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On the expression of joint moments during gait
Gait & Posture 25 (2007) 440–452 www.elsevier.com/locate/gaitpost
On the expression of joint moments during gait Anthony G. Schache a,b,*, Richard Baker a,b a
b
Hugh Williamson Gait Laboratory, Royal Children’s Hospital, Parkville, Vic., Australia Murdoch Childrens Research Institute, Royal Children’s Hospital, Parkville, Vic., Australia Received 15 May 2006; accepted 15 May 2006
Abstract The purpose of the current study was to examine the effect of different reference frames on lower limb joint moments during gait with a view to identifying a recommended convention for clinical purposes. Data were collected from 10 subjects (nine able-bodied adults and one child with diplegic cerebral palsy) whilst walking at a self-selected speed. Calculations utilised a three-dimensional inverse dynamics model. For each joint, moments were expressed in four different reference frames. Three of the frames were orthogonal: laboratory frame; anatomical frame of proximal segment; anatomical frame of distal segment. The fourth reference frame was a non-orthogonal joint coordinate system (JCS). Significant differences in the joint moment profiles during gait were found with alternative references frames. This was apparent primarily for the transverse plane joint moments for able-bodied adult gait. For the pathological gait pattern presented, there were also marked differences in the frontal plane joint moments and more subtle ones in the sagittal plane. Whilst it is recognised that all possible reference frames for the expression of the net moment vector are mathematically valid, a decision needs to be made as to which one is more clinically useful. It is proposed that the non-orthogonal JCS is most logical on the basis of what, biomechanically, the joint moment actually represents. # 2006 Elsevier B.V. All rights reserved. Keywords: Gait analysis; Inverse dynamics; Lower limb; Joint coordinate system
1. Introduction There are four possible reference frames for the expression of the net moment vector in quantitative gait analysis. Three of these possibilities are orthogonal frames: the laboratory (or global) frame (LF); the proximal segment anatomical frame (AF); the distal segment AF. Another possibility is a nonorthogonal frame or joint coordinate system (JCS). When reviewing the previous literature evaluating lower limb joint moments during gait, each reference frame has been implemented in at least one study [1–11]. Thus, no consensus currently exists regarding an accepted standard. This makes it difficult to compare joint moment data across studies. Few studies have investigated the differences in lower limb joint moments during gait when expressed in alternative reference frames [12–14]. Of those that have, only * Corresponding author at: Hugh Williamson Gait Laboratory, 3rd Floor, Main Block, Royal Children’s Hospital, Flemington Road, Parkville, Vic. 3052, Australia. Tel.: +61 03 9345 5354; fax: +61 03 9345 5447. E-mail address: [email protected] (A.G. Schache). 0966-6362/$ – see front matter # 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.gaitpost.2006.05.018
able-bodied gait has been evaluated and not all possible reference frames have been considered. In contrast, the effect of different inertial parameter sets on lower limb joint moment calculations has been well investigated [15–19]. This is surprising given that, for relatively slow speed movements such as gait, lower limb joint moments are far more likely to be sensitive to a change in reference frame than they are to a change in the magnitude of an inertial parameter set. The decision to adopt a given reference frame has typically been based upon preference rather than objective evidence. To our knowledge, Winter et al. [20,21] provide the only formal attempt to justify a preferred convention. Two theoretical arguments were provided. First, as the dominant velocity of the centre of mass is in the plane of progression and the balance of the trunk in both the sagittal and frontal planes is dictated by gravity, both the centre of mass and trunk are tightly regulated to have trajectories in the plane of progression. Second, even when externally rotated, the lower limb segments do not follow trajectories in a local AF but rather move forward in the plane of progression. Given that under experimental conditions the
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plane of progression will be aligned with one of the planes of the LF, it was therefore concluded that the net moment vector should be expressed in the LF. Despite this viewpoint, few studies have actually adopted the LF as a preferred convention [2,7,9,10]. Most have used an orthogonal or non-orthogonal local AF [1,3–6,8,11]. This would suggest that additional clinical factors, such as anatomical interpretation and sensitivity to change post treatment, are also considered by many to be important criteria for making judgments regarding a preferred reference frame. The aim of the current study was to therefore provide a definitive evaluation of the effect of different reference frames on lower limb joint moments during gait. It was considered likely that such differences would be more prominent for abnormal gait, thus both able-bodied and pathological gait patterns were investigated. An additional aim was to use these results as evidence for identifying a recommended convention for clinical purposes.
2. Materials and methods 2.1. Subjects Ten subjects were voluntarily recruited. Approval was obtained from the Royal Children’s Hospital Ethics in Human Research Committee prior to commencement and subjects signed a consent form. The able-bodied adult group comprised of two men and seven women aged 19.8 years (S.D. 2.1) with a mean height of 164.5 cm (S.D. 8.5) and body mass of 60.0 kg (S.D. 1.1). The subject with spastic
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diplegic cerebral palsy was a 10-year-old boy who was 146.1 cm tall and weighed 39.7 kg. 2.2. Instrumentation Kinematic data were acquired using a 3D motion analysis system (VICON 512, Oxford Metrics, Oxford, England) with six 120 Hz cameras. The LF was defined such that the positive x direction was in the forward direction, the positive y direction was orientated to the left and the positive z direction was orientated upwards. Two AMTI force plates (Advanced Mechanical Technology Inc., Watertown, MA, USA) captured ground reaction force data at a sampling rate of 1080 Hz. 2.3. Frame definitions The 3D pose of the seven body segments of interest (pelvis; left and right thighs; left and right shanks; both feet) were obtained by tracking the trajectories of small spherical retro-reflective markers (25 mm diameter) mounted as outlined in Table 1. These markers allowed the reconstruction of a technical frame (TF) for each of the body segments (Table 2). Given the potential arbitrary relationship between the defined TFs and the anatomy of the underlying bone, a static anatomical landmark calibration trial was performed to reconstruct the various AFs. Respective AF definitions are detailed in Table 3. The knee joint flexion–extension axis was defined using a dynamic optimisation procedure as described by Schache et al. [22]. The vertical (z) axis of the femur was first defined (knee joint centre (KJC) to hip joint centre (HJC)) and then the mediolateral (y) axis (or knee joint
Table 1 Specific marker locations and orientations Static and dynamic trials LASIS (RASIS) SACR LTH1 (RTH1) LTH2 (RTH2) LTH3 (RTH3) LSH1 (RSH1) LSH2 (RSH2) LANK (RANK) LCAL1 (RCAL1) LMID (RMID) LLATMID (RLATMID) Static anatomical landmark calibration trial only LMFE (RMFE) LLFE (RLFE) LTHIROT (RTHIROT) LMED (RMED) LCAL2 (RCAL2) LTOE (RTOE)
Anterior to left (and right) anterior superior iliac spine (ASIS) lying in plane containing left and right ASIS and the midpoint between both posterior superior iliac spines (PSIS) Posterior to the midpoint between both PSISs lying in plane containing left and right ASISs and the midpoint between both PSISs Distal and anterior aspect of left (and right) thigh Distal and lateral aspect of left (and right) thigh Distal and posterior aspect of left (and right) thigh Proximal end of left (and right) anterior tibia just distal to tibial tubercle Distal end of left (and right) anterior tibia Left (and right) lateral malleolus aligned with bimalleolar axis Bisection of the distal aspect of the left (and right) posterior calcaneum Left (and right) medial midfoot over the distal and dorsomedial aspect of the navicular Left (and right) lateral midfoot over the dorsal and distal aspect of the cuboid Most prominent palpable aspect of left (and right) medial femoral epicondyle (MFE) Most prominent palpable aspect of left (and right) lateral femoral epicondyle (LFE) Virtual point, defined as rotated position of LTH2 (or RTH2) marker (see text for further explanation) Left (and right) medial malleolus aligned with bimalleolar axis Bisection of the proximal aspect of the left (and right) posterior calcaneum Dorsal surface of the left (and right) distal forefoot at the midpoint between the second and third metatarsophalangeal joints
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Table 2 Technical frame definitions Pelvis Origin Mediolateral (y) axis Anterior–posterior (x) axis Vertical (z) axis Thigh Origin Anterior–posterior (x) axis Mediolateral (y) axis Vertical (z) axis Shank Origin Vertical (z) axis Mediolateral (y) axis Anterior–posterior (x) axis Foot Origin Anterior–posterior (x) axis Mediolateral (y) axis
Vertical (z) axis
Midpoint between LASIS and RASIS markers In direction from RASIS to LASIS markers Perpendicular to mediolateral (y) axis in plane containing LASIS, RASIS and SACR markers Mutual perpendicular to other two axes Midpoint between LTH1 (or RTH1) and LTH3 (or RTH3) markers In direction from LTH3 (or RTH3) to LTH1 (or RTH1) markers Perpendicular to anterior–posterior (x) axis in plane containing LTH1 (or RTH1), LTH2 (or RTH2) and LTH3 (or RTH3) markers Mutual perpendicular to other two axes LSH2 (or RSH2) marker In direction from LSH2 (or RSH2) marker to LSH1 (or RSH1) marker Perpendicular to vertical (z) axis in plane containing LSH1 (or RSH1) marker, LSH2 (or RSH2) marker and LANK (or RANK) marker Mutual perpendicular to other two axes LCAL1 (or RCAL1) marker In direction from LCAL1 (or RCAL1) marker to LLATMID (or RLATMID) marker Perpendicular to anterior–posterior (x) axis in plane containing LCAL1 (or RCAL1) marker, LLATMID (or RLATMID) marker and LMID (or RMID) marker Mutual perpendicular to other two axes
flexion–extension axis) was rotated in the plane perpendicular to the vertical (z) axis through an angle u, whereby u represented the degree of rotation necessary to minimise the variance in the dynamic knee varus–valgus kinematic profile. 2.4. Procedures Anthropometric parameters required for estimating the location of the HJC using the method of Davis et al. [23] were first measured. Markers were then placed on each subject’s pelvis and lower limbs as previously described. The same tester (AS) performed all marker placements. Each test session commenced with the capture of the static anatomical landmark calibration trial. Calibration markers were then removed and dynamic trials were captured. Subjects walked at their natural speed through the middle of a walkway with a calibrated field approximately five metres in length. The able-bodied adult subjects walked at a speed of 1.2 0.1 m/s, whilst the child with cerebral palsy walked independently at a speed of 1.1 m/s. A successful trial was one in which the left and right heels successfully struck the two adjacent force plates in isolation where no obvious force plate targeting was observed by the tester. A single walking trial was captured for each subject. 2.5. Data analysis Coordinate data were filtered using Woltring’s general cross-validatory quintic smoothing spline [24] with a predicted mean-squared error of 15 mm. Kinematic data
