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Repeatability and sources of variability in multi-center assessment of segmental foot kinematics in normal adults
Gait & Posture 31 (2010) 32–36
Contents lists available at ScienceDirect
Gait & Posture journal homepage: www.elsevier.com/locate/gaitpost
Repeatability and sources of variability in multi-center assessment of segmental foot kinematics in normal adults Jason T. Long a,*, Daniel C. Eastwood b, Adam R. Graf c, Peter A. Smith c, Gerald F. Harris a,c a
Orthopaedic and Rehabilitation Engineering Center (Marquette University/Medical College of Wisconsin), Milwaukee, WI, United States Department of Biostatistics, Medical College of Wisconsin, Milwaukee, WI, United States c Shriners Hospital for Children, Chicago, IL, United States b
A R T I C L E I N F O
A B S T R A C T
Article history: Received 13 October 2008 Received in revised form 10 August 2009 Accepted 31 August 2009
Multi-site application of biomechanical models can be a powerful tool as quantitative methods are employed to improve clinical care and to assess larger populations for research purposes. However, the use of such models depends on adequate validation to assure reliability in inter-site measures. We assessed repeatability and sources of variability associated with the assessment of segmental foot kinematics using the Milwaukee Foot Model during multiple testing sessions at two sites. Six healthy ambulators were instrumented and tested during comfortable ambulation; data were analyzed with variance components analysis using a mixed effects linear model. Results indicated that the largest source of variability was inter-subject; measurement error associated with Site and Session fell below 3.58 in over 80% of position measurements and below 2.58 in over 80% of ROM measurements. These findings support the continued use of the segmental foot model at multiple sites for clinical and research purposes. ß 2009 Elsevier B.V. All rights reserved.
Keywords: Multisegmental foot/ankle model Inter-site reliability Repeatability Variance components analysis
1. Introduction The kinematic analysis of the lower extremities during gait is generally accepted as a well-tested and validated tool, appropriate for both clinical and research applications. Similar analysis of the multiple segments of the foot and ankle is becoming more prevalent in the research literature, with a number of different models having been reported over the past 20 years [1–8]. The acceptance of these new models across laboratories in the clinical and research arenas is contingent on validations which demonstrate sufficient fidelity to the behavior being analyzed and sufficient repeatability so as to be useful across a wide range of users. The adjusted coefficient of multiple determination (CMD; R2a ) has been used extensively to evaluate similarities between kinematic and kinetic waveforms. The positive root of the CMD, known as the coefficient of multiple correlation (CMC), is also used for this purpose. Kadaba first reported good intra- and intersession repeatability in lower extremity biomechanics in subjects walking at a self-selected speed, and these findings supported the further use of gait analysis in clinical decision making [9]. These
analytical methods were later adopted by Leardini et al. [10], Woodburn et al. [5], and Jenkyn and Nicol [8] in the reports of their respective multisegmental foot models. Carson et al. assessed four components of variability in their foot model using a custom protocol [1]. Kidder et al. [3] and Myers et al. [11] reported on linear and angular accuracy and resolution in their validations of the Milwaukee Foot Model for adult and pediatric populations, respectively. These reports all provided important information regarding the strengths and limitations of the models described; however, none of these reports considered the implications of employing the model on a multi-center basis. The present study was designed to validate the use of the Milwaukee Foot Model (MFM) between two separate testing sites. The MFM is a four segment model which represents the lower leg and foot as the tibia, hindfoot (calcaneus), forefoot (metatarsals), and hallux [3,11]. The MFM is unique in that it employs measurements from weightbearing X-rays to index the orientations of skin-mounted markers to the orientation of the underlying bony anatomy. These methods allow the model to account for bony deformities (e.g. hallux valgus, pes planus) and provide a crucial means of evaluating populations with pathology [12–14]. 2. Methods
* Corresponding author at: Medical College of Wisconsin, Department of Orthopaedic Surgery, 9200 W Wisconsin Ave, Milwaukee, WI 53226, United States. Tel.: +1 414 805 7456; fax: +1 414 805 7488. E-mail address: [email protected] (J.T. Long). 0966-6362/$ – see front matter ß 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.gaitpost.2009.08.240
Six healthy young ambulators took part in the testing (4M, 2F; age 21.2 2.5 years). Subjects had passed clinical screen for inclusion in a pool of healthy ambulators for a larger study; normal foot posture was confirmed for all subjects via clinical and radiographic analysis. Power analysis found that based on the chi-square distribution
J.T. Long et al. / Gait & Posture 31 (2010) 32–36 and equal tailed 95% confidence intervals for the standard deviation, a sample size of n = 6 would provide an estimated standard deviation within 62–245% of the measured standard deviation [15]. While this range appears large, it is based on estimates of the variability of the variance, which is inherently greater than the variability of the mean. This method also does not account for increased power due to the repeated measurements performed in the current study. Power increases due to repeated measures are considerable, but difficult to predict. The study was approved by the Institutional Review Board of the Medical College of Wisconsin, and all subjects provided informed consent prior to data collection. Each subject underwent two data capture sessions in each of two different facilities. Motion data was captured at each facility with a Vicon system (Vicon 524 at the Medical College of Wisconsin (MCW); Vicon MX at Shriners Hospital Chicago (SHC)). For each testing session, the subject was instrumented with reflective markers for multisegmental analysis of foot kinematics as described by the MFM [3]. A delay of at least 90 min was imposed between successive test sessions; markers were completely removed following the first session and reattached prior to the second session. Trained personnel specific to each site conducted all instrumentation and data collection; MCW personnel were not involved in test procedures at SHC, nor vice versa. Communications between the two sites for purposes of testing was limited to administrative topics (e.g. scheduling). Following instrumentation, each subject stood in a comfortable position on a piece of heavy cardboard in the middle of the data capture volume. The subject’s feet were traced onto the cardboard to create a permanent record of weightbearing foot posture (‘‘footprint template’’). Static reference data were then captured using the motion capture system, followed by walking trials at a self-selected speed along a data collection corridor (length 6 m). To restrict sources of variability to those involved in subject instrumentation and testing, a single set of X-rays was collected and measured for each subject at the MCW site. The set included standing A/P and lateral views, as well as a modified coronal plane view (Milwaukee view [16]) designed to facilitate a measurement of the rotation of the calcaneus about its long axis. For each X-ray, the footprint template was used to reposition the feet into the same weightbearing posture adopted during the static motion capture trial. Intersegmental angles were then measured from the weightbearing X-rays to develop the bone-based matrices defined by the MFM; a single investigator (JTL) performed all measurements. The intra- and inter-rater reliability of these measurements has been established previously [16,17] and they were not considered as a source of variability in this study. Data from the four sessions were processed using angular measurements from the X-ray session. Markers and key events (heel strike, toe off) were identified in the software workspace, and custom MFM software was used to calculate intersegmental kinematics of the hindfoot, forefoot, and hallux in each of the three clinical planes; tibia kinematics were calculated relative to the global reference frame. Kinematic data were further reduced by subdividing each gait cycle into the seven phases of gait as defined by Perry [18]; within each phase, key summary measures (minimum position, maximum position, mean position, and range) were extracted and tabulated for statistical analysis. 2.1. Statistical analysis For each subject, data from four sessions were included in the full data set. Each session data set was comprised of four summary measures (minimum position, maximum position, mean position, and ROM) from each of the seven phases of the gait cycle, for each of the four segments (tibia, hindfoot, forefoot, hallux) in each of the three planes (sagittal, coronal, transverse). Four temporal–spatial measures were also included (walking speed, stride length, cadence, and stance duration). This led to 340 measures for each of the four sessions. All statistical analyses were performed in SAS v9.1 (SAS Institute Inc., Cary, NC). A mixed effects linear model was used to perform variance components analysis on each summary measurement (minimum, maximum, mean, and range). The model included random effects for Subject, Site, Residual (measurement error) and Session, and a fixed effect for Site, as described in:
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confidence interval for the variance. The variance and interval estimate were then transformed to create an approximate confidence interval for the standard deviation. Estimates close to zero (‘‘near zero’’ factors) were noted to represent a small part of TME. For comparison to other studies, intra- and inter-session CMCs were calculated for each subject using methods previously described by Kadaba et al. [9]; these values were calculated across all data collection sessions both with and without regard for testing site. Intra- and inter-subject CMCs were calculated for the pool of subjects using methods previously described by Jenkyn and Nichols [8]; these are a variation of the methods described by Kadaba.
3. Results Intra- and inter-session CMCs were calculated for each subject at each site and across all sites. Intra- and inter-subject CMCs were also calculated across all sites. These values are presented in Table 1, along with comparison values from earlier studies which evaluated intra- and inter-subject repeatability for their respective multisegmental foot models. A total of 340 measures were evaluated during the statistical analysis (four measures per each of seven gait phases, calculated for each of four segments within each of three motion planes). In considering the fixed effects portion of the analysis, 55 measures (16%) demonstrated significant average differences between sites (p < 0.05). Significant inter-Site differences ranged from 0.748 to 4.648; most of these measures (23 of 55, 42%) were in the hindfoot, followed by the tibia (16 of 55, 29%) and forefoot (15 of 55, 27%). Hallux motion showed minimal significant inter-site differences. In addition, most significant differences occurred during stance (phases 1–4). Few of these significantly different measures occurred in such a way as to suggest a trend in measurement differences between sites. No temporal–spatial parameters demonstrated any change between sites, and with the exception of tibial rotational position during loading response (Site #2 values demonstrated an external rotation shift of approximately 38), no other measures, planes, or segments demonstrated differences between sites that were consistent or present across consecutive phases of the gait cycle. The statistical use of a mixed model allows the consideration of both random and fixed effects. For each kinematic and temporal– spatial measure, the model attributes variance in the data to either inter-subject differences (‘‘Subject’’), inter-session differences (‘‘Session’’), inter-site differences (‘‘Site’’), or measurement error Table 1 CMC values calculated within- and between-sessions and within- and betweensubjects. All values are calculated without regard for site. For intra/inter-subject CMCs, select values from Leardini et al. [10] and Jenkyn and Nichol [8] are provided for comparison. Blank spaces indicate that no comparative segment/motion plane was available for comparison. Segment Plane
Session CMC
Subject CMC
Current study
Current study
Leardini et al. [10]
Intra
Intra
Intra Inter Intra Inter
yi jkl ¼ b0 þ bi þ b j þ bl þ ei jkl where b0 represents an overall mean. bi represents random Subject error with Normal distribution (m = 0, s 2 ¼ s 21 ). bj represents random Site error with Normal distribution (m = b2, s 2 ¼ s 22 ). bl represents random Session error with Normal distribution (m = 0, s 2 ¼ s 23 ). eijkl represents random Residual (measurement) error with Normal distribution (m = 0, s 2 ¼ s 24 ). b2 represents the average difference between sites. A variance components covariance structure was used to provide estimates of variability for each of the random effects in the model. Variability was reported as the estimated standard deviation associated with each random factor after the removal of the fixed effect, and as a percentage of the total variance remaining after the removal of the fixed effect. The totals of Site, Session, and Residual error were used to calculate total measurement error (TME), representing the total variability of a given measurement, excluding between-subject variability. The random effects portion of the model provided estimates of the variance (assumed to be independent and normally distributed) as well as the standard error of the variance. The standard error was used to calculate a standard normal
Tibia
Inter
Inter
Jenkyn and Nichol [8]
Sagittal 0.9960 0.9925 0.9933 0.9868 Coronal 0.9394 0.8429 0.8632 0.6037 Transverse 0.8893 0.7784 0.8391 0.6296
Hindfoot Sagittal 0.9647 0.8991 0.9058 0.5548 0.91 0.61 0.92 0.71 Coronal 0.9445 0.8917 0.9518 0.3165 0.85 0.36 0.71 0.31 Transverse 0.9581 0.8718 0.8951 0.3250 0.76 0.35 0.58 0.41 Forefoot Sagittal 0.9069 0.7323 0.7264 0.2202 Coronal 0.9621 0.9157 0.9525 0.8045 Transverse 0.9457 0.8813 0.8918 0.4943 Hallux
Sagittal 0.9742 0.9503 0.9553 0.8030 0.95 0.65 Coronal 0.9744 0.8992 0.9090 0.7703 0.76 0.36 Transverse 0.9644 0.8930 0.9071 0.6418 0.89 0.62
0.85 0.70
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J.T. Long et al. / Gait & Posture 31 (2010) 32–36
(‘‘Residual’’). Variance estimates are based on the random sample of two sites, four sessions (two per site), and six subjects. Variability attributed to one factor (e.g. Site) is not included in the estimated variance for the other factors (e.g. Session and Subject). By modeling a fixed effect for Site, any overall differences between sites are initially removed and variances are calculated as if the site means were equal. The fixed effect for Site is then tested to determine if there was a difference between the sites. Breaking out individual variance components for different phases of the gait cycle allows a simple representation of variability sources and their magnitudes. Visual depictions such as those presented in Figs. 1 and 2 highlight the magnitude of variability attributed to each of the sources of variation. As this representation is intended to represent variability in clinically relevant units (degrees), the standard deviation of the variance (square root) is used. For the random effects, the largest variability in measurement was attributed to Subject. The relative levels of variability for each of the sources of variation were assessed given the maximum inter-subject variability observed (12.708, observed in transverse plane hindfoot ROM during midswing). Measures greater than 80% of this maximum were identified as high variability measures (HVMs), and measures lower than 20% of this maximum were identified as low variability measures (LVMs). Random effects variance estimates due to Subject, Site, Session, and Residual are presented for mean position and ROM measures in Supplemental Tables S1 and S2; the standard deviation of the variance is again used to present these values in clinically relevant units. No measures of variability attributed to Residual, Session, or Site were HVMs; the majority of these measures were LVMs (86% of Residual measures, 93% of Session measures, 97% of Site measures). Measurement variability attributed to Subject was relatively higher, particularly in measures of the hindfoot in the transverse plane and the forefoot in the sagittal plane. These high variability measures were present throughout the gait cycle without any clear bias toward stance or swing. Analysis of variability due to the Site, Session, and Residual random effects (TME) found that 80% of the variance in mean position measurements was below 3.368, and 80% of variance in ROM measurements was below 2.478. This is presented in histogram form in Fig. 3.
