Multiscale modeling of calcified polymer hydrogels

水凝胶是一组重要的高度水合的聚合物，代表了骨折再生的潜在应用的最佳选择，这可以追溯到它们的生物活性、对生物活性蛋白的亲和力以及与骨组织的相容性。然而，这类材料也显示出严重的缺点，即它通过溶胀而失去其机械强度。这使得它很难直接使用，并促使开发不同的增强程序。用于此目的的最现代的技术之一是钙化，或者在更一般的意义上，矿化。 这种方法的灵感来自于骨生长的自然过程，其中碱性磷酸酶通过从有机分子中裂解磷酸盐来引起骨的矿化。类似的过程诱导水凝胶的均匀矿化并增加其机械强度。最近，光学和电子显微镜显示，钙化产生不同类型的微观结构，这取决于底层聚合物的类型，因此已经清楚地表明，计算建模可以显着有助于有效的行为和材料参数的有针对性的调查。 断裂能和扩散率是这方面的两个特别重要的方面。前者被认为是材料延展性的主要衡量标准，代表了钙化水凝胶的弱点。为了解决这个具有挑战性的问题，灵感再次来自于天然材料及其层次结构。大分子溶液中扩散的研究受到许多生物医学应用以及其在蛋白质组装和间隙运输中的关键作用的推动。该项目还研究了矿化过程的设计，其中包括两个基本步骤：理解控制微观结构发展的机制，随后对其进行优化。扩散率和矿化的调查需要对纳米尺度上的过程有深刻的了解。这当然有力地证实了计算机模拟，因为即使是最现代的显微镜技术也无法实现这种过程。适用的方法包括多尺度有限元法、相场法、模型降阶策略和有限差分法。

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.