Data-Driven Computational Simulation in Bone Mechanics

Multiscale Analysis of Composite Structures with Artificial Neural Network Support for Micromodel Stress Determination

Structures made of heterogeneous materials, such as composites, often require a multiscale approach when their behavior is simulated using the finite element method. By solving the boundary value problem of the macroscale model, for previously homogenized material properties, the resulting stress maps can be obtained. However, such stress results do not describe the actual behavior of the material and are often significantly different from the actual stresses in the heterogeneous microstructure. Finding high-accuracy stress results for such materials leads to time-consuming analyses in both scales. This paper focuses on the application of machine learning to multiscale analysis of structures made of composite materials, to substantially decrease the time of computations of such localization problems. The presented methodology was validated by a numerical example where a structure made of resin epoxy with randomly distributed short glass fibers was analyzed using a computational multiscale approach. Carefully prepared training data allowed artificial neural networks to learn relationships between two scales and significantly increased the efficiency of the multiscale approach.

Structural optimization of 3D-printed patient-specific ceramic scaffolds for in vivo bone regeneration in load-bearing defects

Tissue engineering has recently gained popularity as an alternative to autografts to stimulate bone tissue regeneration through structures called scaffolds. Most of the in vivo experiments on long-bony defects use internally-stabilized generic scaffolds. Despite the wide variety of computational methods, a standardized protocol is required to optimize ceramic scaffolds for load-bearing bony defects stabilized with flexible fixations. An optimization problem was defined for applications to sheep metatarsus defects. It covers biological parameters (porosity, pore size, and the specific surface area) and mechanical constraints based on in vivo and in vitro results reported in the literature. The optimized parameters (59.30% of porosity, 5768.91 m^-1 of specific surface area, and 360.80 μm of pore size) and the compressive strength of the selected structure were validated in vitro by means of tomographic images and compression tests of six 3D-printed samples. Divergences between the design and measured values of the optimized parameters, mainly due to manufacturing defects, are consistent with the previous studies. Using the mixed experimental-mathematical scaffold-design procedure described, they could be implanted in vivo with instrumented external fixators, therefore facilitating biomechanical monitoring of the regeneration process.