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Prescribing joint co-ordinates during model preparation to improve inverse kinematic estimates of elbow joint angles
Author’s Accepted Manuscript Prescribing Joint Co-ordinates during Model Preparation to Improve Inverse Kinematic Estimates of Elbow Joint Angles D.J.M. Wells, J.A. Alderson, J. Dunne, B.C. Elliott, C.J. Donnelly www.elsevier.com/locate/jbiomech
PII: DOI: Reference:
S0021-9290(16)31236-2 http://dx.doi.org/10.1016/j.jbiomech.2016.11.057 BM8018
To appear in: Journal of Biomechanics Accepted date: 19 November 2016 Cite this article as: D.J.M. Wells, J.A. Alderson, J. Dunne, B.C. Elliott and C.J. Donnelly, Prescribing Joint Co-ordinates during Model Preparation to Improve Inverse Kinematic Estimates of Elbow Joint Angles, Journal of Biomechanics, http://dx.doi.org/10.1016/j.jbiomech.2016.11.057 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting galley proof before it is published in its final citable form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
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Prescribing Joint Co-ordinates during Model Preparation to Improve
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Inverse Kinematic Estimates of Elbow Joint Angles
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Wells, D. J. M., 1Alderson J. A., 2Dunne, J, 1Elliott, B. C., and 1*Donnelly, C. J.
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School of Sport Science, Exercise and Health, the University of Western Australia, Perth, Australia
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Department of Bioengineering, Stanford University, Stanford, California, USA
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*Cyril J. Donnelly, M.Sc., PhD
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Assistant Professor
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School of Sport Science Exercise and Health
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Faculty of Life and Physical Sciences
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University of Western Australia
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CRAWLEY, WA, Australia, 6009
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P: +61 8 6488 3919; F: +61 8 6488 1039; E: [email protected]
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Word Count (Introduction – Discussion): 2,693
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Abstract
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To appropriately use inverse kinematic (IK) modelling for the assessment of human motion, a
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musculoskeletal model must be prepared to 1) match participant segment lengths (scaling) and 2) to
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align the model’s virtual markers positions with known, experimentally derived kinematic marker
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positions (marker registration). The purpose of this study was to investigate whether prescribing
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joint co-ordinates during the marker registration process (within the modelling framework OpenSim)
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will improve IK derived elbow kinematics during an overhead sporting task. To test this, the upper
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limb kinematics of eight cricket bowlers were recorded during two testing sessions, with a different
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tester each session. The bowling trials were IK modelled twice: once with an upper limb
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musculoskeletal model prepared with prescribed participant specific co-ordinates during marker
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registration - MRPC - and once with the same model prepared without prescribed co-ordinates – MR;
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and by an established direct kinematic (DK) upper limb model. Whilst both skeletal model
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preparations had strong inter-tester repeatability (MR: Statistical Parametric Mapping (SPM1D) = 0%
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different; MRPC: SPM1D = 0% different), when compared with DK model elbow FE waveform
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estimates, IK estimates using the MRPC model (RMSD = 5.2 ±2.0°, SPM1D = 68% different) were in
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closer agreement than the estimates from the MR model (RMSD = 44.5 ±18.5°, SPM1D = 100%
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different). Results show that prescribing participant specific joint co-ordinates during the marker
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registration phase of model preparation increases the accuracy and repeatability of IK solutions
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when modelling overhead sporting tasks in OpenSim.
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Key Words: OpenSim; upper limb modelling; sports biomechanics; SPM; cricket
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Introduction
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It has been suggested that inverse kinematic (IK) modelling may mitigate the influence of soft tissue
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artefact (STA) (Lu and O’Connor, 1999, Roux et al., 2002). With open access to these computational
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methods through the musculoskeletal modelling framework OpenSim (Delp et al., 2007), movement
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scientists are more often using IK as an alternative kinematic modelling approach for the analysis of
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high velocity tasks (Donnelly et al., 2012, McConnell et al., 2011, Morgan et al., 2014).
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Inverse kinematic modelling requires preparing a generic rigid-body skeletal model (with predefined
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degrees of freedom and ranges of motion) to match individual participants, through segment scaling
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(i.e. lengths and inertial properties) and marker registration. During marker registration, 1) the
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skeletal model is transformed through the adjustment of its generalised co-ordinates (i.e. joint
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angles) to best-fit selected experimental data, and 2) model virtual markers are mapped to the
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experimental marker positions in the global frame. Once repositioned, virtual markers are fixed
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within the relevant skeletal model segment frame. During IK, both segment lengths and virtual
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marker positions (within the segment reference frames) are fixed, so the accuracy of an IK solution is
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dependent on how well skeletal model preparation is performed. Lathrop et al. (2011) demonstrate
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that when IK modelling, the availability of participant-specific co-ordinate data during marker
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registration is an important source of error. They observed that due to the generic nature of skeletal
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models used for such processes, more effort is required to incorporate participant-specific data
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during model preparation.
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The musculoskeletal modelling framework OpenSim allows users to perform marker registration
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with or without specifying participant-specific segment orientation information (prescribing co-
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ordinates). The least-squared error optimisation process employed by OpenSim for marker
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registration can orientate the segments in any manner within the model’s pre-defined degrees of
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freedom and ranges of motion. It is proposed that an additional constraint of prescribed participant-
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specific co-ordinates can remove the ambiguity of the automated least squared optimisation process
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used to orient the segments of a rigid skeletal model.
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A ilot study by Dunne et al. (2013) investigated whether prescribing co-ordinates during marker
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registration improved IK estimates of lower limb gait kinematics from an actuated robot. Prescribing
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co-ordinates was found to reduce root mean square differences (RMSD) by 3.8°, 2.6° and 1.7° for the
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hip, knee and ankle joints respectively, but the process is yet to be verified among human
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participants.
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The aim of this study was to determine if prescribing participant-specific co-ordinates during marker
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registration could improve the 1) accuracy, and 2) inter-tester repeatability of IK derived elbow FE
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angles during a dynamic overhead task. Cricket bowling was the overhead sporting task and was in
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part selected based on pilot data presented in Appendix A. To test the accuracy of IK derived
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kinematic solutions, marker registration was performed with prescribed co-ordinates (MRPC) and
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without (MR) prescribed co-ordinates, then IK modelled elbow FE angles were calculated from each
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model preparation approach and compared with a criterion upper limb direct kinematic (DK) model.
