ARTICLE IN PRESS Journal of Biomechanics 36 (2003) 1159–1168 Repeatability of gait data using a functional hip joint centre and a mean helical knee axis Thor F. Besier, Daina L. Sturnieks, Jacque A. Alderson, David G. Lloyd* School of Human Movement and Exercise Science, University of Western Australia, 35 Stirling Highway, Crawley, WA 6907, Australia Accepted 7 February 2003Abstract Repeatability of traditional kinematic and kinetic models is affected by the ability to accurately locate anatomical landmarks(ALs) to deﬁne joint centres and anatomical coordinate systems. Numerical methods that deﬁne joint centres and axes of rotationindependent of ALs may also improve the repeatability of kinematic and kinetic data. The purpose of this paper was to compare therepeatability of gait data obtained from two models, one based on ALs (AL model), and the other incorporating a functionalmethod to deﬁne hip joint centres and a mean helical axis to deﬁne knee joint ﬂexion/extension axes (FUN model). A footcalibration rig was also developed to deﬁne the foot segment independent of ALs. The FUN model produced slightly morerepeatable hip and knee joint kinematic and kinetic data than the AL model, with the advantage of not having to accurately locateALs. Repeatability of the models was similar comparing within-tester sessions to between-tester sessions. The FUN model may alsoproduce more repeatable data than the AL model in subject populations where location of ALs is difﬁcult. The foot calibration rigemployed in both the AL and FUN model provided an easy alternative to deﬁne the foot segment and obtain repeatable data,without accurately locating ALs on the foot.r 2003 Elsevier Science Ltd. All rights reserved.Keywords: Kinematics; Kinetics; Repeatability; Gait analysis1. Introduction et al., 1999; Stagni et al., 2000). Errors associated with the imprecise location of ALs have been noted as the Efforts have been made to reduce errors associated greatest source of error in motion analysis, compared towith photogrammetric techniques and skin movement instrument error or skin movement artefact (Dellaartefacts during motion analysis, to accurately deter- Croce et al., 1997). These ﬁndings raise concernsmine the position and orientation of body segments. regarding the repeatability of models using ALs toSkin movement artefact has been shown to be reduced deﬁne an ACS, which from a clinical perspective, is ofby employing a ‘CAST’ technique, whereby three or paramount importance. Methods to reduce any varia-more clusters of markers are placed on each segment to bility in locating ALs and deﬁning the ACS thereforecreate technical coordinate systems (TCSs) (Cappozzo warrant investigation.et al., 1995). Anatomical landmarks (ALs) are then Numerical methods can be used to determine jointdeﬁned relative to the TCSs in a static trial to centres and axes of rotation relative to marker clusters,reconstruct an anatomical coordinate system (ACS) without the need to accurately locate ALs. Techniquesduring a dynamic trial (Cappozzo et al., 1995; Lucchetti have been previously established to estimate jointet al., 1998). However, imprecise location of ALs can centres for the hip (Cappozzo, 1984; Shea et al., 1997;lead to mislocation of the ACS and subsequent joint Leardini et al., 1999), and the shoulder (Stokdijk et al.,centres, which propagates to errors in joint kinematics 2000), by moving the joint through a functional range ofand kinetics (Holden and Stanhope, 1998; Della Croce motion, assuming a true ‘ball-and-socket’ articulation. Methods have also been developed to determine *Corresponding author. Tel.: +61-9-380-3919; fax: +61-9-380- ‘optimal’ axes or mean helical axes of rotation for the1039. knee (Boyd and Ronsky, 1998; Churchill et al., 1998) E-mail address: firstname.lastname@example.org (D.G. Lloyd). ! and elbow (Cheze et al., 1998; Stokdijk et al., 1999)0021-9290/03/$ - see front matter r 2003 Elsevier Science Ltd. All rights reserved.doi:10.1016/S0021-9290(03)00087-3
