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

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 acq...

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Published in:Scientific reports Vol. 15; no. 1; pp. 31436 - 25
Main Authors: 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
Format: Journal Article
Language:English
Published: London Nature Publishing Group UK 26.08.2025
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ISSN:2045-2322, 2045-2322
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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 ( ), achieves a performance of , representing a 75% improvement over the mean of all candidate configurations. Subsequent hyperparameter tuning with Optuna reduces this value to , 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 provided the best result in 19 cases, achieving an average of , 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 , , and are sensitive to the applied force via a statistical analysis, while 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.
AbstractList 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.
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.
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.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.
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.
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 ( ), achieves a performance of , representing a 75% improvement over the mean of all candidate configurations. Subsequent hyperparameter tuning with Optuna reduces this value to , 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 provided the best result in 19 cases, achieving an average of , 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 , , and are sensitive to the applied force via a statistical analysis, while 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.
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 ( ), achieves a performance of , representing a 75% improvement over the mean of all candidate configurations. Subsequent hyperparameter tuning with Optuna reduces this value to , 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 provided the best result in 19 cases, achieving an average of , 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 , , and are sensitive to the applied force via a statistical analysis, while 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.
ArticleNumber 31436
Author Cruz-Duarte, Jorge M.
Zárate-Triviño, Diana G.
Avina-Cervantes, Juan Gabriel
Menchaca, Jorge Luis
Duque-Gimenez, Grecia C.
Zambrano-Gutierrez, Daniel F.
Ortiz-Bayliss, José Carlos
Rodriguez-Nieto, Maricela
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  fullname: Rodriguez-Nieto, Maricela
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  givenname: Diana G.
  surname: Zárate-Triviño
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  givenname: Juan Gabriel
  surname: Avina-Cervantes
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BackLink https://www.ncbi.nlm.nih.gov/pubmed/40858862$$D View this record in MEDLINE/PubMed
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Issue 1
Keywords Viscoelasticity
Atomic force microscopy
Metaheuristic
Fractional-order zener model
Automated algorithm design
Cells
Hyper-heuristic
Language English
License 2025. The Author(s).
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Snippet Understanding the viscoelastic properties of cells is essential for studying their mechanical behavior and identifying disease-related biomechanical markers....
Abstract Understanding the viscoelastic properties of cells is essential for studying their mechanical behavior and identifying disease-related biomechanical...
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SubjectTerms 639/166/985
639/705/117
Algorithms
Atomic force microscopy
Automation
Biomechanical Phenomena
Biomechanics
Bone cancer
Calculus
Cell Line, Tumor
Cells
Coefficient of variation
Design
Elasticity
Fractional-order zener model
Heuristic
Humanities and Social Sciences
Humans
Hyper-heuristic
Laplace transforms
Mechanical properties
Metaheuristic
Microscopy, Atomic Force
multidisciplinary
Optimization
Osteosarcoma
Osteosarcoma - pathology
Parameter estimation
Physiology
Science
Science (multidisciplinary)
Statistical analysis
Viscoelasticity
Viscosity
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Title Viscoelastic characterization of the human osteosarcoma cancer cell line MG-63 using a fractional-order zener model through automated algorithm design and configuration
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