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Inter-tester repeatability was tested by comparing elbow FE estimates calculated by MRPC and MR
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skeletal models across two testing sessions. It was hypothesised: 1) the MRPC model preparation
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process will improve the accuracy of IK solutions and subsequently report lower IK marker error
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(distance between skeletal model and corresponding experimental kinematic marker data) than
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when using a MR model preparation process; and, 2) the MRPC model preparation will demonstrate
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increased inter-tester repeatability of IK derived elbow FE kinematics when compared with the MR
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model estimates.
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Methods
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Eight (seven male; one female) international level, cricket bowlers were recruited (22.6 ±3.6 yrs;
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height 184.9 ±8.5 cm; mass 75.6 ±9.5 kg). Informed consent was obtained prior to participation, with
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experimental protocols approved by the University of Western Australia Human Research Ethics
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Committee (RA/4/1/5927).
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Each bowler participated in two independent testing sessions within a single day (session 1 and
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session 2) at which their upper limb kinematics were recorded using an external marker set (Figure
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1). Each testing session comprised of: one static A-pose trial with the elbows at maximum extension
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and shoulders abducted 45°; two static pointer trials to digitise the elbow epicondyles (Chin et al.,
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2009); and 12 dynamic bowling trials.
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All data were collected at 250 Hz by an 18-camera combined Vicon MX-13/MX-40 system. Bowling
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trial kinematic data was low pass filtered with a fourth order zero-lag Butterworth at participant-
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specific cut-off frequencies (19-21 Hz), as determined by a residual analysis method (Winter, 2005)
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and visual inspection.
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Direct Kinematic Modelling
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The upper limb DK model selected for comparison was chosen as it was purposely developed for the
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kinematic analysis of cricket bowling (Campbell et al., 2008; Chin et al., 2009, Lloyd et al., 2000). The
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model is representative of upper arm and forearm segments, connected by a six degree of freedom
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elbow joint. Relevant joint centres were estimated (Table 1.1), from which the anatomical co-
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ordinate systems were defined (Table 1.2).
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From static A-pose trials, the DK model calculated upper limb joint centre locations, and baseline
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elbow FE and abduction angles. The DK model was then applied to the dynamic bowling trials to
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derive elbow FE waveforms. Vicon Nexus (1.8.5) software was used for all computations involving DK
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modelling.
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Inverse Kinematic Modelling
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Experimental marker data were imported into OpenSim 3.2. Experimental marker data for static A-
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pose trials comprised of external marker positions, recorded during motion capture, and joint centre
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positions, estimated by the DK model; experimental marker data for the bowling trials comprised of
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external marker positions only.
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A Holzbaur Upper Limb Model (Holzbaur et al., 2005) was reduced to three segments (humerus,
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ulna, radius), two joints (elbow, radioulnar) and three degrees of freedom (elbow FE, elbow
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abduction/adduction, radioulnar pronation/supination). No shoulder-related kinematics were
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reported. The modified Holzbaur et al. (2005) model acted as a template, which was duplicated and
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prepared twice for each participant and session. In each preparation, the segment scaling process
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was identical; segment lengths were scaled to match the participant-specific DK modelled joint
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centre positions within static A-pose trials. During the marker registration stage, one scaled model
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underwent unmodified marker registration (MR). The second scaled model underwent marker
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registration with the additional constraint of prescribing participant specific elbow FE and abduction
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angle joint co-ordinates (MRPC) calculated by the DK model. Elbow abduction was only reported
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during scaling. IK was then performed using both MR and MRPC prepared models, producing two
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independent IK solutions for each trial. Consistent marker weightings were used throughout model
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preparation and IK (see Appendix B). No participant-specific co-ordinates were provided during IK.
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Marker error reported by OpenSim was recorded following the IK modelling of each trial for both MR
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and MRPC skeletal models.
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Analysis
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For each bowling trial, the time-varying elbow FE waveforms were calculated for each of the IK
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models, as well as the established DK upper limb model (Figure 2). These data were normalised to
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the ‘delivery phase’, beginning at upper arm horizontal (0%) and ending at ball release (100%) (Lloyd
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et al., 2000).
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Discrete elbow FE estimates within the delivery phase were extracted from MR, MRPC and DK
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modelled data: upper arm horizontal, maximum flexion, minimum flexion, ball release. Elbow
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extension range was calculated, i.e. maximum flexion minus minimum flexion.
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Statistics
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The first analysis compared MR and MRPC modelled elbow FE with criterion measure estimates. The
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second analysis assessed the inter-tester repeatability of each IK model (MR and MRPC)
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independently, comparing session 1 results with session 2. Each investigation involved analyses of
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both elbow FE waveforms and discrete elbow FE variables.
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Analyses involving elbow FE waveforms comprised both a time-independent zero dimensional (0D -
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RMSD) and a time-dependent one dimensional (1D - statistical parametric mapping (SPM1D))
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statistical tests (Li et al., 2016, Pataky et al., 2013). SPM1D analysis allows for the comparison of time
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normalised vector or scalar waveforms. Further information regarding SPM1D is provided in
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Appendix C.
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Discrete elbow FE events were analysed by one-way ANOVA and intra-class correlation (ICC) tests.
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Correlations were interpreted as weak (< 0.2), moderate (0.2 – 0.8) or strong (> 0.8) (Cohen, 1988).
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Static A-pose trial elbow FE and abduction angles recorded following MR model preparation were
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compared with DK modelled values using a paired samples t-test.
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Marker error was reported as RMSD for each frame (n = 2679) of bowling trial data for both MR and
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MRPC IK modelling approaches. Mean, maximum and cumulative RMSD marker errors were
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calculated over the bowling delivery. A two tailed, independent t-test was used to compare maker
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error values between IK modelling methods. An alpha of 0.05 was used for all statistical tests.
