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Determination of vertical ground reaction forces under each foot during walking a
a
G.M. Meurisse & G.J. Bastien a
Université catholique de Louvain, Louvain-la-Neuve, 1348, Belgium Published online: 30 Jul 2014.
Click for updates To cite this article: G.M. Meurisse & G.J. Bastien (2014) Determination of vertical ground reaction forces under each foot during walking, Computer Methods in Biomechanics and Biomedical Engineering, 17:sup1, 110-111, DOI: 10.1080/10255842.2014.931483 To link to this article: http://dx.doi.org/10.1080/10255842.2014.931483
PLEASE SCROLL DOWN FOR ARTICLE Taylor & Francis makes every effort to ensure the accuracy of all the information (the “Content”) contained in the publications on our platform. However, Taylor & Francis, our agents, and our licensors make no representations or warranties whatsoever as to the accuracy, completeness, or suitability for any purpose of the Content. Any opinions and views expressed in this publication are the opinions and views of the authors, and are not the views of or endorsed by Taylor & Francis. The accuracy of the Content should not be relied upon and should be independently verified with primary sources of information. Taylor and Francis shall not be liable for any losses, actions, claims, proceedings, demands, costs, expenses, damages, and other liabilities whatsoever or howsoever caused arising directly or indirectly in connection with, in relation to or arising out of the use of the Content. This article may be used for research, teaching, and private study purposes. Any substantial or systematic reproduction, redistribution, reselling, loan, sub-licensing, systematic supply, or distribution in any form to anyone is expressly forbidden. Terms & Conditions of access and use can be found at http:// www.tandfonline.com/page/terms-and-conditions
Computer Methods in Biomechanics and Biomedical Engineering, 2014 Vol. 17, No. S1, 110–111, http://dx.doi.org/10.1080/10255842.2014.931483
Determination of vertical ground reaction forces under each foot during walking G.M. Meurisse* and G.J. Bastien Physiology and Biomechanics of Locomotion Laboratory, Institute of Neuroscience, Universite´ catholique de Louvain, Louvain-la-Neuve 1348, Belgium Keywords: gait; vertical GRF; reconstruction
Downloaded by [Erciyes University] at 11:48 26 December 2014
1.
Introduction
In gait analysis, the quantification of the ground reaction force (GRF) acting under each foot is often required for a deep and complete analysis of the double contact phase (DC) in walking. However, using a single force plate or an instrumented treadmill, only the resultant GRF acting on both feet is available. The aim of this study is to develop an algorithm allowing (a) the detection of the limits of DC: from the foot contact (FC) of the front foot to the foot off (FO) of the rear foot and (b) the reconstruction of the individual vertical GRF profiles of each foot.
2.
single step; the limits of a step being determined when the fore –aft GRF is equal to zero during the simple contact phase. As illustrated in Figure 1(b), FC corresponds to the minimum of dpath curve and FO to its maximum. The vertical GRF reconstruction, inspired from Davis and Cavanagh (1993), is based on the three equations. One describing the equilibrium of forces in the vertical direction: F sum ¼ F back þ F front Two describing the equilibrium of moments about a transversal axis (Mx) in the force plate top surface horizontal plane where the CoP is calculated:
Methods
Twenty-seven subjects walked across multiple plates of the same size at speeds between 0.83 and 1.94 ms21. The data were collected on force plates measuring forces in three directions (vertical, foreaft and lateral). The data were collected independently at two locations, and two different models of force plates were used: either eight 1000 £ 1000 mm force plates as described in Genin et al study (2010) or four Arsalis 800*500 mm force plates (Arsalis SPRL., Glabais, Belgium). A complete step was selected for analysis only when the feet were on different force plates and when the subject was walking at a relatively constant speed. The vertical GRFs components were summed to obtain vertical GRFs resultant values (Fsum) in order to simulate that they were collected with a single force plate. The GRFs produced by the back leg (Fback) and produced by the front leg (Ffront) are reconstructed from the Fsum using a mathematical algorithm detailed below. The FC and FO are determined by computation of the distance covered by the centre of pressure (CoP) (PathCoP) and by the difference between PathCoP and the reference line on one step (dpath, see Figure 1(a)). The reference line simply joins the initial and final PathCoP value on one
*Corresponding author. Email: [email protected] q 2014 Taylor & Francis
M x ¼ CoPyback *F back þ CoPyfront *F front M x ¼ CoPysum *F sum where: CoPysum is the point of application of Fsum in the fore– aft direction. CoPyback is the point of application in the fore – aft direction of Fback, the force applied by the rear foot. During DC, CoPyback is defined as CoPysum measured just before FC. CoPyfront is the point of application in the fore – aft direction of Ffront, the force applied by the front foot. During DC, CoPyfront is defined as CoPysum just after FO.
3.
