Rodríguez Cristian F, Quezada Valentina, Guzmán-Sastoque Paula, Orozco Juan Camilo, Reyes Luis H, Osma Johann F, Muñoz-Camargo Carolina, Cruz Juan C
Department of Biomedical Engineering, Universidad de Los Andes, Cra. 1E No. 19a-40, 111711, Bogotá, Colombia.
Neuroscience Group of Antioquia, Cellular and Molecular Neurobiology Area, School of Medicine, SIU, University of Antioquia, Medellín, Colombia.
Sci Rep. 2025 Jun 5;15(1):19765. doi: 10.1038/s41598-025-04495-2.
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.
体外组织模型对于再生医学、药物发现以及减少动物实验至关重要。三维生物打印，特别是在利用细胞球体的磁操纵时，能够对组织结构进行精确控制。然而，现有的数学模型缺乏精确性，无法捕捉球体融合过程中生物动力学和磁力之间的相互作用。本研究开发并验证了一种新型数学模型，该模型模拟了磁辅助球体融合，同时考虑了细胞迁移、粘附以及外部磁场的影响。该模型整合了细胞力学、流体动力学和静磁学原理，并在COMSOL Multiphysics中实现。实验验证使用了用超顺磁性氧化铁纳米颗粒（SPIONs）生物打印的HeLa细胞球体。使用共聚焦显微镜监测有无外部磁场时的球体融合情况。采用严格的统计分析（平均绝对误差、均方根误差、平均绝对百分比误差、决定系数、卡方检验、布兰德 - 奥特曼分析和方差加权指标）来评估模型性能。该模型准确预测了磁操纵下的加速融合，将融合时间从大约7天（无磁场）减少到2天。高决定系数值（双球体融合时>0.99，多球体系统时>0.97）和狭窄的置信区间表明模拟结果与实验结果高度一致。系统复杂性的增加导致误差变异性略有提高，但该模型仍保持强大的预测能力。在四球体情况下观察到了球体解体，突出了磁力与细胞重组之间复杂的相互作用。这个经过验证的高精度模型代表了组织工程领域的一项重大进展，为优化生物打印方案、设计复杂组织构建体以及推进体外模型开发提供了一个强大的工具。这一突破对再生医学和药物发现具有重要意义，同时也凸显了解决纳米颗粒安全问题的重要性。
