Quantitative Load Dependency Analysis of Local Trabecular Bone Microstructure to Understand the Spatial Characteristics in the Synthetic Proximal Femur.

Analysis of the dependency of the trabecular structure on loading conditions is essential for understanding and predicting bone structure formation. Although previous studies have investigated the relationship between loads and structural adaptations, there is a need for an in-depth analysis of this relationship based on the bone region and load specifics. In this study, the load dependency of the trabecular bone microstructure for twelve regions of interest (ROIs) in the synthetic proximal femur was quantitatively analyzed to understand the spatial characteristics under seven different loading conditions. To investigate the load dependency, a quantitative measure, called the load dependency score (LDS), was established based on the statistics of the strain energy density (SED) distribution. The results showed that for the global model and epiphysis ROIs, bone microstructures relied on the multiple-loading condition, whereas the structures in the metaphysis depended on single or double loads. These results demonstrate that a given ROI is predominantly dependent on a particular loading condition. The results confirm that the dependency analysis of the load effects for ROIs should be performed both qualitatively and quantitatively.

Framework of sampling the subject-specific static loads from the gait cycle of interindividual variation.

BACKGROUND AND OBJECTIVE: Numerous techniques for bone remodeling simulation have been developed based on Wolff's law. However, most studies have been conducted with empirically determined static loads, which cannot reflect subject-specific characteristics. We recently proposed a new concept of representative static loads (RSLs) to efficiently consider the effect of cyclically repeated dynamic loads on bone remodeling simulation. Based on this concept, the goal of this study is to sample the subject-specific static loads (SSL) from a general gait cycle of interindividual variation. METHODS: A total of 15 gait cycles (ten normal and five abnormal cycles) obtained from the public database were used in this study. Each gait cycle was applied to a femur FE model constructed from the clinical CT scan data to evaluate the strain energy distribution as a reference. Then, a natural coordinate was introduced to maintain the predefined locations of extreme points (i.e., two peaks and one valley) for both normal and abnormal gait cycles. To determine the RSLs in the natural coordinate, five out of ten normal gait cycles were used. Through an inverse transformation for each gait cycle, the RSLs in the natural coordinate were converted to the SSLs in the original coordinate. Topology optimization results with the proposed SSLs were compared with those with a single full gait cycle (reference). For comparison, topology optimization was also conducted with empirically determined loads (EDLs) which have been widely used in the literature. RESULTS: For normal gait cycles, the proposed SSLs reduced the average computing cost by 95.86% while suppressing the errors of bone mass distribution and apparent stiffness below maximum 4.24% and 1.72%, respectively. Even for abnormal gait cycles, the errors of bone mass distribution and apparent stiffness were suppressed below maximum 9.49% and 2.12%, respectively. Conversely, the conventional EDLs (peak loads selected in this study) showed significantly larger errors of maximum 47.28% and 30.31% in bone mass distribution and apparent stiffness for normal gait cycles. CONCLUSION: By virtue of using the coordinate transformation for each gait cycle, the proposed SSLs achieved a higher accuracy in the bone mass distribution and apparent stiffness than the previous RSLs and EDLs. Furthermore, this approach can be used for abnormal gait cycles which have higher interindividual variation.

Determination of the representative static loads for cyclically repeated dynamic loads: a case study of bone remodeling simulation with gait loads.

BACKGROUND AND OBJECTIVE: Bone has the self-optimizing capability to adjust its structure in order to efficiently support external loads. Bone remodeling simulations have been developed to reflect the above characteristics in a more effective way. In most studies, however, only a set of static loads have been empirically determined although both static and dynamic loads affect bone remodeling phenomenon. The goal of this study is to determine the representative static loads (RSLs) to efficiently consider the statically equivalent effect of cyclically repeated dynamic loads on bone remodeling simulation. METHODS: Based on the concept of two-scale approach, the RSLs for the gait cycles are determined from five subjects. First, the gait profiles at the hip joint are selected from the public database and then are preprocessed. The finite element model of the proximal femur is constructed from the clinical CT scan data to determine the strain energy distribution during the gait cycles. An optimization problem is formulated to determine the candidate static loads that minimize the errors of the spatial strain energy distribution for five gait profiles. Then, all candidate static loads from five gait profiles are partitioned into multiple clusters. The RSLs and the corresponding coefficients can be determined at the center of the densest cluster. For verification, topology optimization is separately conducted with the whole gait cycle (reference), empirically determined loads (conventional), and the RSLs (proposed). The strain energy density-based bone remodeling simulation is also conducted for another comparison. RESULTS: For the gait loads, the use of the RSLs enables a 99% reduction of the function calls with negligible errors in the bone spatial distribution (6.75% for two representative static loads and 6.24% for three representative static loads) and apparent stiffness (4.84% for two representative static loads and 4.47% for three representative static loads), compared with the use of a whole gait cycle as reference. CONCLUSION: This study shows the feasibility of the RSLs and provides a theoretical foundation for investigating the relationship between static and dynamic loads in the aspect of bone remodeling simulation.