- Email: [email protected]
Assumption of a ‘gravity only region’ for gravity correction of passive joint moment data may be problematic
Journal of Biomechanics 43 (2010) 2653–2656
Contents lists available at ScienceDirect
Journal of Biomechanics journal homepage: www.elsevier.com/locate/jbiomech www.JBiomech.com
LETTERS TO THE EDITOR
Letter to the Editor regarding ‘‘All joint moments significantly contribute to trunk angular acceleration’’ At the outset let me congratulate the authors on their use of recent advancements in 3D measurements and biomechanical modeling to demonstrate the influence of all three lower limb moments on the trunk angular acceleration. Previous analysis by McKinnon and Winter (1993) using a ‘‘top-down’’ model of the HAT in the frontal plane showed that the trunk angular was a function of the gravitational moment, the hip ab/abd moment and the hip joint vertical and horizontal accelerations. This model recognized in these two joint accelerations the net contributions of the moments of the two distal joints. A similar top-down sagittal plane model of HAT balance was reported in Winter (1995). The significant contribution in this new paper is that it represents a much more difficult ‘‘bottom-up’’ approach and partitions the contributions of all joint moments and their reaction joint force coupling contributions to the HAT angular accelerations in both planes. Of particular interest is the contribution of the large plantarflexor ankle moment to the trunk’s angular acceleration. As far as the total body analysis is concerned it is important to put this trunk angular acceleration in perspective regarding the accelerations that the head experience. During gait it is important that the head linear accelerations are a minimum because the head is the platform for the visual and vestibular systems. The linear acceleration of the pelvis in the A/P direction is 71.91 m s 2 and that combined with the trunk’s angular acceleration reduces the head acceleration to 70.48 m s 2. However we must also recognize that the head and trunk do not form a single rigid segment. An analysis of the motor control of the head and vertebrae showed a phased difference in EMG activity of the paraspinal muscles from the C7 level down to the L4 level (Prince et al., 1994). They demonstrated a ‘‘top-down’’ anticipatory control showing the head being stabilized first, then the cervical level, the thoracic level and final the lumbar level. For example, the C7 EMG profile was 70 ms in advance of the L4 profile. Thus with the
contribution of this new paper we can now say that the head’s acceleration is under motor control of all muscles from the ankle up to the neck. Finally a small note of correction. The authors erroneously described the trunk angular acceleration analysis by McKinnon and Winter (1993) as being only sagittal plane analysis; it was a frontal plane analysis done with frontal plane data and a frontal plane model. Also the authors assumed that treadmill gait was the same as overground gait but we have not found that to be true (Winter et al., 1980). In that paper we recorded large fluctuations in treadmill motor power during the gait stride: during weight acceptance the belt and motor slowed down and motor power increased, during push off the belt and motor sped up and motor power decreased.
Conflict of interest statement None.
References MacKinnon, C.D., Winter, D.A., 1993. Control of whole body balance in the frontal plane during human walking. J. Biomech. 26, 633–644. Prince, F., Winter, D.A., Stergiou, P., Walt, S.E., 1994. Anticipatory control of upper body balance during human locomotion. Gait Posture 2, 19–25. Winter, D.A., Arsenault, B., Woolley, S., 1980. Step-to-step fluctuations in treadmill gait. Proc. Hum. Locomotion 1, 28–29 London, Ont. Winter, D.A., 1995. Human balance and posture control during standing and walking. Gait Posture 3, 193–214.
David A. Winter n University of Waterloo, Waterloo, Ont., Canada E-mail address: [email protected]
22 May 2010
DOI of original articles: 10.1016/j.jbiomech.2010.04.044 doi:10.1016/j.jbiomech.2010.05.025
Assumption of a ‘gravity only region’ for gravity correction of passive joint moment data may be problematic Many devices used to collect joint moment data create gravitational moments due to the masses of the device and the limb being tested. Where a significant gravitational moment is present in the recorded moment-angle data, it may be necessary to correct for (remove) the gravitational moment component. In a recent article in this journal, Anderson et al. (2010) proposed a computationally elegant method for gravity correction of joint
n
Tel.: + 1 519 747 0077.