were calculated using a joint coordinate system convention. The JCS for the hip and knee corresponded to the standard convention whereby the mediolateral (y) axis was fixed in the proximal segment, the vertical (z) axis was fixed in the distal segment and the anteroposterior (x) axis was the mutual perpendicular [25]. For the ankle, the mediolateral (y) axis was fixed in the distal tibia, the anteroposterior (x) axis was fixed in the foot and the vertical (z) axis was the mutual perpendicular [26]. Left-sided data were chosen for analysis. Lower limb internal joint moments were calculated using a standard inverse dynamics approach. Adapted inertial parameters as per De Leva [27] were used for computing joint moments for the able-bodied adults, whilst dual energy X-ray absorptiometry based inertial parameters from Ganley and Powers [17] were used for computing joint moments for the child with cerebral palsy. For each joint, moments were expressed in each of four frames of reference: the LF, the proximal segment AF, the distal segment AF and the JCS. All computations were performed using Bodybuilder software (Oxford Metrics Ltd.). Joint moments were normalised by dividing by subject’s body mass. Temporal events defining the gait cycle were identified from the ground reaction force data. Each stride was time normalised to 101 points representing equal intervals from 0% to 100% using Polygon software (Oxford Metrics Ltd.). Discrete parameters were extracted from the able-bodied adult joint moment profiles for statistical analysis (Table 4). The parameters were selected based on those used previously by Benedetti et al. [4]. Given the number of dependent variables analysed, a conservative level of
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Table 3 Anatomical frame definitions Pelvis Origin Mediolateral (y) axis Anterior–posterior (x) axis Vertical (z) axis Virtual point Femur Origin Vertical (z) axis Mediolateral (y) axis
Anterior–posterior (x) axis Virtual points Tibia (proximal) Origin Vertical (z) axis Mediolateral (y) axis Anterior–posterior (x) axis Virtual point Tibia (distal) Origin Vertical (z) axis Mediolateral (y) axis Anterior–posterior (x) axis Virtual point Foot Origin Anterior–posterior (x) axis
Vertical (z) axis Mediolateral (y) axis Virtual point
Midpoint between LASIS and RASIS markers In direction from RASIS to LASIS markers Perpendicular to mediolateral (y) axis in plane containing LASIS, RASIS, SACR markers Mutual perpendicular to other two axes LHJC (or RHJC), defined relative to pelvic anatomical frame as per Davis et al. [23] LKJC (or RKJC), defined as midpoint between LLFE (or RLFE) marker and LMFE (or RMFE) marker In direction from LKJC (or RKJC) to LHJC (or RHJC) Perpendicular to vertical (z) axis in plane containing LKJC (or RKJC), LHJC (or RHJC), and LTHI (RTHI) marker, rotated by angle u about vertical (z) axis, whereby u represents degree of rotation required to minimise variance in dynamic knee varus–valgus kinematic profile Mutual perpendicular to other two axes LKJC (or RKJC) and LTHIROT (or RTHIROT) as defined above LAJC (or RAJC), defined as midpoint between LANK (or RANK) marker and LMED (or RMED) marker In direction from LAJC (or RAJC) to LKJC (or RKJC) location Perpendicular to vertical (z) axis and parallel to femur mediolateral (y) axis when in anatomical landmark calibration configuration Mutual perpendicular to other two axes LAJC (or RAJC) as defined above LAJC (or RAJC), defined as midpoint between LANK (or RANK) marker and LMED (or RMED) marker In direction from LAJC (or RAJC) to LKJC (or RKJC) location Perpendicular to vertical (z) axis in plane containing LKJC (or RKJC), LMED (or RMED) and LANK (or RANK) markers Mutual perpendicular to other two axes LAJC (or RAJC) as defined above LAJC (or RAJC), defined as midpoint between LANK (or RANK) marker and LMED (or RMED) marker In direction from LCAL1 (or RCAL1) marker to LTOE (or RTOE) marker but rotated in plane containing LCAL1 (or CAL1), LCAL2 (or RCAL2) and LTOE (or RTOE) markers until parallel with floor (horizontal plane of laboratory frame) Perpendicular to anterior–posterior (x) axis in plane containing LCAL1 (or CAL1), LCAL2 (or RCAL2) and LTOE (or RTOE) markers Mutual perpendicular to other two axes LAJC (or RAJC) as defined above
NB. HJC, hip joint centre; KJC, knee joint centre; AJC, ankle joint centre.
significance was set at a = 0.01 for all tests. One-way repeated measures ANOVA tests were used to determine if significant differences in the dependent variables occurred for different reference frames. When significant F-ratios
were obtained, post hoc pairwise comparisons (paired t-test) were used to determine differences between each reference frame. All statistical computations were performed using a commercial statistics software package (SPSS, USA).
Table 4 Joint moment parameters Hip joint moment parameters
Knee joint moment parameters
Ankle joint moment parameters
HM1 HM2 HM3 HM4 HM5 THM5 HM6 THM6
KM1 KM2 KM3 KM4 KM5 KM6 KM7 KM8 TKM8 KM9 TKM9
AM1 AM2 AM3 TAM3 AM4 TAM4 AM5 TAM5 AM6 TAM6
Peak stance extensor moment Peak stance flexor moment First peak stance abductor moment Second peak stance abductor moment Peak stance internal rotator moment Time HM5 (gait cycle%) Peak stance external rotator moment Time HM5 (gait cycle%)
Unless stated otherwise all parameters are in Nm/kg.
First peak stance flexor moment First peak stance extensor moment Second peak stance flexor moment Second peak stance extensor moment Peak stance varus moment First peak stance valgus moment Second peak stance valgus moment Peak stance internal rotator moment Time KM8 (gait cycle%) Peak stance external rotator moment Time KM9 (gait cycle%)
Peak stance dorsi-flexor moment Peak stance plantar flexor moment Peak stance adductor moment Time AM3 (gait cycle%) Peak stance abductor moment Time AM4 (gait cycle%) Peak stance invertor moment Time AM5 (gait cycle%) Peak stance evertor moment Time AM6 (gait cycle%)
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The able-bodied adults displayed typical kinematic patterns in each plane for each joint (Fig. 1). In contrast, the child with cerebral palsy had an increased rearfoot valgus alignment in standing (15.48 compared to 3.5 4.98 for the able-bodied adults) and walked with excessive hip internal rotation (Fig. 1) and foot adduction or toe in (Fig. 2).
ankle rotation moment in the foot AF and the ankle invertor– evertor moment in the LF where a degree of inter-subject variability was present. Lower limb joint moments for CP gait are also illustrated in Figs. 3–5. Whilst some general characteristic features associated with diplegic CP gait were evident, such as a prolonged stance phase hip extensor moment and a reduced plantar flexor moment, other features were dependent upon the particular reference frame. These results will be discussed further below.
3.2. Joint moment profiles
3.3. Effect of different reference frame
Lower limb joint moments for able-bodied adult gait are illustrated in Figs. 3–5. Most joint moments were found to display characteristic profiles that were systematic across subjects as indicated by the relatively small standard deviation bands. This was not the case, however, for the
Significant differences in the joint moment profiles during gait were found with alternative reference frames. There were three general findings. First, differences in the joint moment profiles with a change in reference frame were apparent for each joint. Second, the frontal and transverse
3. Results 3.1. Joint kinematic profiles
Fig. 1. Hip, knee and ankle joint kinematics during able-bodied adult gait (mean curve and standard deviation band) and CP gait (dashed line). The dashed vertical line indicates toe off.
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Fig. 2. Foot rotation angles (ab/adduction or toe in/out) with respect to the LF for able-bodied adult gait (mean curve and standard deviation band) and CP gait (dashed line). The dashed vertical line indicates toe off.
plane joint moments were more sensitive to a change in reference frame than the sagittal plane joint moments. Third, the joint moments for CP gait were more sensitive to a change in reference frame than the joint moments for ablebodied adult gait.
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Differences in the hip joint moment profiles with a change in reference frame were mainly evident in the transverse plane for able-bodied adult gait (Fig. 3). Only two of the eight hip joint parameters examined (THM5 and THM6) were found to be significantly different and these were both transverse plane parameters (Table 5). The timing of the peak hip internal rotator joint moment (THM5) was significantly later during stance when expressed in the LF compared to the femoral AF, whilst the timing of the peak hip external rotator joint moment (THM6) was significantly earlier during stance when expressed in both the LF and pelvis AF compared to the femoral AF (Fig. 3). In contrast, differences in the hip joint moment profiles with a change in reference frame were detectable in all planes for CP gait (Fig. 3). In the sagittal plane, the prolonged hip extensor moment displayed a distinctly different pattern when expressed in the femoral AF compared to the LF and pelvis AF. In the frontal plane, the magnitude of the late stance hip abductor moment was substantially greater when expressed in the femoral AF compared to the LF, pelvis AF or JCS. Finally, in the transverse plane, joint moment profiles were markedly different between the four reference frames. Differences in the knee joint moment profiles with a change in reference frame were apparent in all planes for both able-bodied adult and CP gait (Table 6 and Fig. 4). In the sagittal plane, the magnitude of the first peak knee extensor moment (KM2) for able-bodied adult gait was
Fig. 3. Hip joint moments when expressed in the four alternative reference frames for both able bodied adult gait (mean curve and standard deviation band) and CP gait (dashed line). The dashed vertical line indicates toe off.
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Fig. 4. Knee joint moments when expressed in the four alternative reference frames for both able-bodied adult gait (mean curve and standard deviation band) and CP gait (dashed line). The dashed vertical line indicates toe off.
significantly greater when expressed in the LF compared to the femoral AF or tibial AF (Table 6). The opposite was found to be true for CP gait and the magnitude of the difference was somewhat greater (Fig. 4). In the frontal plane, differences between reference frames for both ablebodied adult and CP gait occurred primarily during initial stance (Fig. 4). For able-bodied adult gait, the magnitude of the first peak knee valgus moment (KM6) was significantly less when expressed in the LF compared to the femoral AF, tibial AF or JCS (Table 6). KM6 was also significantly less when expressed in the femoral AF compared to the JCS (Table 6). For CP gait, the magnitude of the peak knee varus moment during initial stance displayed considerable variability across reference frames (Fig. 4). In the transverse plane, differences across reference frames were evident for the magnitude of the peak knee external rotator moment (KM9) for both able-bodied adult and CP gait (Fig. 4). For able-bodied adult gait, KM9 was significantly less when expressed in the LF compared to the femoral AF and tibial AF (Table 6). KM9 was also significantly less when expressed in the femoral AF compared to the tibial AF (Table 6). These same differences were found for CP gait (Fig. 4). Differences in the ankle joint moment profiles with a change in reference frame were mainly apparent in the frontal plane for able-bodied adult gait (Fig. 5). The peak
ankle invertor moment, in terms of both magnitude (AM5) and time (TAM5), was found to differ significantly across reference frames (Table 7). AM5 was significantly greater when expressed in the LF compared to the tibial AF or foot AF, whilst TAM5 occurred significantly later during stance when expressed in the LF compared to the foot AF (Table 7). For CP gait, differences in the ankle joint moment profiles with a change in reference frame were apparent in both the frontal and transverse planes (Fig. 5). In the frontal plane, a large ankle evertor moment was measured when expressed in the LF compared to the tibial AF or foot AF. In the transverse plane, a large ankle adductor moment was measured when expressed in the foot AF compared to the LF, tibial AF or JCS.
4. Discussion Consistent with previous studies [2,4,28], most joint moments for able-bodied adult gait were found to display characteristic profiles that were systematic across subjects. Two joint moments, however, were associated with a degree of inter-subject variability: the ankle rotation moment in the foot AF and the ankle invertor–evertor moment in the LF. This is in agreement with findings from a previous study [12].
