Viscoelastic characterization of the human osteosarcoma cancer cell line MG-63 using a fractional-order zener model through automated algorithm design and configuration

Abstract

Abstract 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 ( $$\text {MH}_{*}^3$$ ), achieves a performance of $$3.00\times 10^{-3}$$ , representing a 75% improvement over the mean of all candidate configurations. Subsequent hyperparameter tuning with Optuna reduces this value to $$2.86\times 10^{-3}\pm 2.43\times 10^{-7}$$ , 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 $$\text {MH}_{*}^3$$ provided the best result in 19 cases, achieving an average of $$3.31\times 10^{-3}$$ , 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 $$E_1$$ , $$\tau$$ , and $$\alpha$$ are sensitive to the applied force via a statistical analysis, while $$E_0$$ 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.