Medical Engineering and Physics 37 (2015) 948–955 Contents lists available at ScienceDirect Medical Engineering and Physics journal homepage: www.elsevier.com/locate/medengphy New equations to calculate 3D joint centres in the lower extremities Martin Sandau a,b,∗ , Rikke V. Heimbürger c , Chiara Villa c , Karl E. Jensen d , Thomas B. Moeslund e , Henrik Aanæs f , Tine Alkjær a , Erik B. Simonsen a a Department of Neuroscience and Pharmacology, University of Copenhagen, 2200 Copenhagen, Denmark b Security Consulting, The Danish Institute of Fire and Security Technology, 2650 Hvidovre, Denmark c Department of Forensic Medicine, University of Copenhagen, 2100 Copenhagen, Denmark d Department of Radiology, Rigshospitalet, 2100 Copenhagen, Denmark e Department of Architecture, Design and Media Technology, Aalborg University, 9200 Aalborg, Denmark f Department of Informatics and Mathematics, Technical University of Denmark, 2800 Kgs. Lyngby, Denmark article info Article history: Received 31 October 2014 Revised 1 June 2015 Accepted 19 July 2015 Keywords: Gait Biomechanics Conventional Gait Model Marker set Motion capture Motion analysis abstract Biomechanical movement analysis in 3D requires estimation of joint centres in the lower extremities and this estimation is based on extrapolation from markers placed on anatomical landmarks. The purpose of the present study was to quantify the accuracy of three established set of equations and provide new improved equations to predict the joint centre locations. The ‘true’ joint centres of the knee and ankle joint were ob- tained in vivo by MRI scans on 10 male subjects whereas the ‘true’ hip joint centre was obtained in 10 male and 10 female cadavers by CT scans. For the hip joint the errors ranged from 26.7 (8.9) to 29.6 (7.5) mm, for the knee joint 5.8 (3.1) to 22.6 (3.3) mm and for the ankle joint 14.4 (2.2) to 27.0 (4.6) mm. This differed significantly from the improved equations by which the error for the hip joint ranged from 8.2 (3.6) to 11.6 (5.6) mm, for the knee joint from 2.9 (2.1) to 4.7 (2.5) mm and for the ankle joint from 3.4 (1.3) to 4.1 (2.0) mm. The coefficients in the new hip joint equations differed significantly between sexes. This difference depends on anatomical differences of the male and female pelvis. © 2015 IPEM. Published by Elsevier Ltd. All rights reserved. 1. Introduction Movement analyses of the lower extremities in three dimensions are typically based on motion capture of markers placed on anatom- ical landmarks according to a marker setup by which the anatomical hip, knee and ankle joint centres are predicted by regression equa- tions. However, the usage of markers has several kinematic and ki- netic limitations due to soft tissue artefacts (STA) and variations in the marker placement [1-7]. Besides STA and variability of the marker placement, errors associated with the regression equations used to calculate the joint centre locations are also considerable [8–10]. The regression equations are either based on functional methods or pre- dictive methods. Functional methods estimate the centre of rotation of a rigid motion between two segments through optimisation [11], but in many patient groups functional calibration has been reported to be difficult [10]. Most biomechanical analysis systems use regres- sion equations based on predictive methods to calculate joint centres. Kadaba et al. [12], Davis et al. [13] and Vaughan et al. [14] (Vaughan I) ∗ Corresponding author: Department of Neuroscience and Pharmacology, Univer- sity of Copenhagen, 2200 Copenhagen, DBI, Jernholmen 12, 2650 Hvidovre, Denmark. Tel: +45 61 20 16 65. E-mail address: msc@dbi-net.dk (M. Sandau). provided detailed descriptions of a marker based systems to calcu- late joint centres in the lower extremities. The marker setup used by Davis et al. [13], Kadaba et al. [12] and Vaughan et al. [15] (Vaughan II) is commonly referred to as Helen Hayes Hospital marker setup and the regression equations are referred to as the Plug-in gait model, VI- CON Clinical Manager or the Conventional Gait Model (CGM). In this study, these equations are referred to as CGM. The first marker setup by Vaughan I was based on 15 markers attached directly on the skin. The joint centre regression equations were estimated from a single subject (N = 1), which implies some bias. In 1999, Vaughan II adopted the marker setup in the CGM to im- prove the limitations of estimating the internal/external rotations as this marker set had a higher sensitivity by using wand markers. How- ever, accurate placement of the wands is difficult and they suffer from vibrations [7]. The original marker setup by Vaughan I is therefore still being used. The regression equations by Vaughan II were based on 12 male subjects but the errors of the joint centre predictions were omitted. The regression equations in the CGM are based on the HJC regression equation by Davis et al. [13] and chord functions to predict the knee and the ankle joint centres [16]. The HJC regression equa- tion was based on 25 male subjects and has been validated in later studies [8-10] showing significant errors, which were corrected with new regression equations. The chord functions predict the knee joint http://dx.doi.org/10.1016/j.medengphy.2015.07.001 1350-4533/© 2015 IPEM. Published by Elsevier Ltd. All rights reserved.