Fig. 2. Estimates of variability due to individual random effects (e.g. variability attributed to Site, Session, Subject, and measurement error Residual) for the specified temporal–spatial parameters. As these estimates are intended to represent variability in clinically relevant units, the standard deviation of the variance (square root) is reported.
4. Discussion
Fig. 1. Estimates of variability due to individual random effects (e.g. variability attributed to Site, Session, Subject, and measurement error Residual) across the gait cycle for mean position of the hindfoot in the coronal plane. As these estimates are intended to represent variability in clinically relevant units (degrees), the standard deviation of the variance (square root) is reported.
The use of multiple testing sites is critical for studying large numbers of subjects in a given population. However, the results of such testing are only as good as the reliability of the testing methods, and previous studies have demonstrated the potential for large errors when inter-site differences are not controlled. The purpose of this study was to examine the reliability of motion analysis testing with the MFM between two clinical foot and ankle test sites.
J.T. Long et al. / Gait & Posture 31 (2010) 32–36
Fig. 3. Distribution of total measurement error (TME) for all segment-plane-phase triplets for each of the four specified measures (minimum position, maximum position, mean position, and ROM). Dashed line indicates the approximate threshold below which 80% of the variability is found for each measure (3.58 for measures of position; 2.58 for ROM).
Many earlier studies of reliability in multisegmental foot models have focused on the repeatability of kinematic waveforms across an entire gait cycle. When compared to these earlier studies, the results of the present study are encouraging. Intra-subject CMC values are equal to or higher than values for similar metrics published previously. This is particularly notable in the coronal and transverse planes, where previously published models noted a fairly large reduction in repeatability. Inter-subject CMC values demonstrate a large decrease from intra-subject values in most measures. The direction and magnitude of this difference agrees with findings of previous studies. In considering measures across sessions, Woodburn et al. have reported intra- and inter-day CMCs on a per-segment basis without distinguishing motion planes. In this study, intra-day measures exceeded 0.910 in the hindfoot, forefoot, and hallux; inter-day measures exceeded 0.900 in the hindfoot and 0.850 in the forefoot, with the exception of transverse plane hindfoot motion (0.677). The findings of the present study compare very well with these reported values. These wide ranges of repeatability measurements may be attributed in part to the methods of neutral referencing. The models reported by Jenkyn and Nichols and Leardini et al. both used subject-specific postures (comfortable standing) to define neutral alignment. In contrast, the study reported by Woodburn et al. used a vertical tibial alignment and heel wand system following the model described by Carson et al. [1], and the present study used weightbearing radiographs to index marker orientations to the underlying bony alignment. It should also be noted that inter-subject assessments of repeatability are inherently sensitive to variations in individuals’ walking patterns. This sensitivity is apparent in the analyses of both Leardini and Jenkyn in the steep falloff between intra-subject CMC and inter-subject CMC values. CMC methods provide efficient ‘‘snapshots’’ of a model’s repeatability across multiple measures. Depending on the type of analysis (cross-session vs. cross-subject), measures with high CMC values may be regarded as highly repeatable and valid for use in clinical and research settings. However, for measures with low CMC values, no additional information is available to provide insight into what is causing the reduced repeatability. This need framed the focus of the statistical analysis conducted in the current study.
