Elsevier

Journal of Biomechanics

Volume 43, Issue 6, 19 April 2010, Pages 1055-1060
Journal of Biomechanics

Optimality principles for model-based prediction of human gait

https://doi.org/10.1016/j.jbiomech.2009.12.012Get rights and content

Abstract

Although humans have a large repertoire of potential movements, gait patterns tend to be stereotypical and appear to be selected according to optimality principles such as minimal energy. When applied to dynamic musculoskeletal models such optimality principles might be used to predict how a patient's gait adapts to mechanical interventions such as prosthetic devices or surgery. In this paper we study the effects of different performance criteria on predicted gait patterns using a 2D musculoskeletal model. The associated optimal control problem for a family of different cost functions was solved utilizing the direct collocation method. It was found that fatigue-like cost functions produced realistic gait, with stance phase knee flexion, as opposed to energy-related cost functions which avoided knee flexion during the stance phase. We conclude that fatigue minimization may be one of the primary optimality principles governing human gait.

Introduction

Dynamic simulation of human gait is a well established research technique but has been mainly applied to track observed human movements (Zajac et al., 2003). Predictive simulations of gait, on the other hand, are based solely on an assumed optimality criterion, e.g. minimal energy, which is used to solve an optimal control problem. Such simulations can help uncover underlying principles of neuromuscular coordination and have potential applications in predicting patient responses to surgical interventions (e.g. a tendon transfer procedure), in the design of prosthetic and orthotic devices, or in the reconstruction of gait for dinosaurs (Sellers and Manning, 2007). Predictive simulation has not yet found widespread application because of its high computational cost (Anderson and Pandy, 2001). In addition, there is no generally accepted optimality criterion for human gait. Previous studies have only used a single optimality criterion and it is not clear how the choice of optimality criterion affects the results.

Energy consumption appears to play a role in the selection of overall gait characteristics, such as step length and cadence, as corroborated by many experimental studies (e.g. Bertram and Ruina, 2001, Ralston, 1976). This, however, does not necessarily imply that minimal energy also governs detailed features of gait such as joint angles and muscle recruitment. Other criteria such as muscle fatigue or peak joint loads might play a role.

In particular, the knee flexion observed in the weight acceptance phase of normal gait raises questions as it requires the activation of the large Quadriceps to prevent knee collapse and may, therefore, be inconsistent with minimal energy criteria. Indeed, stance phase knee flexion appears to be absent in several energy-based predictive gait simulations (Sellers et al., 2005, Nagano et al., 2005).

In this context, the objective of this paper is to shed some light into the effects of the cost function choice on the predicted kinematics and muscle recruitment patterns of gait. A series of predictive simulations of gait are performed utilizing a family of cost functions representative of a large range of performance criteria traditionally adopted in the literature.

Section snippets

Musculoskeletal model

The musculoskeletal dynamics model (Gerritsen et al., 1998, Hardin et al., 2004) consists of seven body segments (trunk, thighs, shanks, and feet) and has nine kinematic degrees of freedom. Eight muscle groups are included in each lower extremity: Iliopsoas, Glutei, Hamstrings, Rectus Femoris, Vasti, Gastrocnemius, Soleus, and Tibialis Anterior. Each muscle is represented by a 3-element Hill-type model, using the equations from McLean et al. (2003) and muscle properties from Gerritsen et al.

Results

Fig. 1, Fig. 2 show the results for the simulations using the muscle volume-based weighting factors, ωi=Vi, corresponding to cost functions J5, J6, J7 and J8, and for the simulations using a unitary weighting factors, ωi=1, corresponding to cost functions J1, J2, J3 and J4 in Table 1, respectively. A comparison of the predicted kinematics on the left and of the ground contact forces on the right is shown for the four different exponents p (1, 2, 3 and 10) in the cost function, Eq. (9). As

Discussion

Different performance criteria led to substantially distinct gait predictions, Fig. 1, Fig. 2, Fig. 3, showing the importance of the choice of an appropriate cost function. Perhaps the most remarkable differences occur in knee flexion angle during initial and mid-stance. Cost functions J2, J3, J4 and J8 led to a maximal knee flexion of 20 or higher in mid-stance, while cost functions J1, J5, J6 and J7 led to a straight-legged pattern, with only very slight knee flexion. As explained in Section

Conflict of interest statement

None declared.

Acknowledgments

This study is supported by the NIH Grant R01 EB006735 and NSF Grant BES 0302259.

References (28)

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Parts of this work were first presented in January 2008 at the Workshop 3 — Biomechanics and Neural Control — Muscle, Limb and Brain, Mathematical Biosciences Institute, Columbus, OH.

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