Machine Learning Approaches for the Automatic Design of Micro-Architected Triply Periodic Minimal Surface Scaffolds for Bone Tissue Engineering

Due to their peculiar architecture, Triply Periodic Minimal Surfaces (TPMS) find applications in many engineering domains. The increasing capability of additive manufacturing (AM) technologies allows the printing of microstructured materials with unparalleled spatial resolution and repeatability. This makes the design of TPMS-based material systems and device a feasible approach. Application of TPMS structure in Bone Tissue Engineering scaffolds design is particularly attractive. Indeed, scaffolds made with bioactive materials like glass ceramics and Hydroxyapatite and with specific morphological (such as porosity, pore interconnectivity, micro-feature characteristic size) and mechanical properties can be designed by taking advantage of the TPMS features.<br/>The design of biomechanically reliable BTE scaffolds, possibly following a patient-specific approach, is still a complex task that is based on multidisciplinary input such as biomechanics, transport properties and mechanobiology. Classical optimization approaches may be unsuitable for such a complex approach in which multiple objectives need to be met simultaneously. For this purpose, the use of Machine Learning methodologies can be a suitable approach to support the selection of a design with prescribed multi-disciplinary properties.<br/>In this study, we assessed whether a ML model may support the identification of TMPS architectures by leveraging biomechanical and morphological parameters as design inputs. The ML model was composed by three components. The first and second ones predict the geometrical parameters whereas the third one identifies the architecture type (i.e. diamond, gyroid and IWP). To do so, two regression and one classification problems were designed. Here, we considered three different TPMS architectures fully parametrized by two geometrical parameters. A dataset of TPMS architectures was created by solving the direct problem, i.e. imposing the geometrical parameters and the architecture type. Elastic and strength properties have been obtained through finite element modeling; while post-processing of the simulated micro-CT images of the TPMS structure was used to assess morphological parameters (the main ones are: wall thickness, wall spacing, volume fractions and geometrical anisotropy). Fluid transport properties were estimated by assessing the effective pore connectivity index. A total amount of 38 features were extracted from each of the 1258 designs (352, 476, 430 designs for diamond, gyroid and IWP, respectively).<br/>The pseudo-experimental dataset was partitioned into a training set (60%), a validation set (20%) and a test set (20%). A ML greedy feed-forward feature selection algorithm was used with the aim of selecting the most informative descriptors. Once the selection of the most relevant features was identified the optimal design was obtained by defining the optimal values of the features.<br/>The effectiveness of the predictive capability of the proposed approach was quantified by comparing the optimal structure obtained through the regressions and the actual values of the features for geometry extracted from the validation sets.<br/>The results obtained through this approach have proven the suitability of the proposed ML algorithm to design suitable TPMS scaffold architectures, allowing for patient specificity which prescribes specific biomechanical (stiffness and strength) and transport properties (mainly related to the morphological parameters).