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Results
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During marker registration of the MR model, the elbow FE angles estimated for the static A-pose
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trials were different to DK model values (MR: -15.1 ±6.1°, DK: 14.1 ±8.1°; t = 10.99, p < 0.001), whilst
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abduction angles were similar (MR: 17.1 ±7.0°, DK: 18.3 ±7.2°; t = -0.71, p = 0.490).
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Performing IK with the MR model resulted in much lower elbow FE angles than the criterion DK
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model through the entire delivery phase (SPM1D = 100% time different; RMSD = 44.5 ±18.5°; Figure
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3.2). The MRPC model elbow FE angles were significantly greater at two independent occasions, from
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7-39% and 64-100% of the delivery phase (SPM1D = 68% time different; RMSD = 5.2 ±2.0°; Figure
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3.4). All discrete elbow FE event values calculated using the MR model were significantly less (p
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<0.001) and poorly correlated (ICC < 0.3) to equivalent DK model estimates. Discrete elbow FE event
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values calculated using the MRPC model were similar (p > 0.05), and moderate-highly correlated (ICC
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> 0.7) to DK model estimates (Table 2).
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The inter-tester analysis of IK modelling approaches showed that both MR (RMSD = 13.4 ±11.3°;
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SPM1D = 0% different, Figure 3.6) and MRPC (RMSD= 4.5 ±2.3°; SPM1D = 0% different, Figure 3.8)
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models produced repeatable elbow FE values. Likewise, no differences were found for either IK
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model following inter-tester analysis of discrete elbow FE variables. MR inter-tester discrete elbow
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FE event correlations were low-moderate (ICC <0.6), while MRPC correlations were high (ICC >0.8).
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Mean marker error (RMSD) during IK modelling when using the MR model was 0.025 ±0.010 m per
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frame (max 0.061 m; sum 65.74 m). Mean marker error when using the MRPC model was 0.022
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±0.008 m per frame (max 0.066 m; sum 59.75 m). None of these estimates were significantly
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different between IK modelling approaches.
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Discussion
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This study investigated whether prescribing participant-specific co-ordinates during marker
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registration improves accuracy (to an established model) and the inter-tester repeatability of IK
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modelled solutions. When compared with the established DK modelling approach, MRPC elbow FE
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estimates were shown to have better agreement than the MR estimates for both the waveform (1D)
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and discrete event (0D) analyses. This was not reflected by marker fitting errors (RMSD) during IK.
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Both MR and MRPC marker registration approaches proved repeatable (inter-tester) for estimating
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elbow FE during cricket bowling.
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Elbow FE values calculated at upper arm horizontal and ball release by the DK and MRPC models align
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with Portus et al. (2006). Portus and colleagues also specify that hyperextension is uncommon, with
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are consistent with the DK and MRPC elbow FE estimates, but not the MR model estimates. Results
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are comparable with Dunne et al. (2013), who reported small (<2°) RMSD values between their MRPC
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and DK model equivalents. When compared to Dunne et al. (2013), the RMSD reported for this study
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between MRPC and DK models (5.2 ±2.0°) was greater, which was likely due to the presence of STA
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among human participants. Our RMSD values also align with data reported by Lathrop et al. (2011),
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who were investigating knee FE calculated by a point cluster DK technique and IK solutions within
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the modelling framework OpenSim (4.8 ±2.5°). Notably, Lathrop and colleagues reported these
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values without the prescription of co-ordinates during marker registration. It is suggested that
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prescribing co-ordinates during marker registration is particularly important for modelling upper
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limb, due to larger ranges of motion possible at the shoulder and the presence of the
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pronation/supination degree of freedom.
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Following the marker registration phase of model preparation, the MR model estimated elbow
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hyperextension for every participant (-15.1 ±6.1°), where the DK model estimated elbow flexion
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(+14.1 ±8.1°). During marker registration, both MR and MRPC segments are fit to match the same
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experimental kinematic marker data while the participant is standing in a quasi-static A-pose. The 10
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rigid skeletal model is fit to corresponding experimental data within pre-defined joint degrees of
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freedom and ranges of motion for both modelling approaches using the same least squared marker
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fit cost function. However, the MRPC modelling approach possesses an additional constraint, which
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is participant-specific joint co-ordinates. The outcome is that virtual marker positions for the MR and
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MRPC models maintain the same relative segmental configurations, however they are oriented
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differently within each segment’s reference frame (i.e., rotated about the long axes of the segment)
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(Figure 4). When estimating the elbow kinematics of the participant while standing in the A-pose
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posture, the MR model estimated elbow hyperextension, where the MRPC model estimated elbow
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flexion, which again aligned with the DK estimates.
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The observed IK derived kinematic ‘offset’ observed between the MR and MRPC models during
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cricket bowling (see Figure 3.1, 3.3) are likely attributed to the aforementioned differences in virtual
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marker orientations following model preparation.
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differences between the MR and MRPC models were due to the simplistic nature of the upper limb
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model used. Specifically, the radius and ulna segments possessed no orientation information from
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the distal end of the kinematic chain as the hand was not modelled. This could explain why research
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by as Lathrop et al (2011) did not observe such large kinematic differences as in this study. Whilst
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the addition of more segments to the upper limb kinematic chain may reduce orientation errors, we
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propose that using prescribed co-ordinates during marker registration provides a repeatable and
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standardised procedure for kinematic chains of different lengths and configurations. These results
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clearly show that prescribing co-ordinates during marker registration substantially improves
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accuracy (to an established model), whilst providing a high degree of inter-tester repeatability for IK
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derived upper limb kinematics during overhead sporting tasks.
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When observing the waveform comparison of MRPC and DK elbow FE, there appears to be a 5° offset
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present (Figure 3.3). Whilst the SPM1D analysis demonstrates that this does fluctuate throughout
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the task (Figure 3.4), a persistent offset is likely explained by the different methods for modelling the
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Additionally, it is suspected the kinematic
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shoulder joint centre throughout the overhead movement. Upper limb kinematic analyses regularly
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recognise the shoulder joint as the largest source of measurement error, due to its complex
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geometry and the presence of many soft tissues (Reid et al., 2010); of which both factors come into
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consideration with dynamic, overhead tasks such as cricket bowling. We encourage future research
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to investigate overhead sporting movements with and without large ranges of glenohumeral,
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scapulothoracic and elbow joint ranges of motion to determine the sensitivity of elbow
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flexion/extension estimates to the modelling specificity of the glenohumeral and scapulothoracic
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joints.
