Anisotropy characteristics of microstructures for bone substitutes and porous implants with application of additive manufacturing in orthopaedic

Porous bone substitutes built with additive manufacturing provide an opportunity for mimicking natural bone with complicated structures and excellent properties. However, the anisotropic discrepancy between microstructure and host bone is still unclear, and the mathematical relationship to design microstructures with controllable anisotropy has not been established. In the study, the numerical method for anisotropic evaluation of microstructures was developed from the generalized Hooke's law by the finite element method and programming. The 3D spatial distributions of effective modulus surfaces for four porous units were analyzed. The mapping relationship between anisotropy coefficient and geometric parameters was built. Finally, the comparison of anisotropy was investigated systematically. The numerical method can characterize the spatial distribution of modulus and anisotropy effectively. Modulus anisotropy can be controlled by adjusting geometric sizes and the response mechanism of modulus spatial distribution caused by the distribution of materials was revealed. The ratio of modulus extremum indicated that is necessary for the accurate evaluation of modulus and the influence of anisotropy on the service performance. This study not only evaluate qualitatively and quantitatively the mechanical anisotropy between porous structures and host bone, but also will lay the foundation for the functional bionic design of 3D printing porous prosthesis. [Display omitted] •Spatial distribution of modulus like that of bone can be obtained by changing the geometrical sizes of microstructure.•Mathematic relationship between anisotropy and geometric sizes was built to design lattices with controlled anisotropy.•The necessary of anisotropic evaluation was highlighted by the extremum ratio of elastic modules from 1.6 to 2.4.•Anisotropy map of microstructures against natural bone was developed to guide the functional design of porous implants.