ARTICLE IN PRESS1160 T.F. Besier et al. / Journal of Biomechanics 36 (2003) 1159–1168throughout a dynamic range of motion. Deﬁning joint Oxford, UK). Gait data were retrieved using customcentres and axes of rotation using these functional software and normalized to 51 points over stride using amethods may improve the repeatability of kinematic and cubic spline within MATLAB (Mathworks, Natick,kinetic data, compared to traditional methods that rely MA).on the accurate location of ALs to deﬁne an ACS. During each session, subjects walked at a self-selected The purpose of this paper was to compare within- pace (observed speeds were between 1.2 and 1.5 m/s)tester and between-tester repeatability of gait data using across an instrumented 10 m walkway. A minimum oftwo different methods of deﬁning a lower limb ACS. six trials with successful force-plate strikes wereThe ﬁrst model utilizes a functional hip joint centre captured for both left and right legs. In addition to the(HJC) and a mean helical axis of the knee (FUN model), walking trials, subjects performed a series of static andwhile the second model uses traditional ALs to deﬁne an dynamic calibration trials to locate ALs and estimateACS (AL model). It was hypothesized that the FUN the location of the HJCs, knee joint centres (KJC) andlower limb model would demonstrate greater repeat- functional ﬂexion/extension axes of each knee.ability of kinematic and kinetic gait data than an ALmodel for both between-tester and within-tester condi-tions. Furthermore, in an effort to reduce the errorassociated with locating ALs on the foot (Della Croce 2.3. Marker set and deﬁnitions of segment and jointet al., 1997), a new technique is demonstrated to deﬁne coordinate systemsthe orientation of the foot segment for gait analysis. To determine the three-dimensional position and orientation of each lower limb segment, clusters of three2. Methods retro-reﬂective markers (20 mm) were ﬁrmly adhered to the subject’s pelvis, thighs, shank, and feet (Fig. 1B). A2.1. Subjects TCS was deﬁned using each thigh, shank, and foot segment cluster such that the ACS and joint centres Ten able-bodied subjects (6 males, 4 females; body could be deﬁned relative to these TCSs. The pelvis,mass 55–89 kg; height 1.64–1.90 m) participated in the femoral, and tibial ACSs were deﬁned the same as thosestudy. Written informed consent was obtained prior toparticipation, as per requirement of the University ofWestern Australia ethics committee. Subjects had nocurrent musculoskeletal injury or disease and were freeof pain.2.2. Gait analysis protocol Gait analyses were performed on each subject in themorning and afternoon of the same day. Two examinersperformed separate gait analyses in the morning (forbetween-tester comparisons), and one of these exami-ners performed a repeat analysis in the afternoon, atleast 4 h following the ﬁrst session (for within-testercomparisons). This procedure resulted in three gaitanalyses for each subject. Five examiners in total wereused, three of which performed the test–retest sessionsfor within-tester comparisons. A six-camera VICON motion analysis system (OxfordMetrics, Oxford, UK) was used in conjunction with twoAMTI force-plates (AMTI, Watertown, MA) to collectmotion data (50 Hz) and ground reaction force data(2000 Hz), respectively. Marker coordinate data wereﬁltered using a GCVSPL routine (Woltring, 1986),which helped to reduce the error in reconstructing thehelical axes parameters (de Lange et al., 1990) and inperforming inverse dynamic calculations. The 7-segment Fig. 1. (A) Pointer device used to locate the medial and lateralFUN and AL kinematic/kinetic models were con- epicondyles of the femur. (B) ACSs of the lower limb model. Figurestructed using BodyBuilder software (Oxford Metrics, produced using SIMM (Musculographics Inc., Evanston, IL).
ARTICLE IN PRESS T.F. Besier et al. / Journal of Biomechanics 36 (2003) 1159–1168 1161used by Kadaba et al. (1989), although a new ACS was method from Spoor and Veldpaus (1980) and Rein-established for the foot. schmidt and van den Bogert (1997). A mean helical axis The pelvis ACS was deﬁned using an origin midway was then calculated for each knee, analogous to thebetween the antero-superior iliac spines (ASISs), a method presented by Stokdijk et al. (1999) for the elbowpositive z-axis along the line of the left ASIS to the joint. The mean helical axis was used to deﬁne theright ASIS, an x-axis along a line from the sacrum ﬂexion/extension