Duque-Gimenez Grecia C, Zambrano-Gutierrez Daniel F, Rodriguez-Nieto Maricela, Menchaca Jorge Luis, Cruz-Duarte Jorge M, Zárate-Triviño Diana G, Avina-Cervantes Juan Gabriel, Ortiz-Bayliss José Carlos
Centro de Investigación en Ciencias Físico Matemáticas, Facultad de Ciencias Físico Matemáticas, Universidad Autónoma de Nuevo León, 66450, San Nicolás de los Garza, Nuevo León, Mexico.
School of Engineering and Sciences, Tecnologico de Monterrey, 64700, Monterrey, Nuevo León, Mexico.
Sci Rep. 2025 Aug 26;15(1):31436. doi: 10.1038/s41598-025-16174-3.
Understanding the viscoelastic properties of cells is essential for studying their mechanical behavior and identifying disease-related biomechanical markers. This paper proposes an integrated framework that combines fractional modeling with automated algorithm design to fit force-relaxation data acquired through atomic force microscopy. We employ the fractional-order zener model to describe cell relaxation curves and formulate the parameter estimation as a black-box optimization problem. To solve it, we implement a Randomized Constructive Hyper-Heuristic with Local Search (RCHH-LS) that automatically generates tailored metaheuristics (MHs) by exploring combinations of search operators. Our results show that the best-performing MH, composed of two swarm-based dynamics and a local random-walk operator ([Formula: see text]), achieves a performance of [Formula: see text], representing a 75% improvement over the mean of all candidate configurations. Subsequent hyperparameter tuning with Optuna reduces this value to [Formula: see text], a further 4.7% gain relative to the untuned version while preserving high stability and repeatability. In an evaluation of 21 instances (force-relaxation curves), the tuned [Formula: see text] provided the best result in 19 cases, achieving an average of [Formula: see text], about 12% better than the best two-operator alternative and a coefficient of variation below 0.01%, underscoring its generalization capability. The FOZ model fitted using this solver generalizes well to independent datasets and captures critical viscoelastic parameters. We also confirm that [Formula: see text], τ, and α are sensitive to the applied force via a statistical analysis, while [Formula: see text] remains stable, reinforcing its association with intrinsic cell properties. These results highlight the effectiveness of combining fractional viscoelastic modeling with automated MH design for robust and interpretable mechanical characterization of cells. The proposed approach reduces manual intervention, ensures generalizability, and offers a scalable solution for computational biomechanics.
了解细胞的粘弹性特性对于研究其力学行为和识别疾病相关的生物力学标志物至关重要。本文提出了一个综合框架，将分数阶建模与自动算法设计相结合，以拟合通过原子力显微镜获得的力松弛数据。我们采用分数阶齐纳模型来描述细胞松弛曲线，并将参数估计表述为一个黑箱优化问题。为了解决这个问题，我们实现了一种带有局部搜索的随机构造超启发式算法（RCHH-LS），该算法通过探索搜索算子的组合来自动生成定制的元启发式算法（MHs）。我们的结果表明，性能最佳的MH由两种基于群体的动力学和一个局部随机游走算子（[公式：见原文]）组成，其性能达到了[公式：见原文]，比所有候选配置的平均值提高了75%。随后使用Optuna进行超参数调整将该值降低到了[公式：见原文]，相对于未调整版本又提高了4.7%，同时保持了高稳定性和可重复性。在对21个实例（力松弛曲线）的评估中，调整后的[公式：见原文]在19个案例中提供了最佳结果，平均达到了[公式：见原文]，比最佳的双算子替代方案高出约12%，变异系数低于0.01%，突出了其泛化能力。使用该求解器拟合的分数阶齐纳（FOZ）模型能够很好地推广到独立数据集，并捕捉到关键的粘弹性参数。我们还通过统计分析证实，[公式：见原文]、τ和α对所施加的力敏感，而[公式：见原文]保持稳定，加强了其与细胞固有特性的关联。这些结果突出了将分数阶粘弹性建模与自动MH设计相结合用于细胞稳健且可解释的力学表征的有效性。所提出的方法减少了人工干预，确保了泛化性，并为计算生物力学提供了一种可扩展的解决方案。
