Department of Information Engineering, University of Padova, Via Gradenigo 6/B, Padova, IT 35131, Italy.
J Biomech. 2012 Feb 2;45(3):595-601. doi: 10.1016/j.jbiomech.2011.10.040. Epub 2011 Dec 15.
We present a robust and computationally inexpensive method to estimate the lengths and three-dimensional moment arms for a large number of musculotendon actuators of the human lower limb. Using a musculoskeletal model of the lower extremity, a set of values was established for the length of each musculotendon actuator for different lower limb generalized coordinates (joint angles). A multidimensional spline function was then used to fit these data. Muscle moment arms were obtained by differentiating the musculotendon length spline function with respect to the generalized coordinate of interest. This new method was then compared to a previously used polynomial regression method. Compared to the polynomial regression method, the multidimensional spline method produced lower errors for estimating musculotendon lengths and moment arms throughout the whole generalized coordinate workspace. The fitting accuracy was also less affected by the number of dependent degrees of freedom and by the amount of experimental data available. The spline method only required information on musculotendon lengths to estimate both musculotendon lengths and moment arms, thus relaxing data input requirements, whereas the polynomial regression requires different equations to be used for both musculotendon lengths and moment arms. Finally, we used the spline method in conjunction with an electromyography driven musculoskeletal model to estimate muscle forces under different contractile conditions, which showed that the method is suitable for the integration into large scale neuromusculoskeletal models.
我们提出了一种强大且计算成本低廉的方法，用于估计人体下肢大量肌肉肌腱驱动器的长度和三维力臂。使用下肢的肌肉骨骼模型，为每个肌肉肌腱驱动器的长度建立了一组值，这些值对应于不同的下肢广义坐标（关节角度）。然后使用多维样条函数对这些数据进行拟合。通过相对于感兴趣的广义坐标对肌肉肌腱长度样条函数进行求导，可以获得肌肉力臂。将这种新方法与以前使用的多项式回归方法进行了比较。与多项式回归方法相比，多维样条方法在整个广义坐标工作空间中估算肌肉肌腱长度和力臂的误差更小。拟合精度也较少受到依赖自由度数量和可用实验数据量的影响。样条方法仅需要肌肉肌腱长度的信息即可估计肌肉肌腱长度和力臂，从而放宽了数据输入要求，而多项式回归则需要为肌肉肌腱长度和力臂使用不同的方程。最后，我们将样条方法与肌电图驱动的肌肉骨骼模型结合使用，以在不同的收缩条件下估算肌肉力，这表明该方法适合于整合到大规模的神经肌肉骨骼模型中。
