Contributions of muscle forces and toe-off kinematics to peak knee flexion during the swing phase of normal gait: an induced position analysis

https://doi.org/10.1016/j.jbiomech.2003.09.018Get rights and content

Abstract

A three-dimensional dynamic simulation of walking was used together with induced position analysis to determine how kinematic conditions at toe-off and muscle forces following toe-off affect peak knee flexion during the swing phase of normal gait. The flexion velocity of the swing-limb knee at toe-off contributed 30° to the peak knee flexion angle; this was larger than any contribution from an individual muscle or joint moment. Swing-limb muscles individually made large contributions to knee angle (i.e., as large as 22°), but their actions tended to balance one another, so that the combined contribution from all swing-limb muscles was small (i.e., less than 3° of flexion). The uniarticular muscles of the swing limb made contributions to knee flexion that were an order of magnitude larger than the biarticular muscles of the swing limb. The results of the induced position analysis make clear the importance of knee flexion velocity at toe-off relative to the effects of muscle forces exerted after toe-off in generating peak knee flexion angle. In addition to improving our understanding of normal gait, this study provides a basis for analyzing stiff-knee gait, a movement abnormality in which knee flexion in swing is diminished.

Introduction

During normal gait, advancement of the swing limb is enabled by flexion of the swing knee. In stiff-knee gait, a movement abnormality observed in persons with cerebral palsy and individuals after stroke, knee flexion during swing is diminished. This inhibits toe-clearance, resulting in tripping or requiring energy-inefficient compensatory movements (Sutherland and Davids, 1993). The diminished knee flexion associated with stiff-knee gait is frequently attributed to abnormal activity of the rectus femoris (Perry, 1987; Sutherland et al., 1990). Accordingly, treatments, such as a rectus femoris transfer surgery (Gage et al., 1987) or injections of neuromuscular blocking agents (Sung and Bang, 2000), are performed to alter the function of this muscle. Unfortunately, not all patients benefit from these treatments. We believe that outcomes may be variable, in part, because factors other than abnormal rectus femoris excitation limit knee flexion in some cases. Understanding the factors that produce knee flexion during the swing phase of normal gait is needed to provide a basis for investigation of the causes of limited knee flexion in stiff-knee gait.

Electromyographic data shows that muscles are active during the swing phase of gait, even though this activity is low relative to stance phase (Winter, 1991; Perry, 1992). However, activation patterns alone do not elucidate how muscles contribute to knee motion during swing due to the complex dynamics of the lower limbs (Zajac and Gordon, 1989). Studies of stiff-knee gait have characterized the roles that swing-limb joint moments and muscles play in generating swing-phase knee flexion. Riley and Kerrigan (1998) used dynamic simulation of stiff-knee kinematics to show that an increase in the hip flexion moment during swing can increase knee flexion. A muscle-driven simulation of normal swing phase (Piazza and Delp, 1996) showed that either an increase in knee extension moment or a decrease in hip flexion moment decreases knee flexion during swing. By calculating the angular accelerations of the knee induced by individual muscles, they found that the rectus femoris acts to accelerate the knee into extension during swing phase, while the biceps femoris short head, hip flexors, and ankle dorsiflexors accelerate the knee into flexion.

Joint angular velocities at toe-off also contribute to swing-phase knee flexion. Dynamic simulations of swing phase performed in the absence of muscular joint torques have approximated normal knee kinematics when the initial joint angular positions and velocities were chosen judiciously (Mochon and McMahon, 1980; Mena et al., 1981). Piazza and Delp (1996) found that the amount of knee flexion achieved during swing phase could be decreased by either increasing hip flexion velocity at toe-off or decreasing knee flexion velocity at toe-off. Goldberg et al. (2003) found that many stiff-knee subjects with cerebral palsy exhibit abnormally low angular knee flexion velocities at toe-off, and that a simulated increase in this velocity results in a normal or above normal range of knee flexion in swing.

A balance between the factors that promote and inhibit knee flexion is required to achieve adequate knee flexion during swing; stiff-knee gait results when this balance is not achieved. However, the factors that contribute to this balance have not been clearly identified or quantified. The purpose of this study was to determine the contributions of individual muscles, joint moments, gravity, Coriolis and centripetal forces, and knee flexion velocity at toe-off to peak knee flexion during the swing phase of normal gait. In particular, we assessed the importance of knee flexion velocity at toe-off relative to the importance of muscle forces exerted after toe-off. These results add to our understanding of normal gait and point to factors that could enable more effective treatment of stiff-knee gait.

Section snippets

Methods

To assess the contributions of individual muscles and other factors to peak knee flexion in swing, we calculated induced positions. As the basis for our analysis, we used a dynamic simulation of normal gait (Anderson and Pandy, 2001) in which the body was modeled as a 10 segment, 23 degree-of-freedom linkage controlled by 54 musculotendon actuators. The first 6 degrees of freedom were used to define the position and orientation of the pelvis relative to the ground. The remaining nine segments

Results

The initial angular velocity of the swing knee made the largest contribution to peak knee flexion. The initial knee flexion velocity (375° s−1) contributed 30° of knee flexion to this change in angle (Fig. 1, dashed black line). The forces applied by all actuators together (actuators include muscles and ligaments) acted to extend the knee by 12° (Fig. 1, thick black line). Gravitational, Coriolis, and centripetal forces each had little influence on peak knee flexion angle; when combined these

Discussion

We used induced positions to quantify how knee flexion velocity at toe-off and the forces due to muscles, gravity, and Coriolis and centripetal effects contribute to peak knee flexion angle during the swing phase of normal gait. Induced positions are an extension of the induced accelerations concept (Hollerbach and Flash, 1982; Zajac and Gordon, 1989). Induced accelerations have been used to understand the muscle coordination of a variety of movements, including jumping, pedaling, and walking

Acknowledgements

The authors are grateful to George Chen for comments on an earlier version of this manuscript. This work was supported by NIH grant R01-HD38962, the Whitaker Foundation, the American Association of University Women, and the International Society of Biomechanics.

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