axis of the knee relative to the thighmarker to the origin (positive being anterior), and a TCS. The KJC in the FUN model was deﬁned relativey-axis orthogonal to the x2z-plane (positive being to the mean helical axis, at a point along the helical axissuperior) (Fig. 1B). that intersected a plane that was normal to the Two different methods were used to determine the transepicondylar line, midway between the epicondyles.HJCs. For the AL model, HJCs were deﬁned relative to As such, the location of the ME and LE in the FUNthe pelvis ACS and estimated using a regression model were only used to deﬁne the medial and lateralequation developed by Shea et al. (1997). For the side of the knee. The femoral ACS in the FUN modelFUN model, a functional method similar to that used by was then deﬁned similar to the AL model, except usingPiazza et al. (2001) was employed, whereby subjects the FUN KJC and ﬂexion/extension axis.were required to consecutively move the right and left The tibial ACS was determined using the position ofthigh through a range of ﬂexion, abduction, adduction, markers placed on the medial malleoli (MM) of theand extension (Piazza et al., 2001). These data were used tibiae and lateral malleoli (LM) of the ﬁbulae, collectedin a constrained optimization program written in during a static trial. Each tibial ACS was deﬁned usingMATLAB (Optimization Toolbox, Mathworks Inc.; an origin at the AJC (midway between the MM andNatick, MA), where spheres were ﬁt to each thigh LM), a y-axis as the line passing from the AJC to themarker to ﬁnd a left and right HJC location relative to KJC (positive being superior), a z-axis being along athe pelvis ACS (xp ; yp ; zp ) and sphere radii. An initial plane deﬁned by the ﬂexion/extension axis of the knee,estimation was obtained using the regression equation of and an x-axis orthogonal to the y2z-axes (positive beingShea et al. (1997) and the optimization was constrained anterior) (Fig. 1B). Subsequently, the tibial ACS wasto be within a 100 mm cube surrounding this position. different for the AL and FUN models due to theThe location of the initial estimate of the HJC respective difference in KJC and knee ﬂexion/extensioncoordinates was randomly perturbed within the axis deﬁnitions.100 mm cube during six consecutive optimizations to The foot segment was deﬁned the same way for bothavoid ﬁnding local minima. AL and FUN models. To overcome large errors in In four static trials, the position of the medial and palpating and placing markers on ALs of the foot (Dellalateral femoral epicondyles (ME and LE, respectively) of Croce et al., 1997), an alignment rig was developed toeach femur were measured. A pointer with ﬁve markers deﬁne the orientation of the foot segment (Fig. 2). Awas used to locate the ME and LE, with marker TCS was deﬁned for the alignment rig using four retro-redundancy used to reduce error in locating the end of reﬂective markers attached to the rig, such that any footthe pointer (Fig. 1A). The femoral ACS, KJCs, and knee ﬂexion/extensionaxis were deﬁned differently for the AL and FUNmodels. In the AL model, the femoral ACS was deﬁnedusing an origin at the KJC (midway between the MEand LE), a y-axis as the line passing through the KJC tothe HJC (positive being superior), a z-axis being along aplane deﬁned by the ME and LE and orthogonal to they-axis (positive pointing from left to right), and anx-axis orthogonal to the y2z-axes (positive beinganterior) (Fig. 1B). For the FUN model, a mean helical axis was used todeﬁne the KJC and ﬂexion/extension axis of each knee.To achieve this, subjects stood on one leg and ﬂexed thecontra-lateral thigh to enable the shank to freely ﬂex andextend about the knee from full extension to B100 ofﬂexion. This was performed for at least three cycles foreach limb. Using the custom MATLAB program, the Fig. 2. Foot calibration rig and rig TCS. Note the goniometer beneathtibia markers were expressed in the femoral TCS and the subjects’ foot to measure foot progression (abduction/adduction)instantaneous helical axes calculated throughout the relative to yRIG. Rear-foot inversion/eversion was also taken whilst therange of motion using a singular value decomposition subject was on the rig using an inclinometer.
