The stabilometric evaluation of the erect stance. Energy-based optimal control in a numerical model

This paper proposes an anthropomorphic model developed in a virtual context, useful to simulate the maintenance of the erect stance. Such a model can be built through a suitable software which can identify the geometry of the articular parts and place mechanical constraints (e.g. joints, spherical links, etc.) between the single elements.

Our approach can be described as the assembly of rigid parts linked at the joints. The control is given by internal torques at the joints and driven by strategy for the balance aimed to the least amount of total muscular energy spent. The anthropomorphic model proposed underlines and solves the typical problems of a system characterized by a multiple number of degree of freedom placed in erect stance and perturbed by phenomena of endogenous and exogenous nature. This model is developed via the coupling of 2 separate bi-dimensional models, one representing the sagittal plane and the other the frontal plane. The numerical tests were validated through experimental tests in a group of healthy volunteers. For this purpose we employed a stabilometric platform (force-plate) to record the statokinesigram (SKG) on the rest surface.

The shapes of the stabilometric plots show a good spatial similarity between the experimental and simulated SKG. Both SKGs present a good range in the frontal plane with concentration of points in some areas (or attractors) in the experimental SKG, but not in the simulated one. The tests also showed a postural oscillation at low frequency (= 0.02Hz), probably due to the differential tiredness of groups of muscles or because of a delayed action of the neurological control.

On the numerical simulations, we claim the suitability of the antropomorphic model for a general description of the maintenance of the erect stance. Despite the simplification, with our approach it is possible to simulate some of the main characteristics of the postural act. In particular, the length and the areas of the simulated SKG's are comparable with those of the experimental tests.