Computational modeling of degradation process of biodegradable magnesium biomaterials

Degradable metals; Finite element method; In silico medicine; Magnesium corrosion; Reaction–diffusion models; Biodegradable magnesiums; Biodegradable metals; Computational model; Degradation process; Element method; Implant design; Magnesium corrosions; Reaction-diffusion models; Chemistry (all); Chemical Engineering (all); Materials Science (all); Computer Science - Computational Engineering; Finance; and Science; Physics - Materials Science; General Materials Science; General Chemical Engineering; General Chemistry

Abstract :

[en] Despite the advantages of using biodegradable metals in implant design, their uncontrolled degradation and release remain a challenge in practical applications. A validated computational model of the degradation process can facilitate tuning implant biodegradation properties. In this study, a mathematical model of the chemistry of magnesium biodegradation was developed and implemented in a 3D computational model. The parameters were calibrated by Bayesian optimization using dedicated experimental data. The model was validated by comparing the predicted and experimentally obtained pH change in saline and buffered solutions, showing maximum 5% of difference, demonstrating the model's validity to be used for practical cases.

Disciplines :

Engineering, computing & technology: Multidisciplinary, general & others

Author, co-author :

Barzegari, Mojtaba ; Biomechanics Section, Department of Mechanical Engineering, KU Leuven, Belgium

Mei, Di ; Institute of Surface Science, Helmholtz-Zentrum Hereon, Geesthacht, Germany ; School of Materials Science and Engineering & Henan Key Laboratory of Advanced Magnesium Alloy, Zhengzhou University, Zhengzhou, China

Lamaka, Sviatlana V. ; Institute of Surface Science, Helmholtz-Zentrum Hereon, Geesthacht, Germany

Geris, Liesbet ; Université de Liège - ULiège > GIGA > GIGA In silico medecine - Biomechanics Research Unit ; Biomechanics Section, Department of Mechanical Engineering, KU Leuven, Belgium

Language :

English

Title :

Computational modeling of degradation process of biodegradable magnesium biomaterials

Publication date :

September 2021

Journal title :

Corrosion Science

ISSN :

0010-938X

Publisher :

Elsevier Ltd

Volume :

190

Pages :

109674

Peer reviewed :

Peer Reviewed verified by ORBi

Additional URL :

https://api.elsevier.com/content/article/PII:S0010938X21004406?httpAccept=text/xml

Funders :

ERC - European Research Council [BE]
Interreg North-West Europe [FR]
FWO - Fonds Wetenschappelijk Onderzoek Vlaanderen [BE]

Funding text :

This research is financially supported by the Prosperos project, funded by the Interreg VA Flanders – The Netherlands program, CCI grant no. 2014TC16RFCB046 and by the Fund for Scientific Research Flanders (FWO) , grant G085018N . LG acknowledges support from the European Research Council under the European Union's Horizon 2020 research and innovation programme, ERC CoG 772418. The computational resources and services used in this work were provided by the VSC (Flemish Supercomputer Center), funded by the Research Foundation – Flanders (FWO) and the Flemish Government – department EWI.This research is financially supported by the Prosperos project, funded by the Interreg VA Flanders – The Netherlands program, CCI grant no. 2014TC16RFCB046 and by the Fund for Scientific Research Flanders (FWO), grant G085018N. LG acknowledges support from the European Research Council under the European Union's Horizon 2020 research and innovation programme, ERC CoG 772418. The computational resources and services used in this work were provided by the VSC (Flemish Supercomputer Center), funded by the Research Foundation – Flanders (FWO) and the Flemish Government– department EWI.

Available on ORBi :