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Fig. 5. Ankle joint moments when expressed in the four alternative reference frames for both able-bodied adult gait (mean curve and standard deviation band) and CP gait (dashed line). The dashed vertical line indicates toe off.
The inter-subject variability of the ankle rotation moment in the foot AF can be explained by its sensitivity to the frontal plane orientation of the posterior calcaneus [12]. As the postural alignment of the posterior calcaneus and its dynamic movement during gait will differ across subjects, the presence of this variability is not surprising. For example, with a varus-aligned rearfoot, the foot AF vertical z axis will be tilted medially and an ankle abductor moment will be generated from mid stance onwards. With a valgus-aligned rearfoot the opposite will be true [14]. This is further illustrated when viewing the CP gait data, characterised by an increased rearfoot valgus alignment and a corresponding large ankle adductor moment during stance (Fig. 5). The inter-subject variability of the ankle invertor–evertor moment in the LF can be explained by its sensitivity to the alignment of the foot in the LF transverse plane (ad/ abduction or toe in/out), which can be expected to vary across subjects. With increased toe out, the cosine projection of the foot into the LF frontal plane will increase, resulting in an increased ankle invertor moment in the LF. Hunt and Smith [12] have previously shown that a linear relationship exists between the magnitude of the ankle invertor moment in the LF and the amount of toe out. This relationship was also apparent for the CP gait data but in the opposite direction. In contrast to the able-bodied adult gait profile, the
child with CP ambulated with increased toe in (Fig. 2). Consequently, a large ankle evertor moment was generated in the LF (Fig. 5). Significant differences in the joint moment profiles for able-bodied adult gait were found with alternative reference frames. Differences were evident at all lower limb joints and were more prominent in the frontal and transverse planes. Previous studies in this area have only considered the LF and the distal segment AF [12–14]. Hunt and Smith [12] investigated differences in ankle joint moments during gait with a change in reference frame for 18 able-bodied adults. Similar results were reported to the current study whereby significant differences were found but were limited to the frontal and transverse planes. Liu and Lockhart [13] also investigated differences in lower limb joint moments during gait with a change in reference frame for 30 able-bodied adults varying in age from 19 to 86 years. Consistent with the current study, differences were found at all lower limb joints. However, in contrast, Liu and Lockhart [13] reported significant differences in all three planes for each joint despite finding the sagittal plane mean lower limb joint moment profiles for the alternative reference frames to be closely matched. This difference with respect to the current study may be a consequence of the larger cohort. Differences in the degree of variability associated with the joint moment profiles for able-bodied adult gait were
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Table 5 Mean (S.D.) for the hip joint moment parameters Parameter
LF
Pelvis AF
Femoral AF
JCSa
p-Value
HM1 (Nm/kg) Adult CP
0.596 (0.113) 0.577
0.594 (0.110) 0.574
0.580 (0.095) 0.615
– –
0.105 –
HM2 (Nm/kg) Adult CP
0.858 (0.231) 0.741
0.905 (0.236) 0.759
0.878 (0.223) 0.683
– –
0.388 –
HM3 (Nm/kg) Adult CP
0.708 (0.133) 0.547
0.687 (0.127) 0.527
0.684 (0.118) 0.360
0.699 (0.123) 0.522
0.335 –
HM4 (Nm/kg) Adult CP
0.628 (0.182) 0.286
0.579 (0.185) 0.165
0.623 (0.158) 0.425
0.578 (0.181) 0.157
0.027 –
HM5 (Nm/kg) Adult CP
0.109 (0.026) 0.121
0.087 (0.038) 0.099
0.095 (0.041) 0.105
– –
0.439 –
– –
0.005b –
– –
0.788 –
– –
0.001c –
THM5 (%) Adult CP HM6 (Nm/kg) Adult CP THM6 (%) Adult CP
40.0 (21.3) 57.0 0.085 (0.016) 0.055 15.8 (15.2) 4.0
36.1 (25.3) 55.0 0.179 (0.054) 0.126 11.7 (2.5) 4.0
12.2 (1.7) 16.0 0.087 (0.023) 0.047 41.3 (1.7) 50.0
a Note that for the hip JCS, by definition, the sagittal plane is the same as that for the pelvis AF and the transverse plane is the same as that for the femoral AF. Thus, only hip JCS frontal plane data were included in statistical analyses. b Significant comparisons ( p < 0.01) for LF vs. femoral AF. c Significant comparisons ( p < 0.01) for LF vs. femoral AF; pelvis AF vs. femoral AF.
also found with alternative reference frames. As previously discussed, both the ankle rotation moment in the foot AF and the ankle invertor–evertor moment in the LF displayed intersubject variability. For the ankle rotation moment, if the net moment vector was instead expressed in a reference frame other than the foot AF, then the measured inter-subject variability was reduced (Fig. 5). Similarly, for the ankle invertor–evertor moment, if the net moment vector was expressed in any of the anatomical reference frames rather than the LF, then the measured inter-subject variability was also reduced (Fig. 5). Susceptibility to inter-subject variability might therefore be one criteria to use for the selection of a preferred reference frame for the expression of the net moment vector. The joint moment profiles for CP gait were more sensitive to a change in reference frame than those for able-bodied gait. To our knowledge, no previous studies have documented this. Quite clear differences were evident in all three planes at the hip and knee joints. At the ankle joint, differences were limited to the frontal and transverse planes but the magnitude of the differences were quite considerable. This would indicate that, certainly for data relating to pathologies such as CP, the choice of reference frame for the expression of the net moment vector is critical. Interpretations regarding the
degree of similarity or disparity between the joint moment profiles for CP and able-bodied gait are reference frame dependent. For example, the child with CP can be seen to have or not have a hip abductor moment during terminal stance depending upon which particular reference frame is considered (Fig. 3). Likewise, for the ankle invertor–evertor moment, the profile for CP gait can be seen to be either opposite or quite similar to that of able-bodied gait (Fig. 5). Other examples of conflicting interpretations can also be found. Thus, at the very least for clinical purposes, it is clear that an accepted standard is required. The question of which reference frame is most appropriate for the expression of the net moment vector has received only limited discussion in the biomechanics literature to date. There has been some debate amongst researchers in the context of quantifying lumbar spine loading during lifting tasks [29–33]. However, for purposes of quantitative gait analysis, this issue has been largely neglected. Whilst the various possible reference frames have been well acknowledged [34–36], very few studies have provided any formal attempt to justify a preferred convention. It is important to note that all four alternative reference frames are mathematically correct. The differences between them do not represent ‘errors’ in determining
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Table 6 Mean (S.D.) for the knee joint moment parameters Parameter
LF
Femoral AF
Proximal tibial AF
JCSa
p-Value
KM1 (Nm/kg) Adult CP
0.209 (0.077) 0.131
0.200 (0.067) 0.106
0.205 (0.074) 0.091
– –
0.030 –
KM2 (Nm/kg) Adult CP
0.500 (0.220) 0.471
0.430 (0.194) 0.638
0.444 (0.187) 0.680
– –
0.005b –
KM3 (Nm/kg) Adult CP
0.215 (0.149) 0.441
0.222 (0.150) 0.463
0.238 (0.152) 0.453
– –
0.019 –
KM4 (Nm/kg) Adult CP
0.269 (0.115) 0.231
0.276 (0.109) 0.198
0.248 (0.102) 0.149
– –
0.117 –
KM5 (Nm/kg) Adult CP
0.036 (0.033) 0.509
0.070 (0.055) 0.298
0.054 (0.047) 0.157
0.071 (0.054) 0.253
0.029 –
KM6 (Nm/kg) Adult CP
0.300 (0.057) 0.160
0.383 (0.101) 0.040
0.384 (0.106) 0.064
0.398 (0.102) 0.070
0.001c –
KM7 (Nm/kg) Adult CP
0.298 (0.105) 0.207
0.295 (0.115) 0.199
0.289 (0.111) 0.239
0.278 (0.112) 0.192
0.053 –
KM8 (Nm/kg) Adult CP
0.056 (0.032) 0.146
0.103 (0.046) 0.114
0.030 (0.012) 0.126
– –
0.038 –
– –
0.019 –
– –
0.000d –
– –
0.920 –
TKM8 (%) Adult CP KM9 (Nm/kg) Adult CP TKM9 (%) Adult CP
33.1 (23.4) 11.0 0.043 (0.018) 0.007 45.4 (10.2) 0
12.0 (1.0) 16.0 0.094 (0.026) 0.030 41.6 (2.4) 50.0
10.3 (2.7) 12.0 0.125 (0.035) 0.059 45.0 (3.6) 54.0
a Note that for the knee JCS, by definition, the sagittal plane is the same as that for the femoral AF and the transverse plane is the same as that for the proximal tibial AF. Thus, only knee JCS frontal plane data were included in statistical analyses. b Significant comparisons ( p < 0.01) for LF vs. femoral AF; LF vs. proximal tibial AF. c Significant comparisons ( p < 0.01) for LF vs. femoral AF; LF vs. proximal tibial AF; LF vs. JCS; femoral AF vs. JCS. d Significant comparisons ( p < 0.01) for LF vs. femoral AF; LF vs. proximal tibial AF; femoral AF vs. proximal tibial AF.
a ‘correct’ value. Rather they represent subtly different biomechanical quantities. The question for quantitative gait analysis is which of the alternative reference frames is most useful in understanding the biomechanics of gait with or without pathology. The decision as to which to use must rest on a consideration of such issues. To our knowledge, Winter et al. [20,21] appear to be the only researchers to have addressed this question. Briefly, Winter et al. [20,21] argued that, as the whole body and its constituent segments are tightly regulated to have trajectories in the plane of progression and that as the plane of progression will correspond to one of the planes of the LF when under experimental conditions, joint moments should be expressed in the LF so as to allow the trajectories to be interpreted in terms of the moments that cause them.
