-PRESENTATION OF THE NET MOMENT DATA
The joint reaction forces and net joint moments that are calculated from an inverse dynamics procedure are 3-D vectors computed in the GCS but are typically resolved into an anatomically meaningful
coor-that are presented. The most straightforward representation would be to leave these signals in the GCS (Bresler and Frankel 1950; Winter et al. 1995). This was suggested on the basis that the individual’s line of progression is generally aligned along one of the planes of the global reference system, and thus the sagittal plane of the lower extremity and the line of progression will be essentially the same.
This interpretation is a 2-D centric view of gait analysis and may be useful for the sagittal plane (e.g.,
moments about the x
-nents of the signals because the LCS is rarely aligned precisely with the GCS in every pose. It is our recommendation, therefore, that users refrain from using this 2-D representation and present the joint forces and moments in a coordinate system that can be readily understood regardless of the subject’s (and individual segment’s) position and orientation in the GCS.
There are four representations of the net joint moment and joint reaction force that have documented four because they all have merit in some context but can sometimes differ dramatically in the results.
Option 1 is to resolve the joint reaction force and net joint moment into the proximal segment LCS (Schache and Baker, 2007). Option 2 is to resolve the signals into the distal segment LCS (Kaufman et al. 2001). Option 3 is to resolve the signals into the joint coordinate system (Schache and Baker 2007;
Astephen et al. 2008). Option 4 is ad hoc, in which the anterior-posterior and inferior-superior moments are projected onto the plane of progression (Mundermann et al. 2005). The confusion for the reader is that each of these representations is mathematically sensible and, depending on the parameters of interest, may be superior to the others in the appropriate context (Schache and Baker 2007; Schache et al. 2008). This confusion extends, also, to the international biomechanics societies in which no inter-national standard has been proposed, let alone adopted. In this chapter, we refrain from advocating a particular option. The researcher, therefore, must take note of the coordinate system in which the moments are presented and be very careful in comparing results from different journal articles. It is unfortunately quite rare for authors to specify the resolution coordinate system for their joint moments, so much of the biomechanics literature contains questionable moment data.
This issue gets more confusing because options 1 and 2 result in the signals’ being vectors, which is consistent with our representations of joint angular velocity, angular acceleration, and joint force, but inconsistent with a JCS representation of joint angles. Option 3 is a nonorthogonal representa-tion, which means that the reaction force and net moments are not vectors, so this representation is consistent with joint angles (which makes it popular with clinical gait analysis) but not with angular velocity, angular acceleration, or joint force. The support moment (described in the previous section) cannot be computed using this approach because only vectors can be added sensibly. Option 4 is not consistent with any of our kinematic measures. Readers, therefore, must be careful that they are only comparing “like” signals: for example, comparing vectors with vectors, and comparing nonorthogonal representations with other consistent nonorthogonal representations.
Hip abd/adduction
Figure 7.8 Net joint moments of the ankle, knee, and hip during a stride cycle of walking based on data from 13 subjects (the subject for the text book data is one of these subjects). The solid line represents the mean value, whereas the gray zone indicates ±1 standard deviation. All joint angles used an XYZ cardan sequence, and the joint moments (with segment mass) were resolved in the proximal segment’s coordinate system. The sign conventions are as follows: hip joint moment (positive flexion, adduction, internal rotation); knee joint moment (positive flexion, adduction, internal rotation); ankle joint moment (positive flexion, adduction, internal rotation).
Just as there is no standard convention for choosing the coordinate system in which to represent joint reaction force and net moment, most published articles differ in choosing normalization (scaling) factors. Scaling the net joint moments is an attempt to remove between-subject differences. In a clini-cal setting in which an individual’s data are being collected and a report is generated on that subject, there is perhaps no need to scale the data. In a research study, however, in which data are collected on multiple subjects in different conditions, it probably is appropriate to scale the data for purposes of
and Todd, 1994).
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E5144/Robertson/fig 7.9/414967, 463151,463152, 463153/TB/R2-alw X ˆ Y
FA X
Y X
Y
Distal Proximal Joint coordinate
system (JCS)
Plane of progression (PoP) X
Figure 7.9 Four anatomical reference frames for the net knee joint moment. 1) Resolve the net moment into the shank coordinate system. 2) Resolve the net moment into the thigh coordinate system. 3) Project the net moment vector onto the unit vectors of the Joint Coordinate System (see chapter 2; typically the flexion/extension axis of the thigh segment, the axial rotation axis of the shank segment, and an axis perpendicular to these two axes, which for gait is close to the abduc-tion/adduction axis). 4) The plane of progression (PoP) frame fixes the flexion axis perpendicular to the plane of progression, whereas the adduction and internal rotation axes are taken from the distal frame and projected onto the plane of progression.
Reprinted from Clinical Biomechanics, Vol. 26(1), S.C. Brandon and K.J. Deluzio, “Robust features of knee osteoarthritis in joint moments are independent of reference frame selection,” pgs. 65-70, copyright 2011, with permission of Elsevier.
FROM THE SCIENTIFIC LITERATURE
Brandon, S.C., and K.J. Deluzio. 2011. Robust features of knee osteoarthritis in joint moments are independent of reference frame selection. Clinical Biomechanics 26(1):65-70.
The physiological interpretation of 3-D joint moments can change when the moments are transformed -tures of the hip, knee, and ankle joint moment waveforms that, regardless of the choice of reference frame, were consistently different between control subjects and subjects with knee osteoarthritis.
Subjects walked at self-selected speed, and external 3-D joint moments were calculated with a stan-dard inverse dynamics approach. Moments were then expressed using the four alternative reference (PoP). Finally, the primary features of variance across all four systems were extracted using principal component analysis.
The magnitude and shape of every joint moment were different between the four reference frames.
However, regardless of the choice of reference frame, subjects with knee osteoarthritis exhibited decreased overall hip adduction moment magnitudes, increased overall knee adduction moment amplitudes, decreased knee internal rotation moment amplitudes, and increased early-stance ankle are characteristics of the pathogenesis of knee osteoarthritis and are not merely artifacts of reference frame selection.
167
% stance % stance % stance
–0.5
Figure 7.10 Four robust changes due to osteoarthritis that are independent of the choice of reference frame, identified using principal component analysis. (a) Mean waveforms, averaged across all anatomical reference frames for control (solid black line) and osteoarthritis (dashed gray line). (b) Loading vectors that indicate biomechanical changes in overall magnitude (hip and knee adduction), amplitude (knee internal rotation), and early-stance magnitude (ankle adduction). (c) Extreme subjects are shown for control (solid black line) and osteoarthritis (dashed gray line) groups to characterize robust group differences. Arrows give the direction of the osteoarthritis group relative to the control group throughout the shaded regions.
Reprinted from Clinical Biomechanics, Vol. 26(1), S.C. Brandon and K.J. Deluzio, “Robust features of knee osteoarthritis in joint moments are independent of reference frame selection,” pgs. 65-70, copyright 2011, with permission of Elsevier.
P P = .83). Not only does the choice of reference frame affect the magnitude and shape of joint moments; it can affect joint moments differently for different subjects.