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The variance components analysis performed by the mixed effects linear model included both fixed and random effects. The fixed effect for Site accounts for any overall difference between the Sites over all subjects, and is used to test for possible bias or average difference in measurement levels. Excluding the fixed effect for Site in the model would lead to this portion of the total variability appearing in the Site error random effect. The random effect of the variance components model allows each subject to vary independently at each of four sessions. The effect of different subjects responding in different ways between sessions or sites is included in the estimated variability of the random effects, rather than the variability of the average difference between sites (the fixed effect). The absence of major fixed effect differences between sites is a primary finding of this study, indicating no inherent bias between sites. Similar findings of low variability due to the Site and Session random effects suggest that the random effect of testing persons at two different sites or across multiple sessions leads to negligible differences in output. As noted earlier, variance in position measurements is overwhelmingly influenced by intersubject variance. The influence of variability associated with Residual increases in ROM measurements; this is reflected in probability testing for variability due to Residual, which suggests that other sources of variability exist in the data. It should be noted, however, that the magnitude of variability imposed by these unidentified sources is relatively small (86% of these measures were LVMs). The largest sources of variability in this investigation were found in inter-subject measurements; most of these were found at the hindfoot (internal/external rotation) and the forefoot (plantar/ dorsiflexion). Variability due to Subject is expected, and attempts to control this type of variability generally deal with protocol planning and specification of subject criteria. The results of this study indicate that the remaining sources of variation (Site, Session, and Residual, Figs. 1 and 2) are generally responsible for variability of a very small magnitude. As noted in Fig. 3, more than 80% of the variability presented in the TRE histograms falls below 3.58 for mean position estimates and below 2.58 for ROM estimates. Considered from the clinical standpoint, these relatively small magnitudes of variability suggest that testing between multiple sites with the MFM can be well-controlled such that differences between measurements are negligible. Given the results of the variance components analysis, it would be useful to derive a simple reliability index to rank-order the spectrum of measurements made in the study. While no single index can adequately represent the multiple layers of information available from the mixed effects linear model, the data reduction provided by such an index would be intuitively useful in the design of clinical and research protocols. We considered the total contribution to variability of the Site, Session, and Residual effects (TME), and calculated the Mean TME Variability across all seven phases of the gait cycle for each segment/plane couplet. Results are presented in Table 2; for brevity, minimum and maximum position measures are not presented because of their similarity to the mean position measure. Results of this rank-ordering suggest that in measurements of segment position, coronal plane tibia position is the least variable measure across the gait cycle, followed by hindfoot position in the coronal, transverse, and sagittal planes. In measurements of ROM, tibia ab/adduction and forefoot plantar/dorsiflexion are the most reliable measure. It should be noted that in all measures of position (minimum, maximum, and mean), the top five segment/plane couplets are the same, and the top three share the same order. These are all measures of either tibia motion (coronal and sagittal planes) or hindfoot motion (all three planes). The rudimentary nature of Mean TME Variability as a reliability index precludes
J.T. Long et al. / Gait & Posture 31 (2010) 32–36
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Table 2 Mean TME variability for each segment-plane couplet calculated across all phases of the gait cycle. Measure
Segment
Plane
Mean TME variability
Mean position
Tibia Hindfoot Hindfoot Hindfoot Tibia Forefoot Forefoot Tibia Hallux Forefoot Hallux Hallux
Cor Cor Tra Sag Sag Tra Sag Tra Tra Cor Cor Sag
1.53 1.60 2.00 2.37 2.37 2.48 2.54 2.70 2.78 2.87 3.63 3.63
Tibia Forefoot Tibia Hindfoot Hindfoot Tibia Hindfoot Forefoot Hallux Hallux Forefoot Hallux
Cor Sag Tra Cor Tra Sag Sag Tra Cor Tra Cor Sag
1.23 1.42 1.56 1.66 1.70 1.87 2.06 2.08 2.23 2.31 2.34 3.34
ROM
extensive speculation as to why this may be the case, but it should be noted that in transforming marker motion to the underlying bony segments, the hindfoot segment is the only one specified by three measures from weightbearing X-rays. Further applications of the MFM across clinical laboratories are supported by the findings of the current study. The minimal contribution of inter-site differences to variance in foot kinematics supports the use of the MFM for multi-center testing. This multi-center testing could take the form of a research application in which a subject pool is reliably enlarged by testing at multiple sites. It could also extend clinical practice by allowing patients to undergo gait analysis at one location and follow up with a practitioner elsewhere. While the present study was limited to two sites, it is reasonable to expect that additional sites could be included given adequate training with the model. Given a clinically relevant benchmark for acceptable inter-site variance, it may be possible to extend the methods described in this study to develop a tool for assessing the success of training. It should be noted, however, that the present study focused on healthy feet with normal posture. While the MFM does provide for the characterization of bony deformity through radiographic referencing, feet with deformity were not included in this study. The use of the MFM in patient populations has been demonstrated previously in characterizing the gait patterns of patients with foot/ankle pathology [14,19–21] and assessing changes following surgical correction [12,13]. Acknowledgments The authors wish to thank the staffs of the motion analysis laboratories at the Medical College of Wisconsin and Shriners Hospital Chicago. In particular we acknowledge the contributions of Kathy Reiners, Vicki Young, Sahar Hassani, and Tamara Cohen.
This study was supported in part by a grant from the Department of Education through the National Institute on Disability and Rehabilitation Research (NIDRR) (H133G060252). Conflict of interest statement None of the authors has any conflicts of interest to report.
Appendix A. Supplementary data Supplementary data associated with this article can be found, in the online version, at doi:10.1016/j.gaitpost.2009.08.240.