The interpretation of a joint moment is worth discussing in the context of evaluating the various reference frames with which to express the net moment vector. A joint moment represents the net activity in the muscle groups crossing a particular joint. It indicates which muscle group is dominant. For example, if an internal knee flexor moment is present, the moment generated by the knee flexor muscle group exceeds that generated by the knee extensor muscle group by the measured amount. It is important to note that the joint moment does not represent the action of the dominant muscle group. The specific action of any particular muscle group is dependent on the behaviour of the entire kinetic chain. For example, it is now well established that the hamstrings can be acting to extend the knee under certain circumstances even though they will
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Table 7 Mean (S.D.) for the ankle joint moment parameters Parameter
LF
Distal tibial AF
Foot AF
JCS a
p-Value
AM1 (Nm/kg) Adult CP
0.143 (0.042) 0.014
0.142 (0.040) 0.016
0.142 (0.041) 0.017
– –
0.240 –
AM2 (Nm/kg) Adult CP
1.330 (0.125) 1.189
1.332 (0.123) 1.216
1.333 (0.122) 1.177
– –
0.440 –
AM3 (Nm/kg) Adult CP
0.034 (0.014) 0.044
0.030 (0.012) 0.127
0.056 (0.038) 0.332
0.031 (0.013) 0.114
0.307 –
TAM3 (%) Adult CP AM4 (Nm/kg) Adult CP TAM4 (%) Adult CP AM5 (Nm/kg) Adult CP TAM5 (%) Adult CP AM6 (%) Adult CP TAM6 (%) Adult CP
20.8 (19.8) 11.0 0.103 (0.026) 0.005 44.7 (3.6) 43.0 0.149 (0.080) 0.003 36.3 (11.0) 0 0.050 (0.055) 0.328 25.7 (28.3) 51.0
9.9 (3.5) 12.0 0.123 (0.036) 0.058 44.6 (3.0) 55.0 0.069 (0.045) 0.155 24.0 (13.7) 32.0 0.128 (0.065) 0.046 54.7 (2.7) 57.0
16.6 (12.8) 35.0 0.146 (0.087) 0.026 47.3 (16.0) 58.0 0.061 (0.027) 0.027 18.0 (8.8) 23.0 0.096 (0.039) 0.107 53.3 (2.3) 54.0
9.7 (2.2) 12.0 0.122 (0.043) 0.055 41.2 (4.1) 55.0
0.131 – 0.261 – 0.417 –
– –
0.007b –
– –
0.001c –
– –
0.018 –
– –
0.018 –
a
Note that for the ankle JCS, by definition, the sagittal plane is the same as that for the distal tibial AF and the frontal plane is the same as that for the foot AF. Thus, only ankle JCS transverse plane data were included in statistical analyses. b Significant comparisons ( p < 0.01) for LF vs. distal tibial AF; LF vs. foot AF. c Significant comparisons ( p < 0.01) for LF vs. foot AF.
always contribute to the generation of an internal knee flexor moment [37]. Consideration of which reference frame to refer the moments to must therefore be based on that which best represents the relative activity of the different muscle groups. This implicit link with muscle activity suggests that an anatomically relevant frame is most desirable. Furthermore, there is no consistent or definable relationship between the muscle groups themselves and the LF and this is clearly indicated by the sensitivity of the LF joint moment profiles to deviations in anatomical alignment (Figs. 3–5). The choice of which of the three anatomical frames (proximal, distal and JCS) then hinges on how one defines the different muscle groups. The simplest definition is in terms of which rotation the muscles would cause if the moment were applied to a joint unconstrained by the forces and moments arising from other components of the musculoskeletal system. For example, if applied to a joint in isolation, the flexors are the muscles that would cause the
joint to flex and the abductors are the muscles that would cause the joint to abduct etc. It is widely accepted that such rotations in the lower limb can be best defined using a nonorthogonal JCS. The JCS has been recommended as a standard convention by the International Society of Biomechanics for the 3D description of lower limb joint kinematics [38,39]. It has also recently been shown to relate to a globographic representation of joint rotations and hence correlate well with conventional clinical terminology [26,40]. Describing joint kinematics and moments with respect to the same reference frame is considered critical [30,41]. Thus, if a joint moment is thought to create a rotation about a joint and the JCS has been used to describe that rotation, then it would follow logically for the net moment vector to be expressed in the JCS as well. This approach has been previously well presented by Fujie et al. [41]. Many biomechanical researchers may feel uncomfortable in using a non-orthogonal reference frame for the expression
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of joint moments. An inevitable consequence, for example, is that the square of the total moment will always be less than the sum of the squares of the three component moments. This, however, may be seen as indicative of the clinical reality that away from the anatomically neutral position, the actions of the different muscle groups cannot be neatly apportioned to acting solely about a given axis. It should also be remembered that this is only being recommended as a framework for presenting and making clinical interpretations of joint moments. All calculations should be conducted in an orthogonal reference frame with moments only being converted to the non-orthogonal frame for the output of the final results. In particular, subsequent manipulation of moments, for example, to calculate joint powers, should be conducted within one of the orthogonal reference frames.
Acknowledgment This project was financially supported by a Health Professional Research Training Fellowship from the Australian National Health and Medical Research Council (Grant ID: 237153).
References [1] Allard P, Lachance R, Aissaoui R, Duhaime M. Simultaneous bilateral 3D able-bodied gait. Hum Mov Sci 1996;15:327–46. [2] Andriacchi TP, Strickland AB. Gait analysis as a tool to assess joint kinetics. In: Berme N, Engin AE, Correia da Silva KM, editors. Biomechanics of normal and pathological human articulating joints. Dordrecht: Martinus Nijhoff Publishers; 1985. p. 83–103. [3] Apkarian J, Naumann S, Cairns B. A three dimensional kinematic model of the lower limb. J Biomech 1989;22:143–55. [4] Benedetti MG, Catani F, Leardini A, Pignotti E, Giannini S. Data management in gait analysis for clinical applications. Clin Biomech 1998;13:204–15. [5] Bowsher KA, Vaughan CL. Effect of foot-progression angle on hip joint moments during gait. J Biomech 1995;28:759–62. [6] Besier TF, Sturnieks DL, Alderson JA, Lloyd DG. Repeatability of gait data using a functional hip joint centre and a mean helical knee axis. J Biomech 2003;36:1159–68. [7] Bresler B, Frankel JP. The forces and moments in the leg during level walking. Trans Am Soc Mech Eng 1950;72:27–36. [8] Crowninshield RD, Johnston RC, Andrews JG, Brand RA. A biomechanical investigation of the human hip. J Biomech 1978; 11:75–85. [9] Eng JJ, Winter DA. Kinetic analysis of the lower limbs during walking: what information can be gained from a three dimensional model? J Biomech 1995;28:753–8. [10] Ramakrishnan KK, Kadaba MP, Wootten ME. Lower extremity joint moments and ground reaction torque in adult gait. In: Stein JL, editor. Biomechanics of normal and prosthetic gait. New York: The American Society of Mechanical Engineers; 1987. p. 87–92. [11] Ounpuu S, Gage JR, Davis RB. Three-dimensional lower extremity joint kinetics in normal pediatric gait. J Pediatr Orthop 1991;11: 341–9. [12] Hunt AE, Smith RM. Interpretation of ankle joint moments during the stance phase of walking: a comparison of two orthogonal axes systems. J Appl Biomech 2001;17:173–80.
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[13] Liu J, Lockhart TE. Comparison of 3D joint moments using local and global inverse dynamics approaches among three different age groups. Gait Posture 2006;23:480–5. [14] Schache AG, Baker R, Vaughan CL. Differences in lower limb transverse plane joint moments during gait when expressed in two alternative reference frames. J Biomech, in press. [15] Fantozzi S, Stagni R, Cappello A, Leardini A. Effect of different inertial parameter sets on joint moment calculation during stair ascending and descending. Med Eng Phys 2005;27:537–41. [16] Ganley KJ, Powers CM. Determination of lower extremity anthropometric parameters using dual energy X-ray absorptiometry: the influence on net joint moments during gait. Clin Biomech 2004;19: 50–6. [17] Ganley KJ, Powers CM. Anthropometric parameters in children: a comparison of values obtained from dual energy X-ray absorptiometry and cadaver-based estimates. Gait Posture 2004;19:133–40. [18] Pearsall DJ, Costigan PA. The effect of segment parameter error on gait analysis results. Gait Posture 1999;9:173–83. [19] Rao G, Amarantini D, Berton E, Favier D. Influence of body segments’ parameters estimation in inverse dynamics solutions during gait. J Biomech 2006;39:1531–6. [20] Winter DA, Ishac MG. Interpretation of 3D moments-of-force during gait. J Biomech 1994;27:818. [21] Winter DA, Eng JJ, Ishac MG. A review of kinetic parameters in human walking. In: Craik RL, Oatis CA, editors. Gait analaysis: theory and application. St. Louis: Mosby; 1995. p. 252–70. [22] Schache AG, Baker R, Lamoreux LW. Defining the knee joint flexionextension axis for purposes of quantitative gait analysis: an evaluation of methods. Gait Posture 2006;24:100–9. [23] Davis RB, Ounpuu S, Tyburski D, Gage JR. A gait analysis data collection and reduction technique. Hum Mov Sci 1991;10:575–87. [24] Woltring HJ. A fortran package for generalised, cross-validatory spline smoothing and differentiation. Adv Eng Software 1986;8: 104–7. [25] Grood ES, Suntay WJ. A joint coordinate system for the clinical description of three-dimensional motions: application to the knee. J Biomech Eng 1983;105:136–44. [26] Baker R. Letter to the editor: ISB recommendation of definition of joint coordinate systems for the reporting of human joint motion. Part 1. Ankle, hip and spine. J Biomech 2003;36:300–2. [27] De Leva P. Adjustments to Zatsiorsky–Seluyanov’s segment inertia parameters. J Biomech 1996;29:1223–30. [28] Kadaba MP, Ramakrishnan ME, Wootten ME, Gainey J, Gorton G, Cochran GVB. Repeatability of kinematic, kinetic, and electromyographic data in normal adult gait. J Orthop Res 1989;7:849–60. [29] Gagnon M, Larrive A, Desjardins P. Strategies of load tilts and shoulders positioning in asymmetrical lifting. A concomitant evaluation of the reference systems of axes. Clin Biomech 2000;15: 478–88. [30] Gagnon M, Desjardins P, Larrive A. Joint coordinate systems of axes for coherence in reporting kinematic and kinetic data. Clin Biomech 2001;16:349–50. [31] Kingma I, van Dieen JH, de Looze MP, Toussaint HM, Dolan P, Baten CTM. On the use of axis systems in quantification of lumbar loading during asymmetric lifting. J Biomech 1999;32:637–8. [32] Plamondon A, Gagnon M, Gravel D. Comments on ‘asymmetric low back loading in asymmetric lifting movements is not prevented by pelvic twist’. J Biomech 1999;32:635. [33] van Dieen JH, Kingma I. Reporting net moments about the lumbar spine. Clin Biomech 2001;16:348–9. [34] Hamill J, Selbie WS. Three-dimensional kinetics. In: Robertson DGE, Caldwell GE, Hamill J, Kamen G, Whittlesey SN, editors. Research methods in biomechanics. Champaign, IL: Human Kinetics; 2004. p. 145–60. [35] Meglan D, Todd F. Kinetics of human locomotion. In: Rose J, Gamble JG, editors. Human walking. Baltimore: Williams & Wilkins; 1994. p. 73–99.
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A.G. Schache, R. Baker / Gait & Posture 25 (2007) 440–452
[36] Ounpuu S, Davis RB, DeLuca PA. Joint kinetics: methods, interpretation and treatment decision-making in children with cerebral palsy and myelomeningocele. Gait Posture 1996;4:62–78. [37] Arnold AS, Anderson FC, Pandy MG, Delp SL. Muscular contributions to hip and knee extension during single limb stance phase of normal gait: a framework for investigating the causes of crouch gait. J Biomech 2005;38:2181–9. [38] Wu G, Cavanagh PR. ISB recommendations for standardization in the reporting of kinematic data. J Biomech 1995;28:1257–61.
[39] Wu G, Siegler S, Allard P, Kirtley C, Leardini A, Rosenbaum D, et al. ISB recommendations on definitions of joint coordinate system of various joints for the reporting of human joint motion. Part 1. Ankle, hip, and spine. J Biomech 2002;35:543–8. [40] Baker R. The globographic representation of three dimensional joint angles. Gait Posture 2005;22:S40–1. [41] Fujie H, Livesay GA, Fujita M, Woo SL-Y. Force and moments in sixDOF at the human knee joint: mathematical description for control. J Biomech 1996;29:1577–85.
