Pal Saikat, Langenderfer Joseph E, Stowe Joshua Q, Laz Peter J, Petrella Anthony J, Rullkoetter Paul J
Computational Biomechanics Lab, Department of Mechanical & Materials Engineering, University of Denver, 2390 S. York, Denver, CO 80208, USA.
Ann Biomed Eng. 2007 Sep;35(9):1632-42. doi: 10.1007/s10439-007-9334-6. Epub 2007 Jun 2.
In musculoskeletal modeling, reliable estimates of muscle moment arms are an important step in accurately predicting muscle forces and joint moments. The degree of agreement between the two common methods of calculating moment arms-tendon excursion (TE) and geometric origin-insertion, is currently unknown for the muscles crossing the knee joint. Further, measured moment arm data are subject to variability in estimation of attachment sites as points from irregular surfaces on the bones, and due to differences in joint kinematics observed in vivo. Thus, the objectives of the present study were to compare moment arms of major muscles crossing the knee joint obtained from TE and geometric methods using a finite element-based lower extremity model, and to quantify the effects of potential muscle origin-insertion and tibiofemoral kinematic variability on the predicted moment arms using probabilistic methods. A semiconstrained, fixed bearing, posterior cruciate-retaining total knee arthroplasty was included due to available in vivo kinematic data. In this study, muscle origin and insertion locations and kinematic variables were represented as normal distributions with standard deviations of 5 mm for origin-insertion locations and up to 1.6 mm and 3.0 degrees for the kinematic parameters. Agreement between the deterministic moment arm calculations from the two methods was excellent for the flexors, while differences in trends and magnitudes were observed for the extensor muscles. Model-predicted deterministic moment arms from both methods agreed reasonably with the experimental values from available literature. The uncertainty in input parameters resulted in substantial variability in predicted moment arms, with the size of 1-99% confidence interval being up to 41.3 and 35.8 mm for the TE and geometric methods, respectively. The sizeable range of moment arm predictions and associated excursions has the potential to affect a muscle's operating range on the force-length curve, thus affecting joint moments. In this study, moment arm predictions were more dependent on muscle origin-insertion locations than the kinematic variables. The important parameters from the TE method were the origin and insertion locations in the sagittal plane, while the insertion location in the sagittal plane was the dominant parameter using the geometric method.
在肌肉骨骼建模中，可靠地估计肌肉力臂是准确预测肌肉力量和关节力矩的重要一步。目前，对于跨越膝关节的肌肉，计算力臂的两种常用方法——肌腱 excursion（TE）法和几何原点 - 止点法之间的一致程度尚不清楚。此外，测量得到的力臂数据会因骨骼不规则表面上附着点估计的变异性以及体内观察到的关节运动学差异而受到影响。因此，本研究的目的是使用基于有限元的下肢模型比较通过 TE 法和几何法获得的跨越膝关节主要肌肉的力臂，并使用概率方法量化潜在的肌肉原点 - 止点和胫股运动学变异性对预测力臂的影响。由于有可用的体内运动学数据，纳入了一个半约束、固定承重、保留后交叉韧带的全膝关节置换模型。在本研究中，肌肉的原点和止点位置以及运动学变量被表示为正态分布，原点 - 止点位置的标准差为 5 毫米，运动学参数的标准差分别高达 1.6 毫米和 3.0 度。两种方法的确定性力臂计算结果在屈肌方面一致性极佳，而在伸肌方面观察到趋势和大小存在差异。两种方法模型预测的确定性力臂与现有文献中的实验值合理相符。输入参数的不确定性导致预测力臂存在显著变异性，TE 法和几何法的 1 - 99% 置信区间大小分别高达 41.3 毫米和 35.8 毫米。力臂预测的相当大的范围以及相关的 excursion 有可能影响肌肉在力 - 长度曲线上的工作范围，从而影响关节力矩。在本研究中，力臂预测对肌肉原点 - 止点位置的依赖性大于对运动学变量的依赖性。TE 法的重要参数是矢状面内的原点和止点位置，而使用几何法时矢状面内的止点位置是主导参数。
