باقی مانده امتیاز : شاخص کیفیت به منظور ارزیابی صحت برآورد مشترک

The determination of an accurate centre of rotation (CoR) from skin markers is essential for the assessment of abnormal gait patterns in clinical gait analysis. Despite the many functional approaches to estimate CoRs, no non-invasive analytical determination of the error in the reconstructed joint location is currently available. The purpose of this study was therefore to verify the residual of the symmetrical centre of rotation estimation (SCoRE) as a reliable indirect measure of the error of the computed joint centre. To evaluate the SCoRE residual, numerical simulations were performed to evaluate CoR estimations at different ranges of joint motion. A statistical model was developed and used to determine the theoretical relationships among the SCoRE residual, the magnitude of the skin marker artefact, the corrections to the marker positions, and the error of the CoR estimations to the known centre of rotation. We found that the equation err=0.5rs provides a reliable relationship among the CoR error, err, and the scaled SCoRE residual, rs, providing that any skin marker artefact is first minimised using the optimal common shape technique (OCST). Measurements on six healthy volunteers showed a reduction of SCoRE residual from 11 to below 6 mm and therefore demonstrated consistency of the theoretical considerations and numerical simulations with the in vivo data. This study also demonstrates the significant benefit of the OCST for reducing skin marker artefact and thus for predicting the accuracy of determining joint centre positions in functional gait analysis. For the first time, this understanding of the SCoRE residual allows a measure of error in the non-invasive assessment of joint centres. This measure now enables a rapid assessment of the accuracy of the CoR as well as an estimation of the reproducibility and repeatability of skeletal motion patterns.

The accurate quantification of skeletal motion is not only important for the assessment of abnormal gait patterns caused by skeletal disorders such as cerebral palsy (Röhrle et al., 1987 and Bowsher et al., 1993), but also plays a key role in predicting musculoskeletal loading (Heller et al., 2001, Heller et al., 2003, Taylor et al., 2004 and Taylor et al., 2006) and the functional evaluation of therapy outcomes (Cappozzo, 1983). Marker-based motion capture has therefore become a common approach for the collection of kinematic data (Leardini et al., 1999), with clinical applications focused on using skin markers to derive internal bone motion (Benoit et al., 2005 and Stagni et al., 2005). The reconstruction of skeletal kinematics, however, is limited by the relative motion of the skin markers over the underlying bones (Cappozzo et al., 1990), an error referred to as soft tissue artefact (STA). In order to reduce the errors in determining skeletal kinematics caused by this soft tissue artefact, a number of numerical approaches have been presented (Andriacchi et al., 1998, Lu and O'Connor, 1998 and Cappello et al., 2005). By generating a rigid marker configuration from the complete segment marker data, the optimal common shape technique (OCST) (Taylor et al., 2005) removes any motion of the markers relative to one another—an artefact generally associated with muscle firing and skin elasticity. The advantages of this approach have been demonstrated directly against skeletal motion using bone pin data in sheep, but how these findings relate to the conditions in humans remains unknown because the assessment of segment and skeletal motion in sheep was restricted by the limited range of joint motion during normal gait and the magnitude of skin marker artefact. Whether, and to what extent, application of the OCST improves identification of the human hip joint centre (HJC) and thus the assessment of skeletal motion, however, has not been investigated in detail (Kornaropoulos et al., 2010 and Taylor et al., 2010). In combination with techniques for reducing skin marker artefact, functional approaches that identify joint centres and axes using the motion of one segment relative to the other, have been proposed as a key element for increasing the accuracy in the non-invasive determination of skeletal motion (Cappozzo, 1984, Leardini et al., 1999, Piazza et al., 2001, Halvorsen, 2003 and Schwartz and Rozumalski, 2005). Although sphere fitting approaches may be the most accurate in determining CoRs if one segment is fixed in space or no STAs are present (Ehrig et al., 2006, MacWilliams, 2008 and Cereatti et al., 2009), the use of the symmetrical centre of rotation estimation (SCoRE) (Ehrig et al., 2006) has been demonstrated to be the most accurate technique when both segments move simultaneously. First applications in vivo demonstrate that the SCoRE method can also be successfully applied for the functional determination of the glenohumeral joint (Monnet et al., 2007). Furthermore this specific numerical approach has also been shown to work significantly faster than other CoR approaches (Rozumalski and Schwartz, 2008). One severe limitation of analyses to determine skeletal kinematics is the ability to evaluate their accuracy in vivo (Rettig et al., 2009). Since anatomical data is generally not available, gait analyses do not commonly include subject specific anatomical reference information ( Kirkwood et al., 1999 and Peters et al., 2010), and are therefore reliant upon the marker data alone. A rapid evaluation of the accuracy of the position of a spherical joint from captured skin marker motion data alone could offer benefits such as improved interpretation of the functional data, the early recognition of measurement errors, and a quantification of the quality of the reconstructed joint in post-processing applications. Such a quality measure could therefore offer additional reliability to ensure that any differences found in clinical longitudinal studies are indeed due to changes in patient functional outcome rather than differences in the evaluation set-up, including marker placement or system calibration. As a result of the minimisation task to optimally determine joint centres using SCoRE, it is possible to calculate a residual value, and therefore an assessment of the divergence of the joint motion compared to a joint that moves in a perfectly spherical manner. In this study, we tested the hypothesis that this SCoRE residual can provide a reliable quantitative assessment of joint quality, and further, that application of the OCST to reduce skin marker artefact is able to improve the identification of the hip joint centre using the SCoRE residual as a quality measure.

