Multiscale modeling of calcified polymer hydrogels

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Hydrogels, a significant group of highly hydrated polymers, represent the best choice for the potential application to bone fracture regeneration, which goes back to their bioactivity, affinity for biologically active proteins and compatibility with the bone tissue. However, this kind of materials also shows a serious disadvantage, namely, it loses its mechanical strength through swelling. This makes its straightforward usage difficult and motivates the development of different enhancement procedures. One of the most modern techniques for this purpose is calcification or, in a more general sense, mineralization. This method is inspired by the natural process of the bone growth where the enzyme alkaline phosphatase causes mineralization of the bone by cleavage of the phosphate from organic molecules. An analogous process induces homogeneous mineralization of a hydrogel and increases its mechanical strength. Recently, optical and electron microscopy has revealed that calcification yields different types of microstructure dependent on the type of the underlying polymer, and thus has clearly indicated that computational modeling can significantly contribute to the targeted investigation of effective behavior and material parameters. Fracture energy and diffusivity are two particularly important aspects in this context. The former is taken as the main measure of material ductility and represents a weak point of calcified hydrogels. In order to solve this challenging problem, inspiration once more comes from natural materials and their hierarchical microstructure. The study of diffusion in macromolecular solutions is motivated by many biomedical applications as well as by its key role for protein assembly and interstitial transport. The project furthermore studies the design of the mineralization process which includes two essential steps: the understanding of the mechanisms governing the microstructure development and subsequently their optimization. The investigation of the diffusivity and of mineralization requires a profound knowledge on the processes on the nanoscale. This of course strongly substantiates computer simulations, since this kind of processes is yet non-accessible even by the most modern microscopy techniques. The spectrum of applicable methods encompasses the multiscale finite element method, the phase field method, the model reduction strategy and the finite difference method.