moment data. The method relies heavily on the assumption that the joint has a region of near-zero stiffness (the ‘gravity-only region’) that spans at least 40% of the range of motion. We provide data that demonstrate this assumption is not satisfied, and therefore that the method is not valid, for the human ankle joint. Consequently, we feel that the new method should not be used to remove gravitational moments from human ankle torque-angle data, and should be used with caution for other joints. We collected ankle torque-angle data from 3 healthy subjects using a protocol approved by the University of Sydney Human
2654
Letters to the Editor / Journal of Biomechanics 43 (2010) 2653–2656
Fig. 1. A: passive ankle moment data for 3 subjects; B: passive moment data for subject 2 showing application of the Anderson et al. method (including the cubic polynomial fit, the centre and range of the ‘gravity only region’ (in bold black) and the resulting gravitational moment function); C: the true apparatus gravitational moment recording and the gravitational moment functions for all 3 subjects using the method proposed by Anderson et al. as an approximation of the apparatus gravitational moment.
Research Ethics Committee. The testing device was similar to the device described by Hoang et al. (2005). Subjects were tested in side-lying with the knee fully extended. The device’s axis of rotation was aligned vertically so that the device and foot did not exert a gravitational moment. Prior to testing, torque was measured as the device was rotated without a foot in the device. This confirmed that the axis was vertical and the dynamometer did not exert a measurable moment (mean torque of 0.06 N m, stiffness o0.0003 N m/deg.; Fig. 1C). Subsequently the subject’s foot was fixed in the device and torque was measured as the ankle was passively rotated through its range. The data shown in Fig. 1A clearly demonstrate the ankle exerts a moment throughout its range. As the device and foot are rotated in a horizontal plane, this must be an elastic moment, not a gravitational moment. Thus the ankle cannot be assumed to have a gravity-only region. This was confirmed statistically. Regression lines fit to the passive ankle moment data from the three subjects in the 40% gravity-only region had gradients of 0.089, 0.178 and 0.081 N m/deg. These gradients were significantly different from zero (po0.001).
For each subject, the gravitational moment was calculated using methods proposed by Anderson et al. Fig. 1B shows the application of Anderson et al.’s method to data from Subject 2, and Fig. 1C shows the calculated gravitational moment functions. Anderson et al.’s method predicts a gravitational moment of up to 6.16 N m in the measured range of motion (Fig. 1C), even though testing was conducted in a horizontal plane, so that there was no gravitational moment. Thus Anderson et al.’s method significantly overestimates the gravitational moment. As Fig. 1A demonstrates, the error in estimation of gravitational moments using Anderson et al.’s method is caused by the assumption that there is a gravity-only region. At least for the human ankle there is no region in which there is not a substantial elastic stiffness. A similar absence of a gravity-only region has also been reported for other joints, such as spinal motions segments (e.g. Thompson et al., 2003; Clarke et al, 2007) under certain conditions. It is possible that other joints, such as the hip and knee joints (which were also investigated in the article by Anderson et al.) may have a gravity-only region. In this case the new method described by Anderson et al. may provide a convenient and accurate method for correcting for gravitational moment. However, the method
Letters to the Editor / Journal of Biomechanics 43 (2010) 2653–2656
described by Anderson et al. should only be used when the presence of a gravity-only region has been confirmed.
2655
Thompson, R.E., Barker, T.M., Pearcy, M.J., 2003. Defining the neutral zone of sheep intervertebral joints during dynamic motions: an in vitro study. Clinical Biomechanics 18, 89–98.
Conflict of interest statement
E.C. Clarke n Research Fellow, The George Institute for International Health, The University of Sydney, PO Box M201, Missenden Rd., Sydney, NSW 2050, Australia E-mail address: [email protected]
No conflicts of interest to disclose.
