Institute of Lightweight Design and Structural Biomechanics, TU Wien, Gumpendorfer Straße 7, Vienna 1060, Austria.
Institute of Lightweight Design and Structural Biomechanics, TU Wien, Gumpendorfer Straße 7, Vienna 1060, Austria; Division Biomechanics, Karl Landsteiner University of Health Sciences, Dr. Karl-Dorrek-Straße 30, Krems 3500, Austria.
Comput Methods Programs Biomed. 2023 Jun;236:107549. doi: 10.1016/j.cmpb.2023.107549. Epub 2023 Apr 13.
Measuring physiological loading conditions in vivo can be challenging, as methods are invasive or pose a high modeling effort. However, the physiological loading of bones is also imprinted in the bone microstructure due to bone (re)modeling. This information can be retrieved by inverse bone remodeling (IBR). Recently, an IBR method based on micro-finite-element (µFE) modeling was translated to homogenized-FE (hFE) to decrease computational effort and tested on the distal radius. However, this bone has a relatively simple geometry and homogeneous microstructure. Therefore, the objective of this study was to assess the agreement of hFE-based IBR with µFE-based IBR to predict hip joint loading from the head of the femur; a bone with more complex loading as well as more heterogeneous microstructure.
hFE-based IBR was applied to a set of 19 femoral heads using four different material mapping laws. One model with a single homogeneous material for both trabecular and cortical volume and three models with a separated cortex and either homogeneous, density-dependent inhomogeneous, or density and fabric-dependent orthotropic material. Three different evaluation regions (full bone, trabecular bone only, head region only) were defined, in which IBR was applied. µFE models were created for the same bones, and the agreement of the predicted hip joint loading history obtained from hFE and µFE models was evaluated. The loading history was discretized using four unit load cases.
The computational time for FE solving was decreased on average from 500 h to under 1 min (CPU time) when using hFE models instead of µFE models. Using more information in the material model in the hFE models led to a better prediction of hip joint loading history. Inhomogeneous and inhomogeneous orthotropic models gave the best agreement to µFE-based IBR (RMSE% <14%). The evaluation region only played a minor role.
hFE-based IBR was able to reconstruct the dominant joint loading of the femoral head in agreement with µFE-based IBR and required considerably lower computational effort. Results indicate that cortical and trabecular bone should be modeled separately and at least density-dependent inhomogeneous material properties should be used with hFE models of the femoral head to predict joint loading.
活体测量生理负荷条件具有挑战性，因为方法具有侵入性或需要大量建模工作。然而，由于骨骼（再）建模，骨骼的生理负荷也会在骨骼微结构中留下痕迹。这种信息可以通过反向骨骼重塑（IBR）来获取。最近，一种基于微有限元（µFE）建模的 IBR 方法被转换为均匀有限元（hFE），以降低计算工作量，并在桡骨远端进行了测试。然而，这种骨骼具有相对简单的几何形状和均匀的微观结构。因此，本研究的目的是评估基于 hFE 的 IBR 与基于 µFE 的 IBR 预测股骨头部髋关节载荷的一致性；股骨头部的骨骼具有更复杂的载荷和更多异质的微观结构。
使用四种不同的材料映射定律，将 hFE 基于 IBR 应用于一组 19 个股骨头部。一个模型中，皮质和松质体积均采用单一均质材料，另外三个模型中，皮质采用分离的材料，分别为均质、密度相关非均质或密度和织构相关各向异性材料。在三个不同的评估区域（整个骨骼、松质骨仅、头部区域）中定义了 IBR 应用的区域。为相同的骨骼创建了 µFE 模型，并评估了从 hFE 和 µFE 模型预测的髋关节加载历史的一致性。使用四个单位载荷情况对加载历史进行离散化。
与使用 µFE 模型相比，使用 hFE 模型平均将 FE 求解的计算时间从 500 小时减少到不到 1 分钟（CPU 时间）。在 hFE 模型中使用更多的材料模型信息可以更好地预测髋关节加载历史。非均质和非均质各向异性模型与基于 µFE 的 IBR 具有最佳的一致性（RMSE%<14%）。评估区域仅起到次要作用。
基于 hFE 的 IBR 能够以与基于 µFE 的 IBR 一致的方式重建股骨头部的主导关节载荷，并且需要的计算工作量要低得多。结果表明，皮质和松质骨应该分开建模，并且至少应该使用密度相关非均质材料特性，以对头骨的 hFE 模型进行关节载荷预测。