On the expression of joint moments during gait Anthony G. Schache a,b,*, Richard Baker a,b a
b
Hugh Williamson Gait Laboratory, Royal Children’s Hospital, Parkville, Vic., Australia Murdoch Childrens Research Institute, Royal Children’s Hospital, Parkville, Vic., Australia Received 15 May 2006; accepted 15 May 2006
Abstract The purpose of the current study was to examine the effect of different reference frames on lower limb joint moments during gait with a view to identifying a recommended convention for clinical purposes. Data were collected from 10 subjects (nine able-bodied adults and one child with diplegic cerebral palsy) whilst walking at a self-selected speed. Calculations utilised a three-dimensional inverse dynamics model. For each joint, moments were expressed in four different reference frames. Three of the frames were orthogonal: laboratory frame; anatomical frame of proximal segment; anatomical frame of distal segment. The fourth reference frame was a non-orthogonal joint coordinate system (JCS). Significant differences in the joint moment profiles during gait were found with alternative references frames. This was apparent primarily for the transverse plane joint moments for able-bodied adult gait. For the pathological gait pattern presented, there were also marked differences in the frontal plane joint moments and more subtle ones in the sagittal plane. Whilst it is recognised that all possible reference frames for the expression of the net moment vector are mathematically valid, a decision needs to be made as to which one is more clinically useful. It is proposed that the non-orthogonal JCS is most logical on the basis of what, biomechanically, the joint moment actually represents. # 2006 Elsevier B.V. All rights reserved. Keywords: Gait analysis; Inverse dynamics; Lower limb; Joint coordinate system
1. Introduction There are four possible reference frames for the expression of the net moment vector in quantitative gait analysis. Three of these possibilities are orthogonal frames: the laboratory (or global) frame (LF); the proximal segment anatomical frame (AF); the distal segment AF. Another possibility is a nonorthogonal frame or joint coordinate system (JCS). When reviewing the previous literature evaluating lower limb joint moments during gait, each reference frame has been implemented in at least one study [1–11]. Thus, no consensus currently exists regarding an accepted standard. This makes it difficult to compare joint moment data across studies. Few studies have investigated the differences in lower limb joint moments during gait when expressed in alternative reference frames [12–14]. Of those that have, only * Corresponding author at: Hugh Williamson Gait Laboratory, 3rd Floor, Main Block, Royal Children’s Hospital, Flemington Road, Parkville, Vic. 3052, Australia. Tel.: +61 03 9345 5354; fax: +61 03 9345 5447. E-mail address: [email protected] (A.G. Schache). 0966-6362/$ – see front matter # 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.gaitpost.2006.05.018
able-bodied gait has been evaluated and not all possible reference frames have been considered. In contrast, the effect of different inertial parameter sets on lower limb joint moment calculations has been well investigated [15–19]. This is surprising given that, for relatively slow speed movements such as gait, lower limb joint moments are far more likely to be sensitive to a change in reference frame than they are to a change in the magnitude of an inertial parameter set. The decision to adopt a given reference frame has typically been based upon preference rather than objective evidence. To our knowledge, Winter et al. [20,21] provide the only formal attempt to justify a preferred convention. Two theoretical arguments were provided. First, as the dominant velocity of the centre of mass is in the plane of progression and the balance of the trunk in both the sagittal and frontal planes is dictated by gravity, both the centre of mass and trunk are tightly regulated to have trajectories in the plane of progression. Second, even when externally rotated, the lower limb segments do not follow trajectories in a local AF but rather move forward in the plane of progression. Given that under experimental conditions the
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plane of progression will be aligned with one of the planes of the LF, it was therefore concluded that the net moment vector should be expressed in the LF. Despite this viewpoint, few studies have actually adopted the LF as a preferred convention [2,7,9,10]. Most have used an orthogonal or non-orthogonal local AF [1,3–6,8,11]. This would suggest that additional clinical factors, such as anatomical interpretation and sensitivity to change post treatment, are also considered by many to be important criteria for making judgments regarding a preferred reference frame. The aim of the current study was to therefore provide a definitive evaluation of the effect of different reference frames on lower limb joint moments during gait. It was considered likely that such differences would be more prominent for abnormal gait, thus both able-bodied and pathological gait patterns were investigated. An additional aim was to use these results as evidence for identifying a recommended convention for clinical purposes.
2. Materials and methods 2.1. Subjects Ten subjects were voluntarily recruited. Approval was obtained from the Royal Children’s Hospital Ethics in Human Research Committee prior to commencement and subjects signed a consent form. The able-bodied adult group comprised of two men and seven women aged 19.8 years (S.D. 2.1) with a mean height of 164.5 cm (S.D. 8.5) and body mass of 60.0 kg (S.D. 1.1). The subject with spastic
441
diplegic cerebral palsy was a 10-year-old boy who was 146.1 cm tall and weighed 39.7 kg. 2.2. Instrumentation Kinematic data were acquired using a 3D motion analysis system (VICON 512, Oxford Metrics, Oxford, England) with six 120 Hz cameras. The LF was defined such that the positive x direction was in the forward direction, the positive y direction was orientated to the left and the positive z direction was orientated upwards. Two AMTI force plates (Advanced Mechanical Technology Inc., Watertown, MA, USA) captured ground reaction force data at a sampling rate of 1080 Hz. 2.3. Frame definitions The 3D pose of the seven body segments of interest (pelvis; left and right thighs; left and right shanks; both feet) were obtained by tracking the trajectories of small spherical retro-reflective markers (25 mm diameter) mounted as outlined in Table 1. These markers allowed the reconstruction of a technical frame (TF) for each of the body segments (Table 2). Given the potential arbitrary relationship between the defined TFs and the anatomy of the underlying bone, a static anatomical landmark calibration trial was performed to reconstruct the various AFs. Respective AF definitions are detailed in Table 3. The knee joint flexion–extension axis was defined using a dynamic optimisation procedure as described by Schache et al. [22]. The vertical (z) axis of the femur was first defined (knee joint centre (KJC) to hip joint centre (HJC)) and then the mediolateral (y) axis (or knee joint
Table 1 Specific marker locations and orientations Static and dynamic trials LASIS (RASIS) SACR LTH1 (RTH1) LTH2 (RTH2) LTH3 (RTH3) LSH1 (RSH1) LSH2 (RSH2) LANK (RANK) LCAL1 (RCAL1) LMID (RMID) LLATMID (RLATMID) Static anatomical landmark calibration trial only LMFE (RMFE) LLFE (RLFE) LTHIROT (RTHIROT) LMED (RMED) LCAL2 (RCAL2) LTOE (RTOE)
Anterior to left (and right) anterior superior iliac spine (ASIS) lying in plane containing left and right ASIS and the midpoint between both posterior superior iliac spines (PSIS) Posterior to the midpoint between both PSISs lying in plane containing left and right ASISs and the midpoint between both PSISs Distal and anterior aspect of left (and right) thigh Distal and lateral aspect of left (and right) thigh Distal and posterior aspect of left (and right) thigh Proximal end of left (and right) anterior tibia just distal to tibial tubercle Distal end of left (and right) anterior tibia Left (and right) lateral malleolus aligned with bimalleolar axis Bisection of the distal aspect of the left (and right) posterior calcaneum Left (and right) medial midfoot over the distal and dorsomedial aspect of the navicular Left (and right) lateral midfoot over the dorsal and distal aspect of the cuboid Most prominent palpable aspect of left (and right) medial femoral epicondyle (MFE) Most prominent palpable aspect of left (and right) lateral femoral epicondyle (LFE) Virtual point, defined as rotated position of LTH2 (or RTH2) marker (see text for further explanation) Left (and right) medial malleolus aligned with bimalleolar axis Bisection of the proximal aspect of the left (and right) posterior calcaneum Dorsal surface of the left (and right) distal forefoot at the midpoint between the second and third metatarsophalangeal joints
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Table 2 Technical frame definitions Pelvis Origin Mediolateral (y) axis Anterior–posterior (x) axis Vertical (z) axis Thigh Origin Anterior–posterior (x) axis Mediolateral (y) axis Vertical (z) axis Shank Origin Vertical (z) axis Mediolateral (y) axis Anterior–posterior (x) axis Foot Origin Anterior–posterior (x) axis Mediolateral (y) axis
Vertical (z) axis
Midpoint between LASIS and RASIS markers In direction from RASIS to LASIS markers Perpendicular to mediolateral (y) axis in plane containing LASIS, RASIS and SACR markers Mutual perpendicular to other two axes Midpoint between LTH1 (or RTH1) and LTH3 (or RTH3) markers In direction from LTH3 (or RTH3) to LTH1 (or RTH1) markers Perpendicular to anterior–posterior (x) axis in plane containing LTH1 (or RTH1), LTH2 (or RTH2) and LTH3 (or RTH3) markers Mutual perpendicular to other two axes LSH2 (or RSH2) marker In direction from LSH2 (or RSH2) marker to LSH1 (or RSH1) marker Perpendicular to vertical (z) axis in plane containing LSH1 (or RSH1) marker, LSH2 (or RSH2) marker and LANK (or RANK) marker Mutual perpendicular to other two axes LCAL1 (or RCAL1) marker In direction from LCAL1 (or RCAL1) marker to LLATMID (or RLATMID) marker Perpendicular to anterior–posterior (x) axis in plane containing LCAL1 (or RCAL1) marker, LLATMID (or RLATMID) marker and LMID (or RMID) marker Mutual perpendicular to other two axes
flexion–extension axis) was rotated in the plane perpendicular to the vertical (z) axis through an angle u, whereby u represented the degree of rotation necessary to minimise the variance in the dynamic knee varus–valgus kinematic profile. 2.4. Procedures Anthropometric parameters required for estimating the location of the HJC using the method of Davis et al. [23] were first measured. Markers were then placed on each subject’s pelvis and lower limbs as previously described. The same tester (AS) performed all marker placements. Each test session commenced with the capture of the static anatomical landmark calibration trial. Calibration markers were then removed and dynamic trials were captured. Subjects walked at their natural speed through the middle of a walkway with a calibrated field approximately five metres in length. The able-bodied adult subjects walked at a speed of 1.2 0.1 m/s, whilst the child with cerebral palsy walked independently at a speed of 1.1 m/s. A successful trial was one in which the left and right heels successfully struck the two adjacent force plates in isolation where no obvious force plate targeting was observed by the tester. A single walking trial was captured for each subject. 2.5. Data analysis Coordinate data were filtered using Woltring’s general cross-validatory quintic smoothing spline [24] with a predicted mean-squared error of 15 mm. Kinematic data
