Predicting the Effective Stiffness of Spinodal-like Trabecular Bone via Finite Element Analysis

Understanding and accurately modelling the mechanical behavior of the trabecular bone remains a fundamental challenge in biomechanics and biomedical engineering, with direct implications for the diagnosis, treatment, and prevention of bone-related diseases such as osteoporosis. Currently, traditional approaches rely on high-resolution micro-computed tomography (micro-CT) scans to reconstruct trabecular architectures, then connected to finite element (FE) analysis to study the mechanical behavior. While these methods provide high fidelity, they are computationally expensive and impractical for large-scale or real-time applications. In recent years, alternative modelling strategies have emerged, seeking to mimic the structural features of trabecular bone with reduced computational demand. Among these, spinodal decomposition—a phases separation process that naturally generates interconnected porous structures—has gained attention due to its ability to replicate the morphology and mechanical anisotropy of trabecular bone. Spinodal-like structures offer advantages such as tunable porosity, efficient transport pathways, and structural similarity to biological tissues. This study investigates the feasibility of using spinodal decomposition models as a surrogate for trabecular bone in mechanical simulations. A database of three-dimensional spinodal structures was generated using MATLAB, systematically varying key morphological parameters to capture a broad spectrum of geometries representative of trabecular bone. Finite element simulations under uniaxial elastic compression were performed in ABAQUS for each configuration. The results of the FE analyses were compared with previously established metrics to identify predictive morphological metrics capable of estimating mechanical stiffness without requiring a full FE simulation. Preliminary findings demonstrate that certain structural descriptors can approximate mechanical performance with high accuracy, offering a computationally efficient pathway for bone analysis. This method holds promise for accelerating virtual biomechanical assessments and could be extended to capture bone plasticity and fractured behavior in future studies.