Acknowledgement
J.H. Martin Prince of Wales Medical Research Institute, University of New South Wales, Sydney, Australia
The authors wish to thank Mr. Kevin Wang for his assistance in conducting the experiments. References
R. Herbert Research Fellow, The George Institute for International Health, The University of Sydney, PO Box M201, Missenden Rd., Sydney, NSW 2050, Australia
Anderson, D.E., Nussbaum, M.A., Madigan, M.L., 2010. A new method for gravity correction of dynamometer data and determining passive elastic moments at the joint. Journal of Biomechanics. doi:10.1016/j.jbiomech.2009.11.036. Clarke, E.C., Appleyard, R., Bilston, L.E., 2007. Immature sheep spines are more flexible than mature spines: an in vitro biomechanical study. Spine 32, 2970–2979. Hoang, P.D., Gorman, R.B., Todd, G., Gandevia, S.C., Herbert, R.D., 2005. A new method for measuring passive length–tension properties of human gastrocnemius muscle in vivo. Journal of Biomechanics 38, 1333–1341. doi:10.1016/j.jbiomech.2010.03.051
Response to ‘‘Assumption of a ‘gravity only region’ for gravity correction of passive joint moment data may be problematic’’ In our recent paper (Anderson et al., 2010) we describe a method for determining the gravitational moment in dynamometer data that also accounts for the passive elastic moment due to passive tissue deformation. Our method assumes that the passive elastic moment is negligible within a middle region of the joint range of motion, which we dubbed the ‘‘gravity-only region’’. In their letter to the Editor entitled ‘‘Assumption of a ‘gravity only region’ for gravity correction of passive joint moment data may be problematic’’, Clarke et al. present data indicating that this assumption is invalid for the ankle, and as a result the method tends to overestimate the magnitude of the gravitational moment at the ankle. We would like to thank Clark et al. for their scrutiny of our method, as this is a critical component of scientific progress. In this response we describe an addition to our method that accounts for the presence of a non-negligible passive elastic moment in the gravity-only region, and as a result should address the valid concern expressed by Clarke et al. We would also like to point out that, based upon the data presented by Clarke et al. and our own retrospection, the term ‘‘gravity-only region’’ that we used in the original work is somewhat of a misnomer for the midrange region of passive moment data. This is because the passive elastic moment in this region, while small, may still be present. As such, this region will henceforth be referred to as the ‘‘mid-range region’’. Clarke et al. reported a passive elastic moment at the ankle that is not uniformly zero in the mid-range region. Based upon their data, this moment could be reasonably approximated by a straight line. Other studies also report non-zero yet linear passive elastic moments in the mid-range region of the knee (McFaull and Lamontagne, 1998) and hip (Yoon and Mansour, 1982). To account for the presence of a non-zero passive elastic moment in this mid-range region, a linear approximation of the passive elastic moment may be incorporated into our previously published method. Thus, when fitting the passive moment data from
30 March 2010
n
Corresponding author. Tel.: + 61 2 9657 0343; fax: + 61 2 9657 0301.
the mid-range region, a line representing the passive elastic moment should be added to the sinusoidal gravitational model (Eq. (1) in Anderson et al., 2010) giving Mmidrange ¼ A1 sinðyÞ þ A2 cosðyÞ þb1 y þ b2 where b1 and b2 are coefficients for the linear passive elastic component. To estimate these coefficients, an iterative approach can be used. In the first iteration, b1 and b2 are set to zero, and the coefficients for gravitational moment (A1 and A2) are found using a least squares fit as described originally. The passive moment data is then corrected for gravity as described originally, but using the equation above with only the A1 and A2 terms (not including the b1 and b2 terms). The passive elastic moment constants (B1, k1, B2, and k2) are then found as described originally. Coefficients b1 and b2 can then be estimated by evaluating the passive elastic moment (Eq. (2) in Anderson et al., 2010) at the ends of the midrange region and determining the equation of the line between those two points. In subsequent iterations, the estimates of b1 and b2 are included when determining A1 and A2, and updated values for B1, k1, B2, k2, b1 and b2 may be found. Iteration continues until the fit is optimized (i.e. the concordance correlation coefficient reaches a maximum). It should be noted that with this approach the final equation for fitting the measured passive moment (Eq. (3) in Anderson et al., 2010) remains the same and does not include the terms b1 and b2. This is because the linear trend of the passive elastic moment within the mid-range region is accounted for in the passive elastic moment equation (Eq. (2) in Anderson et al., 2010). In testing using data from a single subject, this addition to the method reduced the magnitude of estimated gravitational moment for the ankle, knee, and hip. The concordance correlation coefficient was optimized for all three joints in three iterations. At the ankle, the largest magnitude gravitational moment in the range of motion was reduced by 1.84 N m or 18.6%. Similarly, gravitational moment was reduced by 0.69 N m (4.1%) at the knee and by 5.55 N m (8.1%) at the hip. Thus, this revised method appears to be less likely to overestimate the magnitude of the gravitational moment.
