Differences in lower limb transverse plane joint moments during gait when expressed in two alternative reference frames

Article Outline

• Abstract
• 1. Introduction
• 2. Materials and methods
  • 2.1. Subjects
  • 2.2. Instrumentation
  • 2.3. Frame definitions
  • 2.4. Procedures
  • 2.5. Data analysis
• 3. Results
• 4. Discussion
• Acknowledgments
• References
• Copyright

Abstract 

When comparing previous studies that have measured the three-dimensional moments acting about the lower limb joints (either external moments or opposing internal joint moments) during able-bodied adult gait, significant variation is apparent in the profiles of the reported transverse plane moments. This variation cannot be explained on the basis of adopted convention (i.e. external versus internal joint moment) or inherent variability in gait strategies. The aim of the current study was to determine whether in fact the frame in which moments are expressed has a dominant effect upon transverse plane moments and thus provides a valid explanation for the observed inconsistency in the literature. Kinematic and ground reaction force data were acquired from nine able-bodied adult subjects walking at a self-selected speed. Three-dimensional hip, knee and ankle joint moments during gait were calculated using a standard inverse dynamics approach. In addition to calculating internal joint moments, the components of the external moment occurring in the transverse plane at each of the lower limb joints were calculated to determine their independent effects. All moments were expressed in both the laboratory frame (LF) as well as the anatomical frame (AF) of the distal segment. With the exception of the ankle rotation moment in the foot AF, lower limb transverse plane joint moments during gait were found to display characteristic profiles that were consistent across subjects. Furthermore, lower limb transverse plane joint moments during gait differed when expressed in the distal segment AF compared to the LF. At the hip, the two alternative reference frames produced near reciprocal joint moment profiles. The components of the external moment revealed that the external ground reaction force moment was primarily responsible for this result. Lower limb transverse plane joint moments during gait were therefore found to be highly sensitive to a change in reference frame. These findings indicate that the different transverse plane joint moment profiles during able-bodied adult gait reported in the literature are likely to be explained on this basis.

Keywords: Gait analysis, Inverse dynamics, Hip, Knee, Ankle

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1. Introduction 

Numerous studies have measured the three-dimensional (3D) moments acting about the lower limb joints (either external moments or opposing internal joint moments) during able-bodied adult gait (Allard et al., 1996; Andriacchi and Strickland, 1985; Benedetti et al., 1998; Besier et al., 2003; Bowsher and Vaughan, 1995; Bresler and Frankel, 1950; Eng and Winter, 1995; Ramakrishnan et al., 1987). Irrespective of the adopted convention (i.e. external versus internal joint moment), all studies in general report consistent joint moment profiles for the sagittal and frontal planes. However, significant variation does exist when comparing the transverse plane joint moment profiles, particularly for the hip. This was first noted by Allard et al. (1996) and is highlighted when comparing two technical notes, the first by Eng and Winter (1995) and the second by Bowsher and Vaughan (1995), both of which were published consecutively in Volume 28, Edition No. 6 of the Journal of Biomechanics. These two studies report 3D internal joint moments at the hip during gait. The sagittal and frontal plane hip joint moments are consistent but the transverse plane joint moments are opposite. Eng and Winter (1995) report an ‘external rotator’ hip joint moment during initial stance followed by an ‘internal rotator’ hip joint moment during terminal stance. Bowsher and Vaughan (1995) report a profile of similar shape but reversed convention. Whilst at first it may be suggested that this inconsistency is merely a product of inherent variability in gait strategies across subjects, such an explanation does not fit the findings. In contrast to this notion, it has been demonstrated that the transverse plane hip joint moment during the stance phase of gait does in fact display a characteristic profile that is remarkably consistent across subjects (Andriacchi and Strickland, 1985; Benedetti et al., 1998; Eng and Winter, 1995; Ramakrishnan et al., 1987). Furthermore, it is rather difficult to comprehend how a change in gait strategy would have almost no effect upon sagittal and frontal plane hip joint moments yet an apparent opposing effect upon the transverse plane hip joint moment. These factors would therefore suggest that an alternative explanation must exist.

