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This study aimed to develop and evaluate an image-based method of obtaining anthropometric measurements for accurate subjectspecific inertia parameter determination using Yeadon’s (1990) inertia model. Ninety five anthropometric measurements were obtained directly from five athletic performers and indirectly from digitization of subjectspecific whole-body still images. The direct and image-based measurements were used as input into Yeadon’s (1990) inertia model. The overall absolute error in predicted whole-body mass achieved using the image-based approach (2.87%) compared well to that achieved using the direct measurements (2.10%). The inclusion of image-based anthropometric measurements obtained from extremity (hand and feet) images was not found to consistently improve model accuracy achieved using whole-body images only. The presented method provides a successful alternative to direct measurement for obtaining anthropometric measurements required for customized inertia modelling. The noninvasive image-based approach is benefited by the potential for obtaining subject-specific measurements from large samples of subjects and elite athletic performers for whom time-consuming data collections may be undesirable.


Introduction
The accuracy of biomechanical analyses can depend upon the extent to which the approximation of the body represents the true anatomical structure. One important set of mechanical properties is body segmental inertia parameters (BSIP) (Pearsall & Reid, 1994) and in many applications, including the analysis of sports performance, a parameter set for the particular individual under study is desirable (Yeadon et al., 1993).
Cadaver data (Clauser et al., 1969;Chandler et al., 1975) have previously been used to estimate the BSIP of individuals if their body mass and stature are known (Forwood et al., 1985). However, de Leva (1993) showed that the generalization of cadaver data, which in the main have been from elderly male Caucasians, leads to large errors in segmental centre of mass estimations when applied to other populations. Zatsiorsky et al. (1990) obtained BSIP for male and female college students using a gamma-ray scanning technique, which de Leva (1996) adjusted so the parameters were determined with reference to more commonly used body landmarks.
The use of ratio and regression methods in determining BSIP has the advantage that the time required with the subject is minimal, although the parameters determined are not fully customized to the individual's geometry. The modelling of body segments as simple shapes can influence BSIP substantially, particularly in segments comprising complex geometries (Rao et al., 2006). Segmental inertia parameter values derived using ratio and regression may be adequate for biomechanical analysis in simple situations. However, as the biomechanical representation of the human body becomes more complex the requirement of specific inertia parameters becomes essential to avoid inaccurate kinetic analyses 3 Journal of Applied Biomechanics. © Human Kinetics, Inc. (Pearsall & Reid, 1994). Joint kinetics describing gait and derived using an inverse dynamics approach have been reported to be particularly sensitive to BSIP (Rao et al., 2006). Given the precision of current motion analysis systems, the accuracy of the inertia parameters is therefore a potentially limiting factor in carrying out accurate dynamic analyses.
Mathematical models, which represent the body segments using a number of geometric solids are capable of estimating values of all BSIP (Yeadon, 1990). Since these models generally require the anthropometric measurements of the individual, the inertia parameters are subject-specific and consider the geometry of the individual under study. The number of measurements taken depends on the number of solids that comprise the model. Yeadon's (1990) model, which estimates total body mass with a maximum error of 2.3% across three subjects, comprises 40 geometric solids, specified by 95 anthropometric measurements. The time to record these measurements can be less than 30 minutes for an experienced operator, although when time with the subject is limited this technique may not be feasible. Jensen (1976) developed an inertia model comprising elliptical zones, the dimensions of which were obtained by digitizing photographic images of the subject. Whilst this method is less time consuming for the subject than direct measurement, reference points need to be marked prior to the subject being photographed. More recently, Baca (1996) developed a method for determining 220 anthropometric measurements from video images to be used as input to Hatze's (1980) model and concluded that the video-based method was useful in situations where ease of application and rapid availability are of importance. The BSIP estimated using the video-based measures of Baca (1996) were similar to those obtained using direct measurement. However, an examination of the 'true' accuracy of the video-based and direct approach in replicating the actual, known BSIP of each subject was not conducted. A quantitative comparison of an actual measure e.g. whole-body mass, with the corresponding predicted measure is desirable to indicate the level of confidence associated with a modelling approach. The aim of this study was to develop a method of obtaining anthropometric measurements from athletic performers, which requires reduced collection time, and to examine the accuracy of the approach in determining actual subject-specific inertia parameters using Yeadon's inertia model.
