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.

Strontium Substituted Tricalcium Phosphate Bone Cement: Short and Long‐Term Time‐Resolved Studies and In Vitro Properties

“…Nonlinear oscillatory behavior of calcium phosphate cements was already observed and described in our previous work. [56] The IR pattern collected at reaction time t = 220 min (about 4 h) looks very similar to the one collected at t = 45 min. This result can be interpreted as a further confirmation that, during this time lapse, no further relevant conversion of the TCP into brushite phase took place and primary crystallization of the cement represented the predominant process.…”

“…Resulting time profile is characterized by a constant increase of max values that are correlated with a constant increase in formation of brushite phase. Correlating the results of the EDXRD and THz-TDS techniques is it possible to infer that during the first time interval (0 ÷ 40 min), the hardening process can be described as a continuous dissolution/disaggregation-precipitation-nucleation process [56,57] giving rise to a constant brushite particles formation. After each modulation (as depicted in Figure 4), a part of the dissolved TCP undergoes a conversion into brushite phase (nucleation), while the remaining unreacted particles reaggregate as the TCP crystallites.…”

Bone Mineral Crystallinity Governs the Orchestration of Ossification and Resorption during Bone Remodeling

“…However, in the nonlinear, feedback-looped systems that bone and other biological tissues and organs are, where health depends on an ongoing and precise orchestration of the mutually antagonistic processes of ossification and resorption, a lower amount of ACP would entail structural sluggishness and resistance to swiftly modify the crystal structure to fit the immediate biological demands. CPs have earlier been shown to display structurally intrinsic nonlinear phenomena, 103 so their engagement in extrinsic feedback loops of this type should not be surprising. For example, an osteoclastic acidification of the microenvironment surrounding an apatite platelet in bone increases the proportion of amorphous domains in it, which promotes resorption and release of ions to be used for various metabolic ends, but also a smoother regrowth, as demonstrated by an earlier FTIR crystallinity analysis, 104 thus providing for a dampening effect that prevents uncontrolled dissolution under these conditions.…”

On Grounds of the Memory Effect in Amorphous and Crystalline Apatite: Kinetics of Crystallization and Biological Response

“…With the calculated value of 1.8, the Avrami constant, n, corresponding to the recrystallization of HAp via an amorphous intermediate, is closest to the integer of 2 (Figure 7) and is in agreement with our previous estimation of this factor for brushite formation during the hardening of a β-TCP cement. 60 This exponent, although having an ambiguous meaning depending on the exact nature of nucleation and its limiting factors (interface vs diffusion), is composed of two additive factors, n d and n n , the former of which represents the dimensionality of the growing units, while the latter represents the time dependence of the nucleation. With the value of n n equaling 0 for heterogeneous nucleation, as opposed to 1 for the homogeneous, n d has the value of 2, denoting planar growth, as in agreement with the platelet morphology of crystals that is typical for apatite in the bone.…”