were calculated using a joint coordinate system convention. The JCS for the hip and knee corresponded to the standard convention whereby the mediolateral (y) axis was fixed in the proximal segment, the vertical (z) axis was fixed in the distal segment and the anteroposterior (x) axis was the mutual perpendicular [25]. For the ankle, the mediolateral (y) axis was fixed in the distal tibia, the anteroposterior (x) axis was fixed in the foot and the vertical (z) axis was the mutual perpendicular [26]. Left-sided data were chosen for analysis. Lower limb internal joint moments were calculated using a standard inverse dynamics approach. Adapted inertial parameters as per De Leva [27] were used for computing joint moments for the able-bodied adults, whilst dual energy X-ray absorptiometry based inertial parameters from Ganley and Powers [17] were used for computing joint moments for the child with cerebral palsy. For each joint, moments were expressed in each of four frames of reference: the LF, the proximal segment AF, the distal segment AF and the JCS. All computations were performed using Bodybuilder software (Oxford Metrics Ltd.). Joint moments were normalised by dividing by subject’s body mass. Temporal events defining the gait cycle were identified from the ground reaction force data. Each stride was time normalised to 101 points representing equal intervals from 0% to 100% using Polygon software (Oxford Metrics Ltd.). Discrete parameters were extracted from the able-bodied adult joint moment profiles for statistical analysis (Table 4). The parameters were selected based on those used previously by Benedetti et al. [4]. Given the number of dependent variables analysed, a conservative level of
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Table 3 Anatomical frame definitions Pelvis Origin Mediolateral (y) axis Anterior–posterior (x) axis Vertical (z) axis Virtual point Femur Origin Vertical (z) axis Mediolateral (y) axis
Anterior–posterior (x) axis Virtual points Tibia (proximal) Origin Vertical (z) axis Mediolateral (y) axis Anterior–posterior (x) axis Virtual point Tibia (distal) Origin Vertical (z) axis Mediolateral (y) axis Anterior–posterior (x) axis Virtual point Foot Origin Anterior–posterior (x) axis
Vertical (z) axis Mediolateral (y) axis Virtual point
Midpoint between LASIS and RASIS markers In direction from RASIS to LASIS markers Perpendicular to mediolateral (y) axis in plane containing LASIS, RASIS, SACR markers Mutual perpendicular to other two axes LHJC (or RHJC), defined relative to pelvic anatomical frame as per Davis et al. [23] LKJC (or RKJC), defined as midpoint between LLFE (or RLFE) marker and LMFE (or RMFE) marker In direction from LKJC (or RKJC) to LHJC (or RHJC) Perpendicular to vertical (z) axis in plane containing LKJC (or RKJC), LHJC (or RHJC), and LTHI (RTHI) marker, rotated by angle u about vertical (z) axis, whereby u represents degree of rotation required to minimise variance in dynamic knee varus–valgus kinematic profile Mutual perpendicular to other two axes LKJC (or RKJC) and LTHIROT (or RTHIROT) as defined above LAJC (or RAJC), defined as midpoint between LANK (or RANK) marker and LMED (or RMED) marker In direction from LAJC (or RAJC) to LKJC (or RKJC) location Perpendicular to vertical (z) axis and parallel to femur mediolateral (y) axis when in anatomical landmark calibration configuration Mutual perpendicular to other two axes LAJC (or RAJC) as defined above LAJC (or RAJC), defined as midpoint between LANK (or RANK) marker and LMED (or RMED) marker In direction from LAJC (or RAJC) to LKJC (or RKJC) location Perpendicular to vertical (z) axis in plane containing LKJC (or RKJC), LMED (or RMED) and LANK (or RANK) markers Mutual perpendicular to other two axes LAJC (or RAJC) as defined above LAJC (or RAJC), defined as midpoint between LANK (or RANK) marker and LMED (or RMED) marker In direction from LCAL1 (or RCAL1) marker to LTOE (or RTOE) marker but rotated in plane containing LCAL1 (or CAL1), LCAL2 (or RCAL2) and LTOE (or RTOE) markers until parallel with floor (horizontal plane of laboratory frame) Perpendicular to anterior–posterior (x) axis in plane containing LCAL1 (or CAL1), LCAL2 (or RCAL2) and LTOE (or RTOE) markers Mutual perpendicular to other two axes LAJC (or RAJC) as defined above
NB. HJC, hip joint centre; KJC, knee joint centre; AJC, ankle joint centre.
significance was set at a = 0.01 for all tests. One-way repeated measures ANOVA tests were used to determine if significant differences in the dependent variables occurred for different reference frames. When significant F-ratios
were obtained, post hoc pairwise comparisons (paired t-test) were used to determine differences between each reference frame. All statistical computations were performed using a commercial statistics software package (SPSS, USA).
Table 4 Joint moment parameters Hip joint moment parameters
Knee joint moment parameters
Ankle joint moment parameters
HM1 HM2 HM3 HM4 HM5 THM5 HM6 THM6
KM1 KM2 KM3 KM4 KM5 KM6 KM7 KM8 TKM8 KM9 TKM9
AM1 AM2 AM3 TAM3 AM4 TAM4 AM5 TAM5 AM6 TAM6
Peak stance extensor moment Peak stance flexor moment First peak stance abductor moment Second peak stance abductor moment Peak stance internal rotator moment Time HM5 (gait cycle%) Peak stance external rotator moment Time HM5 (gait cycle%)
Unless stated otherwise all parameters are in Nm/kg.
First peak stance flexor moment First peak stance extensor moment Second peak stance flexor moment Second peak stance extensor moment Peak stance varus moment First peak stance valgus moment Second peak stance valgus moment Peak stance internal rotator moment Time KM8 (gait cycle%) Peak stance external rotator moment Time KM9 (gait cycle%)
Peak stance dorsi-flexor moment Peak stance plantar flexor moment Peak stance adductor moment Time AM3 (gait cycle%) Peak stance abductor moment Time AM4 (gait cycle%) Peak stance invertor moment Time AM5 (gait cycle%) Peak stance evertor moment Time AM6 (gait cycle%)
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The able-bodied adults displayed typical kinematic patterns in each plane for each joint (Fig. 1). In contrast, the child with cerebral palsy had an increased rearfoot valgus alignment in standing (15.48 compared to 3.5 4.98 for the able-bodied adults) and walked with excessive hip internal rotation (Fig. 1) and foot adduction or toe in (Fig. 2).
ankle rotation moment in the foot AF and the ankle invertor– evertor moment in the LF where a degree of inter-subject variability was present. Lower limb joint moments for CP gait are also illustrated in Figs. 3–5. Whilst some general characteristic features associated with diplegic CP gait were evident, such as a prolonged stance phase hip extensor moment and a reduced plantar flexor moment, other features were dependent upon the particular reference frame. These results will be discussed further below.
3.2. Joint moment profiles
3.3. Effect of different reference frame
Lower limb joint moments for able-bodied adult gait are illustrated in Figs. 3–5. Most joint moments were found to display characteristic profiles that were systematic across subjects as indicated by the relatively small standard deviation bands. This was not the case, however, for the
Significant differences in the joint moment profiles during gait were found with alternative reference frames. There were three general findings. First, differences in the joint moment profiles with a change in reference frame were apparent for each joint. Second, the frontal and transverse
3. Results 3.1. Joint kinematic profiles
Fig. 1. Hip, knee and ankle joint kinematics during able-bodied adult gait (mean curve and standard deviation band) and CP gait (dashed line). The dashed vertical line indicates toe off.
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Fig. 2. Foot rotation angles (ab/adduction or toe in/out) with respect to the LF for able-bodied adult gait (mean curve and standard deviation band) and CP gait (dashed line). The dashed vertical line indicates toe off.
plane joint moments were more sensitive to a change in reference frame than the sagittal plane joint moments. Third, the joint moments for CP gait were more sensitive to a change in reference frame than the joint moments for ablebodied adult gait.
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Differences in the hip joint moment profiles with a change in reference frame were mainly evident in the transverse plane for able-bodied adult gait (Fig. 3). Only two of the eight hip joint parameters examined (THM5 and THM6) were found to be significantly different and these were both transverse plane parameters (Table 5). The timing of the peak hip internal rotator joint moment (THM5) was significantly later during stance when expressed in the LF compared to the femoral AF, whilst the timing of the peak hip external rotator joint moment (THM6) was significantly earlier during stance when expressed in both the LF and pelvis AF compared to the femoral AF (Fig. 3). In contrast, differences in the hip joint moment profiles with a change in reference frame were detectable in all planes for CP gait (Fig. 3). In the sagittal plane, the prolonged hip extensor moment displayed a distinctly different pattern when expressed in the femoral AF compared to the LF and pelvis AF. In the frontal plane, the magnitude of the late stance hip abductor moment was substantially greater when expressed in the femoral AF compared to the LF, pelvis AF or JCS. Finally, in the transverse plane, joint moment profiles were markedly different between the four reference frames. Differences in the knee joint moment profiles with a change in reference frame were apparent in all planes for both able-bodied adult and CP gait (Table 6 and Fig. 4). In the sagittal plane, the magnitude of the first peak knee extensor moment (KM2) for able-bodied adult gait was
Fig. 3. Hip joint moments when expressed in the four alternative reference frames for both able bodied adult gait (mean curve and standard deviation band) and CP gait (dashed line). The dashed vertical line indicates toe off.
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Fig. 4. Knee joint moments when expressed in the four alternative reference frames for both able-bodied adult gait (mean curve and standard deviation band) and CP gait (dashed line). The dashed vertical line indicates toe off.
significantly greater when expressed in the LF compared to the femoral AF or tibial AF (Table 6). The opposite was found to be true for CP gait and the magnitude of the difference was somewhat greater (Fig. 4). In the frontal plane, differences between reference frames for both ablebodied adult and CP gait occurred primarily during initial stance (Fig. 4). For able-bodied adult gait, the magnitude of the first peak knee valgus moment (KM6) was significantly less when expressed in the LF compared to the femoral AF, tibial AF or JCS (Table 6). KM6 was also significantly less when expressed in the femoral AF compared to the JCS (Table 6). For CP gait, the magnitude of the peak knee varus moment during initial stance displayed considerable variability across reference frames (Fig. 4). In the transverse plane, differences across reference frames were evident for the magnitude of the peak knee external rotator moment (KM9) for both able-bodied adult and CP gait (Fig. 4). For able-bodied adult gait, KM9 was significantly less when expressed in the LF compared to the femoral AF and tibial AF (Table 6). KM9 was also significantly less when expressed in the femoral AF compared to the tibial AF (Table 6). These same differences were found for CP gait (Fig. 4). Differences in the ankle joint moment profiles with a change in reference frame were mainly apparent in the frontal plane for able-bodied adult gait (Fig. 5). The peak
ankle invertor moment, in terms of both magnitude (AM5) and time (TAM5), was found to differ significantly across reference frames (Table 7). AM5 was significantly greater when expressed in the LF compared to the tibial AF or foot AF, whilst TAM5 occurred significantly later during stance when expressed in the LF compared to the foot AF (Table 7). For CP gait, differences in the ankle joint moment profiles with a change in reference frame were apparent in both the frontal and transverse planes (Fig. 5). In the frontal plane, a large ankle evertor moment was measured when expressed in the LF compared to the tibial AF or foot AF. In the transverse plane, a large ankle adductor moment was measured when expressed in the foot AF compared to the LF, tibial AF or JCS.
4. Discussion Consistent with previous studies [2,4,28], most joint moments for able-bodied adult gait were found to display characteristic profiles that were systematic across subjects. Two joint moments, however, were associated with a degree of inter-subject variability: the ankle rotation moment in the foot AF and the ankle invertor–evertor moment in the LF. This is in agreement with findings from a previous study [12].