Contents lists available at ScienceDirect
Journal of Biomechanics journal homepage: www.elsevier.com/locate/jbiomech www.JBiomech.com
LETTERS TO THE EDITOR
Letter to the Editor regarding ‘‘All joint moments significantly contribute to trunk angular acceleration’’ At the outset let me congratulate the authors on their use of recent advancements in 3D measurements and biomechanical modeling to demonstrate the influence of all three lower limb moments on the trunk angular acceleration. Previous analysis by McKinnon and Winter (1993) using a ‘‘top-down’’ model of the HAT in the frontal plane showed that the trunk angular was a function of the gravitational moment, the hip ab/abd moment and the hip joint vertical and horizontal accelerations. This model recognized in these two joint accelerations the net contributions of the moments of the two distal joints. A similar top-down sagittal plane model of HAT balance was reported in Winter (1995). The significant contribution in this new paper is that it represents a much more difficult ‘‘bottom-up’’ approach and partitions the contributions of all joint moments and their reaction joint force coupling contributions to the HAT angular accelerations in both planes. Of particular interest is the contribution of the large plantarflexor ankle moment to the trunk’s angular acceleration. As far as the total body analysis is concerned it is important to put this trunk angular acceleration in perspective regarding the accelerations that the head experience. During gait it is important that the head linear accelerations are a minimum because the head is the platform for the visual and vestibular systems. The linear acceleration of the pelvis in the A/P direction is 71.91 m s 2 and that combined with the trunk’s angular acceleration reduces the head acceleration to 70.48 m s 2. However we must also recognize that the head and trunk do not form a single rigid segment. An analysis of the motor control of the head and vertebrae showed a phased difference in EMG activity of the paraspinal muscles from the C7 level down to the L4 level (Prince et al., 1994). They demonstrated a ‘‘top-down’’ anticipatory control showing the head being stabilized first, then the cervical level, the thoracic level and final the lumbar level. For example, the C7 EMG profile was 70 ms in advance of the L4 profile. Thus with the
contribution of this new paper we can now say that the head’s acceleration is under motor control of all muscles from the ankle up to the neck. Finally a small note of correction. The authors erroneously described the trunk angular acceleration analysis by McKinnon and Winter (1993) as being only sagittal plane analysis; it was a frontal plane analysis done with frontal plane data and a frontal plane model. Also the authors assumed that treadmill gait was the same as overground gait but we have not found that to be true (Winter et al., 1980). In that paper we recorded large fluctuations in treadmill motor power during the gait stride: during weight acceptance the belt and motor slowed down and motor power increased, during push off the belt and motor sped up and motor power decreased.
Conflict of interest statement None.
References MacKinnon, C.D., Winter, D.A., 1993. Control of whole body balance in the frontal plane during human walking. J. Biomech. 26, 633–644. Prince, F., Winter, D.A., Stergiou, P., Walt, S.E., 1994. Anticipatory control of upper body balance during human locomotion. Gait Posture 2, 19–25. Winter, D.A., Arsenault, B., Woolley, S., 1980. Step-to-step fluctuations in treadmill gait. Proc. Hum. Locomotion 1, 28–29 London, Ont. Winter, D.A., 1995. Human balance and posture control during standing and walking. Gait Posture 3, 193–214.
David A. Winter n University of Waterloo, Waterloo, Ont., Canada E-mail address: [email protected]
22 May 2010
DOI of original articles: 10.1016/j.jbiomech.2010.04.044 doi:10.1016/j.jbiomech.2010.05.025
Assumption of a ‘gravity only region’ for gravity correction of passive joint moment data may be problematic Many devices used to collect joint moment data create gravitational moments due to the masses of the device and the limb being tested. Where a significant gravitational moment is present in the recorded moment-angle data, it may be necessary to correct for (remove) the gravitational moment component. In a recent article in this journal, Anderson et al. (2010) proposed a computationally elegant method for gravity correction of joint
n
Tel.: + 1 519 747 0077.
