Abstract
This chapter discusses the development of computational degradation models for different bioresorbable composite materials. The models were developed in a two-stage process. Firstly, a general modelling framework was generated and analysed and secondly, this general framework was particularised for specific ceramic fillers yielding the degradation models.
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Notes
- 1.
In this work, acid dissociation constants are always expressed in terms of concentrations instead of in terms of activity and therefore \(K_\text {a}\) has concentration units [4], usually reported as mol/ L which can be easily converted to mol m\(^{-3}\).
- 2.
In this work, dimensionless units are expressed with the symbol “1” and usually displayed between parentheses: (1).
- 3.
The definition and mathematical expression of the solubility product \(K_\text {sp}\) is given in Appendix A.2.
- 4.
Information about the definition and description of the average degree of pseudo-polymerisation, \(N_\text {dp0}\), can be found in Appendix A.4.
- 5.
Information about the definition and calculation of the ceramic solubility product can be found in Appendix A.2.
- 6.
Information about the definition and calculation of the ceramic calcium equilibrium concentration can also be found in AppendixA.2.
- 7.
- 8.
The description and mathematical derivation of the Sauter mean diameter, \(d_{32}\), can be found in Appendix A.5.
References
Pan, J., Han, X., Niu, W., & Cameron, R. E. (2011). A model for biodegradation of composite materials made of polyesters and tricalcium phosphates. Biomaterials, 32(9), 2248–2255.
Pan, J. (2014). Modelling degradation of bioresorbable polymeric medical devices. Elsevier.
Bergwerf, H. (2014). MolView online application. Retrieved September 1, 2016 from http://molview.org/.
Popov, K., Rönkkömäki, H., & Lajunen, L. H. (2006). Guidelines for NMR measurements for determination of high and low p\({K}_\text{a}\) values (IUPAC Technical Report). Pure and Applied Chemistry, 78(3), 663–675.
Wang, Y., Pan, J., Han, X., Sinka, C., & Ding, L. (2008). A phenomenological model for the degradation of biodegradable polymers. Biomaterials, 29(23), 3393–3401.
Wang, Y. (2009). Modelling degradation of bioresorbable polymeric devices. Ph.D. thesis, Department of Engineering, University of Leicester.
Wang, L., & Nancollas, G. H. (2008). Calcium orthophosphates: crystallization and dissolution. Chemical Reviews, 108(11), 4628–4669.
Wang, L., Tang, R., Bonstein, T., Orme, C. A., Bush, P. J., & Nancollas, G. H. (2005). A new model for nanoscale enamel dissolution. The Journal of Physical Chemistry B, 109(2), 999–1005.
Tang, R., Orme, C. A., & Nancollas, G. H. (2004a). Dissolution of crystallites: surface energetic control and size effects. ChemPhysChem, 5(5), 688–696.
Tang, R., Wang, L., & Nancollas, G. H. (2004b). Size-effects in the dissolution of hydroxyapatite: an understanding of biological demineralization. Journal of Materials Chemistry, 14(14), 2341–2346.
Hayakawa, S. (2015). In vitro degradation behavior of hydroxyapatite. In M. Mucalo (Ed.), Hydroxyapatite (HAp) for biomedical applications (Vol. 4, pp. 85–105). Elsevier.
Grizzi, I., Garreau, H., Li, S., & Vert, M. (1995). Hydrolytic degradation of devices based on poly(DL-lactic acid) size-dependence. Biomaterials, 16(4), 305–311.
Dorozhkin, S. V. (2010). Bioceramics of calcium orthophosphates. Biomaterials, 31(7), 1465–1485.
Marshall, W. L., & Franck, E. (1981). Ion product of water substance, 0–1000 \(^\circ \)C, 1–10,000 bars new international formulation and its background. Journal of Physical and Chemical Reference Data, 10(2), 295–304.
Morse, J. W., Arvidson, R. S., & Lüttge, A. (2007). Calcium carbonate formation and dissolution. Chemical Reviews, 107(2), 342–381.
Harned, H. S., & Scholes, S. R, Jr. (1941). The ionization constant of HCO\(_3^-\) from 0 to 50\(^\circ \). Journal of the American Chemical Society, 63(6), 1706–1709.
Harned, H. S., & Davis, R., Jr. (1943). The ionization constant of carbonic acid in water and the solubility of carbon dioxide in water and aqueous salt solutions from 0 to 50\(^\circ \). Journal of the American Chemical Society, 65(10), 2030–2037.
Bohner, M., Lemaître, J., & Ring, T. A. (1997). Kinetics of dissolution of \(\beta \)-tricalcium phosphate. Journal of Colloid and Interface Science, 190(1), 37–48.
Gleadall, A., Pan, J., Kruft, M.-A., & Kellomäki, M. (2014a). Degradation mechanisms of bioresorbable polyesters. Part 1. Effects of random scission, end scission and autocatalysis. Acta Biomaterialia, 10(5), 2223–2232.
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Moreno-Gomez, I. (2019). Degradation of Bioresorbable Composites: The Models. In: A Phenomenological Mathematical Modelling Framework for the Degradation of Bioresorbable Composites. Springer Theses. Springer, Cham. https://doi.org/10.1007/978-3-030-04990-4_3
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