Studying trabecular bone samples demonstrates a power law relation between deteriorated structure and mechanical properties - a study combining 3D printing with the finite element method

Introduction: The bone volume fraction (BV/TV) significantly contributes to the mechanical properties of trabecular bone. However, when studies compare normal trabeculae against osteoporotic trabeculae (in terms of BV/TV decrease), only an “average” mechanical result has been determined because of the limitation that no two trabecular structures are the same and that each unique trabecular structure can be mechanically tested only once. The mathematic relation between individual structural deterioration and mechanical properties during aging or the osteoporosis process has yet to be further clarified. Three-dimensional (3D) printing and micro-CT-based finite element method (μFEM) can assist in overcoming this issue.

Methods: In this study, we 3D printed structural-identical but BV/TV value-attenuated trabecular bones (scaled up ×20) from the distal femur of healthy and ovariectomized rats and performed compression mechanical tests. Corresponding μFEM models were also established for simulations. The tissue modulus and strength of 3D printed trabecular bones as well as the effective tissue modulus (denoted as Ez) derived from μFEM models were finally corrected by the side-artifact correction factor.

Results: The results showed that the tissue modulus corrected, strength corrected and Ez corrected exhibited a significant power law function of BV/TV in structural-identical but BV/TV value-attenuated trabecular samples.

Discussion: Using 3D printed bones, this study confirms the long-known relationship measured in trabecular tissue with varying volume fractions. In the future, 3D printing may help us attain better bone strength evaluations and even personal fracture risk assessments for patients who suffer from osteoporosis.