It is possible that transverse plane joint moments during gait are highly sensitive to the reference frame in which they are expressed. A comparison of lower limb transverse plane joint moment profiles during gait from previous studies would suggest that this is feasible. Studies that have expressed the net moment vector in the transverse plane of the laboratory frame (LF) (Andriacchi and Strickland, 1985; Bresler and Frankel, 1950; Eng and Winter, 1995; Ramakrishnan et al., 1987) report markedly different lower limb transverse plane joint moment profiles during gait when compared to studies that have expressed the net moment vector in the transverse plane of the distal segment anatomical frame (AF) (Allard et al., 1996; Benedetti et al., 1998; Besier et al., 2003; Bowsher and Vaughan, 1995). Based on this, it was hypothesised that the contrasting transverse plane hip joint moment profiles during gait from Eng and Winter (1995) and Bowsher and Vaughan (1995) could be explained on the basis of differing reference frames. The aim of the current study was to therefore test this hypothesis and compare lower limb transverse plane joint moments during gait when expressed in the LF versus the distal segment AF. If this hypothesis proved to be true, then an additional aim was to analyse the relative effects of each component of the external moment acting in the transverse plane at the lower limb joints in an endeavour to provide a thorough explanation for this finding.

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2. Materials and methods 

2.1. Subjects 

Nine able-bodied adults (two males; seven females) with a mean height of 164.5 (SD 8.5) cm, body mass of 60.0 (SD 11.1) kg and age of 19.8 (SD 2.1) years 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.

2.2. Instrumentation 

Kinematic data were acquired using a 3D motion analysis system (VICON, Oxford Metrics, Oxford, England) with six cameras operating at a sampling rate of 120Hz. 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) were used to capture ground reaction force data at a sampling rate of 1080Hz.

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 non-rigid clusters of small spherical retro-reflective markers (25mm diameter) mounted in a non-colinear fashion as outlined in Table 1. These markers allowed the reconstruction of technical frames (TF) embedded in 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. (2005). 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 flexion–extension axis) was rotated about the vertical (z) axis through an angle θ, whereby θ represented the degree of rotation necessary to minimise the variance in the dynamic knee varus-valgus kinematic profile.

Table 1. Specific marker locations and orientations

Table 2. Technical frame definitions

Table 3. Anatomical frame definitions

NB: HJC, hip joint centre; KJC, knee joint centre; AJC, ankle joint centre.

2.4. Procedures 

Anthropometric parameters required for estimating the location of the HJC using the method of Davis et al. (1991) 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. Testing commenced with the capture of the static anatomical landmark calibration trial. Calibration markers were then removed and dynamic gait trials were captured. Subjects walked at a self-selected speed (1.2±0.1m/s) through the middle of a walkway with a calibrated field approximately 5m in length. A single gait trial was captured for each subject, whereby the left and right heels successfully struck the two adjacent force plates in isolation with no evident force plate targeting as observed by the tester.

2.5. Data analysis 

Coordinate data were filtered using Woltring's general cross-validatory quintic smoothing spline (Woltring, 1986) with a predicted mean-squared error of 15mm. Kinematic data were calculated using a joint coordinate system convention (Grood and Suntay, 1983). Net internal joint moments were calculated using an inverse dynamics approach with adapted inertial parameters as per De Leva (1996). In addition, the components of the external moment occurring in the transverse plane at each joint were calculated to determine their independent effects. The two components of the external moment calculated were: (a) the moment due to the resultant ground reaction force acting at a distance to the joint centre (external GRF moment) and (b) the free moment of rotation acting about a vertical axis through the centre of pressure (external Free moment). The component of the external moment due to segment weight and inertia in the transverse plane was considered to be extremely small and thus its independent effect was not calculated. All moments were normalised by dividing by subject's body mass and were expressed in both the LF as well as the AF of the distal segment (i.e. the femoral AF for hip joint moments; the proximal tibial AF for knee joint moments; the foot AF for ankle joint moments). The kinematic and kinetic computations were performed using Bodybuilder software (Oxford Metrics Ltd, Oxford, England). 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, Oxford, England).

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3. Results 

Lower limb transverse plane internal joint moments during gait are illustrated in Fig. 1. Except for the ankle rotation moment expressed in the foot AF, the patterns were found to be quite consistent across subjects, as indicated by the relatively small standard deviation bands. The transverse plane joint moments expressed in the distal segment AF displayed dramatically different patterns to the equivalent moments expressed in the LF. For the hip joint in particular, the two reference frames produced near reciprocal profiles. In contrast, the particular reference frame had little influence on the profiles for the sagittal plane hip, knee and ankle joint moments as well as the frontal plane hip and knee joint moments.

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• Fig. 1. 

  Lower limb transverse plane internal joint moments during gait: (a) expressed in the distal segment AF and (b) expressed in the LF. Solid line: right side, dashed line: left side. Shaded area indicates the standard deviation band about the group mean.

