Institute of Biomedical Engineering, National Taiwan University, Taipei, Taiwan.
Biomed Eng Online. 2013 Mar 7;12:20. doi: 10.1186/1475-925X-12-20.
Predictions of the forces transmitted by the redundant force-bearing structures in the knee are often performed using optimization methods considering only moment equipollence as a result of simplified knee modeling without ligament contributions. The current study aimed to investigate the influence of model complexity (with or without ligaments), problem formulation (moment equipollence with or without force equipollence) and optimization criteria on the prediction of the forces transmitted by the force-bearing structures in the knee.
Ten healthy young male adults walked in a gait laboratory while their kinematic and ground reaction forces were measured simultaneously. A validated 3D musculoskeletal model of the locomotor system with a knee model that included muscles, ligaments and articular surfaces was used to calculate the joint resultant forces and moments, and subsequently the forces transmitted in the considered force-bearing structures via optimization methods. Three problem formulations with eight optimization criteria were evaluated.
Among the three problem formulations, simultaneous consideration of moment and force equipollence for the knee model with ligaments and articular contacts predicted contact forces (first peak: 3.3-3.5 BW; second peak: 3.2-4.2 BW; swing: 0.3 BW) that were closest to previously reported theoretical values (2.0-4.0 BW) and in vivo data telemetered from older adults with total knee replacements (about 2.8 BW during stance; 0.5 BW during swing). Simultaneous consideration of moment and force equipollence also predicted more physiological ligament forces (< 1.0 BW), which appeared to be independent of the objective functions used. Without considering force equipollence, the calculated contact forces varied from 1.0 to 4.5 BW and were as large as 2.5 BW during swing phase; the calculated ACL forces ranged from 1 BW to 3.7 BW, and those of the PCL from 3 BW to 7 BW.
Model complexity and problem formulation affect the prediction of the forces transmitted by the force-bearing structures at the knee during normal level walking. Inclusion of the ligaments in a knee model enables the simultaneous consideration of equations of force and moment equipollence, which is required for accurately estimating the contact and ligament forces, and is more critical than the adopted optimization criteria.
在考虑膝关节冗余力承载结构传递力的预测时，通常使用优化方法，仅考虑简化的膝关节模型中韧带贡献缺失时的力矩等效，而不考虑韧带贡献。本研究旨在探讨模型复杂性（带或不带韧带）、问题公式化（力或力矩等效）和优化标准对膝关节力承载结构传递力预测的影响。
10 名健康年轻男性在步态实验室中行走，同时测量他们的运动学和地面反作用力。使用经过验证的包含肌肉、韧带和关节表面的运动系统 3D 骨骼肌肉模型来计算关节合力和力矩，然后通过优化方法计算所考虑力承载结构中的力传递。评估了三种问题公式化和八种优化标准。
在三种问题公式化中，同时考虑带韧带和关节接触的膝关节模型的力矩和力等效，预测接触力（第一峰值：3.3-3.5 BW；第二峰值：3.2-4.2 BW；摆动：0.3 BW），最接近之前报道的理论值（2.0-4.0 BW）和从全膝关节置换的老年患者中遥测的体内数据（站立时约 2.8 BW；摆动时 0.5 BW）。同时考虑力矩和力等效还预测了更生理的韧带力（<1.0 BW），这似乎与所使用的目标函数无关。不考虑力等效时，计算的接触力从 1.0 到 4.5 BW 不等，摆动时高达 2.5 BW；计算的 ACL 力范围从 1 BW 到 3.7 BW，PCL 力范围从 3 BW 到 7 BW。
模型复杂性和问题公式化会影响正常步行时膝关节力承载结构传递力的预测。在膝关节模型中纳入韧带可以同时考虑力和力矩等效方程，这是准确估计接触力和韧带力所必需的，比采用的优化标准更为关键。
