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On intrinsic equivalences of the finite helical axis, the instantaneous helical axis, and the SARA approach. A mathematical perspective

On intrinsic equivalences of the finite helical axis, the instantaneous helical axis, and the SARA approach. A mathematical perspective
On intrinsic equivalences of the finite helical axis, the instantaneous helical axis, and the SARA approach. A mathematical perspective
Accurate determination of joint axes is essential for understanding musculoskeletal function. Whilst numerous algorithms to compute such axes exist, the conditions under which each of the methods performs best remain largely unknown. Typically, algorithms are evaluated for specific conditions only limiting the external validity of conclusions regarding their performance. We derive exact mathematical relationships between three commonly used algorithms for computing joint axes from motion data: finite helical axes (FHA), instantaneous helical axes (IHA) and SARA (symmetrical axis of rotation approach), including relationships for an extension to the mean helical axes methods that facilitate determining joint centres and axes. Through the derivation of a sound mathematical framework to objectively compare the algorithms we demonstrate that the FHA and SARA approach are equivalent for the analysis of two time frames. Moreover, we show that the position of a helical axis derived from the IHA using positional data is affected by a systematic error perpendicular to the true axis direction, whereas the axis direction is identical to those computed with either the FHA or SARA approach (true direction). Finally, with an appropriate choice of weighting factors the mean FHA (MFHA) method is equivalent to the Symmetrical Centre of Rotation Estimation (SCoRE) algorithm for determination of a Centre of Rotation (CoR), and similarly, equivalent to the SARA algorithm for determination of an Axis of Rotation (AoR). The deep understanding of the equivalences between methods presented here enables readers to choose numerically efficient, robust methods for determining AoRs and CoRs with confidence.
Functional gait analysis , Joint axes, Joint centres, SARA, SCoRE, Helical Axes
0021-9290
Ehrig, R.M.
7f6eeae1-ec9f-4a97-8467-f83c84f99cc5
Heller, M.O.
3da19d2a-f34d-4ff1-8a34-9b5a7e695829
Ehrig, R.M.
7f6eeae1-ec9f-4a97-8467-f83c84f99cc5
Heller, M.O.
3da19d2a-f34d-4ff1-8a34-9b5a7e695829

Ehrig, R.M. and Heller, M.O. (2019) On intrinsic equivalences of the finite helical axis, the instantaneous helical axis, and the SARA approach. A mathematical perspective. Journal of Biomechanics. (doi:10.1016/j.jbiomech.2018.12.034).

Record type: Article

Abstract

Accurate determination of joint axes is essential for understanding musculoskeletal function. Whilst numerous algorithms to compute such axes exist, the conditions under which each of the methods performs best remain largely unknown. Typically, algorithms are evaluated for specific conditions only limiting the external validity of conclusions regarding their performance. We derive exact mathematical relationships between three commonly used algorithms for computing joint axes from motion data: finite helical axes (FHA), instantaneous helical axes (IHA) and SARA (symmetrical axis of rotation approach), including relationships for an extension to the mean helical axes methods that facilitate determining joint centres and axes. Through the derivation of a sound mathematical framework to objectively compare the algorithms we demonstrate that the FHA and SARA approach are equivalent for the analysis of two time frames. Moreover, we show that the position of a helical axis derived from the IHA using positional data is affected by a systematic error perpendicular to the true axis direction, whereas the axis direction is identical to those computed with either the FHA or SARA approach (true direction). Finally, with an appropriate choice of weighting factors the mean FHA (MFHA) method is equivalent to the Symmetrical Centre of Rotation Estimation (SCoRE) algorithm for determination of a Centre of Rotation (CoR), and similarly, equivalent to the SARA algorithm for determination of an Axis of Rotation (AoR). The deep understanding of the equivalences between methods presented here enables readers to choose numerically efficient, robust methods for determining AoRs and CoRs with confidence.

Text
Demystifying helical axes J Biomech author accepted version - Accepted Manuscript
Restricted to Repository staff only until 3 January 2020.
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De-mystifying helical axes J Biomech Supplementary material author accepted version
Restricted to Repository staff only until 3 January 2020.
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More information

Accepted/In Press date: 19 December 2018
e-pub ahead of print date: 3 January 2019
Keywords: Functional gait analysis , Joint axes, Joint centres, SARA, SCoRE, Helical Axes

Identifiers

Local EPrints ID: 427239
URI: https://eprints.soton.ac.uk/id/eprint/427239
ISSN: 0021-9290
PURE UUID: 9f49df09-c35b-4e0f-98d9-26ddf495d1f6
ORCID for M.O. Heller: ORCID iD orcid.org/0000-0002-7879-1135

Catalogue record

Date deposited: 09 Jan 2019 17:30
Last modified: 15 Aug 2019 00:36

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