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Best Practices in Developing a Workflow for Uncertainty Quantification for Modeling the Biodegradation of Mg-Based

Tamadur AlBaraghtheh^1,2, Regine Willumeit-Römer¹, Berit Zeller-Plumhoff^1,3

¹Institute of Metallic Biomaterials, Helmholtz-Zentrum hereon GmbH, Max-Planck-Straße 1, 21502, Geesthacht, Germany.

Advanced Science (Weinheim, Baden-Wurttemberg, Germany)

|October 25, 2024

Summary

Quantifying uncertainty in magnesium implant biodegradation models is crucial. This study introduces a workflow using surrogate models, finding Kriging efficient for calibration and polynomial chaos methods better for predicting uncertainties.

Keywords:

UQ biodegradable Mg‐implants propagation surrogate model uncertainty

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Area of Science:

Biomaterials Science
Computational Modeling
Materials Engineering

Background:

Computational models for magnesium (Mg)-based implant biodegradation are essential but face significant uncertainty.
Iterative evaluations are needed to quantify this uncertainty, posing a challenge for complex, multiscale models.
Surrogate models offer a computationally efficient alternative to high-cost, complex models, but their application to biodegradation is understudied.

Purpose of the Study:

To develop and evaluate a workflow for quantifying uncertainties in Mg-based implant biodegradation models.
To compare the performance of three surrogate models: Kriging, polynomial chaos expansion (PCE), and polynomial chaos Kriging (PCK).
To assess the suitability of these surrogate models for global sensitivity analysis and uncertainty propagation.

Main Methods:

Implementation of a workflow for uncertainty quantification in biodegradation models.
Construction and evaluation of Kriging, PCE, and PCK surrogate models.
Testing surrogate models against three computational models of Mg-based implant biodegradation.
Application of global sensitivity analysis and uncertainty propagation.

Main Results:

Kriging demonstrated effectiveness in calibrating computational models with reduced computational time and cost.
Polynomial chaos expansion and polynomial chaos Kriging showed superior capability in predicting propagated uncertainties.
The study successfully quantified different types of uncertainty within the biodegradation models.

Conclusions:

The developed workflow provides a robust method for uncertainty quantification in Mg-based implant biodegradation.
Kriging is recommended for model calibration due to its efficiency, while PCE and PCK are better suited for uncertainty propagation analysis.
This research addresses the understudied application of surrogate modeling for complex degradation processes in biomedical implants.