Computational Methods for the Predictive Design of Bone Tissue Engineering Scaffolds
The design of bone tissue engineering materials and scaffold structures made thereof is a delicate task, owing to the various, sometimes contradicting requirements that must be fulfilled. The traditional approach is based on a trial-and-error strategy, which may result in a lengthy and inefficient process. Aiming at improvement of this unsatisfactory situation, computer simulations, based on sound mathematical modeling of the involved processes, have been identified as promising complement to experimental testing. After giving a brief overview of available modeling and simulation concepts, the core of this chapter is presented, namely recent examples of multiscale, continuum micromechanics-based homogenization approaches developed in relation to bone tissue engineering. First, the fundamentals of continuum micromechanics are introduced, in order to lay the groundwork for the subsequently elaborated stiffness and strength homogenization approach related to a hydroxyapatite-based granular bone tissue engineering material. For the latter, the derivation of an upscaling scheme allowing for estimating the macroscopic stiffness and the macroscopic strength is demonstrated. Finally, avenues to utilization of this method in the design process of such materials are pointed out.
In the context of the research presented in Sect. 3.3 of this chapter, the partial financial support by the European Research Council (ERC), in the framework of the project Multiscale poromicromechanics of bone materials, with links to biology and medicine (project number FP7-257023), as well as the partial financial support by the Russian Science Foundation (grant number 15-13-00108), are gratefully acknowledged. Furthermore, COST-action MP1005, NAMABIO – From nano to macro biomaterials (design, processing, characterization, modeling) and applications to stem cells regenerative orthopedic and dental medicine has provided means for a sustainable collaboration over several years.
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