A mathematical phase field model predicts superparamagnetic nanoparticle accelerated fusion of HeLa spheroids for field guided biofabrication
Abstract In vitro tissue models are crucial for regenerative medicine, drug discovery, and the reduction of animal testing. 3D bioprinting, particularly when utilizing magnetic manipulation of cell spheroids, provides precise control over tissue architecture. However, existing mathematical models la...
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| Format: | Article |
| Language: | English |
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Nature Portfolio
2025-06-01
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| Series: | Scientific Reports |
| Online Access: | https://doi.org/10.1038/s41598-025-04495-2 |
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| author | Cristian F. Rodríguez Valentina Quezada Paula Guzmán-Sastoque Juan Camilo Orozco Luis H. Reyes Johann F. Osma Carolina Muñoz-Camargo Juan C. Cruz |
| author_facet | Cristian F. Rodríguez Valentina Quezada Paula Guzmán-Sastoque Juan Camilo Orozco Luis H. Reyes Johann F. Osma Carolina Muñoz-Camargo Juan C. Cruz |
| author_sort | Cristian F. Rodríguez |
| collection | DOAJ |
| description | Abstract In vitro tissue models are crucial for regenerative medicine, drug discovery, and the reduction of animal testing. 3D bioprinting, particularly when utilizing magnetic manipulation of cell spheroids, provides precise control over tissue architecture. However, existing mathematical models lack the precision to capture the interplay between biological dynamics and magnetic forces during spheroid fusion. This study developed and validated a novel mathematical model that simulates magnetically assisted spheroid fusion, taking into account cell migration, adhesion, and the effects of external magnetic fields. The model integrates principles of cell mechanics, fluid dynamics, and magnetostatics, implemented in COMSOL Multiphysics. Experimental validation used HeLa cell spheroids bioprinted with superparamagnetic iron oxide nanoparticles (SPIONs). Spheroid fusion was monitored with and without an external magnetic field using confocal microscopy. Rigorous statistical analysis (MAE, RMSE, MAPE, R², Chi-Square, Bland-Altman, and variance-weighted metrics) was used to evaluate model performance. The model accurately predicted accelerated fusion under magnetic manipulation, reducing fusion time from approximately 7 days (without field) to 2 days. High R² values (> 0.99 for two-spheroid fusion and > 0.97 for multi-spheroid systems) and narrow confidence intervals demonstrated strong agreement between the simulation and the experiment. Increased system complexity introduced slightly higher error variability, but the model maintained robust predictive capabilities. Spheroid disassembly was observed in the four-spheroid case, highlighting the complex interplay of magnetic forces and cellular reorganization. This validated, high-precision model represents a significant advancement in tissue engineering, providing a powerful tool for optimizing bioprinting protocols, designing complex tissue constructs, and advancing in vitro model development. This breakthrough has implications for regenerative medicine and drug discovery while also highlighting the importance of addressing nanoparticle safety concerns. |
| format | Article |
| id | doaj-art-b6d41bc59fce41cfa35600029c697fa3 |
| institution | DOAJ |
| issn | 2045-2322 |
| language | English |
| publishDate | 2025-06-01 |
| publisher | Nature Portfolio |
| record_format | Article |
| series | Scientific Reports |
| spelling | doaj-art-b6d41bc59fce41cfa35600029c697fa32025-08-20T03:10:36ZengNature PortfolioScientific Reports2045-23222025-06-0115112910.1038/s41598-025-04495-2A mathematical phase field model predicts superparamagnetic nanoparticle accelerated fusion of HeLa spheroids for field guided biofabricationCristian F. Rodríguez0Valentina Quezada1Paula Guzmán-Sastoque2Juan Camilo Orozco3Luis H. Reyes4Johann F. Osma5Carolina Muñoz-Camargo6Juan C. Cruz7Department of Biomedical Engineering, Universidad de Los AndesDepartment of Biomedical Engineering, Universidad de Los AndesDepartment of Biomedical Engineering, Universidad de Los AndesCentro de Microscopia (MicroCore), Vicerrectoría de investigación y creación, Universidad de Los AndesGrupo de Diseño de Productos y Procesos (GDPP), Department of Chemical Engineering, Universidad de Los AndesDepartment of Biomedical Engineering, Universidad de Los AndesDepartment of Biomedical Engineering, Universidad de Los AndesDepartment of Biomedical Engineering, Universidad de Los AndesAbstract In vitro tissue models are crucial for regenerative medicine, drug discovery, and the reduction of animal testing. 3D bioprinting, particularly when utilizing magnetic manipulation of cell spheroids, provides precise control over tissue architecture. However, existing mathematical models lack the precision to capture the interplay between biological dynamics and magnetic forces during spheroid fusion. This study developed and validated a novel mathematical model that simulates magnetically assisted spheroid fusion, taking into account cell migration, adhesion, and the effects of external magnetic fields. The model integrates principles of cell mechanics, fluid dynamics, and magnetostatics, implemented in COMSOL Multiphysics. Experimental validation used HeLa cell spheroids bioprinted with superparamagnetic iron oxide nanoparticles (SPIONs). Spheroid fusion was monitored with and without an external magnetic field using confocal microscopy. Rigorous statistical analysis (MAE, RMSE, MAPE, R², Chi-Square, Bland-Altman, and variance-weighted metrics) was used to evaluate model performance. The model accurately predicted accelerated fusion under magnetic manipulation, reducing fusion time from approximately 7 days (without field) to 2 days. High R² values (> 0.99 for two-spheroid fusion and > 0.97 for multi-spheroid systems) and narrow confidence intervals demonstrated strong agreement between the simulation and the experiment. Increased system complexity introduced slightly higher error variability, but the model maintained robust predictive capabilities. Spheroid disassembly was observed in the four-spheroid case, highlighting the complex interplay of magnetic forces and cellular reorganization. This validated, high-precision model represents a significant advancement in tissue engineering, providing a powerful tool for optimizing bioprinting protocols, designing complex tissue constructs, and advancing in vitro model development. This breakthrough has implications for regenerative medicine and drug discovery while also highlighting the importance of addressing nanoparticle safety concerns.https://doi.org/10.1038/s41598-025-04495-2 |
| spellingShingle | Cristian F. Rodríguez Valentina Quezada Paula Guzmán-Sastoque Juan Camilo Orozco Luis H. Reyes Johann F. Osma Carolina Muñoz-Camargo Juan C. Cruz A mathematical phase field model predicts superparamagnetic nanoparticle accelerated fusion of HeLa spheroids for field guided biofabrication Scientific Reports |
| title | A mathematical phase field model predicts superparamagnetic nanoparticle accelerated fusion of HeLa spheroids for field guided biofabrication |
| title_full | A mathematical phase field model predicts superparamagnetic nanoparticle accelerated fusion of HeLa spheroids for field guided biofabrication |
| title_fullStr | A mathematical phase field model predicts superparamagnetic nanoparticle accelerated fusion of HeLa spheroids for field guided biofabrication |
| title_full_unstemmed | A mathematical phase field model predicts superparamagnetic nanoparticle accelerated fusion of HeLa spheroids for field guided biofabrication |
| title_short | A mathematical phase field model predicts superparamagnetic nanoparticle accelerated fusion of HeLa spheroids for field guided biofabrication |
| title_sort | mathematical phase field model predicts superparamagnetic nanoparticle accelerated fusion of hela spheroids for field guided biofabrication |
| url | https://doi.org/10.1038/s41598-025-04495-2 |
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