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Fig. 5. Ankle joint moments when expressed in the four alternative reference frames for both able-bodied adult gait (mean curve and standard deviation band) and CP gait (dashed line). The dashed vertical line indicates toe off.
The inter-subject variability of the ankle rotation moment in the foot AF can be explained by its sensitivity to the frontal plane orientation of the posterior calcaneus [12]. As the postural alignment of the posterior calcaneus and its dynamic movement during gait will differ across subjects, the presence of this variability is not surprising. For example, with a varus-aligned rearfoot, the foot AF vertical z axis will be tilted medially and an ankle abductor moment will be generated from mid stance onwards. With a valgus-aligned rearfoot the opposite will be true [14]. This is further illustrated when viewing the CP gait data, characterised by an increased rearfoot valgus alignment and a corresponding large ankle adductor moment during stance (Fig. 5). The inter-subject variability of the ankle invertor–evertor moment in the LF can be explained by its sensitivity to the alignment of the foot in the LF transverse plane (ad/ abduction or toe in/out), which can be expected to vary across subjects. With increased toe out, the cosine projection of the foot into the LF frontal plane will increase, resulting in an increased ankle invertor moment in the LF. Hunt and Smith [12] have previously shown that a linear relationship exists between the magnitude of the ankle invertor moment in the LF and the amount of toe out. This relationship was also apparent for the CP gait data but in the opposite direction. In contrast to the able-bodied adult gait profile, the
child with CP ambulated with increased toe in (Fig. 2). Consequently, a large ankle evertor moment was generated in the LF (Fig. 5). Significant differences in the joint moment profiles for able-bodied adult gait were found with alternative reference frames. Differences were evident at all lower limb joints and were more prominent in the frontal and transverse planes. Previous studies in this area have only considered the LF and the distal segment AF [12–14]. Hunt and Smith [12] investigated differences in ankle joint moments during gait with a change in reference frame for 18 able-bodied adults. Similar results were reported to the current study whereby significant differences were found but were limited to the frontal and transverse planes. Liu and Lockhart [13] also investigated differences in lower limb joint moments during gait with a change in reference frame for 30 able-bodied adults varying in age from 19 to 86 years. Consistent with the current study, differences were found at all lower limb joints. However, in contrast, Liu and Lockhart [13] reported significant differences in all three planes for each joint despite finding the sagittal plane mean lower limb joint moment profiles for the alternative reference frames to be closely matched. This difference with respect to the current study may be a consequence of the larger cohort. Differences in the degree of variability associated with the joint moment profiles for able-bodied adult gait were
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Table 5 Mean (S.D.) for the hip joint moment parameters Parameter
LF
Pelvis AF
Femoral AF
JCSa
p-Value
HM1 (Nm/kg) Adult CP
0.596 (0.113) 0.577
0.594 (0.110) 0.574
0.580 (0.095) 0.615
– –
0.105 –
HM2 (Nm/kg) Adult CP
0.858 (0.231) 0.741
0.905 (0.236) 0.759
0.878 (0.223) 0.683
– –
0.388 –
HM3 (Nm/kg) Adult CP
0.708 (0.133) 0.547
0.687 (0.127) 0.527
0.684 (0.118) 0.360
0.699 (0.123) 0.522
0.335 –
HM4 (Nm/kg) Adult CP
0.628 (0.182) 0.286
0.579 (0.185) 0.165
0.623 (0.158) 0.425
0.578 (0.181) 0.157
0.027 –
HM5 (Nm/kg) Adult CP
0.109 (0.026) 0.121
0.087 (0.038) 0.099
0.095 (0.041) 0.105
– –
0.439 –
– –
0.005b –
– –
0.788 –
– –
0.001c –
THM5 (%) Adult CP HM6 (Nm/kg) Adult CP THM6 (%) Adult CP
40.0 (21.3) 57.0 0.085 (0.016) 0.055 15.8 (15.2) 4.0
36.1 (25.3) 55.0 0.179 (0.054) 0.126 11.7 (2.5) 4.0
12.2 (1.7) 16.0 0.087 (0.023) 0.047 41.3 (1.7) 50.0
a Note that for the hip JCS, by definition, the sagittal plane is the same as that for the pelvis AF and the transverse plane is the same as that for the femoral AF. Thus, only hip JCS frontal plane data were included in statistical analyses. b Significant comparisons ( p < 0.01) for LF vs. femoral AF. c Significant comparisons ( p < 0.01) for LF vs. femoral AF; pelvis AF vs. femoral AF.
also found with alternative reference frames. As previously discussed, both the ankle rotation moment in the foot AF and the ankle invertor–evertor moment in the LF displayed intersubject variability. For the ankle rotation moment, if the net moment vector was instead expressed in a reference frame other than the foot AF, then the measured inter-subject variability was reduced (Fig. 5). Similarly, for the ankle invertor–evertor moment, if the net moment vector was expressed in any of the anatomical reference frames rather than the LF, then the measured inter-subject variability was also reduced (Fig. 5). Susceptibility to inter-subject variability might therefore be one criteria to use for the selection of a preferred reference frame for the expression of the net moment vector. The joint moment profiles for CP gait were more sensitive to a change in reference frame than those for able-bodied gait. To our knowledge, no previous studies have documented this. Quite clear differences were evident in all three planes at the hip and knee joints. At the ankle joint, differences were limited to the frontal and transverse planes but the magnitude of the differences were quite considerable. This would indicate that, certainly for data relating to pathologies such as CP, the choice of reference frame for the expression of the net moment vector is critical. Interpretations regarding the
degree of similarity or disparity between the joint moment profiles for CP and able-bodied gait are reference frame dependent. For example, the child with CP can be seen to have or not have a hip abductor moment during terminal stance depending upon which particular reference frame is considered (Fig. 3). Likewise, for the ankle invertor–evertor moment, the profile for CP gait can be seen to be either opposite or quite similar to that of able-bodied gait (Fig. 5). Other examples of conflicting interpretations can also be found. Thus, at the very least for clinical purposes, it is clear that an accepted standard is required. The question of which reference frame is most appropriate for the expression of the net moment vector has received only limited discussion in the biomechanics literature to date. There has been some debate amongst researchers in the context of quantifying lumbar spine loading during lifting tasks [29–33]. However, for purposes of quantitative gait analysis, this issue has been largely neglected. Whilst the various possible reference frames have been well acknowledged [34–36], very few studies have provided any formal attempt to justify a preferred convention. It is important to note that all four alternative reference frames are mathematically correct. The differences between them do not represent ‘errors’ in determining
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Table 6 Mean (S.D.) for the knee joint moment parameters Parameter
LF
Femoral AF
Proximal tibial AF
JCSa
p-Value
KM1 (Nm/kg) Adult CP
0.209 (0.077) 0.131
0.200 (0.067) 0.106
0.205 (0.074) 0.091
– –
0.030 –
KM2 (Nm/kg) Adult CP
0.500 (0.220) 0.471
0.430 (0.194) 0.638
0.444 (0.187) 0.680
– –
0.005b –
KM3 (Nm/kg) Adult CP
0.215 (0.149) 0.441
0.222 (0.150) 0.463
0.238 (0.152) 0.453
– –
0.019 –
KM4 (Nm/kg) Adult CP
0.269 (0.115) 0.231
0.276 (0.109) 0.198
0.248 (0.102) 0.149
– –
0.117 –
KM5 (Nm/kg) Adult CP
0.036 (0.033) 0.509
0.070 (0.055) 0.298
0.054 (0.047) 0.157
0.071 (0.054) 0.253
0.029 –
KM6 (Nm/kg) Adult CP
0.300 (0.057) 0.160
0.383 (0.101) 0.040
0.384 (0.106) 0.064
0.398 (0.102) 0.070
0.001c –
KM7 (Nm/kg) Adult CP
0.298 (0.105) 0.207
0.295 (0.115) 0.199
0.289 (0.111) 0.239
0.278 (0.112) 0.192
0.053 –
KM8 (Nm/kg) Adult CP
0.056 (0.032) 0.146
0.103 (0.046) 0.114
0.030 (0.012) 0.126
– –
0.038 –
– –
0.019 –
– –
0.000d –
– –
0.920 –
TKM8 (%) Adult CP KM9 (Nm/kg) Adult CP TKM9 (%) Adult CP
33.1 (23.4) 11.0 0.043 (0.018) 0.007 45.4 (10.2) 0
12.0 (1.0) 16.0 0.094 (0.026) 0.030 41.6 (2.4) 50.0
10.3 (2.7) 12.0 0.125 (0.035) 0.059 45.0 (3.6) 54.0
a Note that for the knee JCS, by definition, the sagittal plane is the same as that for the femoral AF and the transverse plane is the same as that for the proximal tibial AF. Thus, only knee JCS frontal plane data were included in statistical analyses. b Significant comparisons ( p < 0.01) for LF vs. femoral AF; LF vs. proximal tibial AF. c Significant comparisons ( p < 0.01) for LF vs. femoral AF; LF vs. proximal tibial AF; LF vs. JCS; femoral AF vs. JCS. d Significant comparisons ( p < 0.01) for LF vs. femoral AF; LF vs. proximal tibial AF; femoral AF vs. proximal tibial AF.
a ‘correct’ value. Rather they represent subtly different biomechanical quantities. The question for quantitative gait analysis is which of the alternative reference frames is most useful in understanding the biomechanics of gait with or without pathology. The decision as to which to use must rest on a consideration of such issues. To our knowledge, Winter et al. [20,21] appear to be the only researchers to have addressed this question. Briefly, Winter et al. [20,21] argued that, as the whole body and its constituent segments are tightly regulated to have trajectories in the plane of progression and that as the plane of progression will correspond to one of the planes of the LF when under experimental conditions, joint moments should be expressed in the LF so as to allow the trajectories to be interpreted in terms of the moments that cause them.
