- Volume 26 Issue 6
DOI QR Code
Comparative Study on Axes of Rotation Data by Within-Subjects Designs
피험자내 설계에 의한 회전축자료의 비교연구
- Kim, Jinuk (Department of Physical Education, Kunsan National University)
- 김진욱 (군산대학교 체육학과)
- Received : 2013.07.11
- Accepted : 2013.10.15
- Published : 2013.12.31
The axis of rotation in biomechanics is a major tool to investigate joint function; therefore, many methods to estimate the axis of rotation have been developed. However, there exist several problems to describe, estimate, and test the axis statistically. The axis is directional data(axial data) and it should not be analyzed with traditional statistics. A proper comparative method should be considered to compare axis estimating methods for the same given data ANOVA (analysis of variance) is a frequently used statistical method to compare treatment means in experimental designs. In case of the axial data response assumed to come from Watson distribution, there are a few ANOVA method options. This study constructed ANOVA models for within-subjects designs of axial data. Two models (one within-subjects factor and two within-subjects factors crossed design) were considered. The empirical data used in this study were instantaneous axes of rotation of flexion/extension at the knee joint and the flexion/extension and pronation/supination at the elbow joint. The results of this study can be further applied to the various analysis of experimental designs.
- Blankevoort, L., Huiskes, R. and de Lange, A. (1990). Helical axes of passive knee joint motions, Journal of Biomechanics, 23, 1219-1229. https://doi.org/10.1016/0021-9290(90)90379-H
- Cerveri, P., Lopomo, N., Pedotti, A. and Ferrigno, G. (2005). Derivation of centers and axes of notation for wrist and fingers in a hand kinematic model: Methods and reliability results, Annals of Biomedical Engineering, 33, 402-412. https://doi.org/10.1007/s10439-005-1743-9
- Chang, L. Y. and Pollard, N. S. (2007). Robust estimation of dominant axis of rotation, Journal of Biomechanics, 40, 2707-2715. https://doi.org/10.1016/j.jbiomech.2007.01.010
- Ehrig, R. M., Taylor, W. R., Duda, G. N. and Heller, M. O. (2007). A survey of formal methods for determining functional joint axes, Journal of Biomechanics, 40, 2150-2157. https://doi.org/10.1016/j.jbiomech.2006.10.026
- Figueiredo, A. (2006). Two-way analysis of variance for data from a concentrated bipolar Watson distribution, Journal of Applied Statistics, 33, 575-581. https://doi.org/10.1080/02664760600679619
- Fisher, N. I., Lewis, T. and Embleton, B. J. J. (1993). Statistical Analysis of Spherical Data, Cambridge University Press, New York.
- Gamage, S. S. H. U. and Lasenby, J. (2002). New least squares solutions for estimating the average center of rotation and the axis of rotation, Journal of Biomechanics, 35, 87-93. https://doi.org/10.1016/S0021-9290(01)00160-9
- Greenwood (2003). Advanced Dynamics,Cambridge University Press, New York.
- Halvorsen, K., Lesser, M. and Lundberg, A. (1999). A new method for estimating the axis of rotation and the center of rotation, Journal of Biomechanics, 32, 1221-1227. https://doi.org/10.1016/S0021-9290(99)00120-7
- Hogg, R. V., McKean, J. W. and Craig, A. T. (2005). Introduction to Mathematical Statistics, (6th ed.). Upper Saddle River, Pearson Education, Inc, NJ.
- Keppel, G. and Wickens, T. D. (2004). Design and Analysis : A Researcher's Handbook, (4th ed.), Upper Saddle River, Pearson Education, Inc, NJ.
- Kim, J. U. (2009). The analysis of axis of rotation of knee joint using directional statistics, The Korean Journal of Physical Education, 48, 615-623.
- Kim, J. U. (2010a). The statistical test on the mean axes of rotation of knee joint consistent with the coordinate axis, The Korean Journal of Physical Education, 49, 419-427.
