Sensitivity Analysis In Implant Materials#
Global sensitivity analysis is a powerful tool in uncertainty quantification that helps to identify which input variables are the most influential in determining the output of a given model. GSA can be used in a wide range of fields, including engineering, finance, environmental science, and many others.
The main goals of sensitivity analysis are to assess the influence of varying the input parameters on the variation in the model output, ascertain some interactions effect within the model. Adding to that, sensitivity analysis is an effective tool to verify and understand the simplification of a model [Böttcher et al., 2021, Sobester et al., 2008]. There are several types of sensitivity analysis techniques available not only to rank the importance of parameters but also to quantify the uncertainty associated with them []. It is important to note that each technique performs differently depending on the system being considered. Thus, sensitivity analysis must be implemented efficiently with the greatest degree of confidence to quantify the uncertainty in the model. To study complex systems such as the degradation of magnesium, no clear guidelines exist.
An analysis of the sensitivity of the degradation model variables provides a measure of confidence in those variables. Moreover, it identifies which parameters contribute to the behaviour of the degradation model [Albaraghtheh et al., 2022]. Furthermore, an analysis of the sensitivity of the degradation system for the Mg-based implant could provide a solution to the dimensionality problem [Albaraghtheh et al., 2022, Zeller-Plumhoff et al., 2022].
As a case study, the application of sensitivity analysis in modelling the Mg-based implants degradation processes can be used as a feedback to the development of the model by ranking the uncertain model parameters with significant impact on the model predictions, the total effect index indicated that for the degradation of Mg in SBF the process is mainly governed by the degradation kinetic, where the contribution of the degradation reaction constant (\(k_{deg}\)) was found higher than other parameters in the system Figure Mg_SA (Mean degradation depth). The amount of precipitated calcium (Ca), for instance, depends on all parameters of the model not only on the reactions rates, which are directly related to Ca precipitation, but also on the reaction rate constants of the formation of \(Mg_3(PO_4)_2.8H_2O\). This can be explain by the competing reaction between phosphate ions and Ca to form hydroxyapatite As a result of the highly correlated parameters of the precipitation model, simplifying this model is a challenge, and it may exacerbate uncertainties [Zeller-Plumhoff et al., 2022] .
(adapted under CC-BY-4.0 license [Zeller-Plumhoff et al., 2022]).#
References#
- AWRomerZP22(1,2)
Tamadur Albaraghtheh, Regine Willumeit-Römer, and Berit Zeller-Plumhoff. In silico studies of magnesium-based implants: a review of the current stage and challenges. Journal of Magnesium and Alloys, 2022.
- BottcherLF+21
Maria Böttcher, Ferenc Leichsenring, Alexander Fuchs, Wolfgang Graf, and Michael Kaliske. Efficient utilization of surrogate models for uncertainty quantification. PAMM, 20(1):e202000210, 2021.
- SFK08
András Sobester, Alexander Forrester, and Andy Keane. Engineering design via surrogate modelling: a practical guide. John Wiley & Sons, 2008.
- ZPAHocheWRomer22(1,2,3)
Berit Zeller-Plumhoff, Tamadur AlBaraghtheh, Daniel Höche, and Regine Willumeit-Römer. Computational modelling of magnesium degradation in simulated body fluid under physiological conditions. Journal of magnesium and alloys, 10(4):965–978, 2022.
Contributors#
Berit Zeller-Plumhoff