid":false,"given":"Stefan","family":"Achtsnicht","sequence":"additional","affiliation":[{"name":"Institute of Biological Information Processing-Biolelectronics (IBI-3), Forschungszentrum J\u00fclich, 52425 J\u00fclich, Germany"},{"name":"Institute of Nano- and Biotechnologies (INB), FH Aachen University of Applied Sciences, 52428 J\u00fclich, Germany"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Mrinal Murali","family":"Nambipareechee","sequence":"additional","affiliation":[{"name":"Institute of Biological Information Processing-Biolelectronics (IBI-3), Forschungszentrum J\u00fclich, 52425 J\u00fclich, Germany"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6143-2702","authenticated-orcid":false,"given":"Andreas","family":"Offenh\u00e4usser","sequence":"additional","affiliation":[{"name":"Institute of Biological Information Processing-Biolelectronics (IBI-3), Forschungszentrum J\u00fclich, 52425 J\u00fclich, Germany"},{"name":"Faculty of Mathematics, Computer Science and Natural Sciences, RWTH Aachen University, 52062 Aachen, Germany"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7526-9894","authenticated-orcid":false,"given":"Hans-Joachim","family":"Krause","sequence":"additional","affiliation":[{"name":"Institute of Biological Information Processing-Biolelectronics (IBI-3), Forschungszentrum J\u00fclich, 52425 J\u00fclich, Germany"},{"name":"Institute of Nano- and Biotechnologies (INB), FH Aachen University of Applied Sciences, 52428 J\u00fclich, Germany"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2021,8,31]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Chen, Y.-T., Kolhatkar, A.G., Zenasni, O., Xu, S., and Lee, T.R. (2017). Biosensing Using Magnetic Particle Detection Techniques. Sensors, 17.","DOI":"10.3390\/s17102300"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"4307","DOI":"10.1021\/acsanm.1c01077","article-title":"Magnetic Nanomaterials in Microfluidic Sensors for Virus Detection: A Review","volume":"4","author":"Jalal","year":"2021","journal-title":"ACS Appl. Nano Mater."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"315","DOI":"10.18383\/j.tom.2020.00043","article-title":"A Perspective on Cell Tracking with Magnetic Particle Imaging","volume":"6","author":"Sehl","year":"2020","journal-title":"Tomography"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"116","DOI":"10.1016\/j.jmr.2012.11.029","article-title":"Magnetic Particle Imaging (MPI) for NMR and MRI Researchers","volume":"229","author":"Saritas","year":"2013","journal-title":"J. Magn. Reson."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"24","DOI":"10.3390\/brainsci11030358","article-title":"Use of Super Paramagnetic Iron Oxide Nanoparticles as Drug Carriers in Brain and Ear: State of the Art and Challenges","volume":"11","author":"Guigou","year":"2021","journal-title":"Brain Sci."},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Jacob, A., and Chakravarthy, K. (2014). Engineering Magnetic Nanoparticles for Thermo-Ablation and Drug Delivery in Neurological Cancers. Cureus.","DOI":"10.7759\/cureus.170"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"512","DOI":"10.1021\/acsanm.7b00025","article-title":"Recent Advances Incorporating Superparamagnetic Nanoparticles into Immunoassays","volume":"1","author":"Ha","year":"2018","journal-title":"ACS Appl. Nano Mater."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"4411","DOI":"10.1007\/s11051-011-0551-4","article-title":"Biochemical and Biomedical Applications of Multifunctional Magnetic Nanoparticles: A Review","volume":"13","author":"Huang","year":"2011","journal-title":"J. Nanoparticle Res."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"134","DOI":"10.1016\/j.snb.2018.12.110","article-title":"Rapid Detection of Salmonella Typhimurium Using Magnetic Nanoparticle Immunoseparation, Nanocluster Signal Amplification and Smartphone Image Analysis","volume":"284","author":"Guo","year":"2019","journal-title":"Sens. Actuators B Chem."},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Liu, P., Jonkheijm, P., Terstappen, L.W.M.M., and Stevens, M. (2020). Magnetic Particles for CTC Enrichment. Cancers, 12.","DOI":"10.3390\/cancers12123525"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"945","DOI":"10.1016\/j.bios.2003.09.005","article-title":"Biomolecular Reactions Studied Using Changes in Brownian Rotation Dynamics of Magnetic Particles","volume":"19","author":"Astalan","year":"2004","journal-title":"Biosens. Bioelectron."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"3678","DOI":"10.1109\/77.622216","article-title":"SQUID Based Remanence Measurements for Immunoassays","volume":"7","author":"Kotitz","year":"1997","journal-title":"IEEE Trans. Appl. Supercond."