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. 2020 Jan 23;10:1035. doi: 10.1038/s41598-020-57912-z

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© The Author(s) 2020

Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/.

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Schematic representation for the calculation of the centre of rotation and its translation on the helical axis. The centre of mass of the talus in (a) neutral, (b) inversion and (c) eversion positions was computed based on the grey-intensity value of the PedCAT images. (d) A sphere-fitting approach was used to define the parameters of a sphere (purple) with centre on the helical axis (dashed line) and with the centre of mass of the talus in the rotated configurations (orange and yellow dots) on its surface. The centre of rotation of the talus relative to the calcaneus was determined as the centre of such sphere (purple dot). (e) The distances from the centre of rotation (CoR) to the centre of mass of the talus in neutral (R_n), inversion (R_i) and eversion (R_e = R_i) positions were computed. (f) The translation of the centre of rotation (i.e. shift) was defined as the difference between such distances (Shift = R_n − R_n′).