Muscular coordination of knee motion during the terminal-swing phase of normal gait

Abstract

Children with cerebral palsy often walk with diminished knee extension during the terminal-swing phase, resulting in a troublesome "crouched" posture at initial contact and a shortened stride. Treatment of this gait abnormality is challenging because the factors that extend the knee during normal walking are not well understood, and because the potential of individual muscles to limit terminal-swing knee extension is unknown. This study analyzed a series of three-dimensional, muscle-driven dynamic simulations to quantify the angular accelerations of the knee induced by muscles and other factors during swing. Simulations were generated that reproduced the measured gait dynamics and muscle excitation patterns of six typically developing children walking at self-selected speeds. The knee was accelerated toward extension in the simulations by velocity-related forces (i.e., Coriolis and centrifugal forces) and by a number of muscles, notably the vasti in mid-swing (passive), the hip extensors in terminal swing, and the stance-limb hip abductors, which accelerated the pelvis upward. Knee extension was slowed in terminal swing by the stance-limb hip flexors, which accelerated the pelvis backward. The hamstrings decelerated the forward motion of the swing-limb shank, but did not contribute substantially to angular motions of the knee. Based on these data, we hypothesize that the diminished knee extension in terminal swing exhibited by children with cerebral palsy may, in part, be caused by weak hip extensors or by impaired hip muscles on the stance limb that result in abnormal accelerations of the pelvis.

Figure 1

Muscle-driven simulation of swing phase that reproduces the gait dynamics of a representative subject, Subject 4. To create this simulation, a musculoskeletal model with 21 degrees of freedom and 92 muscle-tendon actuators was scaled to the mass (31.7 kg) and height (1.4 m) of an 11-year-old subject who walked at a self-selected speed of 1.3 m/s. The simulation is shown at the instants just prior to toe-off (left), just prior to initial contact (right), and at peak swing-phase knee flexion (center).

Figure 2

Sagittal plane hip, knee, and ankle angles vs. time as determined experimentally (dotted lines) and as generated by the muscle-driven simulation (solid lines) for Subject 4. Averaged data ± 2 SD for a group of 29 unimpaired subjects (shaded region) are shown for comparison. For each of the six subjects in this study, data from gait analysis were collected for two or more successive strides. Simulations were generated that accurately tracked each subject's measured kinematics from toe-off (TO) through the end of the swing phase (IC) of the first stride.

Figure 3

Sagittal plane hip, knee, and ankle moments vs. time as determined experimentally (dotted lines) and as generated by the muscle-driven simulation (solid lines) for Subject 4. Averaged data ± 2 SD for a group of 29 unimpaired subjects (shaded region) are shown for comparison.

Figure 4

Activation patterns for 42 of the 92 muscle-tendon actuators on the swing limb (left) and stance limb (right) used to drive the simulation of Subject 4. The activation patterns of muscles with similar actions (e.g., iliacus and psoas) and muscles represented by multiple compartments (e.g., gluteus medius) are displayed on the same plot (represented by different line types). Corresponding EMG on/off times published by Perry (1992), scaled to the subject's measured stance and swing phases, are overlaid for comparison (solid bars; the thinner bars indicate inconsistencies in EMG timing as documented by Perry). Note that our model has the isometric force-generating capacity of an adult, while Subject 4 has the anthropometry of an 11-year-old child. The magnitudes of the muscle activations, therefore, reflect the relatively small activations (and forces) needed to track the subject's gait dynamics.

Figure 5

Knee flexion angle (A) and angular acceleration during the swing phase as determined experimentally (B) and as generated by the muscle-driven simulation of Subject 4 (C). Prior to toe-off, the knee is rapidly accelerated toward flexion. Shortly after toe-off, the knee stops accelerating toward flexion, and starts accelerating toward extension due to the actions of muscles and velocity-related forces. In late swing, the knee stops accelerating toward extension and starts accelerating toward flexion due to the actions of muscles. The extension phase is defined as the interval during which the knee is accelerated toward extension; the braking phase is defined as the interval during which the knee is accelerated toward flexion.

