A mathematical model for incorporating biofeedback into human postural control

Biofeedback of body motion can serve as a balance aid and rehabilitation tool. To date, mathematical models considering the integration of biofeedback into postural control have represented this integration as a sensory addition and limited their application to a single degree-of-freedom representation of the body. This study has two objectives: 1) to develop a scalable method for incorporating biofeedback into postural control that is independent of the model’s degrees of freedom, how it handles sensory integration, and the modeling of its postural controller; and 2) to validate this new model using multidirectional perturbation experimental results.

Biofeedback was modeled as an additional torque to the postural controller torque. For validation, this biofeedback modeling approach was applied to a vibrotactile biofeedback device and incorporated into a two-link multibody model with full-state-feedback control that represents the dynamics of bipedal stance. Average response trajectories of body sway and center of pressure (COP) to multidirectional surface perturbations of subjects with vestibular deficits were used for model parameterization and validation in multiple perturbation directions and for multiple display resolutions. The quality of fit was quantified using average error and cross-correlation values.

The mean of the average errors across all tactor configurations and perturbations was 0.24° for body sway and 0.39 cm for COP. The mean of the cross-correlation value was 0.97 for both body sway and COP.

The biofeedback model developed in this study is capable of capturing experimental response trajectory shapes with low average errors and high cross-correlation values in both the anterior-posterior and medial-lateral directions for all perturbation directions and spatial resolution display configurations considered. The results validate that biofeedback can be modeled as an additional torque to the postural controller without a need for sensory reweighting. This novel approach is scalable and applicable to a wide range of movement conditions within the fields of balance and balance rehabilitation. The model confirms experimental results that increased display resolution does not necessarily lead to reduced body sway. To our knowledge, this is the first theoretical confirmation that a spatial display resolution of 180° can be as effective as a spatial resolution of 22.5°.