ARTICLE IN PRESS1162 T.F. Besier et al. / Journal of Biomechanics 36 (2003) 1159–1168measurements were made with respect to this coordinate mean gait variables of testing sessions 1–3, and 2–3, thussystem (Fig. 2). The subject stood on the alignment rig giving an indication of the systematic error within testerin a comfortable stance with their heels against a small and between testers.metal plate at the rear of the rig. The long axis (x) of the Two-factor ANOVA’s (model type: AL orfoot segment was assumed to be parallel to the x2z FUN Â examiner: within-tester or between-tester factor)(horizontal) plane of the rig coordinate system (Fig. 2). with repeated measures on subject were then used toIt was assumed that the x-axis of the foot was rotated compare the CMD values and systematic error betweenaround the rig y-axis. This rotation was measured using models and examiner conditions (po0:05). Tests werea goniometer ﬁxed to the alignment rig (Fig. 2), which performed independently on data from each limb.was deﬁned by the line bisecting the calcaneus and themidpoint between the 2nd and 3rd metatarsal heads.The foot was then assumed to be rotated in inversion/ 3. Resultseversion about the x-axis of the foot, which was a rear-foot angle measured relative to the x À z plane of the rig, 3.1. Joint kinematicsperpendicular to the x-axis of the foot. This rear-footinversion/eversion angle was taken using an inclin- Both AL and FUN models produced highly repea-ometer (Dasco Pro Inc., Rochford, IL). These sequences table sagittal plane kinematic data with r2 0:85 (Tableof rotations, in accordance with the ISB standard (Wu 1). Frontal plane kinematics were highly repeatable forand Cavanagh, 1995), were used to deﬁne the foot ACS, the hip joint (r2 0:85), moderately repeatable for thefrom which two virtual markers were then created and knee (r2 between 0.54 and 0.74) and less repeatable forexpressed relative to the foot TCS (Fig. 2). In subse- the ankle (r2 0:42). Rotations in the transverse planequent dynamic trials, the calcaneus-marker and the two were quite repeatable at the knee (r2 0:64) and anklevirtual markers were used to deﬁne the foot ACS. (r2 0:53) and less repeatable at the hip (r2 between 0.28 The convention used to describe the kinematics of the and 0.47).hip, knee, and ankle joints followed the ISB standard There were no signiﬁcant interactions between model(Wu and Cavanagh, 1995). The sequence of rotations type and examiner conditions, except for left kneewas: ﬂexion/extension about the z-axis of the proximal internal rotation kinematics of the left leg. Thissegment; then adduction/abduction about a ﬂoating generally suggests that repeatability of the gait datax-axis; followed by internal/external rotation about the was independent of the examiner administering the testy-axis of the distal segment. Joint kinetics were (Tables 1 and 2).expressed in the ACS of the distal segment. The FUN model demonstrated better repeatability in frontal plane knee kinematics than the AL model, with2.4. Statistics an average r2 of 0.73 compared to 0.57 (Table 1), although this result was only signiﬁcant for the Coefﬁcients of Multiple Determination (CMD or r2 ; comparison of the right leg (po0:05). Similarly, theKadaba et al., 1989) were calculated between testing FUN model produced greater repeatability of internal/sessions 1–3, 1–2, and 2–3 using time normalized external rotation of the knee compared to the AL modelkinematic and kinetic curves. The CMD was reported, (mean r2 of 0.74 and 0.67, respectively), but did notas opposed to the Coefﬁcient of Multiple Correlation reach signiﬁcance for individual limb comparisons(CMC, or r), as an r2 value indirectly refers to the (Table 1).percentage variance accounted for within the data. In Repeatability of ankle joint kinematic and kineticthis fashion, repeatability of each model was measured, data was similar within tester and between testers, forbetween testers and within tester. both AL and FUN models (Tables 1 and 2), which was The systematic error of the two models was deter- expected as the calibration rig was used to deﬁne themined similar to the ‘static daily offset’ calculated by foot segment for both models. Ankle dorsi/plantarKadaba et al. (1989) and Growney et al. (1997), which ﬂexion angles were most repeatable with a mean r2 ofoccurs due to the re-application of markers. This error 0.89, whereas ankle inversion/eversion and abduction/term was calculated using the following: adduction angles were moderately repeatable, with mean r2 of 0.47 and 0.59, respectively. 