The components of the external moment (external GRF moment and external Free moment) along with their combined effect (external Total moment) in the transverse plane at each of the lower limb joints during gait are illustrated in Fig. 2, Fig. 3. The data highlight three important points. First, for each joint, the external Total moment was virtually equivalent to the reciprocal of the respective internal joint moment expressed in the same reference frame (Fig. 2(c) versus Fig. 1(b); Fig. 3(c) versus Fig. 1(a)). This meant that in the transverse plane the component of the external moment due to segment weight and inertia alone did not have an appreciable effect and thus could be ignored for the purposes of this analysis. Second, the effect of the external Free moment was near identical when expressed in either the LF or the distal segment AF (Fig. 2(b) versus Fig. 3(b)). The external Free moment itself therefore could not be used to explain the observed inconsistencies in the lower limb transverse plane joint moments when expressed in the two different reference frames. Third, in contrast to the external Free moment, the effect of the external GRF moment in the transverse plane was found to be highly sensitive to a change in reference frame (Figs. 2(a) versus Fig. 3(a)). The external GRF moment had differing effects at each of the lower limb joints during gait when expressed in the LF compared to the AF of the distal segment. For example, at the hip joint, the effect of the external GRF moment in the femoral AF was opposite to its effect in the LF. The observed differences in the lower limb transverse plane joint moments when expressed in the two reference frames (Fig. 1(a) and (b)) could therefore be explained with consideration to the effect of the external GRF moment.

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• Fig. 2. 

  The components of the external moment in the transverse plane, expressed in the LF, at each of the lower limb joints during gait: (a) the resultant ground reaction force acting at a distance to the joint centre (external GRF moment); (b) the free moment of rotation acting about a vertical axis through the centre of pressure (external Free moment); (c) the external GRF and Free moments combined excluding the component of the external moment due to segment weight and inertia (external Total moment). The external Free moment and the external GRF moment can be seen to have complimentary effects at the ankle joint but opposing effects at the hip and knee joints. Solid line: right side, Dashed line: left side. Shaded area indicates the standard deviation band about the group mean.

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• Fig. 3. 

  The components of the external moment in the transverse plane, expressed in the distal segment AF, at each of the lower limb joints during gait: (a) the resultant ground reaction force acting at a distance to the joint centre (external GRF moment); (b) the free moment of rotation acting about a vertical axis through the centre of pressure (external Free moment); (c) the external GRF and Free moments combined excluding the component of the external moment due to segment weight and inertia (external Total moment). The external Free moment and the external GRF moment can be seen to have complimentary effects at all lower limb joints. Solid line: right side, dashed line: left side. Shaded area indicates the standard deviation band about the group mean.

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4. Discussion 

There are two major findings from this study. First, with the exception of the ankle rotation moment in the foot AF, lower limb transverse plane joint moments during gait displayed characteristic profiles that were consistent across subjects. This is in accordance with previous studies (Andriacchi and Strickland, 1985; Benedetti et al., 1998; Eng and Winter, 1995; Ramakrishnan et al., 1987). Second, lower limb transverse plane joint moments during gait differed when expressed in the distal segment AF compared to the LF. This was not the case for the sagittal plane hip, knee and ankle joint moments as well as the frontal plane hip and knee joint moments.

The ankle rotation moment in the foot AF displayed the greatest degree of variability across subjects (Fig. 1(a)), consistent with a previous study (Hunt and Smith, 2001). This moment is a product of forces acting about the defined vertical (z) axis of the foot AF. As this axis was aligned with the bisection of the posterior calcaneus (Table 3 and Fig. 4), the ankle rotation moment in the foot AF was therefore highly sensitive to the orientation of the posterior calcaneus in the frontal plane (Hunt and Smith, 2001). Given that both static posterior calcaneal alignment and dynamic inversion–eversion movements during gait can vary considerably across subjects, it is not surprising that this moment was variable across subjects. As the ankle rotation moment in the foot AF is dependent upon the specific foot model, this moment can also be expected to vary somewhat across studies.

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• Fig. 4. 

  Coronal view of the foot AF. Point A depicts the bi-malleolar axis, point B depicts the bisection of the posterior calcaneus and AJC indicates the ankle joint centre. Note the dependency of the foot AF vertical (z) axis on the alignment of the posterior calcaneus which medially inclines the foot AF transverse plane with respect to the LF for an ‘everted’ rearfoot.