Results and discussion
In order to quantify the quality of the reconstruction, we compared the reconstructed GRFs with the real forces measured with individual force plates. We observed an absolute mean difference of 1.76% for our set of 27 subjects (^ 0.77%, n ¼ 374, max ¼ 4.72%). It is noteworthy that this difference error is only due to the uncertainty of the CoP under each foot during the whole
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111
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the fore – aft axis. Indeed, the walking progression of the subject implies a displacement in the fore – aft direction; and thus clear different CoP locations for each foot along the fore –aft axis. While on the other hand, the CoP locations along the lateral axis can be similar under each foot when the subject walks with a narrowed sustentation base and, in that case, the computation of the individual forces is flawed. Also, the generalisation of this method to the individual lateral and fore – aft forces reconstruction cannot be done ‘as is’ since both components influence the equilibrium of moments and the equations become more complex.
Figure 1. From top to bottom as function of time. (a) The distance covered by the centre of pressure (PathCoP). (b) The difference between PathCoP and the reference line (dpath). (c) The total and individual reconstructed GRFs and jF 2F measured j (d) The relative error calculated as 1F ð%Þ ¼ reconstructed F max where Fmax is the maximum measured force under the foot. GRF, ground reaction force; DC, double contact phase; FC, foot contact; FO, foot off.
period of DC and furthermore, is independent from the walking speed. Unlike Davis and Cavanagh (1993), the equilibrium of the moment is calculated relative to the lateral axis and not
4. Conclusions The reconstructed GRFs are equal to the measured forces within 2% accuracy. The proposed algorithm yields an excellent reconstruction of the individual vertical GRF under each foot. The observed maximal error in our data is below 5% and much lower compared with the force reconstruction proposed by Ballaz et al. (2013) using spline functions.
References Ballaz L, Raison M, Detrembleur C. 2013. Decomposition of the vertical ground reaction forces during gait on a single force plate. J Musculoskelet Neuronal Interact. 13(2):236– 243. Davis BL, Cavanagh PR. 1993. Decomposition of superimposed ground reaction forces into left and right force profiles. J Biomech. 26(4– 5):593– 597. doi: 0021-9290(93)90020-F [pii] Genin JJ, Willems PA, Cavagna GA, Lair R, Heglund NC. 2010. Biomechanics of locomotion in Asian elephants. J Exp Biol. 213(5):694– 706. doi: 10.1242/jeb.035436
Computer Methods in Biomechanics and Biomedical Engineering Publication details, including instructions for authors and subscription information: http://www.tandfonline.com/loi/gcmb20
Determination of vertical ground reaction forces under each foot during walking a
a
G.M. Meurisse & G.J. Bastien a
Université catholique de Louvain, Louvain-la-Neuve, 1348, Belgium Published online: 30 Jul 2014.
Click for updates To cite this article: G.M. Meurisse & G.J. Bastien (2014) Determination of vertical ground reaction forces under each foot during walking, Computer Methods in Biomechanics and Biomedical Engineering, 17:sup1, 110-111, DOI: 10.1080/10255842.2014.931483 To link to this article: http://dx.doi.org/10.1080/10255842.2014.931483
PLEASE SCROLL DOWN FOR ARTICLE Taylor & Francis makes every effort to ensure the accuracy of all the information (the “Content”) contained in the publications on our platform. However, Taylor & Francis, our agents, and our licensors make no representations or warranties whatsoever as to the accuracy, completeness, or suitability for any purpose of the Content. Any opinions and views expressed in this publication are the opinions and views of the authors, and are not the views of or endorsed by Taylor & Francis. The accuracy of the Content should not be relied upon and should be independently verified with primary sources of information. Taylor and Francis shall not be liable for any losses, actions, claims, proceedings, demands, costs, expenses, damages, and other liabilities whatsoever or howsoever caused arising directly or indirectly in connection with, in relation to or arising out of the use of the Content. This article may be used for research, teaching, and private study purposes. Any substantial or systematic reproduction, redistribution, reselling, loan, sub-licensing, systematic supply, or distribution in any form to anyone is expressly forbidden. Terms & Conditions of access and use can be found at http:// www.tandfonline.com/page/terms-and-conditions
Computer Methods in Biomechanics and Biomedical Engineering, 2014 Vol. 17, No. S1, 110–111, http://dx.doi.org/10.1080/10255842.2014.931483
Determination of vertical ground reaction forces under each foot during walking G.M. Meurisse* and G.J. Bastien Physiology and Biomechanics of Locomotion Laboratory, Institute of Neuroscience, Universite´ catholique de Louvain, Louvain-la-Neuve 1348, Belgium Keywords: gait; vertical GRF; reconstruction
Downloaded by [Erciyes University] at 11:48 26 December 2014
1.