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"436","DOI":"10.1016\/j.jmmm.2006.10.1164","article-title":"Magnetic Particle Detection by Frequency Mixing for Immunoassay Applications","volume":"311","author":"Krause","year":"2007","journal-title":"J. Magn. Magn. Mater."},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Pietschmann, J., Spiegel, H., Krause, H.-J., Schillberg, S., and Schr\u00f6per, F. (2020). Sensitive Aflatoxin B1 Detection Using Nanoparticle-Based Competitive Magnetic Immunodetection. Toxins, 12.","DOI":"10.3390\/toxins12050337"},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Pietschmann, J., Dittmann, D., Spiegel, H., Krause, H.-J., and Schr\u00f6per, F. (2020). A Novel Method for Antibiotic Detection in Milk Based on Competitive Magnetic Immunodetection. Foods, 9.","DOI":"10.3390\/foods9121773"},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Achtsnicht, S., Neuendorf, C., Fa\u00dfbender, T., N\u00f6lke, G., Offenh\u00e4usser, A., Krause, H.-J., and Schr\u00f6per, F. (2019). Sensitive and Rapid Detection of Cholera Toxin Subunit B Using Magnetic Frequency Mixing Detection. PLoS ONE, 14.","DOI":"10.1371\/journal.pone.0219356"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"259","DOI":"10.1016\/j.jmmm.2006.10.1175","article-title":"Francisella Tularensis Detection Using Magnetic Labels and a Magnetic Biosensor Based on Frequency Mixing","volume":"311","author":"Meyer","year":"2007","journal-title":"J. Magn. Magn. Mater."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"973","DOI":"10.1016\/j.bios.2006.04.001","article-title":"CRP Determination Based on a Novel Magnetic Biosensor","volume":"22","author":"Meyer","year":"2007","journal-title":"Biosens. Bioelectron."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"3039","DOI":"10.1128\/AEM.03667-14","article-title":"Simple and Portable Magnetic Immunoassay for Rapid Detection and Sensitive Quantification of Plant Viruses","volume":"81","author":"Rettcher","year":"2015","journal-title":"Appl. Environ. Microbiol."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"13686","DOI":"10.1021\/acsami.0c00815","article-title":"Magnetic Particle Spectroscopy for Detection of Influenza A Virus Subtype H1N1","volume":"12","author":"Wu","year":"2020","journal-title":"ACS Appl. Mater. Interfaces"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"5611","DOI":"10.1021\/ac5010458","article-title":"Fluorescent Probe-Based Lateral Flow Assay for Multiplex Nucleic Acid Detection","volume":"86","author":"Xu","year":"2014","journal-title":"Anal. Chem."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"e180323","DOI":"10.1155\/2014\/180323","article-title":"Rapid and Sensitive PCR-Dipstick DNA Chromatography for Multiplex Analysis of the Oral Microbiota","volume":"2014","author":"Tian","year":"2014","journal-title":"BioMed Res. Int."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"124","DOI":"10.1007\/s12274-012-0193-6","article-title":"Multiplexed Dot Immunoassay Using Ag Nanocubes, Au\/Ag Alloy Nanoparticles, and Au\/Ag Nanocages","volume":"5","author":"Panfilova","year":"2012","journal-title":"Nano Res."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"2360","DOI":"10.1039\/b926041m","article-title":"Magnetic Relaxation-Based Platform for Multiplexed Assays","volume":"135","author":"Ling","year":"2010","journal-title":"Analyst"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"20637","DOI":"10.1073\/pnas.0810822105","article-title":"Multiplex Protein Assays Based on Real-Time Magnetic Nanotag Sensing","volume":"105","author":"Osterfeld","year":"2008","journal-title":"Proc. Natl. Acad. Sci. USA"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"455101","DOI":"10.1088\/0957-4484\/21\/45\/455101","article-title":"Simultaneous Quantification of Multiple Magnetic Nanoparticles","volume":"21","author":"Rauwerdink","year":"2010","journal-title":"Nanotechnology"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"2587","DOI":"10.1118\/1.3426294","article-title":"Harmonic Phase Angle as a Concentration-Independent Measure of Nanoparticle Dynamics: Harmonic Phase Angle as Measure of Nanoparticle Dynamics","volume":"37","author":"Rauwerdink","year":"2010","journal-title":"Med. Phys."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"1136","DOI":"10.1118\/1.3549762","article-title":"Concurrent Quantification of Multiple Nanoparticle Bound States","volume":"38","author":"Rauwerdink","year":"2011","journal-title":"Med. Phys."},{"key":"ref_29","doi-asserted-by":"crossref","unstructured":"Achtsnicht, S., T\u00f6dter, J., Niehues, J., Tel\u00f6ken, M., Offenh\u00e4usser, A., Krause, H.