since 29 June 2022

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Bibliography

Zheng, Y., Gu, X., Witte, F., Biodegradable metals. Mater. Sci. Eng. R Rep. 77 (2014), 1–34, 10.1016/j.mser.2014.01.001.
Chen, Y., Xu, Z., Smith, C., Sankar, J., Recent advances on the development of magnesium alloys for biodegradable implants. Acta Biomater. 10:11 (2014), 4561–4573, 10.1016/j.actbio.2014.07.005.
Zhao, D., Witte, F., Lu, F., Wang, J., Li, J., Qin, L., Current status on clinical applications of magnesium-based orthopaedic implants: a review from clinical translational perspective. Biomaterials 112 (2017), 287–302, 10.1016/j.biomaterials.2016.10.017.
Qin, Y., Wen, P., Guo, H., Xia, D., Zheng, Y., Jauer, L., Poprawe, R., Voshage, M., Schleifenbaum, J.H., Additive manufacturing of biodegradable metals: current research status and future perspectives. Acta Biomater. 98 (2019), 3–22, 10.1016/j.actbio.2019.04.046.
Riaz, U., Shabib, I., Haider, W., The current trends of mg alloys in biomedical applications—a review. J. Biomed. Mater. Res. Part B: Appl. Biomater., 2018, 10.1002/jbm.b.34290.
Xin, Y., Huo, K., Tao, H., Tang, G., Chu, P.K., Influence of aggressive ions on the degradation behavior of biomedical magnesium alloy in physiological environment. Acta Biomater. 4:6 (2008), 2008–2015, 10.1016/j.actbio.2008.05.014.
Gastaldi, D., Sassi, V., Petrini, L., Vedani, M., Trasatti, S., Migliavacca, F., Continuum damage model for bioresorbable magnesium alloy devices — application to coronary stents. J. Mech. Behav. Biomed. Mater. 4:3 (2011), 352–365, 10.1016/j.jmbbm.2010.11.003.
Ahmed, S., Ward, J., Liu, Y., Numerical modelling of effects of biphasic layers of corrosion products to the degradation of magnesium metal in vitro. Materials, 11(1), 2017, 1, 10.3390/ma11010001.
Grogan, J., Leen, S., McHugh, P., A physical corrosion model for bioabsorbable metal stents. Acta Biomater. 10:5 (2014), 2313–2322, 10.1016/j.actbio.2013.12.059.
Shen, Z., Zhao, M., Bian, D., Shen, D., Zhou, X., Liu, J., Liu, Y., Guo, H., Zheng, Y., Predicting the degradation behavior of magnesium alloys with a diffusion-based theoretical model and in vitro corrosion testing. J. Mater. Sci. Technol. 35:7 (2019), 1393–1402, 10.1016/j.jmst.2019.02.004.
Wilder, J.W., Clemons, C., Golovaty, D., Kreider, K.L., Young, G.W., Lillard, R.S., An adaptive level set approach for modeling damage due to galvanic corrosion. J. Eng. Math. 91:1 (2014), 121–142, 10.1007/s10665-014-9732-3.
Gartzke, A.-K., Julmi, S., Klose, C., Waselau, A.-C., Meyer-Lindenberg, A., Maier, H.J., Besdo, S., Wriggers, P., A simulation model for the degradation of magnesium-based bone implants. J. Mech. Behav. Biomed. Mater., 101, 2020, 103411, 10.1016/j.jmbbm.2019.103411.
Sun, W., Liu, G., Wang, L., Wu, T., Liu, Y., An arbitrary lagrangian–eulerian model for studying the influences of corrosion product deposition on bimetallic corrosion. J. Solid State Electrochem. 17:3 (2012), 829–840, 10.1007/s10008-012-1935-9.
Bajger, P., Ashbourn, J.M.A., Manhas, V., Guyot, Y., Lietaert, K., Geris, L., Mathematical modelling of the degradation behaviour of biodegradable metals. Biomech. Model. Mechanobiol. 16:1 (2016), 227–238, 10.1007/s10237-016-0812-3.
Sanz-Herrera, J., Reina-Romo, E., Boccaccini, A., In silico design of magnesium implants: macroscopic modeling. J. Mech. Behav. Biomed. Mater. 79 (2018), 181–188, 10.1016/j.jmbbm.2017.12.016.
Gao, Y., Wang, L., Gu, X., Chu, Z., Guo, M., Fan, Y., A quantitative study on magnesium alloy stent biodegradation. J. Biomech. 74 (2018), 98–105, 10.1016/j.jbiomech.2018.04.027.
Wang, Y., Pan, J., Han, X., Sinka, C., Ding, L., A phenomenological model for the degradation of biodegradable polymers. Biomaterials 29:23 (2008), 3393–3401.
Mei, D., Lamaka, S.V., Lu, X., Zheludkevich, M.L., Selecting medium for corrosion testing of bioabsorbable magnesium and other metals – a critical review. Corros. Sci., 171, 2020, 108722, 10.1016/j.corsci.2020.108722.
Grindrod, P., The Theory and Applications of Reaction–Diffusion Equations: Patterns and Waves. 1996, Oxford University Press.
Crank, J., Free and Moving Boundary Problems. 1987, OUP Oxford.
Ronald Fedkiw, S.O., Level Set Methods and Dynamic Implicit Surfaces. 2002, Springer, New York.
Wang, C., Mei, D., Wiese, G., Wang, L., Deng, M., Lamaka, S.V., Zheludkevich, M.L., High rate oxygen reduction reaction during corrosion of ultra-high-purity magnesium. NPJ Mater. Degrad., 4(1), 2020 dec, 10.1038/s41529-020-00146-1.
Strebl, M., Bruns, M., Virtanen, S., Editors’ choice—respirometric in situ methods for real-time monitoring of corrosion rates: Part I. Atmospheric corrosion. J. Electrochem. Soc., 167(2), 2020, 021510, 10.1149/1945-7111/ab6c61.
