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J Biomed Eng. 1990 Mar;12(2):143-9.

Evaluation of Euler's angles with a least squares method for the study of lumbar spine motion.

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Département d'Education Physique, Université de Montréal, Québec, Canada.


To analyse intervertebral movements, methods with a high level of accuracy are required. Stereoradiographic methods have been used for a number of years to describe intervertebral movements, but their major problem is to identify the same anatomical landmarks, not only on the pair of radiographs used for three-dimensional reconstruction, but also on all the pairs used to analyse the displacements. To minimize the errors due to the incorrect identification of anatomical landmarks, a least squares method to resolve the parameters of Euler's angles was validated by means of measurements made on a spine obtained from a cadaver. The accuracy of this method varied between 0.69 degrees and 0.71 degrees in rotation and between 0.28 mm and 0.77 mm in translation. In addition, this method significantly corrected the position of the anatomical landmarks. Euler's angles, used with a least squares estimate, can provide accurate and precise results.

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