Marius Zeinhofer: Mathematical Analysis of Scaffold Mediated Bone Growth

I present a simple, efficient, three dimensional, time dependent model for bone regeneration in the presence of porous scaffolds to bridge critical size bone defects. The essential processes are an interplay between the mechanical and biological environment which we model by a coupled system of PDEs and ODEs. The mechanical environment is represented by a linear elastic equation and the biological environment through reaction-diffusion equations as well as as logistic ODEs, modelling signalling molecules and cells/bone respectively. Material properties are incorporated using homogenized quantities not resolving any scaffold microstructure. This makes the model efficient in computations, thus suitable as a forward equation in optimization algorithms and opening up the possibility of patient specific scaffold design and this model is used as a PDE constraint for the optimization of polymer scaffold porosities. Our numerical findings show that our model for example recovers and quantifies clinically relevant stress shielding effects that appear in vivo due to external fixation of the scaffold at the defect site.

This talk is part of the Mechanics Lunch Seminar series. Bring-your-own-lunch and lots of questions.