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Individual contributions of the lower limb muscles to the
position of the centre of pressure during gait
Florent Moissenet, Raphaël Dumas
To cite this version:
Florent Moissenet, Raphaël Dumas. Individual contributions of the lower limb muscles to the position of the centre of pressure during gait. 42ème congrès de la Société de Biomécanique, Nov 2017, REIMS, France. pp. S137-S138, �10.1080/10255842.2017.1382899�. �hal-01769107�
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Computer Methods in Biomechanics and Biomedical
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Individual contributions of the lower limb muscles
to the position of the centre of pressure during
gait
F. Moissenet & R. Dumas
To cite this article: F. Moissenet & R. Dumas (2017) Individual contributions of the lower limb muscles to the position of the centre of pressure during gait, Computer Methods in Biomechanics and Biomedical Engineering, 20:sup1, 137-138, DOI: 10.1080/10255842.2017.1382899
To link to this article: https://doi.org/10.1080/10255842.2017.1382899
© 2017 The Author(s). Published by Informa UK Limited, trading as Taylor & Francis Group
Published online: 27 Oct 2017.
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Computer methods in BiomeChaniCs and BiomediCal engineering, 2017 Vol. 20, no. s1, s137–s138
https://doi.org/10.1080/10255842.2017.1382899
Individual contributions of the lower limb muscles to the position of the centre of
pressure during gait
F. Moisseneta and R. Dumasb
alaboratoire d’analyse du mouvement et de la posture, Centre national de rééducation Fonctionnelle et de réadaptation – rehazenter,
luxembourg; biFsttar, lBmC, univ lyon, université Claude Bernard lyon 1, lyon, France
KEYWORDS musculoskeletal modelling; inverse dynamics; pseudo-inverse method; non-central axis; level ground walking
1. Introduction
To better understand the mechanisms underlying the dynamics of gait, it is important to investigate how individual muscles contribute to the ground reaction force and to the acceleration of the centre of mass (i.e. progression, balance, and support). This was analysed in numerous studies using forward dynamics and perturbation analysis (e.g. Arnold et al. 2007; Allen and Neptune 2012; Correa and Pandy 2013). Only one study (Moissenet et al. 2017) investigated how individual muscles contribute to ground reaction force and moment using inverse dynamics (Moissenet et al. 2014) and pseudo-inverse (Lin et al. 2011) methods. Still, only the con-tributions to the vertical component of the ground reaction moment were analysed (Moissenet et al. 2017) while knowing all the components of the ground reaction force and moment opened the way to the further analysis of the position of the centre of pressure (CoP). The objective of the present study is, therefore, to investigate the individual muscle contributions to the position of the CoP. The results of this study may give access to a deeper understanding of the impacts of motor impairments on CoP and on the dynamic balance during gait in a pathological context.
2. Methods
A previously described (Moissenet et al. 2014, 2016) 3D lower limb musculoskeletal model consisting of five segments (i.e. pelvis, thigh, patella, shank and foot) and 5 joint degrees of freedom was used to perform this study and leaded to the dynamics equation: 𝐆 ̈𝐐 + 𝐊T𝛌 = 𝐑 + 𝐏 + 𝐋𝐟, where 𝐆 was the matrix of generalised masses, 𝐐̈ was the vector of
generalised accelerations, 𝐊 was the Jacobian matrix of both
kinematic and rigid body constraints, 𝛌 was the vector of
Lagrange multipliers, 𝐑 was the vector of generalised ground
reaction (i.e. including the vectors of force 𝐅0and moment 𝐌0 at the CoP), 𝐏 was the vector of generalised weights, 𝐋
was the matrix of generalised muscular lever arms and 𝐟 was
the vector of musculo-tendon forces.
The musculo-tendon forces and a selection of joint con-tact, ligament and bone forces were introduced in a one-step optimisation procedure in order to solve the muscular redundancy problem:
where J was the objective function, 𝐖 a diagonal matrix
composed of the optimisation weights associated to the unknowns [ 𝐟 𝛌1
]T
and 𝐙𝐊T
2 the orthogonal basis of
the null space of the Jacobian sub-matrix 𝐊T2. As an inverse
dynamics procedure, no foot-floor contact model is required. Once the musculo-tendon forces were computed, a pseu-do-inverse method (Moissenet et al. in press; Lin et al. 2011) was used to compute the contributions of each musculo-ten-don force to ground reaction force and moment at the CoP,
𝐅f
j
0, 𝐌 fj
0. The contributions of each segment weight 𝐅 mi𝐠
0 , 𝐌 mi𝐠
0
was estimated a similar way. In a previous study (Moissenet et al. in press), these contributions to the ground reaction force were compared to the ones reported in the literature (Pandy and Andriacchi 2010; Lin et al. 2011) and demon-strated good agreements.