Numerous studies have measured lower limb transverse plane joint moments during able-bodied adult gait (Allard et al., 1996; Andriacchi and Strickland, 1985; Benedetti et al., 1998; Besier et al., 2003; Bowsher and Vaughan, 1995; Bresler and Frankel, 1950; Eng and Winter, 1995; Ramakrishnan et al., 1987). Andriacchi and Strickland (1985), Bresler and Frankel (1950), Eng and Winter (1995) and Ramakrishnan et al. (1987) all expressed the net moment vector in the LF. The transverse plane joint moment profiles from these studies are consistent with those from the current study when expressed in the LF. Allard et al. (1996), Benedetti et al. (1998), Besier et al. (2003) and Bowsher and Vaughan (1995) all expressed the net moment vector in the distal segment AF. The transverse plane joint moment profiles from these studies are consistent with those from the current study when expressed in the distal segment AF. This suggests that the conflicting transverse plane joint moment profiles reported in the literature are likely to be explained on the basis of alternative reference frames rather than inherent variability in gait strategies.

For a given lower limb joint (hip, knee or ankle) and reference frame (LF or distal segment AF), an analysis of the relative effects of each of the components of the external moment in the transverse plane makes it possible to determine which are dominant. As segment weight and inertia were not found to have an appreciable effect, the dominant components were the external GRF and Free moments. In general, the magnitude of the external GRF moment exceeded that of the external Free moment (Fig. 2, Fig. 3). The addition of these two moments (external Total moment) was able to provide a reasonable reflection of the net effect of the external moment in the transverse plane during stance. From this one can deduce the expected internal joint moments, which should then match the measured data from the inverse dynamics solution. Inspection of the data demonstrated this to be the case. For a particular lower limb joint and reference frame, the profile of the stance phase internal joint moment (Fig. 1) was virtually equivalent to the reciprocal of the respective external Total moment (Fig. 2, Fig. 3).

Due to the relative dominance of the external GRF moment, its effect can be used to explain the observed differences in the lower limb transverse plane joint moments during gait when expressed in alternative reference frames (Fig. 1(a) and (b)). The external GRF moment had quite different effects at all lower limb joints when expressed in the LF compared to the distal segment AF, whereas the action of the external Free moment remained unaffected. To explain the sensitivity of the external GRF moment to a change in reference frame, an appreciation of the orientation of the GRF vector with respect to the relevant joint centre for a given lower limb joint and reference frame is required.

At the hip, the GRF vector was medial to the HJC during stance, irrespective of the reference frame, as both conventions calculated an ‘abductor’ internal hip joint moment. In the LF transverse plane, the GRF vector was antero-medial to the HJC pointing postero-medially during initial stance whilst postero-medial to the HJC pointing antero-medially during terminal stance (Fig. 5, Fig. 6). The external GRF moment would therefore be expected to induce an ‘internal rotator’ external hip joint moment during initial stance and an ‘external rotator’ external hip joint moment during terminal stance, which is consistent with Fig. 2(a). Alternatively, in the femoral AF transverse plane, the GRF vector was postero-medial to the HJC pointing antero-medially during initial stance whilst antero-lateral to the HJC pointing postero-medially during terminal stance (Fig. 5, Fig. 6). The external GRF moment would therefore be expected to induce an ‘external rotator’ external hip joint moment during initial stance and an ‘internal rotator’ external hip joint moment during terminal stance, which is consistent with Fig. 3(a).

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• Fig. 5. 

  Orientation of the resultant GRF vector in the LF sagittal plane for the left lower limb during (a) initial stance and (b) terminal stance. The GRF vector is indicated by the thick solid line.

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• Fig. 6. 

  Orientation of the resultant GRF vector projected into (a) the LF transverse plane, (b) the femoral AF transverse plane and (c) the tibial (proximal) AF transverse plane during initial stance and terminal stance for the left lower limb. The projected GRF vector is indicated by the thick solid line. Note that LF (HJC) and LF (KJC) represent the translated LF such that the origin is located at the HJC and KJC respectively.

