Modeling the neuro-mechanics of human balance when recovering from a fall: a continuous-time approach

Abstract

Background: Balance control deteriorates with age and nearly 30% of the elderly population in the United States reports stability problems. Postural stability is an integral task to daily living reliant upon the control of the ankle and hip. To this end, the estimation of joint parameters can be a useful tool when analyzing compensatory actions aimed at maintaining postural stability.

Methods: Using an analytical approach, this study expands on previous work and analyzes a two degrees of freedom human model. The first two modes of vibration of the system are represented by the neuro-mechanical parameters of a second-order, time-varying Kelvin-Voigt model actuated at the ankle and hip. The model is tested using a custom double inverted pendulum and healthy volunteers who were subjected to a positional step-like perturbation during quiet standing. An in silico sensitivity analysis of the influence of inertial parameters was also performed.

Results: The proposed method is able to correctly identify the time-varying visco-elastic parameters of of a double inverted pendulum. We show that that the parameter estimation method can be applied to standing humans. These results appear to identify a subject-independent strategy to control quiet standing that combines both the modulation of stiffness, and the use of an intermittent control.

Conclusions: This paper presents the analysis of the non-linear system of differential equations representing the control of lumped muscle-tendon units. It utilizes motion capture measurements to obtain the estimates of the system's control parameters by constructing a simple time-dependent regressor for estimating the time-varying parameters of the control with a single perturbation. This work is a step forward into the understanding of the neuro-mechanical control parameters of human recovering from a fall. In previous literature, the analysis is either restricted to the first vibrational mode of an inverted-pendulum model or assumed to be time-invariant. The proposed method allows for the analysis of hip related movement for stability control and highlights the importance of core training.

Keywords: Dynamic model; Human balance; Parameter estimation.

Fig. 1

Mechanical representation of the hip balancing strategy: a A sagittal view of the hip balancing strategy, while b is a representation of the human body modeled as a double inverted pendulum

Fig. 2

Prototype built to validate the parameter estimation procedure. The stiffness at the joints was simulated using linear springs between the joints. To reduce friction, all contact surfaces were covered with Teflon

Fig. 3

Stiffness around the joints axis of the constructed double pendulum. The blue line shows the estimated stiffness value considering constant linear springs and a changing moment arm. The black markers represent the estimated parameter obtained using a KF. The dashed red line shows the best fit of the estimated parameter values as a function of joint angle

Fig. 4

Estimated values for the visco-elastic parameters obtained using simulated data. The continuous blue line is the parameter value used to generate the data set, the dashed red line is parameter value estimated using a least squares approach, and the yellow line gives the time changing values obtained using a Kalman filter estimation

Fig. 5

Estimation errors for three simulated subjects with three different rise velocities on the joint stiffness parameters

Fig. 6

Experimental visco-elastic parameters estimation for a representative subject. a Stiffness of the ankle joint $k_1$. b Stiffness of the hip joint $k_2$. c Damping of the ankle joint $c_1$. d Damping of the hip joint $c_2$

Fig. 7

Estimated joint stiffness as a function of joint angle for 10 human subjects. Each subject is represented by a different colored line while the large circular marker represents the estimation for the parameter value at the first iterations of the Kalman filter. a Stiffness of the ankle joint $k_1$ with respect to the measured ankle joint angle. b Stiffness of the ankle joint $k_1$ with respect to the measured hip joint angle. c Stiffness of the hip joint $k_2$ with respect to the measured ankle joint angle. d Stiffness of the ankle joint $k_2$ with respect to the measured hip joint angle

Fig. 8

Estimated segment orientation obtained through a simulation. As shown in c the ankle stiffness was allowed to take negative values. Results a and b show that this strategy can result in a stable system. Additionally c shows that the implemented KF is capable of tracking joint stiffness very rapidly

Fig. 9

Different rise velocities of joint stiffness as a function of the parameter $\eta$

Fig. 10

Simulated angular value for the orientation of each of the model’s segment. The full blue line represents the noisy angular values while the red dashed line shows the values after the application of the zero-phase Butterworth filter

Fig. 11

Experimental setup for the estimation of joint visco-elastic parameters using the hold and release method. a Shows the subject leaning onto the examiner. b The subject is suddenly released and must maintain balance in order to achieve a standing posture. c The subject has recovered a vertical posture