- Kim, J. U. (2010b). The validity test of upper.forearm coordinate system and the exploratory analysis of the interactive effect between flexion/extension and pronation/supination during elbow joint motion, Korean Journal of Sport Biomechanics, 20, 117-127. https://doi.org/10.5103/KJSB.2010.20.2.117
- Kuehl, R. (2000). Design of experiments : Statistical principles of research design and analysis, (2nd ed). Pacific Groove, Duxbury Press, CA.
- Leitch, J., Stebbins, J. and Zavatsky, A. B. (2010). Subject-specific axes of the ankle joint complex, Journal of Biomechanics, 43, 2923-2928. https://doi.org/10.1016/j.jbiomech.2010.07.007
- MacWilliams, B. A. (2008). A comparison of four functional methods to determine centers and axes of rotations, Gait & Posture, 28, 673-679. https://doi.org/10.1016/j.gaitpost.2008.05.010
- MacWilliams, B. A., Sardelli, M. C. and Tashjian, R. Z. (2010). A functional axis of based upper extremity model and associated calibration procedure, Gait & Posture, 31, 289-291. https://doi.org/10.1016/j.gaitpost.2009.10.017
- Mardia, K. V. and Jupp, P. (2000). Directional statistics, (2nd ed.). West Sussex, John Wiley and Sons Ltd, England.
- Metzger, M. F., Faruk Senan, N. A., O'Reilly, O. M. and Lotz, J. C. (2010). Minimiaing errors associated with calculating the location of the helical axis for spinal motions, Journal of Biomechanics, 43, 2822-2829. https://doi.org/10.1016/j.jbiomech.2010.05.034
- Schache, A. G., Baker, R. and Lamoreux, L. W. (2006). Defining the knee joint flexion-extension axis for purposes of quantitative gait analysis: An evaluation of methods, Gait & Posture, 24, 100-109. https://doi.org/10.1016/j.gaitpost.2005.08.002
- Schwartz, M. H. and Rozumalski, A. (2005). A new method for estimating joint parameter from motion data, Journal of Biomechanics, 38, 107-116. https://doi.org/10.1016/j.jbiomech.2004.03.009
- Sheehan, F. T. (2007). The finite helical axis of the knee joint: A non-invasive in vivo study using fast-PC MRI, Journal of Biomechanics, 40, 1038-1047. https://doi.org/10.1016/j.jbiomech.2006.04.006
- Soderkvist, I. and Wedin, p. (1993). Determining the movements of the skeleton using well-configured markers, Journal of Biomechanics, 26, 1473-1477. https://doi.org/10.1016/0021-9290(93)90098-Y
- Stephens, M. A. (1982). Use of the von Mises distribution to analyse continuous proportions, Biometrika, 69, 197-203. https://doi.org/10.1093/biomet/69.1.197
- Strang, G. (2003). Introduction to Linear Algebra, (3rd ed.). Wellesley, MA : Wellesley-Cambridge Press.
- Tay, S. C., van Riet, R., Kazunari, T., Amrami, K. K., An, K. N. and Berger, R. A. (2010). In-vivo kinematic analysis of forearm rotation using helical axis analysis, Clinical Biomechanics, 25, 655-659. https://doi.org/10.1016/j.clinbiomech.2010.03.010
- Watson, G. S. and Williams, E. J. (1956). On the construction of significance tests on the circle and the sphere, Biometrika, 43, 344-352. https://doi.org/10.1093/biomet/43.3-4.344
- Weerahandi, S. (2004). Generalized Inference in Repeated Measures: Exact Methods in MANOVA and Mixed Models, Hoboken, John Wiley & Sons, Inc., NJ.
- Woltring, H. J. (1990). Data Processing and Error Analysis,. In N. Berme, & A. Cappozzo (Eds.), Biomechanics of human movement : Applications in rehabilitation, Sport and Ergonomics (pp. 203-237). Washington, Bertec Corporation, OH.