References [1] Carson MC, Harrington ME, Thompson N, O’Connor JJ, Theologis TN. Kinematic analysis of a multi-segment foot model for research and clinical applications: a repeatability analysis. J Biomech 2001;34:1299–307. [2] Leardini A, Benedetti MG, Berti L, Bettinelli D, Nativo R, Giannini S. Rear-foot, mid-foot and fore-foot motion during the stance phase of gait. Gait Posture 2007;25:453–62. [3] Kidder SM, AF Jr S, Harris GF, Johnson JE. A system for the analysis of foot and ankle kinematics during gait. IEEE Trans Rehabil Eng 1996;4:25–32. [4] MacWilliams BA, Cowley M, Nicholson DE. Foot kinematics and kinetics during adolescent gait. Gait Posture 2003;17:214–24. [5] Woodburn J, Nelson KM, Siegel KL, Kepple TM, Gerber LH. Multisegment foot motion during gait: proof of concept in rheumatoid arthritis. J Rheumatol 2004;31:1918–27. [6] Kitaoka HB, Crevoisier XM, Hansen D, Katajarvi B, Harbst K, Kaufman KR. Foot and ankle kinematics and ground reaction forces during ambulation. Foot Ankle Int 2006;27:808–13. [7] Tome J, Nawoczenski DA, Flemister A, Houck J. Comparison of foot kinematics between subjects with posterior tibialis tendon dysfunction and healthy controls. J Orthop Sports Phys Ther 2006;36:635–44. [8] Jenkyn TR, Nicol AC. A multi-segment kinematic model of the foot with a novel definition of forefoot motion for use in clinical gait analysis during walking. J Biomech 2007;40:3271–8. [9] Kadaba MP, Ramakrishnan HK, Wootten ME, Gainey J, Gorton G, Cochran GV. Repeatability of kinematic, kinetic, and electromyographic data in normal adult gait. J Orthop Res 1989;7:849–60. [10] Leardini A, Benedetti MG, Catani F, Simoncini L, Giannini S. An anatomically based protocol for the description of foot segment kinematics during gait. Clin Biomech 1999;14:528–36. [11] Myers KA, Wang M, Marks RM, Harris GF. Validation of a multisegment foot and ankle kinematic model for pediatric gait. IEEE Trans Neural Syst Rehabil Eng 2004;12:122–30. [12] Canseco K, Long J, Marks R, Khazzam M, Harris G. Quantitative motion analysis in patients with hallux rigidus before and after cheilectomy. J Orthop Res 2009;27:128–34. [13] Marks RM, Long JT, Ness ME, Khazzam M, Harris GF. Surgical reconstruction of posterior tibial tendon dysfunction: Prospective comparison of flexor digitorum longus substitution combined with lateral column lengthening or medial displacement calcaneal osteotomy. Gait Posture 2009;29:17–22. [14] Khazzam M, Long JT, Marks RM, Harris GF. Kinematic changes of the foot and ankle in patients with systemic rheumatoid arthritis and forefoot deformity. J Orthop Res 2007;25:319–29. [15] Casella G, Berger RL. Statistical Inference, 2nd ed., Duxbury Press; 2001. [16] Johnson JE, Lamdan R, Granberry WF, Harris GF, Carrera GF. Hindfoot coronal alignment: a modified radiographic method. Foot Ankle Int 1999;20:818–25. [17] Taranto MJ, Taranto J, Bryant A, Singer KP. Radiographic investigation of angular and linear measurements including first metatarsophalangeal joint dorsiflexion and rearfoot to forefoot axis angle. J Foot Ankle Surg 2005; 44:190–9. [18] Perry J. Gait analysis: normal and pathologic function. Thorofare, NJ: SLACK, Inc.; 1992. [19] Canseco KC, Long JT, Marks RM, Khazzam M, Harris GF. Quantitative characterization of gait kinematics in patients with hallux rigidus using the Milwaukee foot model. J Orthop Res 2008;26:419–27. [20] Ness ME, Long J, Marks R, Harris G. Foot and ankle kinematics in patients with posterior tibial tendon dysfunction. Gait Posture 2008;27:331–9. [21] Khazzam M, Long JT, Marks RM, Harris GF. Preoperative gait characterization of patients with ankle arthrosis. Gait Posture 2006;24:85–93.
Contents lists available at ScienceDirect
Gait & Posture journal homepage: www.elsevier.com/locate/gaitpost
Repeatability and sources of variability in multi-center assessment of segmental foot kinematics in normal adults Jason T. Long a,*, Daniel C. Eastwood b, Adam R. Graf c, Peter A. Smith c, Gerald F. Harris a,c a
Orthopaedic and Rehabilitation Engineering Center (Marquette University/Medical College of Wisconsin), Milwaukee, WI, United States Department of Biostatistics, Medical College of Wisconsin, Milwaukee, WI, United States c Shriners Hospital for Children, Chicago, IL, United States b
A R T I C L E I N F O
A B S T R A C T
Article history: Received 13 October 2008 Received in revised form 10 August 2009 Accepted 31 August 2009
Multi-site application of biomechanical models can be a powerful tool as quantitative methods are employed to improve clinical care and to assess larger populations for research purposes. However, the use of such models depends on adequate validation to assure reliability in inter-site measures. We assessed repeatability and sources of variability associated with the assessment of segmental foot kinematics using the Milwaukee Foot Model during multiple testing sessions at two sites. Six healthy ambulators were instrumented and tested during comfortable ambulation; data were analyzed with variance components analysis using a mixed effects linear model. Results indicated that the largest source of variability was inter-subject; measurement error associated with Site and Session fell below 3.58 in over 80% of position measurements and below 2.58 in over 80% of ROM measurements. These findings support the continued use of the segmental foot model at multiple sites for clinical and research purposes. ß 2009 Elsevier B.V. All rights reserved.
Keywords: Multisegmental foot/ankle model Inter-site reliability Repeatability Variance components analysis
1. Introduction The kinematic analysis of the lower extremities during gait is generally accepted as a well-tested and validated tool, appropriate for both clinical and research applications. Similar analysis of the multiple segments of the foot and ankle is becoming more prevalent in the research literature, with a number of different models having been reported over the past 20 years [1–8]. The acceptance of these new models across laboratories in the clinical and research arenas is contingent on validations which demonstrate sufficient fidelity to the behavior being analyzed and sufficient repeatability so as to be useful across a wide range of users. The adjusted coefficient of multiple determination (CMD; R2a ) has been used extensively to evaluate similarities between kinematic and kinetic waveforms. The positive root of the CMD, known as the coefficient of multiple correlation (CMC), is also used for this purpose. Kadaba first reported good intra- and intersession repeatability in lower extremity biomechanics in subjects walking at a self-selected speed, and these findings supported the further use of gait analysis in clinical decision making [9]. These
analytical methods were later adopted by Leardini et al. [10], Woodburn et al. [5], and Jenkyn and Nicol [8] in the reports of their respective multisegmental foot models. Carson et al. assessed four components of variability in their foot model using a custom protocol [1]. Kidder et al. [3] and Myers et al. [11] reported on linear and angular accuracy and resolution in their validations of the Milwaukee Foot Model for adult and pediatric populations, respectively. These reports all provided important information regarding the strengths and limitations of the models described; however, none of these reports considered the implications of employing the model on a multi-center basis. The present study was designed to validate the use of the Milwaukee Foot Model (MFM) between two separate testing sites. The MFM is a four segment model which represents the lower leg and foot as the tibia, hindfoot (calcaneus), forefoot (metatarsals), and hallux [3,11]. The MFM is unique in that it employs measurements from weightbearing X-rays to index the orientations of skin-mounted markers to the orientation of the underlying bony anatomy. These methods allow the model to account for bony deformities (e.g. hallux valgus, pes planus) and provide a crucial means of evaluating populations with pathology [12–14]. 2. Methods
* Corresponding author at: Medical College of Wisconsin, Department of Orthopaedic Surgery, 9200 W Wisconsin Ave, Milwaukee, WI 53226, United States. Tel.: +1 414 805 7456; fax: +1 414 805 7488. E-mail address: [email protected] (J.T. Long). 0966-6362/$ – see front matter ß 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.gaitpost.2009.08.240
Six healthy young ambulators took part in the testing (4M, 2F; age 21.2 2.5 years). Subjects had passed clinical screen for inclusion in a pool of healthy ambulators for a larger study; normal foot posture was confirmed for all subjects via clinical and radiographic analysis. Power analysis found that based on the chi-square distribution