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Contrary to our hypothesis, MR and MRPC marker error were similar, aligning with observations
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made by Dunne et al. (2013). It is recommended that marker error should only be used to assess
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how well a rigid skeletal model ‘fits’ the experimental data, and not as a validation of an IK solution.
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This research was limited by excluding the shoulder girdle during modelling. The greatest differences
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were observed at the shoulder during 90% of the delivery phase (Figure 3.6, 3.8), when the arm was
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at maximal circumduction and elevation. More advanced upper limb models (Seth et al., 2016), may
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allow investigation of shoulder girdle movement during overhead tasks. Another limitation was
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adopting a DK model as a criterion measure, however can be justified as there is currently no
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alternate gold standard model available for estimating the upper limb kinematics of cricket bowling
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(Lathrop et al., 2011) (see Leardini et al., 2005 and Della Croce et al., 2005).
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Conclusion
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Prescribing participant-specific joint co-ordinates during the marker registration phase of model
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preparation in OpenSim increases the accuracy and maintains the inter-tester repeatability of IK
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solutions when modelling dynamic overhead tasks. Additionally, marker error reported in OpenSim
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following IK should not be used as a measure of kinematic accuracy nor repeatability.
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Acknowledgements
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The authors wish to acknowledge the contribution to this study of Mr Tony Robey for continued
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technical support.
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Conflict of Interest
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The authors report no financial or personal relationships with other people or organizations that
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could have biased the presented work.
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Table 1: The joint centre (1.1), segment reference frame (1.2) and angle decomposition (1.3) definitions for the DK modelling approach
317 1.1: Joint Centre definition Shoulder Joint Centre (SJC)
Regression equation (as per Campbell et al., 2008) during static A-pose, stored within acromion and proximal upper arm technical frames. During bowling trials the joint centre is recreated virtually within both technical frames, with the mean deemed the final joint centre
Elbow Joint Centre
Lateral and medial elbow epicondyle locations (LE, ME) digitised using a “pointer” (as per
(EJC)
Chin et al., 2009) and stored as markers within distal upper arm technical frame. During bowling trials the joint centre is the midpoint of elbow epicondyles
Wrist Joint Centre (WJC)
Midpoint of markers placed on the medial and lateral styloid processes of the wrist (MWR, LWR) 1.2: Segment Frame: Line Order and Definition
Upper Arm
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Origin: EJC
1 (Y-axis): unit vector from EJC to SJC (superior positive) 2 (X-axis): cross-product of Y-axis and unit vector from LE and ME (anterior positive) 3 (Z-axis): orthogonal to X-Y plane (positive left to right) Origin: WJC Forearm
1 (Y-axis): unit vector from WJC to EJC (superior positive) 2 (X-axis): cross-product between Y-axis and unit vector from LWR to MWR (anterior positive) 3 (Z-axis): orthogonal to the X-Y plane (positive to right) 1.3: Angle Decomposition Estimated by decomposing the child segment (forearm) relative to the parent (upper arm) in accordance with the ISB standard:
Elbow
1: FE (Z axis) 2: Abduction/adduction (X axis) 3: Pronation/supination (Y axis) A negative (below zero) FE value indicates elbow hyperextension
318 319
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320 321
Table 2: Discrete Elbow FE Events Analysis: DK Comparison. ANOVA and ICC results comparing elbow FE events from each of the IK approaches with the DK modelling approach equivalents.
322 Mean (St dev) Elbow FE
ANOVA F
MRPC – DK
MR – DK
(p value)
p value
p value
0.941
MRPC
MR
DK
29.2°
-12.5°
26.9°
54.911
(±12.6°)
(±11.7°)
(±13.5°)
(<0.001)*
43.9°
0.0°
41.3°
103.021
(±11.8°)
(±14.2°)
(±13.8°)
(<0.001)*
20.6°
-17.1°
14.5°
54.737
(±6.1°)
(±10.5°)
(±6.7°)
(<0.001)*
20.7°
-4.8°
14.8°
59.589
(±6.1°)
(±7.6°)
(±6.9°)
(<0.001)*
Extension
23.3°
4.3°
26.7°
15.339
Range
(±12.8°)
(±9.6°)
(±14.2°)
(<0.001)*
Event UAH
Max
Min
BR
* indicates statistical significance p < 0.05
323
324 325 326
18
Sidǎk Post-Hoc Test
ICC MRPC - DK
MR - DK
<0.001*
0.964
0.065
0.107
<0.001*
0.723
0.038
0.924
<0.001*
0.960
0.090
0.059
<0.001*
0.739
0.136
0.821
<0.001*
0.977
0.265
327 328
19
329 330
20
331
21
Fig. 1: External Marker Set. Description of the external marker set configuration. Fig. 2: Graphical Representation of Data Collection and Workflow. Fig. 3: Waveform and SPM analyses. Comparison of each marker registration method and the criterion measure (Figures 3.1–3.4) and inter-tester repeatability analysis (Figures 3.5–3.8). Mean and standard deviation plots of each comparison are on the left, and SPM1D analyses are visualised on the right. The two comparisons to the criterion measure (Figures 3.2, 3.4) result in some periods of statistical difference, represented by the grey shaded areas and accompanied by a unique p-value. Fig. 4: A demonstration of how the marker registration methods result in different virtual marker positions within segment reference frames. An MR and an MRPC prepared skeletal model have been overlayed with neutral general co-ordinates (0° for all joint angles, 0 m for all translations) such that their segment reference frames are aligned; however, the virtual marker positions are visibly different, rotated about the long axes of the segments. Thus, when the MR and MRPC skeletal models are both used to model the same experimental data, they will require different elbow angle combinations to best-fit the recorded marker positions, and present with alternative IK solutions.