-J., and Schr\u00f6per, F. (2019). 3D Printed Modular Immunofiltration Columns for Frequency Mixing-Based Multiplex Magnetic Immunodetection. Sensors, 19.","DOI":"10.3390\/s19010148"},{"key":"ref_30","doi-asserted-by":"crossref","unstructured":"Achtsnicht, S., Pourshahidi, A.M., Offenh\u00e4usser, A., and Krause, H.-J. (2019). Multiplex Detection of Different Magnetic Beads Using Frequency Scanning in Magnetic Frequency Mixing Technique. Sensors, 19.","DOI":"10.3390\/s19112599"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"251","DOI":"10.1016\/j.jmmm.2014.10.034","article-title":"Colorize Magnetic Nanoparticles Using a Search Coil Based Testing Method","volume":"380","author":"Wu","year":"2015","journal-title":"J. Magn. Magn. Mater."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"155001","DOI":"10.1088\/0022-3727\/47\/15\/155001","article-title":"Magnetic Nanoparticles Colourization by a Mixing-Frequency Method","volume":"47","author":"Tu","year":"2014","journal-title":"J. Phys. Appl. Phys."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"4972","DOI":"10.1021\/acsanm.0c00890","article-title":"Magnetic Particle Spectroscopy: A Short Review of Applications Using Magnetic Nanoparticles","volume":"3","author":"Wu","year":"2020","journal-title":"ACS Appl. Nano Mater."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"1639","DOI":"10.1016\/j.jmmm.2009.02.104","article-title":"Multiparametric Magnetic Immunoassays Utilizing Non-Linear Signatures of Magnetic Labels","volume":"321","author":"Lenglet","year":"2009","journal-title":"J. Magn. Magn. Mater."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"786","DOI":"10.1016\/j.snb.2010.04.009","article-title":"Different Signatures between Chemically and Biologically Synthesized Nanoparticles in a Magnetic Sensor: A New Technology for Multiparametric Detection","volume":"147","author":"Lijeour","year":"2010","journal-title":"Sens. Actuators B Chem."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"6274","DOI":"10.1021\/acsomega.0c05845","article-title":"Investigation of Commercial Iron Oxide Nanoparticles: Structural and Magnetic Property Characterization","volume":"6","author":"Wu","year":"2021","journal-title":"ACS Omega"},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"156","DOI":"10.1016\/j.jmmm.2016.11.003","article-title":"Dual-frequency magnetic particle imaging of the Brownian particle contribution","volume":"427","author":"Viereck","year":"2017","journal-title":"J. Magn. Magn. Mater."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"083001","DOI":"10.1088\/1367-2630\/aad44b","article-title":"Viscosity quantification using multi-contrast magnetic particle imaging","volume":"20","author":"Meins","year":"2018","journal-title":"New J. Phys."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"074001","DOI":"10.1088\/1361-6560\/ab0fc9","article-title":"Discriminating nanoparticle core size using multi-contrast MPI","volume":"64","author":"Shasha","year":"2019","journal-title":"Phys. Med. Biol."},{"key":"ref_40","doi-asserted-by":"crossref","unstructured":"Krishnan, K.M. (2016). Fundamentals and Applications of Magnetic Materials, Oxford University Press.","DOI":"10.1093\/acprof:oso\/9780199570447.001.0001"},{"key":"ref_41","doi-asserted-by":"crossref","unstructured":"Engelmann, U.M., Shalaby, A., Shasha, C., Krishnan, K.M., and Krause, H.-J. (2021). Comparative Modeling of Frequency Mixing Measurements of Magnetic Nanoparticles Using Micromagnetic Simulations and Langevin Theory. Nanomaterials, 11.","DOI":"10.3390\/nano11051257"},{"key":"ref_42","unstructured":"Engelmann, U.M., Fitter, J.L., and Baumann, M. (2019). Assessing Magnetic Fluid Hyperthermia: Magnetic Relaxation Simulation, Modeling of Nanoparticle Uptake inside Pancreatic Tumor Cells and in Vitro Efficacy, Infinite Science Publishing."},{"key":"ref_43","doi-asserted-by":"crossref","unstructured":"Nocedal, J., and Wright, S.J. (1999). Numerical Optimization, Springer.","DOI":"10.1007\/b98874"},{"key":"ref_44","unstructured":"Murty, K.G. (1988). Linear Complementarity, Linear and Nonlinear Programming, Heldermann."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/21\/17\/5859\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T06:53:06Z","timestamp":1760165586000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/21\/17\/5859"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,8,31]]},"references-count":44,"journal-issue":{"issue":"17","published-online":{"date-parts":[[2021,9]]}},"alternative-id":["s21175859"],"URL":"https:\/\/doi.org\/10.3390\/s21175859","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,8,31]]}}}