Approval for the study was provided by the University's Research Ethics Committee and each subject gave written informed consent. Subjects, who were of various morphologies, wore only tight-fitting shorts, allowing identification of body segment landmarks.
Ninety five anthropometric (direct) measurements, detailed for Yeadon's (1990) inertia model, were taken from each subject by an experienced researcher.
Measurements were obtained using a tape measure and anthropometric callipers.
The whole-body mass ( Table 1)   Images were cropped to a maximum resolution of 720 x 576 pixels using Zoom Browser EX (Canon Inc., version 5.7), converted to .avi format using DVgate Plus (Sony Corporation, version 2.2.01), then imported into Peak Motus (Vicon Motion Systems, version 9.0.0.27-GM) for digitizing. Each image was digitized for ten fields to obtain two-dimensional (2D) coordinate data of the calibration object and the body segment contours at 45 defined landmarks as detailed by Yeadon (1990).
Coordinates were reconstructed using the 2D Direct Linear Transformation (Walton, 1981), then used to obtain lengths, perimeters, widths and depths corresponding to the measurements required by Yeadon's (1990) inertia model. Perimeter measurements were not obtainable directly from the images, so 2D width and depth images were used to derive perimeter measurements required as input into the inertia model.
Coordinate data from the left and right whole-body sagittal plane images were used to obtain depths at each landmark (i) such that: where d i = segment depth, and xa i and xp i = x coordinate of the most anterior and posterior location on the segment, respectively, at each landmark.
The frontal plane whole-body image data defined image-based lengths and widths of body segments so that: where l i = length measure at respective landmark, z i = z coordinate of respective landmark and z i-1 = z coordinate of preceding landmark and: where w i = width, and ym i and yl i = y coordinate of the most medial and lateral location on the segment, respectively, at each landmark.
Perimeter measurements required for the body segments modelled with circular cross-sectional areas (head, neck and limbs) in Yeadon's (1990) inertia model were derived using the 2D depths and widths such that: where p hnli =perimeter measure, d hnli = depth and w hnli = width, at the respective head, neck or limb landmark. Perimeter measurements required for the body segments comprising stadium solids (trunk and extremities) were derived using the 2D depths and widths so that: where p tei =perimeter measure, d tei = depth and w tei = width, at the respective trunk or extremity landmark. The image-derived measurements of the extremities were 7 Journal of Applied Biomechanics. © Human Kinetics, Inc.
obtained firstly using only the whole-body images and secondly using the extremity images.
The measurements derived directly, using whole-body images only and wholebody images combined with the extremity images were independently input into Yeadon's (1990) inertia model. Density values from Dempster (1955) were combined with Yeadon's (1990) inertia model to provide three sets of customized BSIP for each subject. The inertia model's accuracy in replicating each subject's measured wholebody mass was derived for the three sets of model input data as the quantified difference (error) between the predicted and measured whole-body mass such that: The accuracy of the image-based approaches for obtaining anthropometric measurements for inertia modelling was compared with the accuracy achieved using direct measurements. Within-and between-digitizer reliability was assessed by comparing the model error produced using whole-body image data derived from repeated digitizations of one subject.
A sensitivity analysis of the model accuracy was conducted using whole-body image-based data comprising circular segment perimeters derived firstly using the mean depths and widths, secondly using only depths and thirdly using only widths.
Only the segments comprising a circular cross-section were modified in the sensitivity analysis.
The levels of agreement between the measured and predicted whole-body mass derived using the inertia model and three sets of anthropometric input data are illustrated in Table 1. On average, the direct measurements produced the most successful replication of the measured whole-body mass compared to the imagebased approaches. Mean ±SD absolute errors were 2.10 ±1.61%, 2.87 ±1.57% and 2.55 ±1.54% using the direct, digitized whole-body and digitized whole-body combined with extremity image measurements, respectively. Within-and betweendigitizer repeatabilities of within 0.20% and 0.35% respectively, of the error produced using the whole-body image data for Subject A (Table 1) were achieved. _________________________Insert Table 1  The inertia modelling approach was favoured over traditional cadaver-based approaches for deriving BSIP due to the associated benefits of obtaining BSIP customized to the geometry of individual subjects.