moment data. The method relies heavily on the assumption that the joint has a region of near-zero stiffness (the ‘gravity-only region’) that spans at least 40% of the range of motion. We provide data that demonstrate this assumption is not satisfied, and therefore that the method is not valid, for the human ankle joint. Consequently, we feel that the new method should not be used to remove gravitational moments from human ankle torque-angle data, and should be used with caution for other joints. We collected ankle torque-angle data from 3 healthy subjects using a protocol approved by the University of Sydney Human
2654
Letters to the Editor / Journal of Biomechanics 43 (2010) 2653–2656
Fig. 1. A: passive ankle moment data for 3 subjects; B: passive moment data for subject 2 showing application of the Anderson et al. method (including the cubic polynomial fit, the centre and range of the ‘gravity only region’ (in bold black) and the resulting gravitational moment function); C: the true apparatus gravitational moment recording and the gravitational moment functions for all 3 subjects using the method proposed by Anderson et al. as an approximation of the apparatus gravitational moment.
Research Ethics Committee. The testing device was similar to the device described by Hoang et al. (2005). Subjects were tested in side-lying with the knee fully extended. The device’s axis of rotation was aligned vertically so that the device and foot did not exert a gravitational moment. Prior to testing, torque was measured as the device was rotated without a foot in the device. This confirmed that the axis was vertical and the dynamometer did not exert a measurable moment (mean torque of 0.06 N m, stiffness o0.0003 N m/deg.; Fig. 1C). Subsequently the subject’s foot was fixed in the device and torque was measured as the ankle was passively rotated through its range. The data shown in Fig. 1A clearly demonstrate the ankle exerts a moment throughout its range. As the device and foot are rotated in a horizontal plane, this must be an elastic moment, not a gravitational moment. Thus the ankle cannot be assumed to have a gravity-only region. This was confirmed statistically. Regression lines fit to the passive ankle moment data from the three subjects in the 40% gravity-only region had gradients of 0.089, 0.178 and 0.081 N m/deg. These gradients were significantly different from zero (po0.001).
For each subject, the gravitational moment was calculated using methods proposed by Anderson et al. Fig. 1B shows the application of Anderson et al.’s method to data from Subject 2, and Fig. 1C shows the calculated gravitational moment functions. Anderson et al.’s method predicts a gravitational moment of up to 6.16 N m in the measured range of motion (Fig. 1C), even though testing was conducted in a horizontal plane, so that there was no gravitational moment. Thus Anderson et al.’s method significantly overestimates the gravitational moment. As Fig. 1A demonstrates, the error in estimation of gravitational moments using Anderson et al.’s method is caused by the assumption that there is a gravity-only region. At least for the human ankle there is no region in which there is not a substantial elastic stiffness. A similar absence of a gravity-only region has also been reported for other joints, such as spinal motions segments (e.g. Thompson et al., 2003; Clarke et al, 2007) under certain conditions. It is possible that other joints, such as the hip and knee joints (which were also investigated in the article by Anderson et al.) may have a gravity-only region. In this case the new method described by Anderson et al. may provide a convenient and accurate method for correcting for gravitational moment. However, the method
Letters to the Editor / Journal of Biomechanics 43 (2010) 2653–2656
described by Anderson et al. should only be used when the presence of a gravity-only region has been confirmed.
2655
Thompson, R.E., Barker, T.M., Pearcy, M.J., 2003. Defining the neutral zone of sheep intervertebral joints during dynamic motions: an in vitro study. Clinical Biomechanics 18, 89–98.
Conflict of interest statement
E.C. Clarke n Research Fellow, The George Institute for International Health, The University of Sydney, PO Box M201, Missenden Rd., Sydney, NSW 2050, Australia E-mail address: [email protected]
No conflicts of interest to disclose.