PII: DOI: Reference:
S0021-9290(16)31236-2 http://dx.doi.org/10.1016/j.jbiomech.2016.11.057 BM8018
To appear in: Journal of Biomechanics Accepted date: 19 November 2016 Cite this article as: D.J.M. Wells, J.A. Alderson, J. Dunne, B.C. Elliott and C.J. Donnelly, Prescribing Joint Co-ordinates during Model Preparation to Improve Inverse Kinematic Estimates of Elbow Joint Angles, Journal of Biomechanics, http://dx.doi.org/10.1016/j.jbiomech.2016.11.057 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting galley proof before it is published in its final citable form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
1
Prescribing Joint Co-ordinates during Model Preparation to Improve
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Inverse Kinematic Estimates of Elbow Joint Angles
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4
1
Wells, D. J. M., 1Alderson J. A., 2Dunne, J, 1Elliott, B. C., and 1*Donnelly, C. J.
5
1
School of Sport Science, Exercise and Health, the University of Western Australia, Perth, Australia
6
2
Department of Bioengineering, Stanford University, Stanford, California, USA
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8
*Cyril J. Donnelly, M.Sc., PhD
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Assistant Professor
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School of Sport Science Exercise and Health
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Faculty of Life and Physical Sciences
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University of Western Australia
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CRAWLEY, WA, Australia, 6009
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P: +61 8 6488 3919; F: +61 8 6488 1039; E: [email protected]
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16
Word Count (Introduction – Discussion): 2,693
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2
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Abstract
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To appropriately use inverse kinematic (IK) modelling for the assessment of human motion, a
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musculoskeletal model must be prepared to 1) match participant segment lengths (scaling) and 2) to
21
align the model’s virtual markers positions with known, experimentally derived kinematic marker
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positions (marker registration). The purpose of this study was to investigate whether prescribing
23
joint co-ordinates during the marker registration process (within the modelling framework OpenSim)
24
will improve IK derived elbow kinematics during an overhead sporting task. To test this, the upper
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limb kinematics of eight cricket bowlers were recorded during two testing sessions, with a different
26
tester each session. The bowling trials were IK modelled twice: once with an upper limb
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musculoskeletal model prepared with prescribed participant specific co-ordinates during marker
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registration - MRPC - and once with the same model prepared without prescribed co-ordinates – MR;
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and by an established direct kinematic (DK) upper limb model. Whilst both skeletal model
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preparations had strong inter-tester repeatability (MR: Statistical Parametric Mapping (SPM1D) = 0%
31
different; MRPC: SPM1D = 0% different), when compared with DK model elbow FE waveform
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estimates, IK estimates using the MRPC model (RMSD = 5.2 ±2.0°, SPM1D = 68% different) were in
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closer agreement than the estimates from the MR model (RMSD = 44.5 ±18.5°, SPM1D = 100%
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different). Results show that prescribing participant specific joint co-ordinates during the marker
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registration phase of model preparation increases the accuracy and repeatability of IK solutions
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when modelling overhead sporting tasks in OpenSim.
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Key Words: OpenSim; upper limb modelling; sports biomechanics; SPM; cricket
42 3
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Introduction
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It has been suggested that inverse kinematic (IK) modelling may mitigate the influence of soft tissue
45
artefact (STA) (Lu and O’Connor, 1999, Roux et al., 2002). With open access to these computational
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methods through the musculoskeletal modelling framework OpenSim (Delp et al., 2007), movement
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scientists are more often using IK as an alternative kinematic modelling approach for the analysis of
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high velocity tasks (Donnelly et al., 2012, McConnell et al., 2011, Morgan et al., 2014).
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Inverse kinematic modelling requires preparing a generic rigid-body skeletal model (with predefined
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degrees of freedom and ranges of motion) to match individual participants, through segment scaling
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(i.e. lengths and inertial properties) and marker registration. During marker registration, 1) the
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skeletal model is transformed through the adjustment of its generalised co-ordinates (i.e. joint
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angles) to best-fit selected experimental data, and 2) model virtual markers are mapped to the
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experimental marker positions in the global frame. Once repositioned, virtual markers are fixed
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within the relevant skeletal model segment frame. During IK, both segment lengths and virtual
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marker positions (within the segment reference frames) are fixed, so the accuracy of an IK solution is
57
dependent on how well skeletal model preparation is performed. Lathrop et al. (2011) demonstrate
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that when IK modelling, the availability of participant-specific co-ordinate data during marker
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registration is an important source of error. They observed that due to the generic nature of skeletal
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models used for such processes, more effort is required to incorporate participant-specific data
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during model preparation.
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The musculoskeletal modelling framework OpenSim allows users to perform marker registration
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with or without specifying participant-specific segment orientation information (prescribing co-
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ordinates). The least-squared error optimisation process employed by OpenSim for marker
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registration can orientate the segments in any manner within the model’s pre-defined degrees of
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freedom and ranges of motion. It is proposed that an additional constraint of prescribed participant-
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specific co-ordinates can remove the ambiguity of the automated least squared optimisation process
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used to orient the segments of a rigid skeletal model.
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A ilot study by Dunne et al. (2013) investigated whether prescribing co-ordinates during marker
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registration improved IK estimates of lower limb gait kinematics from an actuated robot. Prescribing
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co-ordinates was found to reduce root mean square differences (RMSD) by 3.8°, 2.6° and 1.7° for the
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hip, knee and ankle joints respectively, but the process is yet to be verified among human
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participants.
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The aim of this study was to determine if prescribing participant-specific co-ordinates during marker
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registration could improve the 1) accuracy, and 2) inter-tester repeatability of IK derived elbow FE
76
angles during a dynamic overhead task. Cricket bowling was the overhead sporting task and was in
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part selected based on pilot data presented in Appendix A. To test the accuracy of IK derived
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kinematic solutions, marker registration was performed with prescribed co-ordinates (MRPC) and
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without (MR) prescribed co-ordinates, then IK modelled elbow FE angles were calculated from each
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model preparation approach and compared with a criterion upper limb direct kinematic (DK) model.
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Inter-tester repeatability was tested by comparing elbow FE estimates calculated by MRPC and MR
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skeletal models across two testing sessions. It was hypothesised: 1) the MRPC model preparation
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process will improve the accuracy of IK solutions and subsequently report lower IK marker error
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(distance between skeletal model and corresponding experimental kinematic marker data) than
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when using a MR model preparation process; and, 2) the MRPC model preparation will demonstrate
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increased inter-tester repeatability of IK derived elbow FE kinematics when compared with the MR
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model estimates.