1 X pﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ N ﬃsystematic error ¼ ðx1n À x2n Þ; N n¼1 3.2. Joint momentswhere N is the number of datapoints, x1n is the mean of Sagittal plane moment data were highly repeatable forvariable x at time point n from testing session 1, x2n is the hip, knee, and ankle, with CMD’s ranging from 0.81the mean of variable x at time point n from testing to 0.97 (Table 2). Hip and knee joint moments in thesession 2. This error term was also calculated using the frontal plane were also very repeatable with r2 values
ARTICLE IN PRESS T.F. Besier et al. / Journal of Biomechanics 36 (2003) 1159–1168 1163Table 1Coefﬁcients of multiple determination (CMD, r2 ) of kinematic data using both anatomical landmark (AL) and functional (FUN) modelsJoint angle AL (left) FUN (left) AL (right) FUN (right)CMD between testersHip ﬂexion/extension 0.94470.030 0.95070.027 0.95770.021 0.96270.016Knee ﬂexion/extension 0.93970.032 0.94570.032 0.96270.021 0.96470.021Ankle dorsi/plantar ﬂexion 0.85570.046 0.86170.046 0.89570.030 0.90270.027Hip abduction/adduction 0.84670.078 0.84870.094 0.86270.050 0.88170.038Knee varus/valgus 0.63570.272 0.60670.252 0.54170.205* 0.74270.166Ankle abduction/adduction 0.49970.240 0.50570.245 0.48770.259 0.42170.249Hip internal/external rotn 0.35170.227 0.35470.261 0.37470.228 0.33270.210Knee internal/external rotn 0.71370.133 0.69970.159 0.68770.164 0.76470.149Ankle inversion/eversion 0.59270.190 0.53970.197 0.63470.194 0.57770.221CMD within testerHip ﬂexion/extension 0.95070.038 0.95670.032 0.96770.014 0.96970.013Knee ﬂexion/extension 0.92670.046 0.93470.042 0.96170.025 0.96270.026Ankle dorsi/plantar ﬂexion 0.84870.070 0.86970.057 0.90070.040 0.89870.038Hip abduction/adduction 0.87170.056 0.85170.077 0.84670.089 0.86870.069Knee varus/valgus 0.64270.254 0.67970.159 0.58970.156* 0.71470.238Ankle abduction/adduction 0.49570.277 0.46370.225 0.44370.294 0.48470.238Hip internal/external rotn 0.38670.160 0.39770.301 0.28070.202 0.46570.230Knee internal/external rotn 0.68670.138 0.76470.093 0.63770.209 0.72070.212Ankle inversion/eversion 0.56170.237 0.53170.229 0.66970.171 0.61170.210Note: Signiﬁcant differences between AL and FUN model are denoted by *(po0:05).Table 2Coefﬁcients of Multiple Determination (CMD, r2 ) of joint moment data using both Anatomical Landmark (AL) and Functional (FUN) modelsJoint moment AL (left) FUN (left) AL (right) FUN (right)CMD between testersHip ﬂexion/extension 0.89670.036 0.89570.048 0.91870.032 0.91970.027Knee ﬂexion/extension 0.81070.111 0.81570.068 0.82170.082 0.83770.084Ankle dorsi/plantar ﬂexion 0.95170.024 0.95170.024 0.96870.010 0.96870.010Hip abduction/adduction 0.88570.042* 0.90470.044 0.89970.036* 0.93370.020Knee varus/valgus 0.82670.090 0.80170.125 0.80470.096 0.76970.149Ankle abduction/adduction 0.36570.236 0.37170.240 0.53470.269 0.53570.269Hip internal/external rotn 0.62170.131 0.64370.127 0.68370.081 0.71170.084Knee internal/external rotn 0.74770.097 0.73670.096 0.76370.126 0.74870.135Ankle inversion/eversion 0.62270.242 0.62470.240 0.70470.193 0.70470.193CMD within testerHip ﬂexion/extension 0.88770.039 0.90370.028 0.91670.027 0.92070.022Knee ﬂexion/extension 0.81070.103 0.83170.062 0.81370.095 0.82370.091Ankle dorsi/plantar ﬂexion 0.94570.025 0.94670.026 0.96470.013 0.96470.013Hip abduction/adduction 0.85770.066* 0.91070.032 0.90670.025* 0.93770.013Knee varus/valgus 0.78770.097 0.80070.120 0.79270.077 0.75070.105Ankle abduction/adduction 0.32570.213 0.33870.216 0.55870.175 0.55770.177Hip internal/external rotn 0.62170.131 0.65270.122 0.66670.082 0.70170.074Knee internal/external rotn 0.72070.090 0.71770.095 0.73170.118 0.71070.128Ankle inversion/eversion 0.63370.226 0.63970.231 0.70570.261 0.70370.260Note: Signiﬁcant differences between AL and FUN models are denoted by *(po0:05).ranging between 0.75 and 0.94. Internal/external rota- The FUN model produced more repeatable hiption moments at the hip and knee were slightly less moments than the AL model in the frontal plane, bothrepeatable than ab/adduction moments, with mean r2 of between testers and within tester (FUN r2 ¼ 0:92; AL0.66 and 0.73 Ankle joint moments had similar r2 ¼ 0:89; po0:05) (Table 2). The FUN model alsorepeatability to the hip and knee joint for inversion/ produced slightly more repeatable hip moments than theeversion, with a mean r2 of 0.67, but displayed less AL model in the transverse plane (mean r2 of 0.68 andrepeatability abduction/adduction moments (mean r2 of 0.65, respectively), although these were not statistically0.48, Table 2). signiﬁcant. As expected, ankle joint moments displayed