In the present study, we further analysed the contribu-tions of each musculo-tendon force (and segment weight) to the position of the CoP. The position of this “induced” CoP
min ⎡ ⎢ ⎢ ⎢ ⎣ 𝐟 𝛌1 ⎤ ⎥ ⎥ ⎥ ⎦ J = 1 2 � 𝐟 𝛌1 �T 𝐖 � 𝐟 𝛌1 � subject to : ⎧ ⎪ ⎪ ⎨ ⎪ ⎪ ⎩ 𝐙T𝐊 2 � 𝐋 −𝐊T1 �� 𝐟 𝛌1 � =𝐙T𝐊 2 � 𝐆 ̈𝐐 − 𝐏 − 𝐑� � 𝐟 𝛌1 � ≥𝟎
© 2017 the author(s). published by informa uK limited, trading as taylor & Francis group.
this is an open access article distributed under the terms of the Creative Commons attribution license (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
CONTACT F. moissenet florent.moissenet@rehazenter.lu
S138 F. MOISSENET AND R. DUMAS
This description seems in line with the previous studies (e.g. Pandy and Andriacchi 2010) describing the individual muscle contributions to support (e.g. hip flexors and exten-sors), balance (e.g. hip adductors) and progression (e.g. ankle plantarflexors). It was interesting to observe that the contri-butions were distributed on both medial and lateral sides of the CoP trajectory. Moreover, most of the contributions were shifted and compressed posteriorly with respect to the CoP trajectory. It is the muscles spanning the ankle joint that mainly contribute to the anterior displacement of the CoP at the end of the stance.
This study has some limitations (i.e. musculoskeletal model of the right lower limb only, one subject, one motor task) and a more detailed analysis of the individual muscles and of the timing of their contributions is needed.
4. Conclusions
The individual muscle contributions to the position of the centre of pressure provide useful insights into the dynamics of human walking. The contributions were largely spread, mostly shifted and compressed posteriorly with respect to the CoP trajectory except for the plantarflexors.
Acknowledgements
No financial or personal relationship with other people or or-ganization have inappropriately influenced this study.
References
Allen JL, Neptune RR. 2012. Three-dimensional modular control of human walking. J Biomech. 45:2157–2163. Arnold AS, Schwartz MH, Thelen DG, Delp SL. 2007.
Contributions of muscles to terminal-swing knee motions vary with walking speed. J Biomech. 40:3660–3671.
Correa TA, Pandy MG. 2013. On the potential of lower limb muscles to accelerate the body’s centre of mass during walking. Comput Method Biomech Biomed Eng. 16:1013– 1021.
Lin YC, Kim HJ, Pandy MG. 2011. A computationally efficient method for assessing muscle function during human locomotion. Int J Numer Methods Biomed Eng. 27:436–449. Moissenet F, Chèze L, Dumas R. 2014. A 3D lower limb
musculoskeletal model for simultaneous estimation of musculo-tendon, joint contact, ligament and bone forces during gait. J Biomech. 47:50–58.
Moissenet F, Chèze L, Dumas R. 2016. Influence of the level of muscular redundancy on the validity of a musculoskeletal model. J Biomech Eng. 138:021019–021019–021016. Moissenet F, Chèze L, Dumas R. 2017. Individual muscle
contributions to ground reaction and to joint contact, ligament and bone forces during normal gait. Multibody Syst Dyn. 40:193–211.
Pandy MG, Andriacchi TP. 2010. Muscle and joint function in human locomotion. Annu Rev Biomed Eng. 12:401–433. Sardain P, Bessonnet G. 2004. Forces acting on a biped robot.
Center of pressure-zero moment point. IEEE Trans Syst Man Cybern A. 34:630–637.
(x0fj, yf0j) was obtained by the equations of the non-central
axis (Sardain and Bessonnet 2004):
where (x0, y0) was the position of the measured CoP and (X0, Y0, Z0) were the axes of the inertial coordinate system (ICS, with Y0 vertical) in which the generalised coordinates Q, the position of the CoP and the ground reaction force and moment (F0, M0 and 𝐅f0j, 𝐌f0j) were expressed. In the present
study, the individual muscle contributions were pooled in hip flexors, extensors, adductors, and abductors, knee flexors and extensors, and ankle plantarflexors and dorsiflexors.
This methods was applied to one gait cycle taken from our previous study (Moissenet et al. in press), i.e. on a male subject of 30 year old, 65 kg, 165 cm walking at preferred speed over level ground. The origin of the ICS was defined at the corner of the force plate.
3. Results and discussion
The contributions of a selection of musculo-tendon force and segment weight to the position of the CoP are depicted in Figure 1. The contributions of the weights of all segments and of the hip adductors tended to be inward with respect to the CoP trajectory, shifted and compressed posteriorly, and diverging medially at the end of the stance. The hip flexors and extensors demonstrated the more spread contributions, going both inward and outward during the stance. The contributions of the hip adductors, knee flexors and extensors were more generally aligned with the CoP trajectory, compressed poste-riorly but shifted laterally, except for the hip abductors which had a short forward contribution almost superimposed with the CoP at the very end of the stance. The contributions of the ankle plantarflexors and dorsiflexors were the more aligned with CoP trajectory and were shifted anteriorly.
⎛ ⎜ ⎜ ⎜ ⎝ xf0j 0 z0fj ⎞ ⎟ ⎟ ⎟ ⎠ = 𝐅 fj 0 ×𝐌 fj 0 � 𝐅f j 0 �2 − � 𝐅f j 0 ⋅ 𝐌 fj 0 � 𝐅f j 0 ×𝐘0 � 𝐅f j 0 ⋅ 𝐘0 �� 𝐅f j 0 �2 + ⎛ ⎜ ⎜ ⎜ ⎝ x0 0 z0 ⎞ ⎟ ⎟ ⎟ ⎠
Figure 1. Contributions of pooled musculo-tendon forces and segment weights to the position of the Cop.
