Modular control of human walking: a simulation study

Abstract

Recent evidence suggests that performance of complex locomotor tasks such as walking may be accomplished using a simple underlying organization of co-active muscles, or "modules", which have been assumed to be structured to perform task-specific biomechanical functions. However, no study has explicitly tested whether the modules would actually produce the biomechanical functions associated with them or even produce a well-coordinated movement. In this study, we generated muscle-actuated forward dynamics simulations of normal walking using muscle activation modules (identified using non-negative matrix factorization) as the muscle control inputs to identify the contributions of each module to the biomechanical sub-tasks of walking (i.e., body support, forward propulsion, and leg swing). The simulation analysis showed that a simple neural control strategy involving five muscle activation modules was sufficient to perform the basic sub-tasks of walking. Module 1 (gluteus medius, vasti, and rectus femoris) primarily contributed to body support in early stance while Module 2 (soleus and gastrocnemius) contributed to both body support and propulsion in late stance. Module 3 (rectus femoris and tibialis anterior) acted to decelerate the leg in early and late swing while generating energy to the trunk throughout swing. Module 4 (hamstrings) acted to absorb leg energy (i.e., decelerate it) in late swing while increasing the leg energy in early stance. Post-hoc analysis revealed an additional module (Module 5: iliopsoas) acted to accelerate the leg forward in pre- and early swing. These results provide evidence that the identified modules can act as basic neural control elements that generate task-specific biomechanical functions to produce well-coordinated walking.

Figure 1

The 2D-sagittal plane musculoskeletal model and optimization framework. The model consistedof a trunk (head, arms, torso and pelvis) and left and right legs (femur, tibia, patella, rear-foot, mid-foot and toes). Only the 13 muscle groups for the right leg are shown, which included GMED (anterior and posterior portion of gluteus medius), IL (iliacus, psoas), RF (rectus femoris), VAS (3-component vastus), TA (tibialis anterior, peroneus tertius), PER (peroneus longus, peroneus brevis), FLXDG (flexor hallucis longus, flexor digitorum longus), EXTDG (extensor hallucis longus, extensor digitorum longus), SOL (soleus, tibialis posterior), GAS (medial and lateral gastrocnemius), BFsh (biceps femoris short head), HAM (medial hamstrings, biceps femoris long head) and GMAX (gluteus maximus, adductor magnus). The Optimization Algorithm fine-tuned the muscle excitation patterns for each muscle group to produce a well-coordinated walking pattern that emulated the experimental data. The excitation patterns were defined by the muscle modules or a block pattern if no EMG data were available. Each Muscle Excitation pattern was parameterized by three parameters, the excitation onset(x₁), offset (x₂) and magnitude (x₃) that allowed the pattern to be scaled in magnitude and temporally shifted during the optimization. As seen in the resulting Optimal Modular Control patterns, the optimization shifted the timing very little. For comparison purposes, the experimental module patterns were normalized to the peak simulation excitation magnitude. Note, the RF excitation is the summed contribution from Modules 1 and 3. The muscle excitation patterns for the small muscles that primarily control the foot (PER, FLXDG, EXTDG) were omitted in the Optimal Module Control comparison. The Compare Output to Experimental Data shows how well the simulation emulated the experimental hip, knee and ankle joint angles, and vertical and horizontal GRFs over the gait cycle (i.e., from right heel-strike to right heel-strike).

Figure 2

Muscle module weightings and activation timing profiles while control subjects walked at 1.2 m/s derived from NNMF. A) Muscle weightings indicate the representation of each muscle within the corresponding module. The black region over each muscle is composed of 28 separate bars (14 subjects × 2 legs) that would form a perfect rectangle if the muscle was maximally associated with that module for both legs in all subjects. B) Activation timing profiles indicate when a muscle module is active during the gait cycle. Gray lines indicate individual profiles for each leg of each subject (28 total, normalized to their maximum value). Thick black lines indicate the group average.

Figure 3

Module contributions to the walking subtasks of body support, forward propulsion and leg swing in the beginning of early stance (∼15% gait cycle), late stance (∼45% gait cycle), early swing (∼70 % gait cycle) and late swing (∼85% gait cycle). Arrows acting on the center-of-mass symbol indicate the resultant module contributions to the horizontal and vertical ground reactions forces that act to accelerate the body center-of-mass to provide body support and forward propulsion. Net energy flow by each individual module to the trunk or leg (“net” total of all modules also presented for leg) is denoted by a “+” (energy increase) or “-” (energy decrease). In early stance, Modules 1 and 2 provide body support while acting to decelerate forward motion while Module 4 and all Other muscles combined to provide a little body support and forward propulsion. In late stance, Module 2 provides both body support and forward propulsion. All Others includes the contributions by BFsh, IL, PER and GMAX.

Figure 4

Module contributions to the horizontal and vertical ground reaction forces. All Others includes the contributions by BFsh, IL, PER and GMAX.

Figure 5

Mechanical power delivered to the trunk and ipsilateral leg by each module over the gait cycle. Total is the summed mechanical power delivered to the trunk, ipsilateral and contralateral leg (small and not shown). All Others includes the contributions by BFsh, IL, PER and GMAX. Positive (negative) power indicates the muscle acted to accelerate (decelerate) the leg in the direction of its motion.

Figure 6

Mechanical power delivered to the trunk and ipsilateral leg by IL over the gait cycle. Positive (negative) power indicates the muscle acted to accelerate (decelerate) the leg in the direction of its motion.