ARTICLE IN PRESS1164 T.F. Besier et al. / Journal of Biomechanics 36 (2003) 1159–1168similar repeatability between models, within tester and models may explain the low repeatability in non-sagittalbetween testers. plane data compared to the AL and FUN model Although the curves were repeatable for both the AL presented here. An investigation is currently underwayand FUN models, differences in the magnitude of the to directly compare the model employed by Kadabakinematic and kinetic data collected with both models et al. (1989) and Growney et al. (1997) with the currentwere observed (Figs. 3 and 4). These differences were models.due to the altered location of the hip and KJCs and axes With regard to the accuracy of frontal and transverseof rotation between models, and mostly affected data in plane rotations using these two models, it is difﬁcult tothe frontal and transverse plane. The magnitude of the ascertain whether our results reﬂect the repeatability ofankle joint moments were not affected by the model segmental rotations, or the repeatability of motionemployed (Fig. 4). artefact, for example, due to skin movement from The systematic error due to the re-application of underlying muscle activation or impact loading of themarkers was similar for both AL and FUN models, with foot at heel strike. However, the knee varus/valgusan average difference of B3.8 and B0.03 Nm/kg angles from both models compare favourably to that ofbetween testing sessions for joint angle and moment Lafortune et al. (1992), who used high speed motiondata, respectively. Systematic error within tester was capture and cortical pins embedded within the femursimilar to the error between testers (Figs. 3 and 4). and tibia to measure knee joint rotations (see dashed lines in Fig. 3). Knee internal/external rotation kine- matics were also similar in shape to that of Lafortune4. Discussion et al. (1992), although a difference in the ACS used by us and Lafortune et al. (1992) may be responsible for the It was hypothesized that the numerical deﬁnition of obvious offset (Fig. 3). The difference in the ACSs mayjoint centres and axes of rotation in the FUN model have also caused our models internal/external andwould improve the repeatability of kinematic and varus/valgus rotations during swing to be slightly largerkinetic data, compared to traditional methods that rely than that reported by Lafortune et al. (1992), possiblyon the location of ALs to deﬁne joint centres and axes of due to cross-talk from knee ﬂexion/extension (Piazzarotation (AL model). This hypothesis was tested using and Cavanagh, 2000). Skin movement may also bewithin-tester and between-tester conditions. Further- responsible for these differences. Similar effects may bemore, in an effort to reduce the error associated with evident in the frontal and transverse plane rotations atlocating ALs on the foot (Della Croce et al., 1997), a the hip and ankle joints.new technique to deﬁne the orientation of the foot The FUN model produced slightly more repeatablesegment was investigated. gait curves than the AL model, in knee joint kinematics Both models presented in this paper produced highly and hip joint moments, thus supporting the hypothesisrepeatable frontal and transverse plane kinematic data of this study. However, the differences in repeatabilitycompared to previous studies (Kadaba et al., 1989; between the AL and FUN model were not asGrowney et al., 1997). For example, Kadaba et al. predominant as expected. The FUN model was also(1989) and Growney et al. (1997) reported between-day expected to be more repeatable than the AL model inCMD values of B0.40 for knee varus/valgus and B0.24 the between-tester condition, as the FUN