Computational modelling of local calcium ions release from calcium phosphate-based scaffolds

Abstract

A variety of natural or synthetic calcium phosphate (CaP)-based scaffolds are currently produced for dental and orthopaedic applications. These scaffolds have been shown to stimulate bone formation due to their biocompatibility, osteoconductivity and osteoinductivity. The release of the \(\hbox {Ca}^{2+}\) ions from these scaffolds is of great interest in light of the aforementioned properties. It can depend on a number of biophysicochemical phenomena such as dissolution, diffusion and degradation, which in turn depend on specific scaffold characteristics such as composition and morphology. Achieving an optimal release profile can be challenging when relying on traditional experimental work alone. Mathematical modelling can complement experimentation. In this study, the in vitro dissolution behaviour of four CaP-based scaffold types was investigated experimentally. Subsequently, a mechanistic finite element method model based on biophysicochemical phenomena and specific scaffold characteristics was developed to predict the experimentally observed behaviour. Before the model could be used for local \(\hbox {Ca}^{2+}\) ions release predictions, certain parameters such as dissolution constant (\(k_{\mathrm{dc}}\)) and degradation constant (\(k_\mathrm{sc}\)) for each type of scaffold were determined by calibrating the model to the in vitro dissolution data. The resulting model showed to yield release characteristics in satisfactory agreement with those observed experimentally. This suggests that the mathematical model can be used to investigate the local \(\hbox {Ca}^{2+}\) ions release from CaP-based scaffolds.

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Acknowledgments

Céline Smekens is gratefully acknowledged for her work as a master student on measuring the \(\hbox {Ca}^{2+}\) ions release using micro ion electrode. Bachelor students Antoine Delacroix and Simon Bruneau (ESEO, Angers, France) are gratefully acknowledged for their work on development of Morphing CiTy (ULg, Liege, Belgium). Varun Manhas and Yann Guyot are funded by Belgian National Fund for Scientific Research (FNRS) Grant FRFC 2.4564.12. Greet Kerckhofs and Yoke Chin Chai are financed by the postdoctoral Grant of the Research Foundation—Flanders (FWO/12R4315N and 1.5.172.13N-Interdisc.—http://www.fwo.be/en/). The research leading to these results has received funding from the European Research Council under the European Union’s Seventh Framework Programme (FP/2007-2013)/ERC Grant Agreement No. 279100. The microCT images have been generated on the X-ray computed tomography facilities of the Department of Materials Engineering of the KU Leuven, financed by the Hercules Foundation (Project AKUL 09/001: Micro- and nanoCT for the hierarchical analysis of materials). This work is part of Prometheus, the KU Leuven R&D Division of Skeletal Tissue Engineering (http://www.kuleuven.be/prometheus).

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Manhas, V., Guyot, Y., Kerckhofs, G. et al. Computational modelling of local calcium ions release from calcium phosphate-based scaffolds. Biomech Model Mechanobiol 16, 425–438 (2017). https://doi.org/10.1007/s10237-016-0827-9

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Keywords

  • Calcium phosphate (CaP)-based scaffold
  • Dissolution
  • Diffusion
  • Degradation
  • Mathematical model
  • Finite element method (FEM)