J.T. Long et al. / Gait & Posture 31 (2010) 32–36 and equal tailed 95% confidence intervals for the standard deviation, a sample size of n = 6 would provide an estimated standard deviation within 62–245% of the measured standard deviation [15]. While this range appears large, it is based on estimates of the variability of the variance, which is inherently greater than the variability of the mean. This method also does not account for increased power due to the repeated measurements performed in the current study. Power increases due to repeated measures are considerable, but difficult to predict. The study was approved by the Institutional Review Board of the Medical College of Wisconsin, and all subjects provided informed consent prior to data collection. Each subject underwent two data capture sessions in each of two different facilities. Motion data was captured at each facility with a Vicon system (Vicon 524 at the Medical College of Wisconsin (MCW); Vicon MX at Shriners Hospital Chicago (SHC)). For each testing session, the subject was instrumented with reflective markers for multisegmental analysis of foot kinematics as described by the MFM [3]. A delay of at least 90 min was imposed between successive test sessions; markers were completely removed following the first session and reattached prior to the second session. Trained personnel specific to each site conducted all instrumentation and data collection; MCW personnel were not involved in test procedures at SHC, nor vice versa. Communications between the two sites for purposes of testing was limited to administrative topics (e.g. scheduling). Following instrumentation, each subject stood in a comfortable position on a piece of heavy cardboard in the middle of the data capture volume. The subject’s feet were traced onto the cardboard to create a permanent record of weightbearing foot posture (‘‘footprint template’’). Static reference data were then captured using the motion capture system, followed by walking trials at a self-selected speed along a data collection corridor (length 6 m). To restrict sources of variability to those involved in subject instrumentation and testing, a single set of X-rays was collected and measured for each subject at the MCW site. The set included standing A/P and lateral views, as well as a modified coronal plane view (Milwaukee view [16]) designed to facilitate a measurement of the rotation of the calcaneus about its long axis. For each X-ray, the footprint template was used to reposition the feet into the same weightbearing posture adopted during the static motion capture trial. Intersegmental angles were then measured from the weightbearing X-rays to develop the bone-based matrices defined by the MFM; a single investigator (JTL) performed all measurements. The intra- and inter-rater reliability of these measurements has been established previously [16,17] and they were not considered as a source of variability in this study. Data from the four sessions were processed using angular measurements from the X-ray session. Markers and key events (heel strike, toe off) were identified in the software workspace, and custom MFM software was used to calculate intersegmental kinematics of the hindfoot, forefoot, and hallux in each of the three clinical planes; tibia kinematics were calculated relative to the global reference frame. Kinematic data were further reduced by subdividing each gait cycle into the seven phases of gait as defined by Perry [18]; within each phase, key summary measures (minimum position, maximum position, mean position, and range) were extracted and tabulated for statistical analysis. 2.1. Statistical analysis For each subject, data from four sessions were included in the full data set. Each session data set was comprised of four summary measures (minimum position, maximum position, mean position, and ROM) from each of the seven phases of the gait cycle, for each of the four segments (tibia, hindfoot, forefoot, hallux) in each of the three planes (sagittal, coronal, transverse). Four temporal–spatial measures were also included (walking speed, stride length, cadence, and stance duration). This led to 340 measures for each of the four sessions. All statistical analyses were performed in SAS v9.1 (SAS Institute Inc., Cary, NC). A mixed effects linear model was used to perform variance components analysis on each summary measurement (minimum, maximum, mean, and range). The model included random effects for Subject, Site, Residual (measurement error) and Session, and a fixed effect for Site, as described in:
33
confidence interval for the variance. The variance and interval estimate were then transformed to create an approximate confidence interval for the standard deviation. Estimates close to zero (‘‘near zero’’ factors) were noted to represent a small part of TME. For comparison to other studies, intra- and inter-session CMCs were calculated for each subject using methods previously described by Kadaba et al. [9]; these values were calculated across all data collection sessions both with and without regard for testing site. Intra- and inter-subject CMCs were calculated for the pool of subjects using methods previously described by Jenkyn and Nichols [8]; these are a variation of the methods described by Kadaba.
3. Results Intra- and inter-session CMCs were calculated for each subject at each site and across all sites. Intra- and inter-subject CMCs were also calculated across all sites. These values are presented in Table 1, along with comparison values from earlier studies which evaluated intra- and inter-subject repeatability for their respective multisegmental foot models. A total of 340 measures were evaluated during the statistical analysis (four measures per each of seven gait phases, calculated for each of four segments within each of three motion planes). In considering the fixed effects portion of the analysis, 55 measures (16%) demonstrated significant average differences between sites (p < 0.05). Significant inter-Site differences ranged from 0.748 to 4.648; most of these measures (23 of 55, 42%) were in the hindfoot, followed by the tibia (16 of 55, 29%) and forefoot (15 of 55, 27%). Hallux motion showed minimal significant inter-site differences. In addition, most significant differences occurred during stance (phases 1–4). Few of these significantly different measures occurred in such a way as to suggest a trend in measurement differences between sites. No temporal–spatial parameters demonstrated any change between sites, and with the exception of tibial rotational position during loading response (Site #2 values demonstrated an external rotation shift of approximately 38), no other measures, planes, or segments demonstrated differences between sites that were consistent or present across consecutive phases of the gait cycle. The statistical use of a mixed model allows the consideration of both random and fixed effects. For each kinematic and temporal– spatial measure, the model attributes variance in the data to either inter-subject differences (‘‘Subject’’), inter-session differences (‘‘Session’’), inter-site differences (‘‘Site’’), or measurement error Table 1 CMC values calculated within- and between-sessions and within- and betweensubjects. All values are calculated without regard for site. For intra/inter-subject CMCs, select values from Leardini et al. [10] and Jenkyn and Nichol [8] are provided for comparison. Blank spaces indicate that no comparative segment/motion plane was available for comparison. Segment Plane
Session CMC
Subject CMC
Current study
Current study
Leardini et al. [10]
Intra
Intra
Intra Inter Intra Inter