model is notfor knee internal/external rotation angles. Repeatability as reliant upon accurate location of ALs to deﬁne jointof hip internal/external rotation angles measured centres and axes of rotation. However, the AL and FUNbetween-days by Kadaba et al. (1989) and Growney models produced similar repeatability of gait dataet al. (1997) were also low, with average r2 of 0.2 and within tester as they did between testers (r2 and0.42, respectively. Reasons for such low between-day systematic error), suggesting that both models producerepeatability of non-sagittal plane angles included skin repeatable results, regardless of whether the samemovement artefact and marker re-application, coupled examiner performs the test–retest gait analysis.with the effects of ‘downstream’ errors associated with Several factors might explain the similarities in theEuler angle calculations (Growney et al., 1997). The use repeatability of gait data between the AL and FUNof marker clusters in the AL and FUN model appears to model, and the repeatability of each model, within testerimprove the repeatability of non-sagittal plane kine- and between testers. Perhaps most importantly, thematic data, which may be partly due to reduced skin examiners performing the gait analyses in this studymovement artefact. Furthermore, the AL and FUN were all very experienced in locating lower limb ALs,model do not appear to have the same propensity for such as the ASISs of the pelvis and epicondyles of theerror from marker re-application as the model of femur. An interesting analysis would be to compare theKadaba et al. (1989) and Growney et al. (1997). The gait data from both models collected by an experienceduse of mid-segment markers to deﬁne joint centres and and a novice examiner. Similar gait data would beaxes of rotation for the knee and ankle in previous expected between-examiners using the FUN model,
50 25 10 Flexion Adduction 3.9˚ 2.1˚ Internal Rotation 7.2˚ 40 20 5 30 15 0 0 20 40 60 80 100 20 10 -5 Hip 10 5 -10 0 0 -15 0 20 40 60 80 100 0 20 40 60 80 100 -10 -5 -20 Extension Abduction External Rotation -20 -10 -25 80 30 30 Flexion Varus 3.7˚ Internal Rotation 3.3˚ 3.5˚ 20 20 60 10 10 40 0 0 Knee 20 0 20 40 60 80 100 0 20 40 60 80 100 -10 -10 0 -20 -20 Joint Angle (deg) 0 20 40 60 80 100 Extension Valgus External Rotation -20 -30 -30 20 20 20 Dorsi Flexion 2.1˚ 3.5˚ Inversion 7.2˚ ARTICLE IN PRESS Adduction 15 15 15 10 10 10 5 5 5 0 0 0 Ankle T.F. Besier et al. / Journal of Biomechanics 36 (2003) 1159–1168 0 20 40 60 80 100 0 20 40 60 80 100 0 20 40 60 80 100 -5 -5 -5 -10 -10 -10 -15 -15 -15 Plantar Flexion Abduction Eversion -20 -20 -20 FUN Heel Strike Toe Off Heel Strike Toe Off Heel Strike Toe Off AL Percentage Stride Lafortune et al. (1992)Fig. 3. Typical joint kinematic data obtained from a single gait analysis session using both AL and Optimized (FUN) joint models. The number on each graph indicates the average systematic error(in degrees) between gait sessions (between testers and within tester) of both models. 1165
0.8 0.2 0.2 1166 Flexion Adduction 0.053 0.043 Internal Rotation 0.027 0.6 0.1 0.15 0.4 0 0.1 0 20 40 60 80 100 0.2 -0.1 0.05 0 -0.2 0 Hip 0 20 40 60 80 100 0 20 40 60 80 100 -0.2 -0.3 -0.05 -0.4 -0.4 -0.1 -0.6 -0.5 -0.15 Extension Abduction External Rotation -0.8 -0.6 -0.2 0.4 0.1 0.06 Flexion 0.04 Varus 0.033 Internal Rotation 0.01 0.3 0.05 0.04 0.2 0 0.02 0 20 40 60 80 100 0.1 -0.05 0 0 20 40 60 80 100 0 -0.1 -0.02 Knee 0 20 40 60 80 100 -0.1 -0.15 -0.04 -0.2 -0.2 -0.06 -0.3 -0.25 -0.08 Extension Valgus External Rotation -0.4 -0.3 -0.1 0.2 0.05 0.06 ARTICLE IN PRESS Dorsi Flexion 0.029 Adduction 0.013 Inversion 0.015 Internal Joint Moment (Nm/kg) 0 0.04 0.04 0 20 40 60 80 100 0.02 -0.2 0.03 0 -0.4 T.F. Besier et al. / Journal of Biomechanics 36 (2003) 1159–1168 0.02 0 20 40 60 80 100 Ankle -0.02 -0.6 0.01 -0.04 -0.8 0 -0.06 Plantar Flexion 0 20 40 60 80 100 Eversion -1 -0.01 Abduction -0.08 Heel Strike Toe Off Heel Strike Toe Off Heel Strike Toe Off FUN AL Percentage StrideFig. 4. Typical joint moment data obtained from a single gait analysis session using both AL and Optimized (FUN) joint models. The number on each graph indicates the average systematic error(in Nm/kg) between gait sessions (between testers and within tester) of both models.
