{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,14]],"date-time":"2026-09-14T20:08:59Z","timestamp":1789416539679,"version":"build-2803163510"},"reference-count":35,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2026,5,15]],"date-time":"2026-05-15T00:00:00Z","timestamp":1778803200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100000780","name":"European Union","doi-asserted-by":"publisher","award":["732678"],"award-info":[{"award-number":["732678"]}],"id":[{"id":"10.13039\/501100000780","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100000780","name":"European Union","doi-asserted-by":"publisher","award":["952183"],"award-info":[{"award-number":["952183"]}],"id":[{"id":"10.13039\/501100000780","id-type":"DOI","asserted-by":"publisher"}]},{"award":["732678"],"award-info":[{"award-number":["732678"]}],"id":[{"id":"https:\/\/ror.org\/019w4f821","id-type":"ROR","asserted-by":"publisher"}]},{"award":["952183"],"award-info":[{"award-number":["952183"]}],"id":[{"id":"https:\/\/ror.org\/019w4f821","id-type":"ROR","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Bioengineering"],"abstract":"<jats:p>Magnetizing living cells with superparamagnetic iron oxide nanoparticles (SPIONs) enables their remote manipulation using external magnetic field. This lays the foundation for magnetically assembling tissue precursors within cell-friendly, proliferation-permissive environments and holds considerable promise for biomedical applications, particularly in the development of complex single- and multicellular tissue constructs for bone and organ reconstruction. However, progress in this field is limited by the lack of robust mathematical tools for accurate control of ensembles of magnetic nano- and micro-objects. In practical printing scenarios, collective behavior and unavoidable statistical heterogeneity\u2014such as variations in SPION size and shape or deviations in cell magnetization\u2014render traditional equation-based modeling inadequate. We developed a hybrid modeling framework integrating conventional physics-based simulations with artificial intelligence-driven image analysis. Dynamic parameters were extracted from video recordings of magnetized cells moving within model microfluidic devices exposed to well-defined magnetic fields and gradients. The AI-based analysis enabled quantitative characterization of ensemble behavior under heterogeneous conditions. The proposed framework successfully captured the collective dynamics of magnetized cell ensembles and enabled accurate control of their spatial organization under external magnetic actuation. The integration of simulation and data-driven analysis provided robust parameter identification despite statistical heterogeneity within the system. This integrated modeling approach provides a practical and effective tool for controlling the three-dimensional magnetic assembly of living cells, with strong potential for applications in tissue engineering.<\/jats:p>","DOI":"10.3390\/bioengineering13050560","type":"journal-article","created":{"date-parts":[[2026,5,19]],"date-time":"2026-05-19T16:07:26Z","timestamp":1779206846000},"page":"560","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Advanced Mathematical Platform for the Control and Manipulation of Magnetized Living Cells"],"prefix":"10.3390","volume":"13","author":[{"given":"Vitaly","family":"Goranov","sequence":"first","affiliation":[{"name":"Institute for Nanostructured Materials, CNR-ISMN, 40129 Bologna, Italy"},{"name":"BioDevice Systems s.r.o., Vr\u0161ovice, 10100 Prague, Czech Republic"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7146-8696","authenticated-orcid":false,"given":"Tatiana","family":"Shelyakova","sequence":"additional","affiliation":[{"name":"Surgical Science and Technologies, IRCCS Istituto Ortopedico Rizzoli, 40136 Bologna, Italy"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jaroslav","family":"Ko\u0161t\u00e1l","sequence":"additional","affiliation":[{"name":"BioDevice Systems s.r.o., Vr\u0161ovice, 10100 Prague, Czech Republic"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Alexander","family":"Makhaniok","sequence":"additional","affiliation":[{"name":"BioDevice Systems s.r.o., Vr\u0161ovice, 10100 Prague, Czech Republic"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7843-5969","authenticated-orcid":false,"given":"Gianluca","family":"Giavaresi","sequence":"additional","affiliation":[{"name":"Surgical Science and Technologies, IRCCS Istituto Ortopedico Rizzoli, 40136 Bologna, Italy"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Valentin Alek","family":"Dediu","sequence":"additional","affiliation":[{"name":"Institute for Nanostructured Materials, CNR-ISMN, 40129 Bologna, Italy"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2026,5,15]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Mirsky, N.A., Ehlen, Q.T., Greenfield, J.A., Antonietti, M., Slavin, B.V., Nayak, V.V., Pelaez, D., Tse, D.T., Witek, L., and Daunert, S. 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