Figure 6

Angular acceleration of the swing-limb knee induced by gravity, velocity-related forces, and muscles, averaged over the extension phase (A) and over the braking phase (B), for the six subjects in this study. Subjects are numbered in order of decreasing walking speed.

Figure 7

Angular acceleration of the swing-limb knee induced by back muscles, swing-limb muscles, and stance-limb muscles, averaged over the extension phase (A) and over the braking phase (B), for the six subjects in this study. Subjects are numbered in order of decreasing walking speed.

Figure 8

Angular acceleration of the swing-limb knee induced by individual muscles or groups of muscles on the swing limb (A) and on the stance limb (B), averaged over the extension phase. DF, the ankle dorsiflexors, includes tibialis anterior, extensor digitorum longus, extensor hallucis longus, and peroneus tertius. HipFlx, the hip flexors, includes iliacus, psoas, tensor fasciae latae, and sartorius. BFSH is the biceps femoris short head. RF is the rectus femoris. VAS includes vastus medialis, vastus intermedius, and vastus lateralis. UPF, the uniarticular ankle plantarflexors, includes soleus, tibialis posterior, flexor digitorum longus, flexor hallucis longus, peroneus longus, and peroneus brevis. HipExt, the stance-limb hip extensors, includes gluteus maximus, hamstrings, and adductor magnus. HipAb, the stance-limb hip abductors, includes gluteus medius and gluteus minimus. Other includes all other muscles of the corresponding limb in the model.

Figure 9

Angular acceleration of the swing-limb knee induced by individual muscles or groups of muscles on the swing limb (A) and on the stance limb (B), averaged over the braking phase. DF, the ankle dorsiflexors, includes tibialis anterior, extensor digitorum longus, extensor hallucis longus, and peroneus tertius. BFSH is the biceps femoris short head. HipFlx, the hip flexors, includes iliacus, psoas, tensor fasciae latae, and sartorius. HAMS, the hamstrings, includes semimembranosus, semitendinosus, and biceps femoris long head. VAS includes vastus medialis, vastus intermedius, and vastus lateralis. UPF, the uniarticular ankle plantarflexors, includes soleus, tibialis posterior, flexor digitorum longus, flexor hallucis longus, peroneus longus, and peroneus brevis. HipExt, the swing-limb hip extensors, includes gluteus maximus and adductor magnus. HipAd, the stance-limb hip adductors, includes pectineus, adductor brevis, adductor longus, and gracilis. HipAb, the stance-limb hip abductors, includes gluteus medius and gluteus minimus. Other includes all other muscles of the corresponding limb in the model.

Figure 10

Motions of the pelvis and swing limb induced by all stance-limb muscles during the extension phase (A) and braking phase (B). Straight arrows represent translational accelerations, and curved arrows represent angular accelerations. All arrows are scaled proportional to their magnitudes. Accelerations of the thigh are calculated relative to the pelvis. Stance-limb muscles accelerated the center of mass of the entire model (not shown) upward and backward during the extension phase, and upward and forward during the braking phase, consistent with previous studies (Liu et al., 2006).

Figure 11

Motions of the pelvis and swing limb induced by all swing-limb muscles during the extension phase (A) and braking phase (B). Straight arrows represent translational accelerations, and curved arrows represent angular accelerations. All arrows are scaled proportional to their magnitudes. Accelerations of the thigh are calculated relative to the pelvis, and accelerations of the shank are calculated relative to the thigh.

Figure 12

Fore-aft acceleration of the swing-limb shank induced by groups of muscles on the swing limb, averaged over the last half of the braking phase. HAMS, the hamstrings, includes the semimembranosus, semitendinosus, and biceps femoris long head. DF, the ankle dorsiflexors, includes tibialis anterior, extensor digitorum longus, extensor hallucis longus, and peroneus tertius. HipExt, the hip extensors, includes gluteus maximus and adductor magnus. BFSH is the biceps femoris short head. HipFlx, the hip flexors, includes iliacus, psoas, tensor fasciae latae, and sartorius. Other includes all other muscles of the swing limb in the model.