At the knee, the GRF vector was slightly medial to the KJC during stance, irrespective of the reference frame, as both conventions calculated an ‘abductor’ internal knee joint moment. In the LF transverse plane, the GRF vector was antero-medial to the KJC pointing postero-medially during initial stance whilst postero-medial to the KJC pointing anteriorly during terminal stance (Fig. 5, Fig. 6). However, at both of these times, the moment arm of the GRF vector and the magnitude of its projection in the LF transverse plane were both considerably small (Fig. 6(a)). The external GRF moment would therefore be expected to induce a small ‘internal rotator’ external knee joint moment during initial stance and a small ‘external rotator’ external knee joint moment during terminal stance, which is consistent with Fig. 2(a). Note though that the effect the external GRF moment in the LF transverse plane at the knee joint was relatively small (Fig. 2(a)) in comparison to the corresponding external Free moment (Fig. 2(b)). Thus, at the knee joint in the LF transverse plane, the resultant profile of the external Total moment was not simply a reflection of the external GRF moment. Alternatively, in the tibial AF transverse plane, the GRF vector was antero-medial to the KJC pointing poster-medially during initial stance (Fig. 5, Fig. 6). Not only was its moment arm quite small at this time but the magnitude of the projected GRF vector in the tibial AF transverse plane was also small because the vertical (z) axis of the tibial AF was closely aligned with the GRF vector in the sagittal plane for a short period following heel strike. As stance progressed, the GRF vector continued to point antero-medially but the magnitude of its projection into the transverse plane of the tibial AF increased (Fig. 6(c)). The external GRF moment would therefore be expected to have little effect during initial stance but induce an increasing ‘internal rotator’ external knee joint moment during terminal stance, which is consistent with Fig. 3(a).

At the ankle in the LF transverse plane, the GRF vector was close to the AJC in the medio-lateral direction during initial stance but shifted lateral to it through mid to late stance phase, as can be determined from Fig. 7(b). During initial stance, the GRF vector was pointing postero-medially but was close to the AJC (Fig. 8(a)). By terminal stance, the GRF vector was pointing antero-medially and had shifted anteriorly along the foot to the first metatarso-phalangeal joint, increasing its LF transverse plane moment arm about the AJC (Fig. 8(b)). The external GRF moment would therefore be expected to have little effect during initial stance but induce an increasing ‘internal rotator’ (adductor) external ankle joint moment during terminal stance, which is consistent with Fig. 2(a).

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• Fig. 7. 

  ‘Invertor-evertor’ internal ankle joint moment during gait expressed in (a) the foot AF and (b) the LF. The orientation of the projected GRF vector in the frontal plane of both the foot AF and LF during mid stance for the left foot is also displayed.

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• Fig. 8. 

  Orientation of the resultant GRF vector projected into the LF transverse plane at the AJC during (a) initial stance and (b) terminal stance for the left foot. The projected GRF vector is indicated by the thick solid line.

At the ankle in the foot AF transverse plane, the GRF vector was slightly lateral to the AJC during initial stance and slightly medial to the AJC during terminal stance, as can be determined from Fig. 7(a). During initial stance, the GRF vector was antero-lateral to the AJC pointing postero-laterally but with a small moment arm (Fig. 9(a)). The external GRF moment would therefore be expected to have little effect during initial stance, which is consistent with Fig. 3(a). By mid stance, the GRF vector had shifted anteriorly along the foot to the first metatarso-phalangeal joint, increasing its foot AF transverse plane arm about the AJC (Fig. 9(b) and (c)). However, the orientation of the GRF vector at this time was variable across subjects and depended upon the frontal plane posterior calcaneal alignment. For a varus alignment, the GRF vector was pointing postero-medially (Fig. 9(b)) whereas for a valgus alignment, the GRF vector was pointing postero-laterally (Fig. 9(c)). From mid stance onwards, the external GRF moment would therefore be expected to induce an ‘internal rotator’ (adductor) external ankle joint moment for a varus alignment and an ‘external rotator’ (abductor) external ankle joint moment for a valgus alignment. This is consistent with Fig. 3(a), which from mid stance onwards displays a high degree inter-subject variability.

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• Fig. 9. 

  Orientation of the resultant GRF vector projected into the foot AF transverse plane at the AJC during (a) initial stance, (b) mid stance for the left foot (varus alignment) and (c) mid stance for the left foot (valgus alignment). The projected GRF vector is indicated by the thick solid line.

It is important to note that the findings of the current study relate specifically to able-bodied adult gait. Whilst the particular reference frame was shown to have little influence on the resulting profiles for the sagittal plane hip, knee and ankle joint moments as well as the frontal plane hip and knee joint moments during able-bodied adult gait, this is unlikely to be the case for pathological gait. For example, children with diplegic cerebral palsy typically walk with increased hip and knee flexion as well as increased hip internal rotation (Gage et al., 1995). In such circumstances, the limbs are no longer approximately aligned with the GRF vector in the sagittal plane and differences between reference frames may become apparent for sagittal and frontal plane joint moments during gait. Further research is required to explore this issue.

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Acknowledgments 

This project was financially supported by a Health Professional Research Training Fellowship from the Australian National Health and Medical Research Council (Grant ID: 237153). We would also like to acknowledge the assistance of Mr Bill Reid from the Educational Resource Centre at the Royal Children's Hospital, Melbourne, Australia for the preparation of the figures presented in this study.

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