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Methods
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Eight (seven male; one female) international level, cricket bowlers were recruited (22.6 ±3.6 yrs;
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height 184.9 ±8.5 cm; mass 75.6 ±9.5 kg). Informed consent was obtained prior to participation, with
5
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experimental protocols approved by the University of Western Australia Human Research Ethics
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Committee (RA/4/1/5927).
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Each bowler participated in two independent testing sessions within a single day (session 1 and
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session 2) at which their upper limb kinematics were recorded using an external marker set (Figure
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1). Each testing session comprised of: one static A-pose trial with the elbows at maximum extension
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and shoulders abducted 45°; two static pointer trials to digitise the elbow epicondyles (Chin et al.,
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2009); and 12 dynamic bowling trials.
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All data were collected at 250 Hz by an 18-camera combined Vicon MX-13/MX-40 system. Bowling
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trial kinematic data was low pass filtered with a fourth order zero-lag Butterworth at participant-
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specific cut-off frequencies (19-21 Hz), as determined by a residual analysis method (Winter, 2005)
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and visual inspection.
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Direct Kinematic Modelling
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The upper limb DK model selected for comparison was chosen as it was purposely developed for the
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kinematic analysis of cricket bowling (Campbell et al., 2008; Chin et al., 2009, Lloyd et al., 2000). The
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model is representative of upper arm and forearm segments, connected by a six degree of freedom
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elbow joint. Relevant joint centres were estimated (Table 1.1), from which the anatomical co-
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ordinate systems were defined (Table 1.2).
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From static A-pose trials, the DK model calculated upper limb joint centre locations, and baseline
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elbow FE and abduction angles. The DK model was then applied to the dynamic bowling trials to
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derive elbow FE waveforms. Vicon Nexus (1.8.5) software was used for all computations involving DK
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modelling.
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Inverse Kinematic Modelling
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Experimental marker data were imported into OpenSim 3.2. Experimental marker data for static A-
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pose trials comprised of external marker positions, recorded during motion capture, and joint centre
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positions, estimated by the DK model; experimental marker data for the bowling trials comprised of
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external marker positions only.
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A Holzbaur Upper Limb Model (Holzbaur et al., 2005) was reduced to three segments (humerus,
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ulna, radius), two joints (elbow, radioulnar) and three degrees of freedom (elbow FE, elbow
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abduction/adduction, radioulnar pronation/supination). No shoulder-related kinematics were
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reported. The modified Holzbaur et al. (2005) model acted as a template, which was duplicated and
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prepared twice for each participant and session. In each preparation, the segment scaling process
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was identical; segment lengths were scaled to match the participant-specific DK modelled joint
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centre positions within static A-pose trials. During the marker registration stage, one scaled model
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underwent unmodified marker registration (MR). The second scaled model underwent marker
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registration with the additional constraint of prescribing participant specific elbow FE and abduction
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angle joint co-ordinates (MRPC) calculated by the DK model. Elbow abduction was only reported
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during scaling. IK was then performed using both MR and MRPC prepared models, producing two
128
independent IK solutions for each trial. Consistent marker weightings were used throughout model
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preparation and IK (see Appendix B). No participant-specific co-ordinates were provided during IK.
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Marker error reported by OpenSim was recorded following the IK modelling of each trial for both MR
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and MRPC skeletal models.
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Analysis
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For each bowling trial, the time-varying elbow FE waveforms were calculated for each of the IK
134
models, as well as the established DK upper limb model (Figure 2). These data were normalised to
7
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the ‘delivery phase’, beginning at upper arm horizontal (0%) and ending at ball release (100%) (Lloyd
136
et al., 2000).
137
Discrete elbow FE estimates within the delivery phase were extracted from MR, MRPC and DK
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modelled data: upper arm horizontal, maximum flexion, minimum flexion, ball release. Elbow
139
extension range was calculated, i.e. maximum flexion minus minimum flexion.
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Statistics
141
The first analysis compared MR and MRPC modelled elbow FE with criterion measure estimates. The
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second analysis assessed the inter-tester repeatability of each IK model (MR and MRPC)
143
independently, comparing session 1 results with session 2. Each investigation involved analyses of
144
both elbow FE waveforms and discrete elbow FE variables.
145
Analyses involving elbow FE waveforms comprised both a time-independent zero dimensional (0D -
146
RMSD) and a time-dependent one dimensional (1D - statistical parametric mapping (SPM1D))
147
statistical tests (Li et al., 2016, Pataky et al., 2013). SPM1D analysis allows for the comparison of time
148
normalised vector or scalar waveforms. Further information regarding SPM1D is provided in
149
Appendix C.
150
Discrete elbow FE events were analysed by one-way ANOVA and intra-class correlation (ICC) tests.
151
Correlations were interpreted as weak (< 0.2), moderate (0.2 – 0.8) or strong (> 0.8) (Cohen, 1988).
152
Static A-pose trial elbow FE and abduction angles recorded following MR model preparation were
153
compared with DK modelled values using a paired samples t-test.
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Marker error was reported as RMSD for each frame (n = 2679) of bowling trial data for both MR and
155
MRPC IK modelling approaches. Mean, maximum and cumulative RMSD marker errors were
156
calculated over the bowling delivery. A two tailed, independent t-test was used to compare maker
157
error values between IK modelling methods. An alpha of 0.05 was used for all statistical tests.
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158
Results
159
During marker registration of the MR model, the elbow FE angles estimated for the static A-pose
160
trials were different to DK model values (MR: -15.1 ±6.1°, DK: 14.1 ±8.1°; t = 10.99, p < 0.001), whilst
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abduction angles were similar (MR: 17.1 ±7.0°, DK: 18.3 ±7.2°; t = -0.71, p = 0.490).
162
Performing IK with the MR model resulted in much lower elbow FE angles than the criterion DK
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model through the entire delivery phase (SPM1D = 100% time different; RMSD = 44.5 ±18.5°; Figure
164
3.2). The MRPC model elbow FE angles were significantly greater at two independent occasions, from
165
7-39% and 64-100% of the delivery phase (SPM1D = 68% time different; RMSD = 5.2 ±2.0°; Figure
166
3.4). All discrete elbow FE event values calculated using the MR model were significantly less (p
167
<0.001) and poorly correlated (ICC < 0.3) to equivalent DK model estimates. Discrete elbow FE event
168
values calculated using the MRPC model were similar (p > 0.05), and moderate-highly correlated (ICC
169
> 0.7) to DK model estimates (Table 2).