For the first time, this study presents an approach to assess the error in the estimation of centres of rotation from motion data, and therefore improve information on the predictability of joint centres in patients. When applied to clinical gait analysis, the SCoRE residual provides an indirect measure to assess skeletal kinematics by providing an estimation of the reproducibility and repeatability of joint centres between studies, but also by removing the uncertainty of approach-induced systematic errors in the longitudinal assessment of patients. Since in functional motion analysis, kinematic data suffer from both individual and collective STAs (Cappozzo et al., 1990, Taylor et al., 2005 and Garling et al., 2007), the SCoRE residual has been evaluated for both kinds of artefacts. In our numerical analysis, kinematic datasets were generated using a standard marker set from the gait laboratory, with different levels of artificial STAs similar to conditions in vivo. The results of the theoretical predictions had a high level of agreement with the simulations, as long as only collective STAs were present. In order to create these conditions, SCoRE was used in combination with the optimal common shape technique (OCST). This technique targets the minimisation of STAs through generating a rigid configuration of the marker set, thereby removing individual marker motion. While its effectiveness has not yet been investigated in humans, its ability to reduce STAs has been demonstrated in vivo against pin marker data in sheep (Taylor et al., 2005). The OCST approach has similarities with the study of Veldpaus et al. (1988), who used the ordinary Procrustes transformation to fit one pose (usually a static standing calibration pose) onto another single pose or series of poses (e.g. each time frame of the activity). The OCST uses the more complex generalised Procrustes analysis to calculate the optimal configuration of the markers from the activity, before using the ordinary Procrustes to transform this optimal common marker set onto each configuration of the activity. In this manner, rather than using e.g. a static standing pose and then transforming this onto the motion data, the OCST is able to extract the optimal form of the marker set from the motion data in question. In cases where the OCST is used to create an optimal rigid configuration of each segment's marker set, the equation err=0.5rs yields an estimate of the mean error of the CoR in global coordinates. Here, it must be noted that the SCoRE residual assesses the sphericity of joint motion rather than any anatomical features or landmarks within the joint itself, and therefore works under the assumption that the CoR of the joint is coincident with the joint centre—in this case the HJC. In this study, the in vivo cohort represented a young and healthy subject group with no hip joint pathologies and one can assume that the HJC and CoR at the hip are close or consistent. In assessing the joints, a linear relationship between collective STAs and CoR error has been demonstrated, but it appears not to hold true when individual marker artefact is present. In practice, it therefore seems that only by using the combination of the OCST together with SCoRE it is possible to not only reduce STAs and accurately determine the centre of joint rotation, but also enable an assessment of accuracy for the CoR estimation. When the in vivo data was examined, the OCST produced a considerable reduction of the SCoRE residual. Although we are not able to directly measure the anatomical hip joint centre and compare it to the functionally determined centre of rotation in this study, our data suggests that the relationship between the SCoRE residual and CoR error established using the simulations and the statistical model also holds for our experimental data. Therefore, with a mean SCoRE residual of 7.2 mm we expect a mean error in the HJC position of below 4 mm. It is certainly possible that additional factors such as muscle firing or skin folding influence the relationship between SCoRE residual and CoR error in vivo, especially in elderly or obese subjects, and these aspects therefore need to be investigated in in vivo studies with a known HJC. CoR estimations without application of the OCST results in a large spread of possible CoR errors and finding the optimal permutation of all possible combinations of three markers on both segments to minimise the error is generally not possible in routine settings. However, when using the OCST, all markers are efficiently and simultaneously considered, and finding the optimal permutation is therefore not required. Furthermore, the current simulations suggest that using more than eight or nine markers on each segment should not bring any significant improvement. Although we are now able to estimate CoR accuracy, the direction vector of the error remains unknown (and presumably changes for each time point); hence the CoR estimation cannot be explicitly corrected. However, the use of the OCST and SCoRE does seem to provide the basis for an improved understanding of the relationships between soft tissue artefact and the underlying joint motion, and may thus allow the elucidation of improved skin marker configurations for targeting the smallest SCoRE residual possible and more optimally accessing skeletal movement. While a number of techniques to reduce individual STAs other than the OCST exist (Andriacchi et al., 1998, Lucchetti et al., 1998, Alexander and Andriacchi, 2001 and Cerveri et al., 2005), the reduction of collective STAs remains difficult. All these techniques suffer from the problem of assessing accuracy in a non-invasive manner. While invasive techniques such as bone pins (Ryu et al., 2009 and Taylor et al., 2005) or radiological image data (Garling et al., 2007) can provide an adequate anatomical reference to the known HJC, the SCoRE residual is now able to provide a solution for quantifying the accuracy of CoR assessment, while avoiding invasive techniques. In this study, we have demonstrated that, in combination with the OCST, the SCoRE residual can produce a reliable indirect measure of the error of CoR locations from skin marker-based measurements, and thus a possible early detection of measurement errors. While further investigation will be needed to verify these conclusions in clinical cohorts, the ability to directly assess the accuracy of skeletal kinematics removes the uncertainty resulting from e.g. marker placement variation, especially in the assessment of patients in longitudinal clinical studies.