Statistical methods are increasingly used in biomechanics for studying bone geometry, bone density distribution and function in the population. However, relating population-based bone variation to strain during activity is computationally challenging. Here, we describe a new method for calculating strain in a population, using the Superposition Principle Method Squared (SPM²), and we demonstrate the method for calculating strain in human femurs. Computed-tomography images and motion capture while walking in 21 healthy adult women were obtained earlier. Variation of femur geometry and bone distribution were modelled using active shape and appearance modelling (ASAM). Femoral strain was modelled as the weighted sum of strain generated by each force in the model plus a strain variation assumed a quadratic function of the ASAM scores. The quadratic coefficients were fitted to 35 instances drawn from the ASAM model by varying each eigenmode by ± 2 SD. The equivalent strain in matched finite-element and SPM² calculations was obtained for 40 frames of walking for three independent cases and 50 ASAM instances. Finite-element and SPM2 solutions for walking were obtained in 44 and 3 min respectively. The SPM2 model accurately predicted strain for the three independent instances (R-squared 0.83–0.94) and the 50 ASAM instances (R-squared 0.95–1.00). The method developed enables fast and accurate calculation of population-based femoral strain.

生物力学中越来越多地使用统计方法来研究人群中的骨骼几何形状，骨骼密度分布和功能。然而，在活动期间将基于人群的骨骼变异与应变相关联在计算上具有挑战性。在这里，我们介绍一种使用叠加原理平方（SPM ^2）来计算总体中应变的新方法。），并演示了计算人股骨应变的方法。较早获得了21位健康成年女性行走时的计算机断层扫描图像和运动捕捉。使用活动形状和外观模型（ASAM）对股骨几何形状和骨骼分布的变化进行建模。股骨应变被建模为模型中每个力产生的应变的加权总和加上假设ASAM得分为二次函数的应变变化。通过将每个本征模改变±2 SD，将二次系数拟合到从ASAM模型得出的35个实例。匹配有限元和SPM ^2中的等效应变对于三个独立的案例和50个ASAM实例，获得了40个行走帧的计算结果。用于步行的有限元和SPM2解决方案分别在44分钟和3分钟内获得。SPM2模型可以准确预测三个独立实例（R平方0.83–0.94）和50个ASAM实例（R平方0.95–1.00）的应变。开发的方法可以快速准确地计算基于人群的股骨应变。