yi jkl ¼ b0 þ bi þ b j þ bl þ ei jkl where b0 represents an overall mean. bi represents random Subject error with Normal distribution (m = 0, s 2 ¼ s 21 ). bj represents random Site error with Normal distribution (m = b2, s 2 ¼ s 22 ). bl represents random Session error with Normal distribution (m = 0, s 2 ¼ s 23 ). eijkl represents random Residual (measurement) error with Normal distribution (m = 0, s 2 ¼ s 24 ). b2 represents the average difference between sites. A variance components covariance structure was used to provide estimates of variability for each of the random effects in the model. Variability was reported as the estimated standard deviation associated with each random factor after the removal of the fixed effect, and as a percentage of the total variance remaining after the removal of the fixed effect. The totals of Site, Session, and Residual error were used to calculate total measurement error (TME), representing the total variability of a given measurement, excluding between-subject variability. The random effects portion of the model provided estimates of the variance (assumed to be independent and normally distributed) as well as the standard error of the variance. The standard error was used to calculate a standard normal
Tibia
Inter
Inter
Jenkyn and Nichol [8]
Sagittal 0.9960 0.9925 0.9933 0.9868 Coronal 0.9394 0.8429 0.8632 0.6037 Transverse 0.8893 0.7784 0.8391 0.6296
Hindfoot Sagittal 0.9647 0.8991 0.9058 0.5548 0.91 0.61 0.92 0.71 Coronal 0.9445 0.8917 0.9518 0.3165 0.85 0.36 0.71 0.31 Transverse 0.9581 0.8718 0.8951 0.3250 0.76 0.35 0.58 0.41 Forefoot Sagittal 0.9069 0.7323 0.7264 0.2202 Coronal 0.9621 0.9157 0.9525 0.8045 Transverse 0.9457 0.8813 0.8918 0.4943 Hallux
Sagittal 0.9742 0.9503 0.9553 0.8030 0.95 0.65 Coronal 0.9744 0.8992 0.9090 0.7703 0.76 0.36 Transverse 0.9644 0.8930 0.9071 0.6418 0.89 0.62
0.85 0.70
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J.T. Long et al. / Gait & Posture 31 (2010) 32–36
(‘‘Residual’’). Variance estimates are based on the random sample of two sites, four sessions (two per site), and six subjects. Variability attributed to one factor (e.g. Site) is not included in the estimated variance for the other factors (e.g. Session and Subject). By modeling a fixed effect for Site, any overall differences between sites are initially removed and variances are calculated as if the site means were equal. The fixed effect for Site is then tested to determine if there was a difference between the sites. Breaking out individual variance components for different phases of the gait cycle allows a simple representation of variability sources and their magnitudes. Visual depictions such as those presented in Figs. 1 and 2 highlight the magnitude of variability attributed to each of the sources of variation. As this representation is intended to represent variability in clinically relevant units (degrees), the standard deviation of the variance (square root) is used. For the random effects, the largest variability in measurement was attributed to Subject. The relative levels of variability for each of the sources of variation were assessed given the maximum inter-subject variability observed (12.708, observed in transverse plane hindfoot ROM during midswing). Measures greater than 80% of this maximum were identified as high variability measures (HVMs), and measures lower than 20% of this maximum were identified as low variability measures (LVMs). Random effects variance estimates due to Subject, Site, Session, and Residual are presented for mean position and ROM measures in Supplemental Tables S1 and S2; the standard deviation of the variance is again used to present these values in clinically relevant units. No measures of variability attributed to Residual, Session, or Site were HVMs; the majority of these measures were LVMs (86% of Residual measures, 93% of Session measures, 97% of Site measures). Measurement variability attributed to Subject was relatively higher, particularly in measures of the hindfoot in the transverse plane and the forefoot in the sagittal plane. These high variability measures were present throughout the gait cycle without any clear bias toward stance or swing. Analysis of variability due to the Site, Session, and Residual random effects (TME) found that 80% of the variance in mean position measurements was below 3.368, and 80% of variance in ROM measurements was below 2.478. This is presented in histogram form in Fig. 3.
Fig. 2. Estimates of variability due to individual random effects (e.g. variability attributed to Site, Session, Subject, and measurement error Residual) for the specified temporal–spatial parameters. As these estimates are intended to represent variability in clinically relevant units, the standard deviation of the variance (square root) is reported.
4. Discussion
Fig. 1. Estimates of variability due to individual random effects (e.g. variability attributed to Site, Session, Subject, and measurement error Residual) across the gait cycle for mean position of the hindfoot in the coronal plane. As these estimates are intended to represent variability in clinically relevant units (degrees), the standard deviation of the variance (square root) is reported.
The use of multiple testing sites is critical for studying large numbers of subjects in a given population. However, the results of such testing are only as good as the reliability of the testing methods, and previous studies have demonstrated the potential for large errors when inter-site differences are not controlled. The purpose of this study was to examine the reliability of motion analysis testing with the MFM between two clinical foot and ankle test sites.
J.T. Long et al. / Gait & Posture 31 (2010) 32–36
Fig. 3. Distribution of total measurement error (TME) for all segment-plane-phase triplets for each of the four specified measures (minimum position, maximum position, mean position, and ROM). Dashed line indicates the approximate threshold below which 80% of the variability is found for each measure (3.58 for measures of position; 2.58 for ROM).
Many earlier studies of reliability in multisegmental foot models have focused on the repeatability of kinematic waveforms across an entire gait cycle. When compared to these earlier studies, the results of the present study are encouraging. Intra-subject CMC values are equal to or higher than values for similar metrics published previously. This is particularly notable in the coronal and transverse planes, where previously published models noted a fairly large reduction in repeatability. Inter-subject CMC values demonstrate a large decrease from intra-subject values in most measures. The direction and magnitude of this difference agrees with findings of previous studies. In considering measures across sessions, Woodburn et al. have reported intra- and inter-day CMCs on a per-segment basis without distinguishing motion planes. In this study, intra-day measures exceeded 0.910 in the hindfoot, forefoot, and hallux; inter-day measures exceeded 0.900 in the hindfoot and 0.850 in the forefoot, with the exception of transverse plane hindfoot motion (0.677). The findings of the present study compare very well with these reported values. These wide ranges of repeatability measurements may be attributed in part to the methods of neutral referencing. The models reported by Jenkyn and Nichols and Leardini et al. both used subject-specific postures (comfortable standing) to define neutral alignment. In contrast, the study reported by Woodburn et al. used a vertical tibial alignment and heel wand system following the model described by Carson et al. [1], and the present study used weightbearing radiographs to index marker orientations to the underlying bony alignment. It should also be noted that inter-subject assessments of repeatability are inherently sensitive to variations in individuals’ walking patterns. This sensitivity is apparent in the analyses of both Leardini and Jenkyn in the steep falloff between intra-subject CMC and inter-subject CMC values. CMC methods provide efficient ‘‘snapshots’’ of a model’s repeatability across multiple measures. Depending on the type of analysis (cross-session vs. cross-subject), measures with high CMC values may be regarded as highly repeatable and valid for use in clinical and research settings. However, for measures with low CMC values, no additional information is available to provide insight into what is causing the reduced repeatability. This need framed the focus of the statistical analysis conducted in the current study.
