Bianchi, L., D. Angelini, G. P. Orani, and F. Lacquaniti. Kinematic coordination in human gait: relation to mechanical energy cost. J. Neurophysiol. 79: 2155–2170, 1998. Twenty-four subjects walked at different, freely chosen speeds ( V) ranging from 0.4 to 2.6 m s−1, while the motion and the ground reaction forces were recorded in three-dimensional space. We considered the time course of the changes of the angles of elevation of the trunk, pelvis, thigh, shank, and foot in the sagittal plane. These angles specify the orientation of each segment with respect to the vertical and to the direction of forward progression. The changes of the trunk and pelvis angles are of limited amplitude and reflect the dynamics of both right and left lower limbs. The changes of the thigh, shank, and foot elevation are ample, and they are coupled tightly among each other. When these angles are plotted one versus the others, they describe regular loops constrained on a plane. The plane of angular covariation rotates, slightly but systematically, along the long axis of the gait loop with increasing V. The rotation, quantified by the change of the direction cosine of the normal to the plane with the thigh axis ( u 3 t ), is related to a progressive phase shift between the foot elevation and the shank elevation with increasing V. As a next step in the analysis, we computed the mass-specific mean absolute power ( P u ) to obtain a global estimate of the rate at which mechanical work is performed during the gait cycle. When plotted on logarithmic coordinates, P u increases linearly with V. The slope of this relationship varies considerably across subjects, spanning a threefold range. We found that, at any given V > 1 m s−1, the value of the plane orientation ( u 3 t ) is correlated with the corresponding value of the net mechanical power ( P u ). On the average, the progressive rotation of the plane with increasing V is associated with a reduction of the increment of P u that would occur if u 3 t remained constant at the value characteristic of low V. The specific orientation of the plane at any given speed is not the same in all subjects, but there is an orderly shift of the plane orientation that correlates with the net power expended by each subject. In general, smaller values of u 3 t tend to be associated with smaller values of P u and vice versa. We conclude that the parametric tuning of the plane of angular covariation is a reliable predictor of the mechanical energy expenditure of each subject and could be used by the nervous system for limiting the overall energy expenditure.
Optimization of gratings in a diffractive waveguide using relative-direction-cosine diagrams