ARTICLE IN PRESS T.F. Besier et al. / Journal of Biomechanics 36 (2003) 1159–1168 1167whereas incorrect location of ALs might lead to to describe motion of one segment relative to another,signiﬁcant differences in the gait data between-exam- care should be taken when using it to describeiners using the AL model. Furthermore, the subjects in pathological joint motion. Abnormal knee kinematics,this study were young and healthy, with minimal body for example, may not be easily identiﬁed from timefat, which would improve the ability to locate ALs, histories of knee joint angles using a mean helical axis,particularly on the pelvis. In subject populations where as the orientation of the helical axis may change relativepalpation of pelvis ALs becomes difﬁcult, the FUN to the anatomy.model would be expected to produce more repeatable In summary, both models produced highly repeatablegait data than the AL model between testing sessions, as lower limb gait data compared to previous modelsit does not rely on the accurate location of pelvis (Kadaba et al., 1989; Growney et al., 1997). The FUNmarkers to deﬁne the HJCs. The FUN model might also model produced slightly more repeatable kinematic andproduce more repeatable knee joint kinematics and kinetic data than the AL model, with the advantage ofkinetics than the AL model in subjects who have bony not having to accurately locate bony landmarks.deformities of the knee joint, where location of the Improved repeatability of the FUN model comparedepicondyles of the femur might prove difﬁcult. to the AL model might be more pronounced with Della Croce et al. (1997) suggested that the largest examiners who are less experienced, in overweighterror in locating ALs of the lower limb occur at the foot, subject populations, where location of bony landmarkswhich might have a negative effect on the repeatability becomes more difﬁcult, or with subjects who have largeof ankle kinematic and kinetic data. Using ALs to deﬁne bony deformities at the knee. These issues requirethe foot segment, Growney et al. (1997) reported an further investigation. The foot calibration rig providesaverage CMD of 0.41 for ankle inversion/eversion an easy alternative to deﬁne the foot segment, withoutangles and 0.23 for ankle abduction/adduction angles. accurately locating ALs of the foot, producing repeat-Hence, the foot calibration rig was developed to deﬁne able results.the foot segment using clinical measures of rear-footinversion/eversion, and foot abduction/adduction,rather than relying on the accurate location of ALs. AcknowledgementsUsing the calibration rig to deﬁne the foot segmentresulted in much higher r2 values than those reported We would like to acknowledge the ﬁnancial supportpreviously (Growney et al., 1997) for ankle inversion/ of the Australian Football League (AFL) and theeversion and abduction/adduction angles and moments. Australian National Health and Medical Research Although the repeatability of the waveform data and Council (NHMRC, ID# 991134).systematic error were quite similar between AL andFUN models, differences in the magnitude of the jointangle and moment data (offsets) were still observed References(Figs. 3 and 4). These were due to the different locationsof the hip and KJCs in each model, and the different Boyd, S.K., Ronsky, J.L., 1998. Instantaneous moment arm determi-ﬂexion/extension axes deﬁned for the knee joint. The nation of the cat knee. Journal of Biomechanics 31, 279–283. Cappozzo, A., 1984. Gait analysis methodology. Human Movementquestion must then be asked, which model provides the Science 3, 27–54.most clinically representative data? Previous investiga- Cappozzo, A., Catani, F., Della Croce, U., Leardini, A., 1995. Positiontions have shown the functional method of locating and orientation in space of bones during movement: anatomicalHJCs to be superior to deﬁnitions based on regression frame deﬁnition and determination. Clinical Biomechanics 10,equations or models of ‘best-ﬁt’ (Leardini et al., 1999). 171–178.Therefore, the FUN model is likely to provide more Ch ze, L., Fregly, B.J., Dimnet, J., 1998. Determination of joint e functional axes from noisy marker data using the ﬁnite helical axis.accurate HJCs compared to the AL model. It is more Human Movement Science 17, 1–15.difﬁcult to ascertain the differences between the knee Churchill, D.L., Incavo, S.J., Johnson, C.C., Beynnon, B.D., 1998.ﬂexion/extension axes deﬁned by the transepicondylar The transepicondylar axis approximates the optimal ﬂexion axisaxis or a mean helical axis. Churchill et al. (1998) found of the knee. Clinical Orthopaedics and Related Research 356,no difference between an ‘optimal’ knee ﬂexion/exten- 111–118. de Lange, A., Huiskes, R., Kauer, J.M.G., 1990. Effects of datasion axis and the transepicondylar axis, which would smoothing on the reconstruction of helical axis parameters insuggest that either model of deﬁning the knee axis would human joint kinematics. Journal of Biomechanical Engineeringproduce similar kinematic and kinetic data. However, 112, 107–113.the deﬁnition of the transepicondylar axis requires the Della Croce, U., Cappozzo, A., Kerrigan, D.C., Lucchetti, L., 1997. Bone position and orientation errors: pelvis and lower limbaccurate location of the epicondyles of the femur, which anatomical landmark identiﬁcation reliability. Gait Posture 5,may be problematic given inexperienced examiners or 156–157.knees with bony deformities. Although the helical axis Della Croce, U., Cappozzo, A., Kerrigan, D.C., 1999. Pelvis andprovides an accurate and convenient frame of reference lower limb anatomical landmark calibration precision and its
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