Acknowledgement
J.H. Martin Prince of Wales Medical Research Institute, University of New South Wales, Sydney, Australia
The authors wish to thank Mr. Kevin Wang for his assistance in conducting the experiments. References
R. Herbert Research Fellow, The George Institute for International Health, The University of Sydney, PO Box M201, Missenden Rd., Sydney, NSW 2050, Australia
Anderson, D.E., Nussbaum, M.A., Madigan, M.L., 2010. A new method for gravity correction of dynamometer data and determining passive elastic moments at the joint. Journal of Biomechanics. doi:10.1016/j.jbiomech.2009.11.036. Clarke, E.C., Appleyard, R., Bilston, L.E., 2007. Immature sheep spines are more flexible than mature spines: an in vitro biomechanical study. Spine 32, 2970–2979. Hoang, P.D., Gorman, R.B., Todd, G., Gandevia, S.C., Herbert, R.D., 2005. A new method for measuring passive length–tension properties of human gastrocnemius muscle in vivo. Journal of Biomechanics 38, 1333–1341. doi:10.1016/j.jbiomech.2010.03.051
Response to ‘‘Assumption of a ‘gravity only region’ for gravity correction of passive joint moment data may be problematic’’ In our recent paper (Anderson et al., 2010) we describe a method for determining the gravitational moment in dynamometer data that also accounts for the passive elastic moment due to passive tissue deformation. Our method assumes that the passive elastic moment is negligible within a middle region of the joint range of motion, which we dubbed the ‘‘gravity-only region’’. In their letter to the Editor entitled ‘‘Assumption of a ‘gravity only region’ for gravity correction of passive joint moment data may be problematic’’, Clarke et al. present data indicating that this assumption is invalid for the ankle, and as a result the method tends to overestimate the magnitude of the gravitational moment at the ankle. We would like to thank Clark et al. for their scrutiny of our method, as this is a critical component of scientific progress. In this response we describe an addition to our method that accounts for the presence of a non-negligible passive elastic moment in the gravity-only region, and as a result should address the valid concern expressed by Clarke et al. We would also like to point out that, based upon the data presented by Clarke et al. and our own retrospection, the term ‘‘gravity-only region’’ that we used in the original work is somewhat of a misnomer for the midrange region of passive moment data. This is because the passive elastic moment in this region, while small, may still be present. As such, this region will henceforth be referred to as the ‘‘mid-range region’’. Clarke et al. reported a passive elastic moment at the ankle that is not uniformly zero in the mid-range region. Based upon their data, this moment could be reasonably approximated by a straight line. Other studies also report non-zero yet linear passive elastic moments in the mid-range region of the knee (McFaull and Lamontagne, 1998) and hip (Yoon and Mansour, 1982). To account for the presence of a non-zero passive elastic moment in this mid-range region, a linear approximation of the passive elastic moment may be incorporated into our previously published method. Thus, when fitting the passive moment data from
30 March 2010
n
Corresponding author. Tel.: + 61 2 9657 0343; fax: + 61 2 9657 0301.
the mid-range region, a line representing the passive elastic moment should be added to the sinusoidal gravitational model (Eq. (1) in Anderson et al., 2010) giving Mmidrange ¼ A1 sinðyÞ þ A2 cosðyÞ þb1 y þ b2 where b1 and b2 are coefficients for the linear passive elastic component. To estimate these coefficients, an iterative approach can be used. In the first iteration, b1 and b2 are set to zero, and the coefficients for gravitational moment (A1 and A2) are found using a least squares fit as described originally. The passive moment data is then corrected for gravity as described originally, but using the equation above with only the A1 and A2 terms (not including the b1 and b2 terms). The passive elastic moment constants (B1, k1, B2, and k2) are then found as described originally. Coefficients b1 and b2 can then be estimated by evaluating the passive elastic moment (Eq. (2) in Anderson et al., 2010) at the ends of the midrange region and determining the equation of the line between those two points. In subsequent iterations, the estimates of b1 and b2 are included when determining A1 and A2, and updated values for B1, k1, B2, k2, b1 and b2 may be found. Iteration continues until the fit is optimized (i.e. the concordance correlation coefficient reaches a maximum). It should be noted that with this approach the final equation for fitting the measured passive moment (Eq. (3) in Anderson et al., 2010) remains the same and does not include the terms b1 and b2. This is because the linear trend of the passive elastic moment within the mid-range region is accounted for in the passive elastic moment equation (Eq. (2) in Anderson et al., 2010). In testing using data from a single subject, this addition to the method reduced the magnitude of estimated gravitational moment for the ankle, knee, and hip. The concordance correlation coefficient was optimized for all three joints in three iterations. At the ankle, the largest magnitude gravitational moment in the range of motion was reduced by 1.84 N m or 18.6%. Similarly, gravitational moment was reduced by 0.69 N m (4.1%) at the knee and by 5.55 N m (8.1%) at the hip. Thus, this revised method appears to be less likely to overestimate the magnitude of the gravitational moment.