Probability-based approach for characterization of microarchitecture and its effect on elastic properties of trabecular bone.

Trabecular bone is a random cellular solid with an interconnected network of plate-like and rod-like components. However, the structural randomness and complexity have hindered rigorous mathematical modeling of trabecular bone microarchitecture. Recent advancements in imaging processing techniques have enabled us to define the size, orientation, and spatial location of individual trabecular plates and rods in trabecular bone. Based on the essential information, this study proposed a probability-based approach to define the size, orientation, and spatial distributions of trabecular plates and rods for trabecular bone cubes (N = 547) acquired from six human cadaver proximal femurs. Using two groups of probability-based parameters, it was attempted to capture microarchitectural details, which could not be captured by the existing histomorphometric parameters, but crucial to the elastic properties of trabecular bone. The elastic properties of the trabecular bone cubes in three principal axes were estimated using microCT based finite element (FE) simulations. Based on the results of multivariate multiple regression modeling, the efficacy of the two groups of probability-based parameters in prediction of the elastic properties was verified in comparison with that of the existing histomorphometric parameters (BV/TV, Tb.Th, Tb.Sp, DA, EF.Med, and Conn.D). The results indicated that the regression models trained using the probability-based parameters had a comparable and even better accuracy (rMSE = 0.621 and 0.548) than that of the histomorphometric parameters (rMSE = 0.647). More importantly, the probability-based parameters could provide more insights into some unexplored microarchitectural features, such as individual trabecular size, orientation, and spatial distributions, which are also critical to the elastic properties of trabecular bone.