Nonlinear oscillatory dynamics of the hardening of calcium phosphate bone cements

Abstract

Here we report on the nonlinear, oscillatory dynamics detected in the evolution of phase composition during the setting of different calcium phosphate cements, two of which evolved toward brushite and one toward hydroxyapatite as the final product. Whereas both brushite-forming cements contained ion-doped β-tricalcium phosphate as the initial phase, the zinc-containing one yielded scholzite as an additional phase during setting and the oscillations between these two products were pronounced throughout the entire 80 h setting period, long after the hardening processes was over from the mechanical standpoint. Oscillations in the copper-containing system involved the amount of brushite as the main product of the hardening reaction and they progressed faster toward an equilibrium point than in the zinc-containing system. Initially detected with the use of in situ energy-dispersive X-ray diffractometry, the oscillations were confirmed with a sufficient level of temporal matching in an in situ Fourier transform infrared spectroscopic analysis. The kinetic reaction analysis based on the Johnson–Mehl–Avrami–Kolmogorov model indicated an edge-controlled nucleation mechanism for brushite. The hydroxyapatite-forming cement comprised gelatin as an additional phase with a role of slowing down diffusion and allowing the detection of otherwise rapid oscillations in crystallinity and in the amount of the apatitic phase on the timescale of minutes. A number of possible causes for these dynamic instabilities were discussed. The classical chemical oscillatory model should not apply to these systems unless in combination with less exotic mechanisms of physicochemical nature. One possibility is that the variations in viscosity, directly affecting diffusion and nucleation rates and accompanying growth and transformation from the lower to the higher interfacial energy per the Ostwald–Lussac rule, are responsible for the oscillatory dynamics. The conception of bone replacement materials and tissue engineering constructs capable of engaging in the dynamics of integration with the natural tissues in compliance with this oscillatory nature may open a new avenue for the future of this type of medical devices. To succeed in this goal, the mechanism of these and similar instabilities must be better understood.