The level of confidence in the image-based approach was assessed by determining the inertia model accuracy in replicating actual whole-body masses compared to that achieved using traditional direct measurements. Individual BSIP are difficult to measure in vivo but may be estimated using direct techniques such as gamma scanning and immersion (Kingma et al., 1996). The use of direct methods in biomechanical analyses estimating BSIP are however inhibited by the complexity and cost of the procedures involved, and minor discrepancies between the actual and derived measure that can still exist (Kwon, 1996). The objectivity and accessibility of the measured whole-body mass was considered beneficial for the accuracy assessment conducted in this investigation. As suggested by Yeadon (1990), the level of agreement between simulations performed using the predicted BSIP and actual performances, may provide insight into the appropriateness of other predicted inertia parameters in the future.
A mean absolute error of 2.10% was obtained using direct measurements, which was comparable to that previously achieved by Yeadon (1990) (2.03%) using direct measurements from three subjects. A higher mean error was achieved using the presented whole-body image-based approach (2.87%) compared to the direct measurements, which suggests that the accurate inertia modelling of whole-body mass ideally requires the use of measurements taken directly from the subject. However, the slightly lower mean error achieved using the direct compared to imagebased measurements was counterbalanced by the substantially longer subject contact time required (direct: 30 minutes; image: 5 minutes). Furthermore, the direct Journal of Applied Biomechanics. © Human Kinetics, Inc. method was not found to provide a consistently improved whole-body mass replication for every subject relative to the image-based approach.
A video-based and direct measurement approach for predicting BSIP using Hatze's (1980) inertia model were previously compared by Baca (1996). Although the video-based approach was benefited by its ease of application and rapid availability, the accuracy of the approach in reproducing actual BSIP was not assessed. In contrast to Baca (1996), this study confirmed that image-based measures can be combined with inertia modelling to reproduce actual BSIP with a comparable accuracy to that achieved using direct measurements. The developed approach was benefited by the achievement of a high level of accuracy in whole-body mass replication using only 95 measurements, which was a notably reduced data set than required by Baca (1996) (220 measurements). The benefits of a reduced measurement set are a shorter processing time integrated with a potentially reduced measurement error across the whole-body profile. Further insight into the sensitivity of the predicted BSIP to the direct measurement error may be alleviated by detailed measurer and digitizer reliability assessments in future investigations.
Limitations in inertia modelling associated with changes in lung volume during the measurement of subjects have previously been highlighted (Yeadon, 1990).
Subjects were asked to maintain tidal breathing during direct measurement and image capture in order to minimise mass discrepancies incurred with possible lung volume alterations. Alongside potential errors associated with anthropometric measurement, the success of the image-based and direct measurement approaches was potentially limited by the homogenous segment density assumption of Yeadon's (1990) model. Future analyses may benefit from integrating component inertia Journal of Applied Biomechanics. © Human Kinetics, Inc. models (e.g. Gittoes & Kerwin, 2006), which consider soft and rigid tissue densities, with the image-based approach to produce improved BSIP replications The presented image-based approach was limited by the need to obtain model-specific three-dimensional anthropometric measurements e.g. limb perimeters.
The sensitivity analysis, however, suggested that the use of combined 2D widths and depths was successful due to the improved whole-body mass replication achieved compared to alternative approaches using only widths and only depths. The imagebased approach was also potentially limited by the level of resolution that could be achieved in reproducing extremity measurements with a whole-body field of view.
Anthropometric measurements were subsequently derived using higher resolution extremity images combined with the whole-body image. Although, a slightly reduced mean absolute error (0.32%) was achieved, the improvement was not consistent across all subjects. Without a substantial and consistent improvement in the wholebody mass replication, the rationale for the inclusion of the extremity images into the image analyses may be weakened due to the additional image collection and digitizing time required.
The presented image-based approach provides a successful alternative to direct measurement for obtaining anthropometric measurements required for customized inertia modelling. The image-based approach is potentially beneficial for indirectly deriving comprehensive anthropometric measurements from large samples of subjects or elite athletic performers for whom time-consuming data collections may be undesirable.