The Cho Chun Shik Graduate School of Green Transportation, Korea Advanced Institute of Science and Technology (KAIST), 193, Munji-ro, Yuseong-gu, Daejeon, Republic of Korea.
The Cho Chun Shik Graduate School of Green Transportation, Korea Advanced Institute of Science and Technology (KAIST), 193, Munji-ro, Yuseong-gu, Daejeon, Republic of Korea.
Comput Methods Programs Biomed. 2021 Mar;200:105924. doi: 10.1016/j.cmpb.2020.105924. Epub 2020 Dec 31.
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.
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.
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.
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.
骨骼具有自我优化能力，可调整其结构以有效支撑外部载荷。骨骼重塑模拟已被开发出来，以更有效地反映上述特征。然而，在大多数研究中，尽管静态和动态载荷都会影响骨骼重塑现象，但仅通过经验确定了一组静态载荷。本研究的目的是确定代表静态载荷（RSL），以有效地考虑周期性重复动态载荷对骨骼重塑模拟的静态等效影响。
基于两尺度方法的概念，从 5 位受试者中确定步态周期的 RSL。首先，从公共数据库中选择髋关节步态曲线，然后进行预处理。根据临床 CT 扫描数据构建股骨近端的有限元模型，以确定步态周期期间的应变能分布。构建一个优化问题，以确定候选静态载荷，使 5 种步态曲线的空间应变能分布误差最小。然后，将来自 5 种步态曲线的所有候选静态载荷划分为多个簇。RSL 和相应的系数可以在最密集簇的中心确定。为了验证，分别使用整个步态周期（参考）、经验确定的载荷（常规）和 RSL（提出）进行拓扑优化。还进行了基于应变能密度的骨骼重塑模拟进行了另一个比较。
对于步态载荷，与使用整个步态周期作为参考相比，使用 RSL 可将函数调用次数减少 99%，而骨骼空间分布的误差可以忽略不计（对于两个代表性的静态载荷为 6.75%，对于三个代表性的静态载荷为 6.24%），并且明显的刚度（对于两个代表性的静态载荷为 4.84%，对于三个代表性的静态载荷为 4.47%）。
本研究表明 RSL 的可行性，并为研究骨骼重塑模拟中静态和动态载荷之间的关系提供了理论基础。
