EFFECT OF TIME-DELAY IN FEEDBACK ON HUMAN POSTURAL STABILITY - A Computer Simulation Study

W. Zhao, G. Wu
Center for Locomotion Studies
Department of Mechanical Engineering
The Pennsylvania State University

Presented at the 20th Annual Meeting of the American Society of Biomechanics
Atlanta, Georgia. October 17-19, 1996

INTRODUCTION

Computer modeling and simulation has long been used in the study of mammalian coordination of movement (Camana et al., 1977, Barin, 1989, and Kuo, 1995). Such biomechanical models provide a rational basis to test and analyze experimentally based hypotheses. However, one fundamental element, time-delay in feedback, has been ignored to simplify the analysis. Feedback time-delays are substantial in mammalian sensory-motor systems primarily because of slow action potential velocities in axons (about 100 m/s maximum), central synaptic delays, and time needed to develop tension once muscle is electrically activated. This amount of time-delay might be long enough to affect the overall performance of a dynamic control system. In turn, it could influence our interpretation on the postural control mechanisms.

A NONLINEAR TIME-DELAY FEEDBACK CONTROL MODEL

The human body is represented by a one-link inverted pendulum rotated around the ankle joint (Fig. 1). The subject stands on a normal support surface and exposes to brief forward horizontal perturbations. The dynamic posture is balanced primarily by moving the body around the ankle joint, as termed by the "ankle strategy" (Horak et al., 1986).

Figure 1: Model structure.

The postural dynamics may be described by:

where all the symbols may be referred to Fig. 1. Body mass m = 75 (kg), and link length l = 1 (m).

Joint torque T is assumed to be regulated by the central nervous system which integrates sensory feedbacks from muscle receptor (sensitive to stretch and stretch speed), joint receptor (sensitive to joint rotation), and cutaneous mechanoreceptor (sensitive to normal ground reaction force). Thus,

where is the time-delay. The minimal feedback loop delay is 70 (ms), which accounts for a minimal neural delay of 30 (ms) (about the latency of the monosynaptic reflex in human calf muscles) plus an additional 40 (ms) to account for the delay between excitation of muscle and resulting increases in muscle tension. Therefore, t, time-delay, was set to be 0 for delay-free and 70 (ms) for time-delay simulations.

Term the dynamic change of normal ground reaction force, may be defined as

The stability of the dynamic system depends on feedback gains, and external perturbations. To make the dynamic postural system to be underdamped under the external perturbations, three gains were chosen k1=-1000, k2=-200, k3=10 as constants.

Three external perturbation movements are selected on actual postural experiments (Horak et al, 1990), as listed in Table 1.

The dynamic equation was solved numerically by 4th Adams-Bashforth predictor and 5th Adams-Moulton corrector integration method. The time step of integration was 0.001 (s). The initial condition is at static upright position.

SIMULATION RESULTS AND DISCUSSIONS

Under three external perturbations and the specific feedback gains, the body behaves as a underdamped dynamic system. This characteristics holds for all the simulation cases. As an example, Fig. 2 and Fig. 3 sketch the time histories of angular displacement responses and the joint reaction torques under the medium perturbation condition, respectively.

Figure 2: Angular displacement responses.

Figure 3: Joint torque at ankle joint.

The time-delay effects are clearly shown in the figures. Under the same perturbation condition and the same feedback gains, the time-delay feedback controller requires much larger joint torque, and displays larger oscillations. Furthermore, a longer setting time is required for the postural response to reach and stay within (5% of its peak value. Joint torque peak-to-peak values and the setting times under three perturbation conditions are summarized in Fig. 4 and 5, respectively. The numbers on the bars indicate the percentage increase of the time-delay cases with respect to the delay-free cases.

Figure 4: Joint torque peak-to-peak values.

Figure 5: Oscillation setting time (s).

Simulation results have shown that joint torques to balance the body are much larger ( > 35%), and setting times of oscillation are much longer ( > 25%) in time-delay cases than those in delay- free cases. Thus, it is more difficult to keep the upright balance when the feedback is delayed in time. This result might help us to understand the fall mechanism in elderly people who are usually associated with sensory degeneration and have longer feedback delays.

This founding shows that the time-delay in feedback significantly affects the performance of the dynamic posture. This suggests that, to interpret the postural control mechanisms, time-delay in feedback is not a negligible factor.

REFERENCES

Barin, K., Biol. Cybern., 61, 37-50, 1989.

Camana, P.C. et at., J. Cybern., 7, 199-255, 1977.

Horak, et al., J. Neurophys., 55, 1369-1381, 1986.

Horak, et al., Exp. Brain Res., 82, 167-177, 1990.

Kuo, A. D., IEEE Trans. Biomed. Eng., 42, 87-101, 1995.

ACKNOWLEDGMENTS

This work was supported in part by a grant from the Whitaker Foundation and by a NIH grant No. 1R29AG11602-01A2.