Exploring the Contribution of Proprioceptive Reflexes to Balance Control in Perturbed Standing

Abstract

Humans control balance using different feedback loops involving the vestibular system, the visual system, and proprioception. In this article, we focus on proprioception and explore the contribution of reflexes based on force and length feedback to standing balance. In particular, we address the questions of how much proprioception alone could explain balance control, and whether one modality, force or length feedback, is more important than the other. A sagittal plane neuro-musculoskeletal model was developed with six degrees of freedom and nine muscles in each leg. A controller was designed using proprioceptive reflexes and a dead zone. No feedback control was applied inside the dead zone. Reflexes were active once the center of mass moved outside the dead zone. Controller parameters were found by solving an optimization problem, where effort was minimized while the neuro-musculoskeletal model should remain standing upright on a perturbed platform. The ground was perturbed with random square pulses in the sagittal plane with different amplitudes and durations. The optimization was solved for three controllers: using force and length feedback (base model), using only force feedback, and using only length feedback. Simulations were compared to human data from previous work, where an experiment with the same perturbation signal was performed. The optimized controller yielded a similar posture, since average joint angles were within 5 degrees of the experimental average joint angles. The joint angles of the base model, the length only model, and the force only model correlated weakly (ankle) to moderately with the experimental joint angles. The ankle moment correlated weakly to moderately with the experimental ankle moment, while the hip and knee moment were only weakly correlated, or not at all. The time series of the joint angles showed that the length feedback model was better able to explain the experimental joint angles than the force feedback model. Changes in time delay affected the correlation of the joint angles and joint moments. The objective of effort minimization yielded lower joint moments than in the experiment, suggesting that other objectives are also important in balance control, which cause an increase in effort and thus larger joint moments.

Keywords: balance control; neuromusculoskeletal simulation; perturbed standing; proprioception; reflexes.

Figure 1

Overview of the system with the reflex controller and the plant, the musculoskeletal model. The musculoskeletal model is standing on a platform, that is perturbed in the sagittal plane by a random square wave signal. The musculoskeletal model has nine degrees of freedom, but effectively six are used because the control is the same in the left and right leg. Each leg is operated by nine muscles. Each muscle is controlled by feedforward activation and reflex loops based on force and length information. These reflex loops are only active when the center of mass (COM) is outside of a dead zone inside the base of support. Three different controllers are created: the base model with length and force feedback, a length feedback model, and a force feedback model. The control outputs nine different signals, one for each muscle in both legs.

Figure 2

Correlation between the simulation controlled with length and force feedback and the experiment for the joint angles (Left) and joint moments (Right) for all three joints.

Figure 3

Joint angles as a function of time for the simulation controlled with length and force feedback (red) and experiment (black). The platform motion is shown in gray for reference.

Figure 4

A zoom-in on the joint angles between 60 and 80 s for the simulation controlled with the base model (red) and experiment (black). The platform motion is shown in gray for reference.

Figure 5

Joint moments as a function of time for the simulation controlled with length and force feedback (red) and experiment (black). The platform motion is shown in gray for reference.

Figure 6

Joint angles as a function of time for the simulation controlled with the force feedback model (red), length feedback model (blue), and experiment (black). The platform motion is shown in gray for reference.

Figure 7

A zoom-in on the joint angles between 60 and 80 s for the simulation controlled with the force feedback model (red), length feedback model (blue), and experiment (black). The platform motion is shown in gray for reference.

Figure 8

Joint moments as a function of time for the simulation controlled with length feedback (red) and experiment (black). The platform motion is shown in gray for reference.