Mathematical Modeling of Bone Engineering (MAMBOing)

The project aims at introducing and validating a new model describing bone engineering (BE) after traumas, osteoporosis, or tumors. Such a model appears to be the first capable of simultaneously taking into consideration both the bulk and the surface mechanisms underlying the bone regeneration, which is indeed crucial in order to characterize bone morphologies and to study their mechanical properties especially when polymeric scaffold are employed to enhance the bone growth. The approach consists in transferring techniques developed for the SDRI model in the context of Materials Science and to justify the model for the BE setting by p hase-field approximations. The new model represents a tool to ultimately improve surgical procedures by, e.g., easing the production of bone scaffolds, and the research risks seem to be manageable by introducing proper specific model modifications.

The aim of the project was to advance the understanding of the mechanisms under which bone tissue defects caused, e.g., by traumas, osteoporosis, or the surgical removal of tumors can be healed especially by promoting bone growth through the implantation of biocompatible synthetic scaffolds. In particular, the focus of the project was on evaluating the applicability in the setting of bone tissue engineering of a variational model previously introduced by the project PI with coauthors in the setting of Stress Driven Rearrangement Instabilities (SDRI). The intent was grounded in the fact that such SDRI model seemed to possess the potential of combining the two approaches used in the literature to describe bone-tissue regeneration, that consist either in growth models based on curvature-driven evolution equations or in elastic models in the framework of continuum mechanics. By significantly extending the applicability of the SDRI model in its original setting of Materials Science the project investigations not only have paved the way to address the project envisioned new application of bone regeneration in Medical Sciences, but also were pivotal to already allow for the reach of promising results for the validation of modifications of the SDRI model in that setting. The project impact has been twofold. On the one hand, by moving in the realm of the calculus of variations the applicability of the SDRI model has been extended in various directions, from allowing to work in higher dimensions (with respect to the previous literature studies in two dimensions) to studying the evolution for the SDRI setting of thin films, and from tackling the multiphase settings to addressing the microscopically justification of the SDRI model. On the other hand, by also adopting numerical techniques the implementation of the SDRI model in the setting of bone regeneration have been tackled with promising results.