# Utilizing Computational Modelling to Bridge the Gap between In Vivo and In Vitro Degradation Rates for Mg-xGd Implants

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## Abstract

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## 1. Introduction

## 2. Materials and Methods

#### 2.1. Model Calibration Data

#### 2.2. Peridynamic Model and Implementation

#### 2.3. Kriging-Based Surrogate Model and Implementation

## 3. Results and Discussion

## 4. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 2.**The sampling domain of ${\chi}_{s}^{2}$ and ${\chi}_{l}^{2}$ generated using the LHS technique.

**Figure 3.**Comparison between the QoI (VL) computed by the PD model and corresponding Kriging surrogate models predictions (

**a**) Mg-5Gd in vitro, (

**b**) Mg-5Gd in vivo. (

**c**) Mg-10Gd in vitro and (

**d**) Mg-10Gd in vivo.

**Figure 4.**(

**a**) Experimental (single data points displaying mean ± standard deviation) and Kriging-based surrogate model simulations of volume loss of in vitro and in vivo for Mg-5Gd and Mg-10Gd, respectively. (

**b**) The degradation rate calculated based on the volume loss. The VL was determined from $\mathsf{\mu}$CT measurements as published in [8,38].

**Table 1.**The optimized parameters of in vitro and in vivo measured via the Kriging-based surrogate models and the MAE with respect to the experimental data.

In Vitro | In Vivo | |||
---|---|---|---|---|

Mg-5Gd | Mg-10Gd | Mg-5Gd | Mg-10Gd | |

${\chi}_{s}^{2}$ [m${}^{2}$/s] | $2.9\times {10}^{-15}$ | $1.78\times {10}^{-15}$ | $7.8\times {10}^{-14}$ | $9.6\times {10}^{-14}$ |

${\chi}_{l}^{2}$ [m${}^{2}$/s] | $8.7\times {10}^{-9}$ | $1.44\times {10}^{-9}$ | $5.4\times {10}^{-8}$ | $8.4\times {10}^{-8}$ |

MAE | 0.03 | 0.08 | 0.31 | 0.44 |

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**MDPI and ACS Style**

Al Baraghtheh, T.; Hermann, A.; Shojaei, A.; Willumeit-Römer, R.; Cyron, C.J.; Zeller-Plumhoff, B.
Utilizing Computational Modelling to Bridge the Gap between In Vivo and In Vitro Degradation Rates for Mg-xGd Implants. *Corros. Mater. Degrad.* **2023**, *4*, 274-283.
https://doi.org/10.3390/cmd4020014

**AMA Style**

Al Baraghtheh T, Hermann A, Shojaei A, Willumeit-Römer R, Cyron CJ, Zeller-Plumhoff B.
Utilizing Computational Modelling to Bridge the Gap between In Vivo and In Vitro Degradation Rates for Mg-xGd Implants. *Corrosion and Materials Degradation*. 2023; 4(2):274-283.
https://doi.org/10.3390/cmd4020014

**Chicago/Turabian Style**

Al Baraghtheh, Tamadur, Alexander Hermann, Arman Shojaei, Regine Willumeit-Römer, Christian J. Cyron, and Berit Zeller-Plumhoff.
2023. "Utilizing Computational Modelling to Bridge the Gap between In Vivo and In Vitro Degradation Rates for Mg-xGd Implants" *Corrosion and Materials Degradation* 4, no. 2: 274-283.
https://doi.org/10.3390/cmd4020014