The interpretation of a joint moment is worth discussing in the context of evaluating the various reference frames with which to express the net moment vector. A joint moment represents the net activity in the muscle groups crossing a particular joint. It indicates which muscle group is dominant. For example, if an internal knee flexor moment is present, the moment generated by the knee flexor muscle group exceeds that generated by the knee extensor muscle group by the measured amount. It is important to note that the joint moment does not represent the action of the dominant muscle group. The specific action of any particular muscle group is dependent on the behaviour of the entire kinetic chain. For example, it is now well established that the hamstrings can be acting to extend the knee under certain circumstances even though they will
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Table 7 Mean (S.D.) for the ankle joint moment parameters Parameter
LF
Distal tibial AF
Foot AF
JCS a
p-Value
AM1 (Nm/kg) Adult CP
0.143 (0.042) 0.014
0.142 (0.040) 0.016
0.142 (0.041) 0.017
– –
0.240 –
AM2 (Nm/kg) Adult CP
1.330 (0.125) 1.189
1.332 (0.123) 1.216
1.333 (0.122) 1.177
– –
0.440 –
AM3 (Nm/kg) Adult CP
0.034 (0.014) 0.044
0.030 (0.012) 0.127
0.056 (0.038) 0.332
0.031 (0.013) 0.114
0.307 –
TAM3 (%) Adult CP AM4 (Nm/kg) Adult CP TAM4 (%) Adult CP AM5 (Nm/kg) Adult CP TAM5 (%) Adult CP AM6 (%) Adult CP TAM6 (%) Adult CP
20.8 (19.8) 11.0 0.103 (0.026) 0.005 44.7 (3.6) 43.0 0.149 (0.080) 0.003 36.3 (11.0) 0 0.050 (0.055) 0.328 25.7 (28.3) 51.0
9.9 (3.5) 12.0 0.123 (0.036) 0.058 44.6 (3.0) 55.0 0.069 (0.045) 0.155 24.0 (13.7) 32.0 0.128 (0.065) 0.046 54.7 (2.7) 57.0
16.6 (12.8) 35.0 0.146 (0.087) 0.026 47.3 (16.0) 58.0 0.061 (0.027) 0.027 18.0 (8.8) 23.0 0.096 (0.039) 0.107 53.3 (2.3) 54.0
9.7 (2.2) 12.0 0.122 (0.043) 0.055 41.2 (4.1) 55.0
0.131 – 0.261 – 0.417 –
– –
0.007b –
– –
0.001c –
– –
0.018 –
– –
0.018 –
a
Note that for the ankle JCS, by definition, the sagittal plane is the same as that for the distal tibial AF and the frontal plane is the same as that for the foot AF. Thus, only ankle JCS transverse plane data were included in statistical analyses. b Significant comparisons ( p < 0.01) for LF vs. distal tibial AF; LF vs. foot AF. c Significant comparisons ( p < 0.01) for LF vs. foot AF.
always contribute to the generation of an internal knee flexor moment [37]. Consideration of which reference frame to refer the moments to must therefore be based on that which best represents the relative activity of the different muscle groups. This implicit link with muscle activity suggests that an anatomically relevant frame is most desirable. Furthermore, there is no consistent or definable relationship between the muscle groups themselves and the LF and this is clearly indicated by the sensitivity of the LF joint moment profiles to deviations in anatomical alignment (Figs. 3–5). The choice of which of the three anatomical frames (proximal, distal and JCS) then hinges on how one defines the different muscle groups. The simplest definition is in terms of which rotation the muscles would cause if the moment were applied to a joint unconstrained by the forces and moments arising from other components of the musculoskeletal system. For example, if applied to a joint in isolation, the flexors are the muscles that would cause the
joint to flex and the abductors are the muscles that would cause the joint to abduct etc. It is widely accepted that such rotations in the lower limb can be best defined using a nonorthogonal JCS. The JCS has been recommended as a standard convention by the International Society of Biomechanics for the 3D description of lower limb joint kinematics [38,39]. It has also recently been shown to relate to a globographic representation of joint rotations and hence correlate well with conventional clinical terminology [26,40]. Describing joint kinematics and moments with respect to the same reference frame is considered critical [30,41]. Thus, if a joint moment is thought to create a rotation about a joint and the JCS has been used to describe that rotation, then it would follow logically for the net moment vector to be expressed in the JCS as well. This approach has been previously well presented by Fujie et al. [41]. Many biomechanical researchers may feel uncomfortable in using a non-orthogonal reference frame for the expression
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of joint moments. An inevitable consequence, for example, is that the square of the total moment will always be less than the sum of the squares of the three component moments. This, however, may be seen as indicative of the clinical reality that away from the anatomically neutral position, the actions of the different muscle groups cannot be neatly apportioned to acting solely about a given axis. It should also be remembered that this is only being recommended as a framework for presenting and making clinical interpretations of joint moments. All calculations should be conducted in an orthogonal reference frame with moments only being converted to the non-orthogonal frame for the output of the final results. In particular, subsequent manipulation of moments, for example, to calculate joint powers, should be conducted within one of the orthogonal reference frames.
Acknowledgment This project was financially supported by a Health Professional Research Training Fellowship from the Australian National Health and Medical Research Council (Grant ID: 237153).
References [1] Allard P, Lachance R, Aissaoui R, Duhaime M. Simultaneous bilateral 3D able-bodied gait. Hum Mov Sci 1996;15:327–46. [2] Andriacchi TP, Strickland AB. Gait analysis as a tool to assess joint kinetics. In: Berme N, Engin AE, Correia da Silva KM, editors. Biomechanics of normal and pathological human articulating joints. Dordrecht: Martinus Nijhoff Publishers; 1985. p. 83–103. [3] Apkarian J, Naumann S, Cairns B. A three dimensional kinematic model of the lower limb. J Biomech 1989;22:143–55. [4] Benedetti MG, Catani F, Leardini A, Pignotti E, Giannini S. Data management in gait analysis for clinical applications. Clin Biomech 1998;13:204–15. [5] Bowsher KA, Vaughan CL. Effect of foot-progression angle on hip joint moments during gait. J Biomech 1995;28:759–62. [6] Besier TF, Sturnieks DL, Alderson JA, Lloyd DG. Repeatability of gait data using a functional hip joint centre and a mean helical knee axis. J Biomech 2003;36:1159–68. [7] Bresler B, Frankel JP. The forces and moments in the leg during level walking. Trans Am Soc Mech Eng 1950;72:27–36. [8] Crowninshield RD, Johnston RC, Andrews JG, Brand RA. A biomechanical investigation of the human hip. J Biomech 1978; 11:75–85. [9] Eng JJ, Winter DA. Kinetic analysis of the lower limbs during walking: what information can be gained from a three dimensional model? J Biomech 1995;28:753–8. [10] Ramakrishnan KK, Kadaba MP, Wootten ME. Lower extremity joint moments and ground reaction torque in adult gait. In: Stein JL, editor. Biomechanics of normal and prosthetic gait. New York: The American Society of Mechanical Engineers; 1987. p. 87–92. [11] Ounpuu S, Gage JR, Davis RB. Three-dimensional lower extremity joint kinetics in normal pediatric gait. J Pediatr Orthop 1991;11: 341–9. [12] Hunt AE, Smith RM. Interpretation of ankle joint moments during the stance phase of walking: a comparison of two orthogonal axes systems. J Appl Biomech 2001;17:173–80.
451
[13] Liu J, Lockhart TE. Comparison of 3D joint moments using local and global inverse dynamics approaches among three different age groups. Gait Posture 2006;23:480–5. [14] Schache AG, Baker R, Vaughan CL. Differences in lower limb transverse plane joint moments during gait when expressed in two alternative reference frames. J Biomech, in press. [15] Fantozzi S, Stagni R, Cappello A, Leardini A. Effect of different inertial parameter sets on joint moment calculation during stair ascending and descending. Med Eng Phys 2005;27:537–41. [16] Ganley KJ, Powers CM. Determination of lower extremity anthropometric parameters using dual energy X-ray absorptiometry: the influence on net joint moments during gait. Clin Biomech 2004;19: 50–6. [17] Ganley KJ, Powers CM. Anthropometric parameters in children: a comparison of values obtained from dual energy X-ray absorptiometry and cadaver-based estimates. Gait Posture 2004;19:133–40. [18] Pearsall DJ, Costigan PA. The effect of segment parameter error on gait analysis results. Gait Posture 1999;9:173–83. [19] Rao G, Amarantini D, Berton E, Favier D. Influence of body segments’ parameters estimation in inverse dynamics solutions during gait. J Biomech 2006;39:1531–6. [20] Winter DA, Ishac MG. Interpretation of 3D moments-of-force during gait. J Biomech 1994;27:818. [21] Winter DA, Eng JJ, Ishac MG. A review of kinetic parameters in human walking. In: Craik RL, Oatis CA, editors. Gait analaysis: theory and application. St. Louis: Mosby; 1995. p. 252–70. [22] Schache AG, Baker R, Lamoreux LW. Defining the knee joint flexionextension axis for purposes of quantitative gait analysis: an evaluation of methods. Gait Posture 2006;24:100–9. [23] Davis RB, Ounpuu S, Tyburski D, Gage JR. A gait analysis data collection and reduction technique. Hum Mov Sci 1991;10:575–87. [24] Woltring HJ. A fortran package for generalised, cross-validatory spline smoothing and differentiation. Adv Eng Software 1986;8: 104–7. [25] Grood ES, Suntay WJ. A joint coordinate system for the clinical description of three-dimensional motions: application to the knee. J Biomech Eng 1983;105:136–44. [26] Baker R. Letter to the editor: ISB recommendation of definition of joint coordinate systems for the reporting of human joint motion. Part 1. Ankle, hip and spine. J Biomech 2003;36:300–2. [27] De Leva P. Adjustments to Zatsiorsky–Seluyanov’s segment inertia parameters. J Biomech 1996;29:1223–30. [28] Kadaba MP, Ramakrishnan ME, Wootten ME, Gainey J, Gorton G, Cochran GVB. Repeatability of kinematic, kinetic, and electromyographic data in normal adult gait. J Orthop Res 1989;7:849–60. [29] Gagnon M, Larrive A, Desjardins P. Strategies of load tilts and shoulders positioning in asymmetrical lifting. A concomitant evaluation of the reference systems of axes. Clin Biomech 2000;15: 478–88. [30] Gagnon M, Desjardins P, Larrive A. Joint coordinate systems of axes for coherence in reporting kinematic and kinetic data. Clin Biomech 2001;16:349–50. [31] Kingma I, van Dieen JH, de Looze MP, Toussaint HM, Dolan P, Baten CTM. On the use of axis systems in quantification of lumbar loading during asymmetric lifting. J Biomech 1999;32:637–8. [32] Plamondon A, Gagnon M, Gravel D. Comments on ‘asymmetric low back loading in asymmetric lifting movements is not prevented by pelvic twist’. J Biomech 1999;32:635. [33] van Dieen JH, Kingma I. Reporting net moments about the lumbar spine. Clin Biomech 2001;16:348–9. [34] Hamill J, Selbie WS. Three-dimensional kinetics. In: Robertson DGE, Caldwell GE, Hamill J, Kamen G, Whittlesey SN, editors. Research methods in biomechanics. Champaign, IL: Human Kinetics; 2004. p. 145–60. [35] Meglan D, Todd F. Kinetics of human locomotion. In: Rose J, Gamble JG, editors. Human walking. Baltimore: Williams & Wilkins; 1994. p. 73–99.
452
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[36] Ounpuu S, Davis RB, DeLuca PA. Joint kinetics: methods, interpretation and treatment decision-making in children with cerebral palsy and myelomeningocele. Gait Posture 1996;4:62–78. [37] Arnold AS, Anderson FC, Pandy MG, Delp SL. Muscular contributions to hip and knee extension during single limb stance phase of normal gait: a framework for investigating the causes of crouch gait. J Biomech 2005;38:2181–9. [38] Wu G, Cavanagh PR. ISB recommendations for standardization in the reporting of kinematic data. J Biomech 1995;28:1257–61.
[39] Wu G, Siegler S, Allard P, Kirtley C, Leardini A, Rosenbaum D, et al. ISB recommendations on definitions of joint coordinate system of various joints for the reporting of human joint motion. Part 1. Ankle, hip, and spine. J Biomech 2002;35:543–8. [40] Baker R. The globographic representation of three dimensional joint angles. Gait Posture 2005;22:S40–1. [41] Fujie H, Livesay GA, Fujita M, Woo SL-Y. Force and moments in sixDOF at the human knee joint: mathematical description for control. J Biomech 1996;29:1577–85.