170
The inter-tester analysis of IK modelling approaches showed that both MR (RMSD = 13.4 ±11.3°;
171
SPM1D = 0% different, Figure 3.6) and MRPC (RMSD= 4.5 ±2.3°; SPM1D = 0% different, Figure 3.8)
172
models produced repeatable elbow FE values. Likewise, no differences were found for either IK
173
model following inter-tester analysis of discrete elbow FE variables. MR inter-tester discrete elbow
174
FE event correlations were low-moderate (ICC <0.6), while MRPC correlations were high (ICC >0.8).
175
Mean marker error (RMSD) during IK modelling when using the MR model was 0.025 ±0.010 m per
176
frame (max 0.061 m; sum 65.74 m). Mean marker error when using the MRPC model was 0.022
177
±0.008 m per frame (max 0.066 m; sum 59.75 m). None of these estimates were significantly
178
different between IK modelling approaches.
9
179
Discussion
180
This study investigated whether prescribing participant-specific co-ordinates during marker
181
registration improves accuracy (to an established model) and the inter-tester repeatability of IK
182
modelled solutions. When compared with the established DK modelling approach, MRPC elbow FE
183
estimates were shown to have better agreement than the MR estimates for both the waveform (1D)
184
and discrete event (0D) analyses. This was not reflected by marker fitting errors (RMSD) during IK.
185
Both MR and MRPC marker registration approaches proved repeatable (inter-tester) for estimating
186
elbow FE during cricket bowling.
187
Elbow FE values calculated at upper arm horizontal and ball release by the DK and MRPC models align
188
with Portus et al. (2006). Portus and colleagues also specify that hyperextension is uncommon, with
189
are consistent with the DK and MRPC elbow FE estimates, but not the MR model estimates. Results
190
are comparable with Dunne et al. (2013), who reported small (<2°) RMSD values between their MRPC
191
and DK model equivalents. When compared to Dunne et al. (2013), the RMSD reported for this study
192
between MRPC and DK models (5.2 ±2.0°) was greater, which was likely due to the presence of STA
193
among human participants. Our RMSD values also align with data reported by Lathrop et al. (2011),
194
who were investigating knee FE calculated by a point cluster DK technique and IK solutions within
195
the modelling framework OpenSim (4.8 ±2.5°). Notably, Lathrop and colleagues reported these
196
values without the prescription of co-ordinates during marker registration. It is suggested that
197
prescribing co-ordinates during marker registration is particularly important for modelling upper
198
limb, due to larger ranges of motion possible at the shoulder and the presence of the
199
pronation/supination degree of freedom.
200
Following the marker registration phase of model preparation, the MR model estimated elbow
201
hyperextension for every participant (-15.1 ±6.1°), where the DK model estimated elbow flexion
202
(+14.1 ±8.1°). During marker registration, both MR and MRPC segments are fit to match the same
203
experimental kinematic marker data while the participant is standing in a quasi-static A-pose. The 10
204
rigid skeletal model is fit to corresponding experimental data within pre-defined joint degrees of
205
freedom and ranges of motion for both modelling approaches using the same least squared marker
206
fit cost function. However, the MRPC modelling approach possesses an additional constraint, which
207
is participant-specific joint co-ordinates. The outcome is that virtual marker positions for the MR and
208
MRPC models maintain the same relative segmental configurations, however they are oriented
209
differently within each segment’s reference frame (i.e., rotated about the long axes of the segment)
210
(Figure 4). When estimating the elbow kinematics of the participant while standing in the A-pose
211
posture, the MR model estimated elbow hyperextension, where the MRPC model estimated elbow
212
flexion, which again aligned with the DK estimates.
213
The observed IK derived kinematic ‘offset’ observed between the MR and MRPC models during
214
cricket bowling (see Figure 3.1, 3.3) are likely attributed to the aforementioned differences in virtual
215
marker orientations following model preparation.
216
differences between the MR and MRPC models were due to the simplistic nature of the upper limb
217
model used. Specifically, the radius and ulna segments possessed no orientation information from
218
the distal end of the kinematic chain as the hand was not modelled. This could explain why research
219
by as Lathrop et al (2011) did not observe such large kinematic differences as in this study. Whilst
220
the addition of more segments to the upper limb kinematic chain may reduce orientation errors, we
221
propose that using prescribed co-ordinates during marker registration provides a repeatable and
222
standardised procedure for kinematic chains of different lengths and configurations. These results
223
clearly show that prescribing co-ordinates during marker registration substantially improves
224
accuracy (to an established model), whilst providing a high degree of inter-tester repeatability for IK
225
derived upper limb kinematics during overhead sporting tasks.
226
When observing the waveform comparison of MRPC and DK elbow FE, there appears to be a 5° offset
227
present (Figure 3.3). Whilst the SPM1D analysis demonstrates that this does fluctuate throughout
228
the task (Figure 3.4), a persistent offset is likely explained by the different methods for modelling the
11
Additionally, it is suspected the kinematic
229
shoulder joint centre throughout the overhead movement. Upper limb kinematic analyses regularly
230
recognise the shoulder joint as the largest source of measurement error, due to its complex
231
geometry and the presence of many soft tissues (Reid et al., 2010); of which both factors come into
232
consideration with dynamic, overhead tasks such as cricket bowling. We encourage future research
233
to investigate overhead sporting movements with and without large ranges of glenohumeral,
234
scapulothoracic and elbow joint ranges of motion to determine the sensitivity of elbow
235
flexion/extension estimates to the modelling specificity of the glenohumeral and scapulothoracic
236
joints.
237
Contrary to our hypothesis, MR and MRPC marker error were similar, aligning with observations
238
made by Dunne et al. (2013). It is recommended that marker error should only be used to assess
239
how well a rigid skeletal model ‘fits’ the experimental data, and not as a validation of an IK solution.