Introduction
In gait analysis, the quantification of the ground reaction force (GRF) acting under each foot is often required for a deep and complete analysis of the double contact phase (DC) in walking. However, using a single force plate or an instrumented treadmill, only the resultant GRF acting on both feet is available. The aim of this study is to develop an algorithm allowing (a) the detection of the limits of DC: from the foot contact (FC) of the front foot to the foot off (FO) of the rear foot and (b) the reconstruction of the individual vertical GRF profiles of each foot.
2.
single step; the limits of a step being determined when the fore –aft GRF is equal to zero during the simple contact phase. As illustrated in Figure 1(b), FC corresponds to the minimum of dpath curve and FO to its maximum. The vertical GRF reconstruction, inspired from Davis and Cavanagh (1993), is based on the three equations. One describing the equilibrium of forces in the vertical direction: F sum ¼ F back þ F front Two describing the equilibrium of moments about a transversal axis (Mx) in the force plate top surface horizontal plane where the CoP is calculated:
Methods
Twenty-seven subjects walked across multiple plates of the same size at speeds between 0.83 and 1.94 ms21. The data were collected on force plates measuring forces in three directions (vertical, foreaft and lateral). The data were collected independently at two locations, and two different models of force plates were used: either eight 1000 £ 1000 mm force plates as described in Genin et al study (2010) or four Arsalis 800*500 mm force plates (Arsalis SPRL., Glabais, Belgium). A complete step was selected for analysis only when the feet were on different force plates and when the subject was walking at a relatively constant speed. The vertical GRFs components were summed to obtain vertical GRFs resultant values (Fsum) in order to simulate that they were collected with a single force plate. The GRFs produced by the back leg (Fback) and produced by the front leg (Ffront) are reconstructed from the Fsum using a mathematical algorithm detailed below. The FC and FO are determined by computation of the distance covered by the centre of pressure (CoP) (PathCoP) and by the difference between PathCoP and the reference line on one step (dpath, see Figure 1(a)). The reference line simply joins the initial and final PathCoP value on one
*Corresponding author. Email: [email protected] q 2014 Taylor & Francis
M x ¼ CoPyback *F back þ CoPyfront *F front M x ¼ CoPysum *F sum where: CoPysum is the point of application of Fsum in the fore– aft direction. CoPyback is the point of application in the fore – aft direction of Fback, the force applied by the rear foot. During DC, CoPyback is defined as CoPysum measured just before FC. CoPyfront is the point of application in the fore – aft direction of Ffront, the force applied by the front foot. During DC, CoPyfront is defined as CoPysum just after FO.
3.
Results and discussion
In order to quantify the quality of the reconstruction, we compared the reconstructed GRFs with the real forces measured with individual force plates. We observed an absolute mean difference of 1.76% for our set of 27 subjects (^ 0.77%, n ¼ 374, max ¼ 4.72%). It is noteworthy that this difference error is only due to the uncertainty of the CoP under each foot during the whole
Computer Methods in Biomechanics and Biomedical Engineering
111
Downloaded by [Erciyes University] at 11:48 26 December 2014
the fore – aft axis. Indeed, the walking progression of the subject implies a displacement in the fore – aft direction; and thus clear different CoP locations for each foot along the fore –aft axis. While on the other hand, the CoP locations along the lateral axis can be similar under each foot when the subject walks with a narrowed sustentation base and, in that case, the computation of the individual forces is flawed. Also, the generalisation of this method to the individual lateral and fore – aft forces reconstruction cannot be done ‘as is’ since both components influence the equilibrium of moments and the equations become more complex.
Figure 1. From top to bottom as function of time. (a) The distance covered by the centre of pressure (PathCoP). (b) The difference between PathCoP and the reference line (dpath). (c) The total and individual reconstructed GRFs and jF 2F measured j (d) The relative error calculated as 1F ð%Þ ¼ reconstructed F max where Fmax is the maximum measured force under the foot. GRF, ground reaction force; DC, double contact phase; FC, foot contact; FO, foot off.
period of DC and furthermore, is independent from the walking speed. Unlike Davis and Cavanagh (1993), the equilibrium of the moment is calculated relative to the lateral axis and not
4. Conclusions The reconstructed GRFs are equal to the measured forces within 2% accuracy. The proposed algorithm yields an excellent reconstruction of the individual vertical GRF under each foot. The observed maximal error in our data is below 5% and much lower compared with the force reconstruction proposed by Ballaz et al. (2013) using spline functions.
References Ballaz L, Raison M, Detrembleur C. 2013. Decomposition of the vertical ground reaction forces during gait on a single force plate. J Musculoskelet Neuronal Interact. 13(2):236– 243. Davis BL, Cavanagh PR. 1993. Decomposition of superimposed ground reaction forces into left and right force profiles. J Biomech. 26(4– 5):593– 597. doi: 0021-9290(93)90020-F [pii] Genin JJ, Willems PA, Cavagna GA, Lair R, Heglund NC. 2010. Biomechanics of locomotion in Asian elephants. J Exp Biol. 213(5):694– 706. doi: 10.1242/jeb.035436
