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A survey of formal methods for determining the centre of rotation of ball joints

机译：确定球形接头旋转中心的正式方法的概述

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The determination of an accurate centre of rotation (CoR) from segment marker positions is of interest across a wide range of applications, but particularly for clinical gait analysis and for estimating the hip joint centre during surgical intervention of the knee, for limb alignment purposes. For the first time in this survey of formal methods, we classify, analyse and compare different methods (geometric, algebraic, bias compensated algebraic, and Pratt sphere fit methods, as well as the centre transformation technique, the Holzreiter approach, the helical pivot technique, the Schwartz transformation techniques, the minimal amplitude point method and the Stoddart approach) for the determination of spherical joint centres from marker position data. In addition, we propose a new method, the symmetrical CoR estimation or SCoRE, in which the coordinates of the joint centre must only remain constant relative to each segment, thus not requiring the assumption that one segment should remain at rest. For each method, 1000 CoR estimations were analysed with the application of isotropic, independent and identically distributed Gaussian noise (standard deviation 0.1 cm) to each of the marker positions, to all markers on the segment simultaneously and the two in combination. For the test conditions used here, most techniques were capable of determining the CoR to within 0.3 cm, as long as the spherical range of motion (RoM) of the joint was 45 degrees or more. Under the most stringent conditions tested, however, the SCoRE was capable of best determining the CoR, to within approximately 1.2mm with a RoM of 20 degrees. The correct selection and application of these methodologies should help improve the accuracy of surgical navigation and clinical kinematic measurement. (c) 2005 Elsevier Ltd. All rights reserved.
机译：在广泛的应用中，从分段标记位置确定准确的旋转中心（CoR）是很有意义的，但是特别是对于临床步态分析以及在膝盖的外科手术中估计髋关节中心（以肢体对齐为目的）。在本次正式方法调查中，我们首次分类，分析和比较了不同的方法（几何，代数，偏差补偿代数和普拉特球体拟合方法，以及中心变换技术，Holzreiter方法，螺旋枢轴技术） ，Schwartz变换技术，最小振幅点方法和Stoddart方法）来从标记位置数据确定球形关节中心。此外，我们提出了一种新的方法，即对称CoR估计或SCoRE，其中，关节中心的坐标仅相对于每个线段必须保持恒定，因此不需要假设一个线段应保持静止。对于每种方法，通过将各向同性，独立且均匀分布的高斯噪声（标准偏差0.1 cm）应用于每个标记位置，同时应用于段上的所有标记以及将两者组合使用，分析了1000次CoR估计。对于此处使用的测试条件，只要关节的球形运动范围（RoM）为45度或以上，大多数技术都可以将CoR确定在0.3 cm以内。但是，在最严格的测试条件下，SCoRE能够以20度的RoM最佳地确定CoR，使其在约1.2mm之内。这些方法的正确选择和应用应有助于提高手术导航和临床运动学测量的准确性。 （c）2005 Elsevier Ltd.保留所有权利。

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