Department of Mechanical Engineering, Katholieke Universiteit Leuven, Division PMA, Celestijnenlaan 300B, B-3001 Heverlee, Belgium.
J Biomech. 2011 Oct 13;44(15):2595-600. doi: 10.1016/j.jbiomech.2011.08.022. Epub 2011 Sep 14.
This paper compares geometry-based knee axes of rotation (transepicondylar axis and geometric center axis) and motion-based functional knee axes of rotation (fAoR). Two algorithms are evaluated to calculate fAoRs: Gamage and Lasenby's sphere fitting algorithm (GL) and Ehrig et al.'s axis transformation algorithm (SARA). Calculations are based on 3D motion data acquired during isokinetic dynamometry. AoRs are validated with the equivalent axis based on static MR-images. We quantified the difference in orientation between two knee axes of rotation as the angle between the projection of the axes in the transversal and frontal planes, and the difference in location as the distance between the intersection points of the axes with the sagittal plane. Maximum differences between fAoRs resulting from GL and SARA were 5.7° and 15.4mm, respectively. Maximum differences between fAoRs resulting from GL or SARA and the equivalent axis were 5.4°/11.5mm and 8.6°/12.8mm, respectively. Differences between geometry-based axes and EA are larger than differences between fAoR and EA both in orientation (maximum 10.6°).and location (maximum 20.8mm). Knee joint angle trajectories and the corresponding accelerations for the different knee axes of rotation were estimated using Kalman smoothing. For the joint angles, the maximum RMS difference with the MRI-based equivalent axis, which was used as a reference, was 3°. For the knee joint accelerations, the maximum RMS difference with the equivalent axis was 20°/s(2). Functional knee axes of rotation describe knee motion better than geometry-based axes. GL performs better than SARA for calculations based on experimental dynamometry.
本文比较了基于几何的膝关节旋转轴(髁间轴和几何中心轴)和基于运动的功能性膝关节旋转轴(fAoR)。评估了两种算法来计算 fAoR:Gamage 和 Lasenby 的球体拟合算法(GL)和 Ehrig 等人的轴变换算法(SARA)。计算基于等速测力时获得的 3D 运动数据。AoRs 通过基于静态 MRI 的等效轴进行验证。我们将两个膝关节旋转轴之间的方向差异量化为轴在横切和额状面中的投影之间的角度,以及轴与矢状面交点之间的位置差异为距离。GL 和 SARA 产生的 fAoR 之间的最大差异分别为 5.7°和 15.4mm。GL 或 SARA 产生的 fAoR 与等效轴之间的最大差异分别为 5.4°/11.5mm 和 8.6°/12.8mm。几何轴与 EA 之间的差异大于 fAoR 与 EA 之间的差异,无论是在方向(最大 10.6°)还是位置(最大 20.8mm)。使用卡尔曼平滑法估计了不同膝关节旋转轴的关节角度轨迹及其对应的加速度。对于关节角度,与基于 MRI 的等效轴的最大 RMS 差异(用作参考)为 3°。对于膝关节加速度,与等效轴的最大 RMS 差异为 20°/s(2)。功能性膝关节旋转轴比基于几何的轴更能描述膝关节运动。GL 在基于实验测力的计算中比 SARA 表现更好。