Artificial lattices were designed using the Voronoi tessellation approach. This method allows the creation of personalized biomimetic bone implants with a porous and interconnected microstructure, such as the one that can be observed in natural bone. Furthermore, this strategy produces topologies that can be directly and precisely fabricated using additive manufacturing techniques. The obtained lattices were characterized to obtain the geometric and elastic properties. For this, homogenization analyses were carried out using a dedicated FFT method. A database was built with information on the volume fraction, elastic properties, and tortuosity of the lattice based on its geometric parameters. From the polynomial interpolations of this database, a response surface (RSM) to be used for the optimization method was constructed that allows rapid calculations of the properties. Additionally, Voronoi lattices were additively manufactured using a laser powder bed fusion system with a Ti6Al4V alloy powder to check the manufacturability and analyse the fatigue life. The results of this work were presented at the “8th European Congress on Computational Methods in Applied Sciences and Engineering”.
To determine the fatigue life of the lattices, a method that makes use of damage accumulation models was developed. The procedure can be summarized as follows: i) a fast Fourier transform model of the lattice subjected to constant uniaxial stress is constructed; ii) the model is run, and the distribution of stress is determined; iii) the remaining life is calculated point by point using the Miner's rule; iv) the strut with the minimum remaining life is removed; v) the process is repeated until total failure of the lattice. This procedure must be performed on different lattices and loading states to determine the stress vs. number of cycles to failure curves throughout the whole porosity range.
While working on MidPoint and after learning about the work being done at the host institution, I realized the importance of studying the biomechanical properties of the bone-implant interface for surgical success. Therefore, I decided to develop a multiscale homogenization model to evaluate the effective elastic properties of bone as a function of the distance to the implant, based on tissue structure and composition at lower scales. The model considers three scales: mineral matrix (nanoscale), ultrastructure (microscale), and bone tissue (mesoscale). The elastic properties and volume fraction of the elemental constituents of the bone matrix (mineral, collagen, and water), the orientation of the collagen fibrils relative to the implant surface, and the porosity at the mesoscale constitute the input data of the model. The effect of a spatiotemporal variation in the orientation of collagen fibrils on the anisotropic properties of bone in the vicinity of the implant was investigated. The findings revealed a strong variation of the components of the effective bone elasticity tensor as a function of the distance to the implant. The results of this work were presented at the “X International Conference on Computational Bioengineering”, and a publication was accepted in the journal “Biomechanics and Modelling in Mechanobiology”.