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The variance components analysis performed by the mixed effects linear model included both fixed and random effects. The fixed effect for Site accounts for any overall difference between the Sites over all subjects, and is used to test for possible bias or average difference in measurement levels. Excluding the fixed effect for Site in the model would lead to this portion of the total variability appearing in the Site error random effect. The random effect of the variance components model allows each subject to vary independently at each of four sessions. The effect of different subjects responding in different ways between sessions or sites is included in the estimated variability of the random effects, rather than the variability of the average difference between sites (the fixed effect). The absence of major fixed effect differences between sites is a primary finding of this study, indicating no inherent bias between sites. Similar findings of low variability due to the Site and Session random effects suggest that the random effect of testing persons at two different sites or across multiple sessions leads to negligible differences in output. As noted earlier, variance in position measurements is overwhelmingly influenced by intersubject variance. The influence of variability associated with Residual increases in ROM measurements; this is reflected in probability testing for variability due to Residual, which suggests that other sources of variability exist in the data. It should be noted, however, that the magnitude of variability imposed by these unidentified sources is relatively small (86% of these measures were LVMs). The largest sources of variability in this investigation were found in inter-subject measurements; most of these were found at the hindfoot (internal/external rotation) and the forefoot (plantar/ dorsiflexion). Variability due to Subject is expected, and attempts to control this type of variability generally deal with protocol planning and specification of subject criteria. The results of this study indicate that the remaining sources of variation (Site, Session, and Residual, Figs. 1 and 2) are generally responsible for variability of a very small magnitude. As noted in Fig. 3, more than 80% of the variability presented in the TRE histograms falls below 3.58 for mean position estimates and below 2.58 for ROM estimates. Considered from the clinical standpoint, these relatively small magnitudes of variability suggest that testing between multiple sites with the MFM can be well-controlled such that differences between measurements are negligible. Given the results of the variance components analysis, it would be useful to derive a simple reliability index to rank-order the spectrum of measurements made in the study. While no single index can adequately represent the multiple layers of information available from the mixed effects linear model, the data reduction provided by such an index would be intuitively useful in the design of clinical and research protocols. We considered the total contribution to variability of the Site, Session, and Residual effects (TME), and calculated the Mean TME Variability across all seven phases of the gait cycle for each segment/plane couplet. Results are presented in Table 2; for brevity, minimum and maximum position measures are not presented because of their similarity to the mean position measure. Results of this rank-ordering suggest that in measurements of segment position, coronal plane tibia position is the least variable measure across the gait cycle, followed by hindfoot position in the coronal, transverse, and sagittal planes. In measurements of ROM, tibia ab/adduction and forefoot plantar/dorsiflexion are the most reliable measure. It should be noted that in all measures of position (minimum, maximum, and mean), the top five segment/plane couplets are the same, and the top three share the same order. These are all measures of either tibia motion (coronal and sagittal planes) or hindfoot motion (all three planes). The rudimentary nature of Mean TME Variability as a reliability index precludes
J.T. Long et al. / Gait & Posture 31 (2010) 32–36
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Table 2 Mean TME variability for each segment-plane couplet calculated across all phases of the gait cycle. Measure
Segment
Plane
Mean TME variability
Mean position
Tibia Hindfoot Hindfoot Hindfoot Tibia Forefoot Forefoot Tibia Hallux Forefoot Hallux Hallux
Cor Cor Tra Sag Sag Tra Sag Tra Tra Cor Cor Sag
1.53 1.60 2.00 2.37 2.37 2.48 2.54 2.70 2.78 2.87 3.63 3.63
Tibia Forefoot Tibia Hindfoot Hindfoot Tibia Hindfoot Forefoot Hallux Hallux Forefoot Hallux
Cor Sag Tra Cor Tra Sag Sag Tra Cor Tra Cor Sag
1.23 1.42 1.56 1.66 1.70 1.87 2.06 2.08 2.23 2.31 2.34 3.34
ROM
extensive speculation as to why this may be the case, but it should be noted that in transforming marker motion to the underlying bony segments, the hindfoot segment is the only one specified by three measures from weightbearing X-rays. Further applications of the MFM across clinical laboratories are supported by the findings of the current study. The minimal contribution of inter-site differences to variance in foot kinematics supports the use of the MFM for multi-center testing. This multi-center testing could take the form of a research application in which a subject pool is reliably enlarged by testing at multiple sites. It could also extend clinical practice by allowing patients to undergo gait analysis at one location and follow up with a practitioner elsewhere. While the present study was limited to two sites, it is reasonable to expect that additional sites could be included given adequate training with the model. Given a clinically relevant benchmark for acceptable inter-site variance, it may be possible to extend the methods described in this study to develop a tool for assessing the success of training. It should be noted, however, that the present study focused on healthy feet with normal posture. While the MFM does provide for the characterization of bony deformity through radiographic referencing, feet with deformity were not included in this study. The use of the MFM in patient populations has been demonstrated previously in characterizing the gait patterns of patients with foot/ankle pathology [14,19–21] and assessing changes following surgical correction [12,13]. Acknowledgments The authors wish to thank the staffs of the motion analysis laboratories at the Medical College of Wisconsin and Shriners Hospital Chicago. In particular we acknowledge the contributions of Kathy Reiners, Vicki Young, Sahar Hassani, and Tamara Cohen.
This study was supported in part by a grant from the Department of Education through the National Institute on Disability and Rehabilitation Research (NIDRR) (H133G060252). Conflict of interest statement None of the authors has any conflicts of interest to report.
Appendix A. Supplementary data Supplementary data associated with this article can be found, in the online version, at doi:10.1016/j.gaitpost.2009.08.240.
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