240
This research was limited by excluding the shoulder girdle during modelling. The greatest differences
241
were observed at the shoulder during 90% of the delivery phase (Figure 3.6, 3.8), when the arm was
242
at maximal circumduction and elevation. More advanced upper limb models (Seth et al., 2016), may
243
allow investigation of shoulder girdle movement during overhead tasks. Another limitation was
244
adopting a DK model as a criterion measure, however can be justified as there is currently no
245
alternate gold standard model available for estimating the upper limb kinematics of cricket bowling
246
(Lathrop et al., 2011) (see Leardini et al., 2005 and Della Croce et al., 2005).
247
Conclusion
248
Prescribing participant-specific joint co-ordinates during the marker registration phase of model
249
preparation in OpenSim increases the accuracy and maintains the inter-tester repeatability of IK
250
solutions when modelling dynamic overhead tasks. Additionally, marker error reported in OpenSim
251
following IK should not be used as a measure of kinematic accuracy nor repeatability.
12
252
Acknowledgements
253
The authors wish to acknowledge the contribution to this study of Mr Tony Robey for continued
254
technical support.
255
256
Conflict of Interest
257
The authors report no financial or personal relationships with other people or organizations that
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could have biased the presented work.
259
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Roux, E., Bouilland, S., Godillon-Maquinghen, A. & Bouttens, D., 2002. Evaluation of the global
308
optimisation method within the upper limb kinematics analysis. Journal of Biomechanics, 35, 1279-
309
1283.
310
Seth, A., Matias, R., Veloso, A. P. & Delp, S. L. 2016. A Biomechanical Model of the Scapulothoracic
311
Joint to Accurately Capture Scapular Kinematics during Shoulder Movements. PloS one, 11.
312
Winter D. Motor Control of Human Movement. 3rd edition. Hoboken, New Jersey: John Wiley & Sons,
313
Inc., 2005. p. 49-50.
314 315 316
Table 1: The joint centre (1.1), segment reference frame (1.2) and angle decomposition (1.3) definitions for the DK modelling approach
317 1.1: Joint Centre definition Shoulder Joint Centre (SJC)
Regression equation (as per Campbell et al., 2008) during static A-pose, stored within acromion and proximal upper arm technical frames. During bowling trials the joint centre is recreated virtually within both technical frames, with the mean deemed the final joint centre
Elbow Joint Centre
Lateral and medial elbow epicondyle locations (LE, ME) digitised using a “pointer” (as per
(EJC)
Chin et al., 2009) and stored as markers within distal upper arm technical frame. During bowling trials the joint centre is the midpoint of elbow epicondyles
Wrist Joint Centre (WJC)
Midpoint of markers placed on the medial and lateral styloid processes of the wrist (MWR, LWR) 1.2: Segment Frame: Line Order and Definition
Upper Arm
16
Origin: EJC
1 (Y-axis): unit vector from EJC to SJC (superior positive) 2 (X-axis): cross-product of Y-axis and unit vector from LE and ME (anterior positive) 3 (Z-axis): orthogonal to X-Y plane (positive left to right) Origin: WJC Forearm
1 (Y-axis): unit vector from WJC to EJC (superior positive) 2 (X-axis): cross-product between Y-axis and unit vector from LWR to MWR (anterior positive) 3 (Z-axis): orthogonal to the X-Y plane (positive to right) 1.3: Angle Decomposition Estimated by decomposing the child segment (forearm) relative to the parent (upper arm) in accordance with the ISB standard:
Elbow
1: FE (Z axis) 2: Abduction/adduction (X axis) 3: Pronation/supination (Y axis) A negative (below zero) FE value indicates elbow hyperextension
318 319
17
320 321
Table 2: Discrete Elbow FE Events Analysis: DK Comparison. ANOVA and ICC results comparing elbow FE events from each of the IK approaches with the DK modelling approach equivalents.
322 Mean (St dev) Elbow FE
ANOVA F
MRPC – DK
MR – DK
(p value)
p value
p value
0.941
MRPC
MR
DK
29.2°
-12.5°
26.9°
54.911
(±12.6°)
(±11.7°)
(±13.5°)
(<0.001)*
43.9°
0.0°
41.3°
103.021
(±11.8°)
(±14.2°)
(±13.8°)
(<0.001)*
20.6°
-17.1°
14.5°
54.737
(±6.1°)
(±10.5°)
(±6.7°)
(<0.001)*
20.7°
-4.8°
14.8°
59.589
(±6.1°)
(±7.6°)
(±6.9°)
(<0.001)*
Extension
23.3°
4.3°
26.7°
15.339
Range
(±12.8°)
(±9.6°)
(±14.2°)
(<0.001)*
Event UAH
Max
Min
BR
* indicates statistical significance p < 0.05
323
324 325 326
18
Sidǎk Post-Hoc Test
ICC MRPC - DK
MR - DK
<0.001*
0.964
0.065
0.107
<0.001*
0.723
0.038
0.924
<0.001*
0.960
0.090
0.059
<0.001*
0.739
0.136
0.821
<0.001*
0.977
0.265
327 328
19
329 330
20
331
21
Fig. 1: External Marker Set. Description of the external marker set configuration. Fig. 2: Graphical Representation of Data Collection and Workflow. Fig. 3: Waveform and SPM analyses. Comparison of each marker registration method and the criterion measure (Figures 3.1–3.4) and inter-tester repeatability analysis (Figures 3.5–3.8). Mean and standard deviation plots of each comparison are on the left, and SPM1D analyses are visualised on the right. The two comparisons to the criterion measure (Figures 3.2, 3.4) result in some periods of statistical difference, represented by the grey shaded areas and accompanied by a unique p-value. Fig. 4: A demonstration of how the marker registration methods result in different virtual marker positions within segment reference frames. An MR and an MRPC prepared skeletal model have been overlayed with neutral general co-ordinates (0° for all joint angles, 0 m for all translations) such that their segment reference frames are aligned; however, the virtual marker positions are visibly different, rotated about the long axes of the segments. Thus, when the MR and MRPC skeletal models are both used to model the same experimental data, they will require different elbow angle combinations to best-fit the recorded marker positions, and present with alternative IK solutions.