A Simple Projection Method to Correlate the Principal Mechanical Direction with the Principal Microstructural Direction of Human Osteoporotic Femoral Heads

The mechanics of the trabecular bone is related to its structure; this work aimed to propose a simple projection method to clarify the correlation between the principal mechanical direction (PMD) and the principal microstructural direction (PMSD) of trabecular bones from osteoporotic femoral heads. A total of 529 trabecular cubes were cropped from five osteoporotic femoral heads. The micro computed tomography (mu CT) sequential images of each cube were first projected onto the three Cartesian coordinate planes to have three overlapped images, and the trabecular orientation distribution in the three images was analyzed. The PMSD corresponding to the greatest distribution frequency of the trabecular orientation in the three images was defined. Then, the voxel finite element (FE) models of the cubes were reconstructed and simulated to obtain their compliance matrices, and the matrices were subjected to transversal rotation to find their maximum elastic constants. The PMD corresponding to the maximum elastic constant was defined. Subsequently, the correlation of the defined PMSD and PMD was analyzed. The results showed that PMSD and PMD of the trabecular cubes did not show a significant difference at the xy- and yz-planes except that at the zx-plane. Despite this, the mean PMSD-PMD deviations at the three coordinate planes were close to 0 degrees, and the PMSD-PMD fitting to the line PMSD = PMD demonstrated their high correlation. This study might be helpful to identify the loading direction of anisotropic trabecular bones in experiments by examining the PMSD and also to guide bone scaffold design for bone tissue repair.