A reference frame alignment method for the consistent interpretation of kinematic signals

Ariana Ortigas Vasquez, William R. Taylor, Barbara Postolka, Pascal Schütz, Allan Maas, Matthias Woiczinski, Thomas M. Grupp, Adrian Sauer
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Abstract

Kinematic analysis involves calculating signals from optical/inertial datapoints to represent the relative movement of joint segments. The exact choice of local segment frame orientation and position has been shown to drastically influence the shape and magnitude of the associated kinematic signals, making the consistent interpretation of the underlying motion a challenge [1,2]. Despite attempts to standardise the reporting of these signals [3], a lack of consensus around joint coordinate frame definitions remains. An approach capable of accommodating different analytical methods and reconciling these differences in frame alignment, while ensuring consistent interpretations, is therefore crucial. Given sets of kinematic data, can mathematical optimisation be leveraged to achieve a consistent interpretation of the underlying movement patterns, independent of joint axis definitions? Here, we assess a REference FRame Alignment MEthod (REFRAME) on the in vivo moving-fluoroscopy-based knee kinematics of 10 healthy subjects (5 trials of stair descent each) [4]. Using three methods of defining the flexion/extension axis (cylindrical axis (CA), functional flexion axis (FFA), and transepicondylar axis (TEA)), three different femoral frames were defined for each trial, in addition to a single tibial frame [1]. Rotations of the tibia relative to the femur were calculated, alongside translational positions of the femoral origins in the tibial frame. By implementing REFRAME (as a constrained nonlinear minimisation of ab/adduction and int/external rotation root-mean-square, in addition to all translation variances), local frames were repositioned and reorientated, to derive a set of "REFRAMEd" signals. Fig. 1 - Knee kinematics (rotations[°]: tibia relative to femur; translations[mm]: femur relative to tibia) during a sample stair descent trial, using three different primary axes, before (raw) and after REFRAME. (CA and FFA partially covered by TEA) Download : Download high-res image (294KB)Download : Download full-size image Across all subjects and trials, before REFRAME implementation, the maximum absolute differences between kinematic signals representing the same underlying movement, but derived using different joint axis approaches, reached 1.61° for flexion/extension, 12.00° for ab/adduction, and 12.02° for int/external rotation, in addition to 2.28 mm for mediolateral, 10.60 mm for anteroposterior, and 12.23 mm for proximodistal translations. After REFRAME, maximum differences peaked at 0.78°, 0.08° and 0.08° for flexion/extension, ab/adduction and int/external rotation, respectively; For translations, values peaked at 0.24 mm, 0.10 mm and 0.13 mm in the mediolateral, anteroposterior and proximodistal directions. Moreover, the three signals converged after REFRAME optimisation (Fig1). For each underlying movement pattern, the analysis approach (method of axis definition) affected the characteristics of the kinematic signals. By implementing REFRAME, tibial and femoral frames associated with each signal set were repositioned and reoriented to a common alignment, without requiring knowledge of the original femoral frames' alignment relative to each other. REFRAME thus enables the consistent interpretation of joint kinematics derived using different approaches.
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一种运动信号一致解释的参考系对齐方法
运动学分析包括计算来自光学/惯性数据点的信号来表示关节段的相对运动。局部片段帧方向和位置的精确选择已被证明会极大地影响相关运动学信号的形状和大小,使得对潜在运动的一致解释成为一项挑战[1,2]。尽管试图将这些信号的报告标准化,但在联合坐标框架定义方面仍然缺乏共识。因此,一种能够适应不同的分析方法和协调框架对齐中的这些差异,同时确保一致的解释的方法是至关重要的。给定一组运动学数据,是否可以利用数学优化来实现对潜在运动模式的一致解释,独立于关节轴定义?在这里,我们评估了参考框架对齐方法(REFRAME)对10名健康受试者(每组5次下楼梯试验)的体内基于移动透视的膝关节运动学的影响。使用三种确定屈伸轴的方法(圆柱轴(CA)、功能性屈伸轴(FFA)和经耻骨髁轴(TEA)),除了单个胫骨框架[1]外,每个试验还定义了三个不同的股骨框架。计算胫骨相对于股骨的旋转,以及胫骨框架内股骨起始点的平移位置。通过实现REFRAME(作为ab/内收和int/外旋转均方根的约束非线性最小化,以及所有平移方差),局部帧被重新定位和重新定向,以导出一组“REFRAMEd”信号。图1 -膝关节运动学(旋转[°]:胫骨相对于股骨;在REFRAME之前和之后,使用三个不同的主轴进行楼梯下降试验。平移[mm]:股骨相对于胫骨)。(CA和FFA部分被TEA覆盖)下载:下载高清图像(294KB)下载:在所有受试者和试验中,在REFRAME实施之前,使用不同关节轴入路获得的代表相同潜在运动的运动学信号之间的最大绝对差异,屈伸为1.61°,腹内收为12.00°,内旋/外旋为12.02°,此外中外侧为2.28 mm,前后位为10.60 mm,近远端平移为12.23 mm。REFRAME后,屈伸、内收和内旋/外旋的最大差异分别为0.78°、0.08°和0.08°;对于平移,中外侧、正前方和近远端方向的值在0.24 mm、0.10 mm和0.13 mm处达到峰值。REFRAME优化后,三个信号收敛(图1)。对于每个潜在的运动模式,分析方法(轴定义方法)影响运动信号的特征。通过实施REFRAME,与每个信号集相关的胫骨和股骨框架被重新定位并重新定向到一个共同的对齐,而不需要了解原始股骨框架相对于彼此的对齐。REFRAME因此可以使用不同的方法对关节运动学进行一致的解释。
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