Silva, E.L., Lamaka, S.V., Mei, D., Zheludkevich, M.L., The reduction of dissolved oxygen during magnesium corrosion. ChemistryOpen 7:8 (2018), 664–668, 10.1002/open.201800076.
Grathwohl, P., Diffusion in Natural Porous Media: Contaminant Transport, Sorption/Desorption and Dissolution Kinetics. 1998, Springer US, 10.1007/978-1-4615-5683-1.
Höche, D., Simulation of corrosion product deposit layer growth on bare magnesium galvanically coupled to aluminum. J. Electrochem. Soc. 162:1 (2014), C1–C11, 10.1149/2.0071501jes.
Barzegari, M., Geris, L., Highly Scalable Numerical Simulation of Coupled Reaction–Diffusion Systems With Moving Interfaces. 2020 arXiv:2008.11057v1.
Scheiner, S., Hellmich, C., Stable pitting corrosion of stainless steel as diffusion-controlled dissolution process with a sharp moving electrode boundary. Corros. Sci. 49:2 (2007), 319–346, 10.1016/j.corsci.2006.03.019.
Mei, D., Lamaka, S.V., Gonzalez, J., Feyerabend, F., Willumeit-Römer, R., Zheludkevich, M.L., The role of individual components of simulated body fluid on the corrosion behavior of commercially pure mg. Corros. Sci. 147 (2019), 81–93, 10.1016/j.corsci.2018.11.011.
Hecht, F., New development in freefem++. J. Numer. Math. 20:3–4 (2012), 251–265, 10.1515/jnum-2012-0013.
Falgout, R.D., Yang, U.M., hypre: a library of high performance preconditioners. Lecture Notes in Computer Science, 2002, Springer Berlin Heidelberg, 632–641, 10.1007/3-540-47789-666.
Saad, Y., Schultz, M.H., Gmres: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM J. Sci. Stat. Comput. 7:3 (1986), 856–869, 10.1137/0907058.
Balay, S., Abhyankar, S., Adams, M.F., Brown, J., Brune, P., Buschelman, K., Dalcin, L., Dener, A., Eijkhout, V., Gropp, W.D., Karpeyev, D., Kaushik, D., Knepley, M.G., May, D.A., McInnes, L.C., Mills, R.T., Munson, T., Rupp, K., Sanan, P., Smith, B.F., Zampini, S., Zhang, H., Zhang, H., PETSc Web page. 2019 https://www.mcs.anl.gov/petsc.
Jolivet, P., Hecht, F., Nataf, F., Prud'homme, C., Scalable domain decomposition preconditioners for heterogeneous elliptic problems. Proceedings of the International Conference on High Performance Computing, Networking, Storage and Analysis, SC’13, 2013, Association for Computing Machinery, New York, NY, USA, 10.1145/2503210.2503212.
Schöberl, J., NETGEN an advancing front 2d/3d-mesh generator based on abstract rules. Comput. Visual. Sci. 1:1 (1997), 41–52, 10.1007/s007910050004.
Ribes, A., Caremoli, C., Salome platform component model for numerical simulation. 31st Annual International Computer Software and Applications Conference – vol. 2 – (COMPSAC 2007), 2007, 10.1109/compsac.2007.185.
Mei, D., Lamaka, S.V., Feiler, C., Zheludkevich, M.L., The effect of small-molecule bio-relevant organic components at low concentration on the corrosion of commercially pure mg and mg-0.8ca alloy: an overall perspective. Corros. Sci. 153 (2019), 258–271, 10.1016/j.corsci.2019.03.039.
Mockus, J., Bayesian Approach to Global Optimization. 1989, Springer Netherlands, 10.1007/978-94-009-0909-0.
Mehrian, M., Guyot, Y., Papantoniou, I., Olofsson, S., Sonnaert, M., Misener, R., Geris, L., Maximizing neotissue growth kinetics in a perfusion bioreactor: an in silico strategy using model reduction and Bayesian optimization. Biotechnol. Bioeng. 115:3 (2017), 617–629, 10.1002/bit.26500.
Lee, S.H., Rasaiah, J.C., Proton transfer and the mobilities of the H+ and OH- ions from studies of a dissociating model for water. J. Chem. Phys., 135(12), 2011, 124505, 10.1063/1.3632990.
Graham, J.S.H., Hill, C., Chemistry in Context – Laboratory Manual. 2001, Oxford University Press.
Abdalla, M., Joplin, A., Elahinia, M., Ibrahim, H., Corrosion modeling of magnesium and its alloys for biomedical applications: review. Corros. Mater. Degrad. 1:2 (2020), 219–248, 10.3390/cmd1020011.
Santucci, R.J., McMahon, M.E., Scully, J.R., Utilization of chemical stability diagrams for improved understanding of electrochemical systems: evolution of solution chemistry towards equilibrium. NPJ Mater. Degrad., 2(1), 2018 jan, 10.1038/s41529-017-0021-2.
Lamaka, S.V., Gonzalez, J., Mei, D., Feyerabend, F., Willumeit-Römer, R., Zheludkevich, M.L., Local pH and its evolution near mg alloy surfaces exposed to simulated body fluids. Adv. Mater. Interfaces, 5(18), 2018, 1800169, 10.1002/admi.201800169.
Deshpande, K.B., Numerical modeling of micro-galvanic corrosion. Electrochim. Acta 56:4 (2011), 1737–1745, 10.1016/j.electacta.2010.09.044.
Dolgikh, O., Simillion, H., Lamaka, S.V., Bastos, A.C., Xue, H.B., Taryba, M.G., Oliveira, A.R., Allély, C., Bossche, B.V.D., Bergh, K.V.D., Strycker, J.D., Deconinck, J., Corrosion protection of steel cut-edges by hot-dip numerical simulations. Mater. Corros. 70:5 (2019), 780–792, 10.1002/maco.201810210.